Answers
Therefore , the solution of the given problem of function comes out to be (g - f)(-1) = 29.
What exactly does function mean?The math lesson covers an extensive variety of subjects, including geometry, integers, one's divisions, construction, and both real and imagined geographic places. A work covers the connections between various variable that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinct results for each input.
Here,
We must first evaluate g(-1) and f(-1) before subtracting the results to obtain (g - f)(-1).
We possess
=> g(x) = 5x + 18
=> g(-1) = 5(-1) + 18 = 13
=> f(x) = x² - 17
=> f(-1) = (-1)² - 17 = -16
Therefore:
=> (g - f)(-1) = g(-1) - f(-1) = 13 - (-16) = 29
So, (g - f)(-1) = 29.
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Related Questions
If x = 11 degrees, how many degrees is Angle y? (Include only numerals in your response.)
Answers
Answer:
79 degrees
Step-by-step explanation:
[tex]x + y = 90 \: degrees \\ 11 + y = 90 \\ y = 90 - 11 \\ y = 79 \: degrees[/tex]
Use the graphs of f and g to find (f+g)(−2).
Answers
Using the graph the value of the function (f + g)(-2) = 5
What are graphs?A graph is a diagrammatic representation of a function
Since we have the graphs of the function f(x) and g(x), we desire to find (f + g)(-2). We proceed as follows.
First, we note that (f + g)(x) = f(x) + g(x)
Now, we need to find (f + g)(-2) = f(-2) + g(-2)
So, we use the graph to find these values.
From the graph
f(-2) = 2 and g(-2) = 3
So, substituting the values of the variables into the equation, we have that
(f + g)(-2) = f(-2) + g(-2)
= 2 + 3
= 5
So, (f + g)(-2) = 5
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15 POINTS!!! Mode and Modal Classwork
Answers
1. We can see here that the modes of the given set of numbers will be: 12, 13, 14, 19.
2. The word in the sentence that is the mode is: the.
3. The mode of x is: 7
The mode of y is: - 2
What is mode?In statistics, the mode is the value or values that occur most frequently in a given dataset. It is one of the most common measures of central tendency, along with the mean and the median.
To find the mode of a dataset, you need to look for the value that appears most often. If there is more than one value that occurs with the same highest frequency, the dataset is said to be bimodal or multimodal.
If no value appears more frequently than any other, the dataset is said to have no mode.
4. Modal class: 4-
Modal class: 12 - 20
5. Knowing the modal size of glass that its customers purchase can provide several benefits for the small company that sells glass. Here are some ways in which the company could benefit:
Better inventory managementMore efficient productionBetter pricing strategies6. We can actually find the total frequency of the other three classes by subtracting the frequency of the first class from the total number of observations:
Total Frequency of the three classes = Total number of observations -Frequency of the first class
= 115 - 84 = 31
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suggest five question for a questionnaire to discover what opinions people have about taking a gap year.
Answers
1. Have you taken a gap year in the past, or are you considering taking one in the future?
2. What do you think are the key benefits of taking a gap year?
3. Do you think taking a gap year is a beneficial educational experience?
4. Are there any downsides to taking a gap year, in your opinion?
5. What advice would you give to someone considering taking a gap year?
6. Do you think taking a gap year would provide skills/experiences that you couldn't gain elsewhere?
4.586 to the nearest cm
Answers
Answer:
See below.
Step-by-step explanation:
We are asked to round 4.586 cm to the nearest cm.
What is Rounding?
Rounding is a simple method used to change a number, and all of the numbers behind it to 0. Rounding is similar to an approximation, in order to show you how I should give you an example.
Example:
Round 459 to the hundreds place.
The hundreds place is where the 4 is. We should look at the 5.
Requirements necessary are that 5 needs to be greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 500.
Rounding is an approximation because it's close to the actual number, in other words, inexact.
Let's use the example as a guide for our problem now.
4.586 to the nearest cm (ones place)
The ones place is the 4. We should look at the 5.
5 is greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 5.000 cm.
Our final answer is 5.000 cm.
The polynomial 32x^2+12x-57 has two real roots.
Answers
True, The polynomial 32x^2+12x-57 has two real roots.
What is a polynomial, exactly?
A polynomial in mathematics is an expression that consists of variables (also known as indeterminates) and coefficients and uses only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
It is an absolutely true statement that the polynomial 32x^2+12x-57 has two real roots. The correct option among all the options that are given in the question is the first option or option "A".
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The complete question is -
The polynomial 32x^2+12x-57 has two real roots.
A. True
B. False The polynomial 32x^2+12x-57 has two real roots.
You've just finished making 3 batches of plastic tumblers: a red batch, a yellow batch, and a purple batch. There are 500 tumblers in each batch. You are now making sets of 3 tumblers that contain 1 tumbler of each color. How many sets can you make?
Answers
Answer: Since there are 500 tumblers in each batch, there are a total of:
500 tumblers/batch × 3 batches = 1500 tumblers
To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:
500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.
However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:
500 sets/batch = 500 sets/batch × 3 batches = 1500 sets
Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.
Step-by-step explanation:
What is you answer and how many solutions for the following 3r- 9=3(r + 3)
Answers
Answer:
0
Step-by-step explanation:
3r-9=3(r+3)
3r-9=3r+9
collect like terms
3r-3r=9-9
r=0
Answer:
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identify how many solutions are possible for r.}[/tex]
[tex]\textsf{First, we should simplify the given equation.}[/tex]
[tex]\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}[/tex]
[tex]\textsf{values \underline{inside} the parentheses.}[/tex]
[tex]\textsf{Let's begin simplifying the equation.}[/tex]
[tex]\large\underline{\textsf{Simplify.}}[/tex]
[tex]\mathtt{3r-9=3(r+3)}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{3r-9=(3 \times r)+(3 \times 3)}[/tex]
[tex]\mathtt{3r-9=3r+9}[/tex]
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
[tex]\large\underline{\textsf{Why?:}}[/tex]
[tex]\textsf{Any value that is substituted into r will \underline{never} make the equation true.}[/tex]
For every dollar spent on summer youth programs in Milltown, 80 cents goes directly to program services. The rest of the budget is spent on staff salaries.
What is the ratio of the amount spent on staff salaries to the total budget for the youth programs?
1:10
1:8
1:5
1:4
1:2
Answers
The ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.
What is the ratiο and prοpοrtiοn?A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).
If 80 cents οf every dοllar gοes directly tο prοgram services, then 20 cents οf every dοllar is spent οn staff salaries.
This can be written as a ratiο οf 20 cents tο 100 cents, οr simplified tο 1:5.
Therefοre, the ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.
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In triangle SRK below, medians SC, KE and RL at M.
Which statement must always be true?
Answers
The statement that must always be true fοr the median οf the triangle is RM = KM.
Why is this statement always be true?The statement that must always be true fοr the centrοid οf the triangle is RM = KM. Since, RM and KM are bοth part οf the median that cοnnect at the centrοid and are divided intο 2 halves.
A median in a triangle is a line segment that jοins οne οf the triangle's vertices tο the midway οf the οther side. There are three medians in every triangle, and they all cοme tοgether at the centrοid. The segment frοm the vertex tο the centrοid is twice as lοng as the segment frοm the centrοid tο the midpοint οf the οppοsing side.
The centrοid is the centre οf mass οf the triangle and splits each median intο twο segments. A median divides a triangle intο six smaller triangles οf equal size, passing thrοugh the centrοid οf each οf these smaller triangles, amοng οther nοtewοrthy qualities.
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Identify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
Answers
The total surface area of the rectangular prism is 94 cm2.
What is surface area?Surface area is the measurement of the total area of a three-dimensional object. It is the sum of all the areas of the faces or surfaces of a 3D shape.
The total surface area of a 3D object is the sum of the areas of all its faces. The formula to calculate the total surface area of a 3D object is:
Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)
Where Length, Width, and Height are the dimensions of the 3D object.
For example, if you have a rectangular prism with Length = 5 cm, Width = 4 cm, Height = 3 cm, then the total surface area is:
Total Surface Area = 2(5 cm x 4 cm) + 2(5 cm x 3 cm) + 2(4 cm x 3 cm)
= 40 cm2 + 30 cm2 + 24 cm2
= 94 cm2
Therefore, the total surface area of the rectangular prism is 94 cm2.
In conclusion, the formula to calculate the total surface area of a 3D object is: Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height). Examples can be used to better understand the concept and apply the formula to solve for the total surface area.
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There are 140 cars in a parking lot bob looks at 15 cars and finds out that 2 of those cars in the parking lot are gray colored?
Answers
Answer:
Step-by-step explanation:
about 18.7
Answer:
18.7
Step-by-step explanation:
2 gray cars / 15 cars = x gray cars / 140 cars
Solving for x, we get:
x = 2 gray cars * 140 cars / 15 cars
x = 18.67 gray cars
Each of the following functions f,g,h, and h represents the amount of money in a bank account in dollars as a function of time x, in years they are each written in form m(x)= a•b
Answers
Answer:
f(x) : exponential growth
g(x); exponential growth
h(x): exponential growth
j(x): exponential decay
Step-by-step explanation:
In an exponential function such as
[tex]m(x) = a \cdot b^x[/tex]
the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative
If b > 1, it is a growth function
If b < 1 then it is a decay function
If b = 1 neither growth or decay function values are constant
In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function
Answer:
O f(x) : exponential growth
O g(x); exponential growth
O h(x): exponential growth
O j(x): exponential decay
Step-by-step explanation: I used to do this before :)
Consider the following function.
h(x)=(x−4)2−1
Step 2 of 4 : Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).
Answers
0 = (x - 4)^2 - 1
Adding 1 to both sides, we get:
1 = (x - 4)^2
Taking the square root of both sides, we get:
±1 = x - 4
Adding 4 to both sides, we get:
x = 4 ± 1
Therefore, the x-intercepts of the function h(x) are (3, 0) and (5, 0).
Osprey Cycles, Inc. projected sales of 67,577 bicycles for the year. The estimated January 1 inventory is 6,048 units, and the desired December 31 inventory is 7,558 units.
What is the budgeted production (in units) for the year?
units
Answers
Therefore, the budgeted production for the year is 69,087 units.
factors
given by the question.
To determine the budgeted production for the year, we need to consider the following factors:
Projected sales for the year: 67,577 bicycles
Estimated January 1 inventory: 6,048 units.
Desired December 31 inventory: 7,558 units
The formula to calculate the budgeted production is:
Budgeted Production = Projected Sales + Desired Ending Inventory - Beginning Inventory
Using the values given in the problem, we can calculate the budgeted production as follows:
Budgeted Production = 67,577 + 7,558 - 6,048
Budgeted Production = 69,087 units
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You need a 35% alcohol solution. On hand, you have a 245 mL of a 10% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution?
You will need mL of the 70% solution
to obtain mL of the desired 35% solution.
Answers
Using percentage, we can get that 7ml of the 70% solution will be needed.
What do you mean by percentage?A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form.
In this context, "%" is read as "percent" or "percentage" to represent a percentage. By "division by 100," the percent symbol can always be changed to a fraction or decimal equivalent.
In the given question we get the equation,
35(245) + 0.75x = 0.4(245+x) = 98 + 0.4x
85.75 + 0.75x = 98 + 0.4x
0.35x = 98-85.75 = 12.25
x = 12.25/.35 = 35 mL of 75% solution
mixed with 245 mL of 35% it yields 280 mL of 40% so,
35 is within 5 of 40
75 is within 35 of 40
35/5 = 7
245/35 = 7
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rolling a number greater than 0 but less than 7
Answers
Probability of rolling a number greater than 0 but less than 7 is 1.
Define probability?The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, probability has also been introduced in mathematics.The probability formula is as follows:
Probability = Favourable outcomes / Total outcomes
Sample space of rolling a dice:
S = {1, 2, 3, 4, 5, 6}
Total outcomes = 6
Favourable outcomes: number greater than 0 but less than 7
Favourable outcomes: 6
Then, probability of rolling a number greater than 0 but less than 7
Probability = Favourable outcomes / Total outcomes
Probability = 6/6
Probability = 1
Thus, probability of rolling a number greater than 0 but less than 7 is 1.
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The complete question is-
A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7
Determine the length of x in the triangle. Give your answer to two decimal places. Show the steps please.
Answers
Given:-
A right angled triangle is given to us .Hypotenuse = x , perpendicular = 12 .To find:-
The value of x .Solution:-
As we know that in a right angled triangle,
[tex]\implies \sin\theta =\dfrac{p}{h} \\[/tex]
And here;
p = 12 h = xOn substituting the respective values, we have;
[tex]\implies \sin20^o = \dfrac{12}{x} \\[/tex]
[tex]\implies 0.342 =\dfrac{12}{x} \\[/tex]
[tex]\implies x = \dfrac{12}{0.342} \\[/tex]
[tex]\implies \underline{\underline{ x = 35.087}} \\[/tex]
Hence the value of x is 35.087 .
and we are done!
The length of the missing side of the given triangle above which is adjacent to angle 20° is 35.09.
How to calculate the length of the missing triangle side?To calculate the length of the missing side of the triangle, the formula given below is used. Such as:
Sin ∅ = opposite/hypothenuse.
Where ∅ = 20°
opposite = 12
hypotenuse = X
That is;
sin 20° = 12/X
make X the subject of formula;
X = 12/sin20°
X = 12/0.342020143
X = 35.09
Therefore the length of the missing part of the given triangle which is adjacent to angle 20° is 35.09.
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Write a multiplication equation that shows how the denominators of and are
related. Explain how this equation helps you write as an equivalent fraction with
a denominator of 4.
Answers
Answer:
The multiplication equation that shows how the denominators of 3/4 and 5/6 are related is:4 × 6 = 24To write an equivalent fraction with a denominator of 4, we need to find a number that, when multiplied by 4, gives us 24. That number is 6. So, we can multiply both the numerator and denominator of 3/4 by 6 to get:(3/4) × (6/6) = 18/2418/24 is equivalent to 3/4, but it has a denominator of 24 instead of 4. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6.(18/6) ÷ (24/6) = 3/4Therefore, the equivalent fraction of 3/4 with a denominator of 4 is 3/4 × 6/6 = 18/24, which simplifies to 3/4.
What is the value of x in a triangle with one side being (4x-4) and the other side being 30
Answers
The value for the x in the triangle with sides (4x - 4) and 30 is obtained as x > 6.8.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Assume that the side length 30 is the greatest of the 3 sides.
Using this fact, we can write an inequality based on the lengths of the sides in the given triangle -
(4x - 4) + x > 30
Simplifying this inequality, we get -
4x + x - 4 > 30
Adding x on LHS, we get -
5x > 34
Dividing both sides by 5, we get -
x > 6.8
Therefore, the value of x is greater than 6.8.
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Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $550 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $5,000 and never have to pay annual membership dues.
Obviously, the lifetime membership isn’t a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it’s a great deal. Suppose that the appropriate annual interest rate is 7.5%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $550 in annual membership dues? (Note: Round your answer up to the nearest year.)
21 years
18 years
14 years
12 years
In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4.5% annual interest rate, what is its value as of 2018 (392 years later)?
$987,122,447.84
$635,647,030.80
$859,993,041.68
$747,820,036.24
Answers
Answer:
For the lifetime membership to be cheaper than paying $550 in annual membership dues, we need to calculate the present value of the lifetime membership and compare it to the present value of the stream of annual payments.
The present value of the lifetime membership can be calculated using the formula for the present value of a lump sum:
PV = FV / (1 + r)^n
where FV is the future value (which is the cost of the lifetime membership today, $5,000), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
The present value of the stream of annual payments can be calculated using the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where A is the annual payment ($550), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
We need to find the minimum number of years for which the present value of the lifetime membership is less than the present value of the stream of annual payments. We can do this by setting the two present values equal to each other and solving for n:
5000 / (1 + 0.075)^n = 550 * [(1 - (1 + 0.075)^-n) / 0.075]
Solving this equation gives n ≈ 18.7 years. Rounded up to the nearest year, this means that Lloyd must remain a member of the ADLA for at least 19 years for the lifetime membership to be cheaper than paying $550 in annual membership dues.
Therefore, the answer is 19 years.
For the second question, we can use the formula for the future value of a lump sum:
FV = PV * (1 + r)^n
where PV is the present value ($24), r is the annual interest rate (4.5%), and n is the number of years (392).
Substituting the given values, we get:
FV = 24 * (1 + 0.045)^392
FV ≈ $859,993,041.68
Therefore, the value of the $24 purchase price as of 2018 is approximately $859,993,041.68.
Solve the system
0.2y=4.6x+1.2
-2.3x=-0.1y+0.6
Answers
The graph of f ( x ) = − 1 /2 ( 1 /2 ) ^x − 3 + 5 is shifted downwards 5 units, and then shifted left 3 units, stretched vertically by a factor of 4 , and then reflected about the x -axis. a . What is the equation of the new function, g ( x ) ? g ( x ) = b . What is the y -intercept? ( , ) c . What is the domain? d . What is the range?
Answers
Answer: a. To shift the graph downwards 5 units, we subtract 5 from the function, to shift it left 3 units, we add 3 to the input (the x-value), to stretch the graph vertically by a factor of 4, we multiply the function by 4, and to reflect it about the x-axis, we multiply the entire function by -1. Thus, the new function is:
g(x) = -4(1/2)^(x+3) - 5
b. To find the y-intercept, we set x=0 in the equation and solve for y:
g(0) = -4(1/2)^(0+3) - 5 = -9
Thus, the y-intercept is (0, -9).
c. The domain of the function g(x) is all real numbers, since there are no restrictions on the input x.
d. The range of the function g(x) is (-∞, -5], since the function is shifted downwards 5 units and stretched vertically by a factor of 4, which means that the maximum value of the function is -5, and it can take any value less than or equal to -5. The reflection about the x-axis does not change the range.
Step-by-step explanation:
For which quotient is x=7
an excluded value?
Answers
Answer:
x=3
Step-by-step explanation
x=7 is an excluded value for the quotient x=3 because 3 is not an integer.
Anju does chores to earn allowance. She earns $3 for each chore. She wrote this equation to find how much money she earns (d) based on how many chores she does (c): 3c=d
Answers
Anju earned $30 by doing 10 chores. So, if Anju does 10 chores, she can earn money up to $30?
What is an equation?An equation is a mathematical statement that indicates the equality of two expressions. It is made up of one or more variables, constants, and mathematical operations. An equation consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=).
The purpose of an equation is to find the value(s) of the variable(s) that satisfy the given conditions. To solve an equation, we need to isolate the variable on one side of the equation and simplify the other side of the equation until we obtain a solution or solutions.
The equation shows that the amount of money Anju earns is directly proportional to the number of chores she does. Each chore is worth $3, so if Anju does c chores, she earns 3c dollars.
For example, if Anju does 5 chores, she can use the equation to find how much money she earned:
3c = d
3(5) = d
15 = d
So, Anju earned $15 by doing 5 chores.
Similarly, if Anju does 10 chores, she can use the same equation to find her earnings:
3c = d
3(10) = d
30 = d
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Answer: independent variable Dependent variable
if you’re on khan it’s all right MARK AS BRAINLIEST PLS
Find the equation for the ellipse
Answers
Using the data points given, the equation is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].
What is an ellipse?
An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).
We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).
We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.
Therefore, we have -
a = 9 - 4 = 5
Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -
c = distance from (4,-2) to (4,3)
c = [tex]\sqrt{((4-4)^2 + (3-(-2))^2}[/tex]
c = 5
Now, we can use the equation of an ellipse -
[tex]\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1[/tex]
where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Plugging in the values we have found, we get -
[tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex]
Therefore, the equation for the ellipse is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].
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Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y
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The electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.
What is an electric field?
An electric field is a region in which an electric charge experiences a force. It is created by an electric charge or a changing magnetic field. Electric fields exist everywhere in nature and are vital to the functioning of many electronic devices. Electric fields are also used to describe the motion of electrons in a conductor and the behavior of electric currents.
The electric field at the origin (x=0, y=0) can be calculated using the equation of electric field,
E = k(q1/r1² + q2/r2²)
Where k is the Coulomb's constant, q1 and q2 are the charges and r1 and r2 are the distances from the charges to the origin.
The electric field at the origin can be calculated by substituting the given values in the equation.
The distance from the charge at y = 4.0 cm to the origin is 5 cm and the distance from the charge at y = -4.0 cm to the origin is also 5 cm.
E = 8.988 X 10⁹ (3.8 X 10⁻⁹/25 + 3.8 X 10⁻⁹/25)
E = 8.99 X 10⁹ (3.8 X 10⁻⁹/25)
E = 1.05 X 10⁷ N/C
Therefore, the electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.
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Right Question:-
Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y, Find electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm?
A cereal box advertises that it contains 20% more. It now contains 18.48 ounces. What was the original cereal box amount?
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Answer:
If the new cereal box contains 20% more than the original cereal box, then the original cereal box contained 100% - 20% = 80% of the new cereal box.
Let X be the original cereal box amount in ounces, then we can set up the following equation:
X + 0.20X = 18.48
Simplifying and solving for X:
1.20X = 18.48
X = 15.40
Therefore, the original cereal box amount was 15.40 ounces.
6. Ulysses throws a football to an open wide receiver. The path of the ball can be modeled by the function f(x) = -6t(t-5). How long is the ball in the air?
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On solving the provided question we cans ay that As a result, the ball function remains in the air for 5 seconds.
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
The function f(x) = -6t(t-5) reflects the football's height at time t. When the football lands, its height will be zero.
To determine the time the ball is in the air, we must first determine when f(t) = 0. As a result, we may set the equation to zero and solve for t:
-6t(t-5) = 0
This equation is valid for t = 0 or t = 5. When the ball is tossed, time t = 0 occurs, and time t = 5 occurs when the ball strikes the ground. The time the ball is in the air is calculated as follows: time in air = t final - t initial = 5 - 0 = 5 seconds.
As a result, the ball remains in the air for 5 seconds.
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please help!! i have no idea how to do this.
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hi!
first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.
on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.
then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.
do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.
i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)
next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.
continue down the table. it is the same with x=-2.
next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(
continue down the table and keep doing that!
next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.
next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).
the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.
i hope this was helpful! :)