I hope this helps you.
how to solve 3(x+6) = x + 8 + x
the solution to the equation is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation
what is distributive property ?
The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,
In the given question,
To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.
Here are the steps:
Distribute the 3 on the left-hand side of the equation:
3(x+6) = 3x + 18
Combine the two x terms on the right-hand side of the equation:
3x + 18 = 2x + 8
Subtract 2x from both sides of the equation:
3x - 2x + 18 = 2x - 2x + 8
Simplifying this expression gives:
x + 18 = 8
Finally, subtract 18 from both sides of the equation:
x + 18 - 18 = 8 - 18
Simplifying this expression gives:
x = -10
Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.
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Determine the effective tax rate for a taxable income of $115,500. Round theginal answer to the nearest hundredth
A) 18.71%
B) 17.20%
C) 24.10%
D) 24.75%
The effective tax rate for a taxable income of $115,500 is A) 18.71%
How to calculate the taxThe introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).
Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,
= 18%
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HELP RAAHHHH
1. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 4 feet with an intal upward velocity of 72 feet per second
The T-shirt is caught 42 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
2. During halftime of a football game, a sing shot launches T-shirts at the crowd
A T-shirt is launched from a height of 3 feet with an intal upward velocity of 80 feet per second
The T-shirt is caught 36 feet above the field
How long will take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Answer:
1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:
h(t) = -16t^2 + 72t + 4
To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:
t = -b/2a = -72/(2(-16)) = 2.25 seconds
To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):
h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet
The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.
2. Using the same kinematic equation as before, we have:
h(t) = -16t^2 + 80t + 3
To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:
t = -b/2a = -80/(2(-16)) = 2.5 seconds
To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):
h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet
The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.
Step-by-step explanation:
Which graph represents the hyperbola x2/52-y2/42 = 1?
For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.
What is a hyperbola?A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.
Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.
For the given equation of the parabola, the value of a and b = 5 and 4.
Thus, we have horizontal length of 5 and vertical width of 4 units
The graph that depicts this hyperbola is: Option B.
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The complete question is:
Use the graph to answer the questions
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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;
1. The vertex point is (50, 630)
2. The solution point are; (20, 0), and (80, 0)
3. Vertex form; f(x) = -0.7·(x - 50)² + 630
4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)
What is a quadratic equation?A quadratic equation is an equation of the form f(x) = a·x² + b·x + c
1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)
The vertex point is; (50, 630)
2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;
The solutions are; (20, 0), and (80, 0)
3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
Therefore;
(h, k) = (50, 630)
f(20) = 0 = a·(20 - 50)² + 630
a·(20 - 50)² = -630
a = -630/((20 - 50)²) = -630/900 = -7/10
a = -7/10 = -0.7
The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630
4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)
r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7
The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)
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A partial table of nutrients and Daily Values (DVS)
based on a 2000-calorie diet is provided. The Sodium row and the Vitamin D row are completed, and each % of the DV is calculated.
Compare each amount with the amount on the given nutrition label. Now use the amount of
saturated fat on the nutrition label to calculate its
% of DV, X. Use the saturated fat amount on the nutrition label
to calculate the %DV for saturated fat.
Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
What is the explanation for the above response?To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.
From the label, we see that the serving size contains 3.5g of saturated fat.
To calculate the %DV for saturated fat, we use the equation:
%DV = (amount of nutrient per serving / DV) x 100%
Plugging in the values for saturated fat, we get:
%DV = (3.5g / 19g) x 100%
%DV = 0.1842 x 100%
%DV ≈ 18%
Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
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Use the box plot showing the ages of those who watch the television show 'The Code" to answer the question that follows.
Which value is the best approximation for the range in ages for the middle 50% of viewers?
A) 10
B) 15
C) 20
D) 45
The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.
What is interqurtile range?The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.
What is Range?Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.
According to the given information:
A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).
To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.
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Primary Level 2 3 4 5 6 7. 8 children/funny monkeys thin/rake strong/ox eagle/aeroplane my room/ clean/ whistle swimmer/fish Exercise 2 Read the story. Look for the simile (as/like) When Mr. Bumble is angry, he shouts as loud as thunder. His eyes look like fire. He bangs his hands which feel as heavy as lead. Mr. Bumble stamps his feet like an et All the pupils keep as quiet as lambs when Mr. Bumble behaves like e
The similes in the story are:
"shouts as loud as thunder""eyes look like fire""hands feel as heavy as lead""stamps his feet like an et""quiet as lambs"What is a Simile?A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.
Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.
Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.
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14. The local credit union is offering a special student checking account. The monthly cost of the account is $15. The first 10 checks are free, and each additional check costs $0.75. You search
the Internet and find a bank that offers a student checking account with no monthly charge. The first 10 checks are free, but each additional check costs $2.50.
a. Assume that you will be writing more than 10 checks a month. Let n represent the number of checks written in a month. Write a function rule for the cost c of each account in terms of n.
b. Write an inequality to determine what number of checks in the bank account would be more expensive than the credit union account.
c. Solve the inequality in part b.
Answer: a. c(n) = 15 + 0.75(n - 10)
b. 15 + 0.75(n - 10) = 2.50(n - 10)=
Simplifying and solving for n, we get:
n = 50
c. n > 50
Step-by-step explanation:
a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:
c(n) = 15 + 0.75(n - 10)
The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
The cost c of the bank account in terms of the number of checks written n can be expressed as:
c(n) = 2.50(n - 10)
The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.
b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:
15 + 0.75(n - 10) = 2.50(n - 10)
Simplifying and solving for n, we get:
n = 50
So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.
c. The solution to the inequality is:
n > 50
This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.
Determine whether the following statements are TRUE or FALSE (do not write down the statements
just state TRUE or FALSE). [7 marks]
a. () ≥ 1 for any event .
b. () = 1 where is the Sample space.
c. If {} is any finite or infinite sequence of disjoint events, then (⋃
=1 ) = ∑ ()
=1 .
d. If ⊆ where and are two events in a sample space, then () ≤ ().
e. If and are two events in a sample space, then ( ∪ ) = () − () + ( ∩ ).
f. If and are two independent events in a sample space, then ( ⁄ ) = (∩)
() .
g. Mutually exclusive events are not independent
a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE
How to determine whether the following statements are TRUE or FALSEa. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.
b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.
c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.
d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.
e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.
f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.
g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.
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Find any solution(s) (refer to attachment) of and select the correct statement.
A. The equation has no solution.
B. The equation has two solutions.
C. The equation has one solution.
D. The equation has one solution and one extraneous solution.
how did slugger mcfist get a black eye
Work out sheet below please
Answer:
-4 + 8 = 4
-2 + 6 = 4
-1 + 5 = 4
So the three pairs are -4 and 8; -2 and 6; and -1 and 5.
LOOK AT THE PHOTO PLS
The next entry on the long division would be 0.054, and 0.0054
How to perform long divisionLong division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:
Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.
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Find the area of the trapezoid 11 yd 11 yd 7 yd
Answer:
Step-by-step explanation:
A=1/2(b1+b2)h
=1/2 (11yd+11yd)(7yd)
=1/2(22yd)(7yd)
=(11yd)(7yd)
=77yd
In 2012, the population of a city was 5.51 million. The exponential growth rate was 3.82% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
helppppppp
Answer:
a) To find the exponential growth function, we can use the formula:
P(t) = P0 * e^(rt)
Where:
P(t) = the population at time t
P0 = the initial population (in this case, 5.51 million)
e = the mathematical constant e (approximately 2.71828)
r = the annual growth rate (in decimal form)
t = the number of years
Substituting the given values, we have:
P(t) = 5.51 * e^(0.0382t)
b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:
P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million
Therefore, the estimated population of the city in 2018 is approximately 6.93 million.
c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:
10 = 5.51 * e^(0.0382t)
e^(0.0382t) = 10/5.51
0.0382t = ln(10/5.51)
t ≈ 11.7 years
Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.
d) To find the doubling time, we can use the formula:
T = ln(2) / r
Where:
T = the doubling time
ln = the natural logarithm
2 = the factor by which the population grows (i.e., doubling)
r = the annual growth rate (in decimal form)
Substituting the given value of r, we have:
T = ln(2) / 0.0382 ≈ 18.1 years
Therefore, the doubling time for the population of the city is approximately 18.1 years.
At Amy's Pizza Palace, the cost of a pizza depends on the number of toppings. The graph shows this relationship.
247
21
Cost of Pizza
(in $)
18-
15-
12-
9
6-
3-
1
2
6
3 4
Number of Toppings
7
TURUDANY
According to this graph, what is the meaning of the v-intercept?
The cost of pizza with no toppings is $6. So correct option is C.
Describe Graph?A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.
There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.
Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.
Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.
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The complete question is:
Help please i need this asap!! I'll give 100 points
The range is expressed in interval notation as (-1, ∞)
How to find the function (f+g)(x)?To find the linear function f(x), let us use the table given.
A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):
[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]
Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:
a = -6, g(a) = 16, b = -3 and, g(b) = 10
Therefore g(x)
[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]
now find the (f+g)(x).
[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]
(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1
The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:
[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]
Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.
As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.
The range is expressed in interval notation as (-1, ∞)
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Charlie invests $325 in an account that pays 8% simple interest for 15 years.
Use the simple interest formula, I = P ∙ r ∙ t, to answer the following questions.
How much interest will Charlie’s initial investment earn over the 15-year period?
How much money does Charlie have after the 15 years?
Answer: To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).
In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.
Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:
I = $325 ∙ 0.08 ∙ 15 = $390
Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.
To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.
The total amount of money that Charlie will have after the 15 years is:
Total amount = Initial investment + Interest earned
Total amount = $325 + $390
Total amount = $715
Therefore, Charlie will have $715 after 15 years.
Step-by-step explanation:
Explain what the constant of proportionality means in the equation 1 over 2 x + y
In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.
What is constant of proportionality?If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.
The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.
The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.
A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.
If x = 0
Then,
1/2(0) + y = c
y = c
The proportionality constant, c, can be seen in the equation
1 over 2 x + y = c.
This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.
The slope of the line connecting the two variables is another name for the constant of proportionality.
Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that
are being compared are represented by these variables.
In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.
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The Complete questions as follows-
Explain what the constant of proportionality means in the equation 1 over 2 x + y = c
Hiya, I need help on a few questions URGENTLY
Boris has a coin collection that contains US, Euro and British coins.If the ratio of US to Euro coins is 5 to 2 and the ratio of Euro to British coins is 5 to 1. What is the ratio of US to British coins?
Amanda works at the local cafe and gets paid £10 per hour (h) and a fixed sum of £50 for a month. Write a formula for the money (m) that she will receive in a month?
A holiday package costs £190, plus £50 a day. What. formula shows the cost of the holiday, C for d days?
The ratio of US to British coins is 25 to 4.
The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
How to solve the Problem?1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.
First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.
Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.
Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.
25 : 10 :: 10 : 2
Multiplying both sides by 2, we get:
50 : 20 :: 10 : 2
Simplifying, we get:
The ratio of US to British coins is 25 to 4.
2. To calculate Amanda's monthly pay, we can use the formula:
m = 10h + 50
where m is the total money Amanda receives in a month, and h is the number of hours she works.
The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
3. To calculate the cost of the holiday package for d days, we can use the formula:
C = 190 + 50d
where C is the cost of the holiday package, and d is the number of days.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
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Naya has a pitcher that contains 3 cups of salted lassi, a yogurt drink with sait and sites. She pours 6 fluid ounces of lassi into each glass. If she uses all of the lassi, how many glasses does Naya use?
A. 2
B. 4
C. 16
D. 18
After 6 fluid ounces , Naya uses 4 glasses as a result.
Define ounces?A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce . A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce
In Naya's pitcher, there are three glasses of salted lassi.
She fills each glass with six fluid ounces of lassi.
By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.
8 fluid ounces make constitute a cup.
Consequently, 3 cups equal 24 fluid ounces (3 x 8).
24 divided by 6 results in:
4 glasses are equal to 24/6.
Naya uses four glasses as a result.
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Evaluate (2-5i)(p+q)(i) when p=2 and q=5i
Answer:
29i
Step-by-step explanation:
While multiplying complex numbers we should remember that i^2=−1.
As p=2 and q=5i,
(2−5i)(p+q)i
= (2−5i)(2+5i)i
= (2×2+2×5i−5i×2−5i×5i)×i
= (4+10i−10i−25×i2)×i
= (4+10i−10i−25×(−1))×i
= (4+25)×i
=29i
Oliver and Mike each place some apples and oranges into the same bowl.
• The ratio of apples to oranges Oliver places in the bowl is 2:3
• The ratio of apples to oranges Mike places in the bowl is 1:2
• They each place 6 oranges in the bowl.
Write the total number of apples and oranges they place in the bowl.
Answer: 5 * 5 = 20
20 divided by 1 = 20
If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.
What is 47/ 30 in mixed numbers I'm giving 10 points must hurry
Answer:
1 17/30.
Step-by-step explanation:
you can find this out by seeing how many 30s go into 47 which is 1.
Then subtract to find how much is leftover still over 30.
47 - 30 = 17
So 1 and 17/30
The most important of the Shinto gods is the sun goddess who gave light to the world, named ______.
Amaterasu
Susanoo
Tsukyomi
Izanagi
Answer: Amaterasu
Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.
ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
A.
A'(0, 3), B'(2, 3), C'(1, 1)
B.
A'(0, -3), B'(3, -2), C'(1, -1)
C.
A'(-3, 0), B'(-3, 2), C'(-1, 1)
D.
A'(0, -3), B'(-2, -3), C'(-1, -1)
The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.
What are coordinates?Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.
We are to find the coordinates of the vertices of the image.
We know that
if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :
(a, b) ⇒ (-a, -b).
So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes
A(-3, 0) ⇒ (3, 0)
B(-2, 3) ⇒ (2, -3)
C(-1, 1) ⇒ (1, -1).
Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).
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A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 56.923 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 14 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:
x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923
Using the formula for the sum of a geometric series, we have:
x(1 - (1.1)^7)/(1 - 1.1) = 56.923
x(1 - 1.1^7)/(-0.1) = 56.923
x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles
Therefore, the hiker traveled approximately 4 miles on the first day.
The equation for Sn, the sum of the first n terms of the sequence, is:Sn = x(1 - r^n)/(1 - r)
where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.
Using the equation for Sn from Part B, we can find the total number of miles the hiker will travel in 14 days:S14 = x(1 - 1.1^14)/(1 - 1.1)
S14 ≈ 167.63
Therefore, the hiker will travel approximately 167.63 miles in 14 days.
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please help me fill these boxes
The measurements for area of Jacobs yard are;
Part A = 6m x 3m = 18m
Part B = 4.5m x 3m = 13 m
Part C = 1/2 x 3m x 3m = 4.5 m²
Total area = 18m² + 13.5m² + 4.5m² = 36m²
How do you identify sections that would help in calculating area?To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.
Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.
For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.
Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?
Part A = .............. x ........... = ...........m
Part B = + .............. x ............. = ............ m
Part C = 1/2 x ................. x ............ = ............... m²
Total area = ................... + ..................... + .................. = ..............m
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A pianist plans to play 3 pieces at a recital from her repertoire of 25 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?
There are 13,800 different recital programs possible.
What is permutation?
In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.
The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:
25 x 24 x 23 = 13,800
There are 13,800 different recital programs possible.
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