The ratio of Murkas age to Ivans age is M : I = 6 : 1
Given data ,
Let Murkas age be M and Ivans age be I
Given that 1/3 of Murka's age is twice as much as Ivan's age
So ,
1/3 ( M ) = 2 ( I )
On simplifying the proportion , we get
Multiply by 3 on both sides , we get
M = 6 ( I )
Divide by I on both sides , we get
M / I = 6
Hence , the proportion is 6 : 1
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Please help me with this question
The graph is a function, the domain is (-∝, ∝), the range is (-∝, 4] and the graph is symmetrical with the y-axis
Determine if the graph represents a functionGiven that we have the graph
As a general rule of the vertical line test
For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once
Using the above as a guide, we have the following:
The graph would not intersect with a line from the x-axis more than once
Hence, the graph is a function
The domain and the rangeThe domain is the set of input values
In this case, we have
Domain = (-∝, ∝) i.e. all set of real values
The range is the set of output values
In this case, we have
Range = (-∝, 4]
The symmetric of the graphWhen the graph is rotated across the y-axis, the graph maintains it orientation
This means that the graph is symmetrical with the y-axis
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A wild horse runs at a rate of 8 miles an hour for 6 hours. Let y be the distance, in miles, the horse
travels for a given amount of time, x, in hours. This situation can be modeled by a function.
Which of these describes the domain of the function?
A. 0≤x≤6
B. 0≤y≤6
C. 0≤x≤ 48
D. 0≤ y ≤ 48
0≤x≤6 best describes the domain of the function.
The domain of a function describes the set of all possible input values.
In this case, the input variable is x, which represents the time in hours.
Since the horse runs for 6 hours, it is not possible for x to be greater than 6.
Additionally, x cannot be negative or zero, since time cannot be negative or zero.
Therefore, the domain of the function is 0 ≤ x ≤ 6.
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what are two numbers have a product of 20 and a sum of 9
Answer:
Step-by-step explanation:
Problems 17, 20 Please
The summation of the given expression is as follows:
17.) = 5
18.) = 1
19.) = 1/2
How to calculate the summation of the given expressions above?For question 17.)
The summation of 2k+3 when K= 1
= 2(1)+3
= 2+3
= 5
For question 18.)
The summation of (3/2)^k where k = 0 would be = 1
For question 19.)
The summation of 1/2^k+1 where k = 0
= 1/2^0+1
=1/2^1
=1/2
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Use the graph to answer the question.
B
3
D
Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 5
Reflection across y = 6
8
C
D'
9
10
E'
11
12
B'
A'
13
The line of reflection of the graph is y = -3
Determining the line of reflection.The given graph is added as an attachment
From the graph, we can see that the shapes are symmetrical about the line y = -3
When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection
This means that the line of reflection is y = -3
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Answer:
The calculated line of reflection of the graph is y = -3
Step-by-step explanation:
two variables appear to have an exponential relationship. what pattern(s) does the scatterplot suggest for the model? select the two correct answers.
a. it is only increasing or only decreasing.
b. it has a point of inflection.
c. it is only concave up or only concave down.
d. it has one or more extrema.
e. it is both concave up and concave down.
The pattern that the scatterplot would suggest, given that they have an exponential relationship is :
a. It is only increasing or only decreasing.c. It is only concave up or only concave down.What is an exponential relationship ?A function expressed as y = ab^x or y = a × e^(kx), where a, b, and k are constants represents an exponential relationship between two variables. Exponential functions demonstrate continuous increase or decrease throughout their entire domain; they do not alter direction.
In the event that the base 'b' is greater than 1, or if 'k' is positive, the function increases its output, otherwise, it will decrease when either or both conditions apply ('b' being between zero and one, or 'k' being negative). The concavity of a function is determined by the second derivative which takes on the form of an exponential function for all exponential functions, producing unchanged concavity throughout its entire domain.
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A water cooler has a storage capacity of 50 litres . If each student on an average consumes 750ml of water. Then how many times cooler tank has to be filled to quench the thirst of 1200 student of school
The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.
We have
Number of students= 1200
Water consumption per student= 750 ml
So, Total water consumption
= Number of students × Water consumption per student
= 1200 × 750 ml
= 900000 ml
= 900 Liter
Now, the time cooler tank has to be filled to quench the thirst
= 900 / 50
= 18 times
Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.
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The table represents a quadratic function f(x).
x f(x)
−4 7
−3 6
−2 7
−1 10
0 15
1 22
2 31
If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
A) 3
B) 6
C) 16
D) 22
Answer:
B) 6
Step-by-step explanation:
Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:
[tex]f(x)=ax^2+bx+c[/tex]
[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]
Therefore:
[tex]f(x)=ax^2+bx+15[/tex]
Substitute the point (1, 22) into the formula and create an equation for a in terms of b:
[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]
Therefore:
[tex]f(x)=(7-b)x^2+bx+15[/tex]
Finally, substitute another point from the table (-3, 6) and solve for b:
[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]
Therefore, the value of b is 6.
Answer:
6
Step-by-step explanation:
PLS HELP! TEST REVIEW AND I DONT UNDERSTAND
(a) Volume of the cylinder is 153 cm³
(b) Volume of the cone is 51 cm³
(c) Volume of the cone = 1/3 × Volume of the cylinder
Calculating the volume of a cylinder and a coneFrom the question, we are to determine the volume of the cylinder and the volume of the cone
The volume of a cylinder can be calculated by using the formula,
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
A = πr² = 17 cm²
A is the area of the base
h = 9 cm
Thus,
V = 17 cm² × 9 cm
V = 153 cm³
Therefore,
Volume of the cylinder is 153 cm³
(b)
For the volume of the cone
V = 1/3 πr²h
Substitute the given parameters
V = 1/3 × 17 cm² × 9 cm
V = 17 cm² × 3 cm
V = 51 cm³
Hence,
Volume of the cone is 51 cm³
(c)
Volume of the cone = 1/3 × Volume of the cylinder
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Find the endpoint of the directed line segment starting at (8,19) that is divided in a 1:5 ratio by the point (13,14)
Please help Image Attached!
A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 4.5 cm. If silver is priced at $5.00 per cm3", how much will the silver cost to make one solid sphere?
Use 3.14 for , and do not round your answer.
Answer:
The silver will cost $1908.5125 to make one solid sphere
Step-by-step explanation:
The formula for the volume of a sphere is:
V = (4/3)πr^3
where r is the radius of the sphere.
Substituting the given value for the radius:
V = (4/3)π(4.5 cm)^3
= (4/3)(3.14)(91.125 cm^3)
= 381.7025 cm^3
The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:
Cost = 381.7025 cm^3 × $5.00/cm^3
= $1908.5125
f) the perpendicular distance of
the point G from the x-axis.
g) the point whose perpendicular distance from y-axis is 2 units.
From the given figure, we have the following:
The coordinates of the points B and F are (-5, -4) and (0, 6). The point identified by the coordinates (1, 1) is D.The abscissa of the points D and H are 1 and 0.The ordinates of the points A and C 1 and 0.The quadrant in which points B and I lie is quadrant III.The perpendicular distance of the point G from the x-axis is 4 units.The perpendicular distance of the point I from the y-axis is 2 units.The point whose perpendicular distance from y-axis is 2 units is point I.What is an ordered pair?In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Based on the cartesian coordinate (grid) above, the coordinates points and quadrants should be identified as follows;
Point A ⇔ (-4, 1) → quadrant II.Point B ⇔ (-5, -4) → quadrant III.Point C ⇔ (-2, 0) → quadrant II.Point D ⇔ (1, 1) → quadrant I.Point E ⇔ (0, -6) → quadrant IV.Point F ⇔ (6, 0) → quadrant I.Point G ⇔ (6, 4) → quadrant I.Point H ⇔ (0, 4) → quadrant I.Read more on ordered pair here: brainly.com/question/25462418
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Complete Question:
From the given figure, write
a) The coordinates of the points B and F. b) The point identified by the coordinates (1,1)
c) The abscissa of the points D and H.
d) The ordinates of the points A and C.
e) The quadrant in which points B and I lie.
f) The perpendicular distance of the point G from the x-axis.
g) The perpendicular distance of the point I from the y-axis.
h) The point whose perpendicular distance from y- axis is 2 units
The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written. The store manager then deposited $956.60. Find the checkbook balance
If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.
To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.
Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.
Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.
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The members of a volleyball team were asked what their favorite colors were. The results are shown in the Venn diagram below.
How many players included red and purple as their favorite colors?
A. 0
B. 2
C. 3
D. 4
The number of players who included red and purple as their favorite colors is 0.
option A.
What is the number of people?
The number of people who included red and purple as their favorite colors are calculated as follows;
We are going to determine this number based on the given Venn diagram.
Check the intersection of red and purple, you will notice it is empty, so there is volleyball team member who included red and purple as their favorite colors.
So the answer is zero (0) since the intersection or connection point between red and purple is empty.
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What is the name of the transformation that maps the pre-image (red) onto the image (blue)?
translation
reflection
rotation
glide reflection
The transformation that maps the pre-image (red) onto the image (blue) is reflection
Naming the transformation of the two trianglesGiven that
the pre-image (red) and the image (blue)
From the figure, we can see that
Both triangles are mirrors of one another
As a general rule
When two shapes with the same orientation and properties mirror one another, then the transformation between the shapes is the reflection transformation
This means that the transformation of the two triangles is a reflection transformation
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Alberto sights the top of a building at an angle of elevation of 70°.
The distance between Alberto and the base of the building is 93.4ft
How far is alberto from the base of the building?We can view this as a right triangle, such that one cathetus (opposite to the known angle) measures:
40ft - 6ft = 34ft
And the known angle is 70°, we want to get the other leg of the right triangle, so we can use the tangent trigonometric relation which is:
tan(angle) = (opposite cathetus)/(adjacent cathetus)
Replacing the things that we know we get:
tan(70) = x/34ft
tan(70)*34ft = x = 93.4ft
That is the distance.
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You are now a competent person monitoring the IETS at your plant. Despite the frustration
of not getting the annual bonus, you know that you cannot simply use extra coagulant
because the additional turbidity might exceed the acceptable level. In that case, determine
the amount of coagulant that gives you the lowest turbidity value. In any relevant method,
use 0.1% as the stopping criterion
A feasible solution to minimizing turbidity value is through the use of an iterative technique, entailing either gradient descent method or simulated annealing method.
How to minimize turbidityThe stopping criterion for this approach would be at 0.1 percent. It involves sequentially determining water turbidity dependent on the coagulant dosages used in adjustment procedures based on preceding calculated values.
By further implementing this process until the specified percentage average is met, ease and accuracy in assessing turbidity levels are achievable.
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y≥−
3
1
x+2
y≥3x
Which graph represents the system of inequalities?
Choose 1 answer:
Choose 1 answer:
Both lines will be solid lines and the intersection of the point will be at (1/3, 1).
Given that:
y ≥ −3x + 2
y ≥ 3x
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The region above the line y ≥ −3x + 2 is considered.
The region above the line y ≥ 3x is considered.
And both lines will be solid lines and the intersection of the point will be at (1/3, 1).
The graph is given below.
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Circle 1 is centered at (−5, 4) and has a radius of 15 units. Circle 2 is centered at (−5, −3) and has a radius of 9 units. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of .
The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.
Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.
Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:
scale factor = radius of Circle 2 / radius of Circle 1
scale factor = 9 / 15
scale factor = 3/5
The center of dilation is the center of Circle 1, since we want to preserve its position.
Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:
(0, -7) followed by dilation with a scale factor of 3/5
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h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is 11.25/(a - 1)
Estimating the average rate of change of the height of the rocketFrom the question, we have the following parameters that can be used in our computation:
h(1) = 23 meters and h(a) = 34.25 meters.
The average rate of change of the height of the rocket is
Rate = Change in height /Time
So, we have
Rate = (34.25 - 23)/(a - 1)
Evaluate
Rate = 11.25/(a - 1)
Hence, the rate = 11.25/(a - 1)
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Complete question
Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.
Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.
What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second
You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library. How far do you live from the library? please explain step by step process.
According to the information, the distance from your starting point to the library is 4 miles.
How to calculate how far do you live from the library?To calculate how far do you live from the library we have to assume that the distance from the starting point to the library is "x" miles.
According to the problem, when you are 75% of the way there, you realize you forgot a book. It means you have traveled 75% of the distance, which is 0.75x miles.
Now, you turn around and bike back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library.
From the starting point, you have traveled 0.75x miles to the point where you forgot the book, and then you traveled back 1/3 of 0.75x miles, which is (1/3)*0.75x = 0.25x miles.
Now you turn around again and bike 3.2 miles to the library. It means that the distance between the point where you realized you don't need the book and the library is 3.2 miles.
Therefore, the total distance from your starting point to the library is:
0.75x + 0.25x + 3.2 = xSimplifying the equation:
1x = 4.0Thus, the distance from your starting point to the library is 4 miles.
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Allen owns 70% of Bull Corp. If the company has 721,250 shares,
3. How many shares does Allen own?
4. If he paid $21.45 per share what was his initial total investment?
5. If the shares are now worth $60.18, what are shares total value now?
6. What would be his capital gain if he sold his shares at the new value?
Answer:
3. 504,875 shares
4. $10,829,568.75
5. $30,383,377.5
Step-by-step explanation:
1. For the first one, you just need to find 70% of 721,250, which we can do several ways:
If Allen owns 70% of Bull Corp, he owns 0.7 x 721,250 = 504,875 shares.
Therefore, Allen owns 504,875 shares of Bull Corp.
you can use cross-multiplication to solve this problem as well. Here's how:
Let X be the number of shares that Allen owns.
According to the problem, Allen owns 70% of the total number of shares, which is 721,250.
So we can write:
X/721,250 = 70/100
To solve for X, we can cross-multiply:
100X = 70 * 721,250
Simplifying the right-hand side:
100X = 50,487,500
Dividing both sides by 100:
X = 504,875
Therefore, Allen owns 504,875 shares of Bull Corp, which is the same answer we got earlier.
I added a picture below.
2. If Allen paid $21.45 PER share we just multiply that by he amount of shares, which is 504,875:
If Allen owns 504,875 shares of Bull Corp, and he paid $21.45 per share, his initial total investment would be:
Total investment = Number of shares * Price per share
Total investment = 504,875 * $21.45
Total investment = $10,829,568.75
Therefore, Allen's initial total investment was $10,830,093.75.
i added a picture for this too.
3. Just replace the 21.45 with 60.18:
If the shares are now worth $60.18, the total value of Allen's shares would be:
Total value = Number of shares * Current price per share
Total value = 504,875 * $60.18
Total value = $30,383,377.5
Therefore, the total value of Allen's shares now is $30,382,078.50.
Added a picture.
The world record in the long jump is 29 feet 4 inches. How many inches short of 10 yards is the record long jump?
The record long jump is 8 inches short of 10 yards.
First, we need to convert 10 yards to inches. Since 1 yard = 3 feet and 1 foot = 12 inches, we have:
10 yards = 30 feet
= 30 x 12 inches
= 360 inches
To find how many inches short of 10 yards the long jump is, we can subtract the length of the long jump from 360 inches:
360 inches - 29 feet 4 inches
= 360 inches - (29 x 12 + 4) inches
= 360 inches - 352 inches
= 8 inches
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The product of six and a number is 108. What is the solution to the equation 1822, 102, 648
The value of the number is 18. Option A
How to determine the valueTo determine the product of the expression, we need to consider that;
Algebraic expressions are described as those mathematical expressions that are composed of terms, their coefficients, the variables and the factors and constant values.
These expressions are also made up of mathematical operations. These operations are;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
The product of six and a number is 108
Let the number be x, we have;
6x = 108
Divide sides by the coefficient
x = 18
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20 Per Question, Algebra 2, Thanks :)
The answer to the expression is (x+3)/(x-1)
What is a quadratic expression?You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0
The given expressions are
(x² - 3x - 18) / (x²- 7x +6
(x²-6x +3x +19) / (x²-x -6x +6)
This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}
⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]
This means that [(x+3)(x-6)] / [(x-6)(x-1)]
Dividing by (x-6) to have
Therefore the value of the expression is (x+3)/(x-1)
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Write the equation of a circle with a diameter endpoints of 13 and -1 and 15 and 9
The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.
Given that:
Endpoints of diameter, (13, -1) and (15, 9)
The equation of the circle when endpoints of diameter are given is written as,
(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0
The equation of the circle is calculated as,
(x - 13)(x - 15) + (y + 1)(y - 9) = 0
x² - 28x + 195 + y² - 8y - 9 = 0
x² + y² - 28x - 8y + 186 = 0
The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.
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Mathematics
Direction. Answer the following questions.
- what is the short meaning of percentage, rate, and base?
- How we use percentage, rate and base in our daily lives. give example for each one.
(P=BxR) , (B=P/R) , (R=P/B)
The concepts of percentage, rate, and base can be defined as follows:
Percentage is the representation of a fraction or portion in relation to a whole expressed as a ratio out of 100.Rate refers to the quantitative measurement of something over a specified period, which is often expressed in terms of specific units like miles per hour or dollars per hour. Base denotes the starting point for any calculation or comparison.How to use the concepts in our daily livesIn our daily lives, we utilize these three concepts in many different ways, some examples of which are outlined below:
When we go shopping, we frequently come across discounts or sale prices offered as percentages off the original price. For example, if an item was initially $40 but is now available at a discount of 20%, it will be priced at $32.
Rates enable us to measure speed when we are driving or running with unit-based measurements. In addition, rates allow us to compare prices during grocery shopping, where we might need to know the cost per pound of apples and/or calculate interests on investments or loans.
Bases have utility while dealing with ratios or proportions. For instance, if we wish to prepare food for eight people instead of four, one can take the existing recipe as a base and adjust ingredient quantities proportionally.
The formulas P = B × R, B = P / R, and R = P / B are basic calculations that correspond to different values based on the given percentage, rate, or base. For instance, P = B × R allows us to obtain the value of P given the input of B and R.
Meanwhile, B = P / R enables us to get the value of B by punching in P and R much like calculating interest paid out each month in compound-interest cases.
Finally, R = P / B yields the value of R using inputs for P and B. These formulas find rampant use in fields like finance, economics, and mathematics.
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If you apply the changes below to the quadratic parent function, F(x) = x²,
what is the equation of the new function?
• Shift 6 units right.
• Shift 4 units down.
A. G(x) = (x-4)² +6
B. G(x) = (x − 4)² – 6
C. G(x) = (x + 6)² − 4
D. G(x) = (x − 6)² – 4
The equation for the translated function is the one in option D:
G(x) = (x - 6)² - 4
What is the equation of the new function?We start with the parent quadratic function:
F(x) = x²
We apply two translations, one of 6 units to the right which can be written as:
G(x) = F(x - 6)
And a translation of 4 units down, which is written as:
G(x) = F(x - 6) - 4
Replacing F(x) we will get:
G(x) = (x - 6)² - 4
The correct option is D.
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Select the correct answer. How many solutions for x does the following equation have? A. 4 B. 0 C. infinite D. 1
The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.
We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.
We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;
Now solving for p,
2 (p+ 7) = 4 - 8
Open the bracket,
2p+ 14 = 4 - 8
Combine the like terms,
2p = -4 - 14
2p = -18
p = -18/2 = -9
Therefore, the equation has only one solution which is -9.
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The acute angle with vertex Q measure 60 degrees. Use an equation to find the keasure if the obtuse angle with vertex P
The measure of the obtuse angle with vertex P is 30 degrees.
We have,
If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.
Let's call the measure of this obtuse angle x.
By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.
Therefore, we can write the equation:
60 degrees + 90 degrees + x = 180 degrees
Simplifying this equation, we get:
x = 180 degrees - 60 degrees - 90 degrees = 30 degrees
Therefore,
The measure of the obtuse angle with vertex P is 30 degrees.
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