Suppose that F(x) = x^2 and G(x) = 2x^2-5. Which statement best compares the graph G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units to the right
B. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down
C. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units to the right
D. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down
Answers
Comparing the graphs of F(x) = [tex]x^2[/tex] and G(x) = [tex]2x^2[/tex] - 5 shows that G(x)'s graph is F(x)'s graph stretched vertically by a factor of 2 and then shifted 5 units down.
There is no horizontal shift involved.
Explanation:Comparing the functions F(x) = [tex]x^2[/tex] and G(x) = [tex]2x^2[/tex] - 5, we observe two main transformations applied to F(x) to obtain G(x).
First, the coefficient 2 in front of[tex]x^2[/tex] in G(x) indicates that the graph of F(x) is stretched vertically by a factor of 2.
This stretching makes the graph of G(x) stretch away from the x-axis, becoming narrower compared to F(x).
Second, the term -5 added to [tex]2x^2[/tex] suggests that the entire graph of F(x) after being stretched is then shifted 5 units down.
It's important to note that this vertical shift is down because of the negative sign in front of 5; there is no horizontal shift involved.
Therefore, the statement that best compares the graph of G(x) to the graph of F(x) is:
D. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.Based on the analysis, the correct statement is:
D. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
1. Identify the base function:
Both F(x) = x^2 and G(x) = 2x^2-5 share the same base function, which is x^2. This means their graphs have the same basic shape, a parabola.
2. Analyze the transformations:
Vertical stretch: The coefficient of x^2 in G(x) is 2, which is a vertical stretch factor of 2 compared to F(x). This stretches the graph of G(x) vertically by a factor of 2, making it narrower.
Vertical shift: The constant term in G(x) is -5, which corresponds to a downward shift of 5 units compared to F(x). This moves the entire graph of G(x) 5 units down.
3. Combine the transformations:
The graph of G(x) is obtained by taking the graph of F(x), stretching it vertically by a factor of 2, and then shifting it down by 5 units.
For graph refer to image:
Related Questions
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate?
Answers
To answer the above question, if the store donates 24 soccer balls the number of basketballs does the store donate is 28 basketballs
Answer:
Step-by-step explanation:
First you have to know that you if you divide 24 by 6 you would have to take 7 multiplied by 4 to get 28
List 12 spherical objects that would be around the home. Please do not list all balls, soccer ball, basket ball, etc.
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1. Which fractions are equivalent to 25/45. Please give two examples.
2. Which describes independent events?
Spinning two fours on a spinner divided into four numbered sections.
Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card.
Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another.
Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.
Answers
Any fraction obtaining by multiplying both numerator and denominator by the same quantity will result in an equivalent fraction.
Examples:
- divide both numerator and denominator by 5 => 5/9 is equivalent
- multiply both numerator and denominator by 2 => 50 / 90 is equivalent
- multiply both numerator and denominator by 10 => 250 / 450 is equivalent.
2)
Spinning two fours on a spinner divided into four numbered sections: these are independent events, becasue one result does not influence the other.
Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card: they are not independent, because if the first card is a king the probability of the second card will be different than if the first card is not a king.
Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another: they are not independent because whether the first two marbles are green or not, make the probabilities for the second event different.
Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.: they are not independent, by similar reason explainded in the two previos options.
when 1600 is increased by 20% and the resulting number is decreased by y% . the answer is 1536
Answers
Use the area model to find the product of 28×32
Answers
Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)
Question 16 options:
3 miles
5 miles
7 miles
9 miles
Answers
For this problem, a = 3, b = 4
c = √(3² + 4²) = √5² = 5
Which of the following is the equation of a line parallel to the line y = 4x + 1, passing through the point (5,1)?
A. 4x + y = 19
B. 4x - y = 19
C. 4x + y = -19
D. -4x - y = 19
...?
Answers
4x-y=19 is the correct answer for this problem
Which answer describes the type of sequence?
3, 4, 5, 6, ...
A. neither arithmetic nor geometric
B. geometric
C. arithmetic
Answers
Tony invested $5,500 in a four-year CD that paid 4.8% interest, but later needed to withdraw $475 early. If the CD’s penalty for early withdrawal was three months’ worth of interest on the amount withdrawn, how much of a penalty did Tony pay?
a.
$5.70
b.
$22.80
c.
$60.30
d.
$66.00
Answers
Answer:
It's A-$5.70 :))))
Step-by-step explanation:
The penalty will be $5.70 which corresponds to option A.
The question is about calculating the penalty for early withdrawal from a Certificate of Deposit (CD). Tony invested $5,500 in a CD at a 4.8% interest rate and withdrew $475 early.
To calculate the penalty, we first need to find three months' worth of interest on the amount withdrawn.
The annual interest on $475 at 4.8% is:
Interest = Principal × Rate × Time
Interest = $475 × 0.048 × 1 = $22.80
Since the penalty is three months' worth, we divide the annual interest by 4 (because there are four 3-month periods in a year):
Penalty = $22.80 / 4
= $5.70
Sara is burdened with debt and runs the risk of defaulting on her car loan. She is also late with her credit card payments. What action should Sara take to help her situation?
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What is bigger 5/6 or 13/18?
Answers
6 goes into 18 three times. If we multiply (5/6) by 3 on top and bottom you get
[tex]\frac{15}{18} [/tex]
Now we can compare numerators, since 15 > 13
[tex]\frac{5}{6} \ \textgreater \ \frac{13}{18}[/tex]
Write five and three eights as an improper fraction and as a mixed number
Answers
43/8 (improper fraction)
5.375 (decimal)
How do I convert 4/5 to a percent
Answers
= 80%
=0.8
Evie was doing a science fair project by surveying her biology class. She found that of the 30 students in the class, 15 had brown hair and 17 had blue eyes and 6 had neither brown hair nor blues eyes. Determine the number of students who had brown hair and blue eyes.
Answers
Let f(x)=x^3-7x^2+25x-39 and let g be the inverse function of f. What is the value of g'(0)? ...?
Answers
Below are the choices that can be found from other sources:
a) -1/25
b) 1/25
c) 1/10
d) 10
e) 25
f(x) = x^3 - 7x^2 + 25x - 39
f'(x) = 3x^2 - 14x + 25
Since g is the inverse function of f
f(g(x)) = x
Differentiate both sides of equation
f'(g(x)) g'(x) = 1
Now f(3) = 0, so g(0) = 3
g'(x) = 1 / f'(g(x))
g'(0) = 1 / f'(g(0))
g'(0) = 1 / f'(3)
g'(0) = 1 / 10
Cody is selling chocolate and white chocolate candy bars for a school fundraiser. 30% of the candy bars sold have been white chocolate. If Cody has sold 24 white chocolate candy bars, how many total candy bars has he sold?
Answers
Answer: The answer is 80
Step-by-step explanation: because first of all divide 24 by 30% which equals 80 and second I took the USATP Test and got it right
If the function has jump discontinuity , infinite discontinuity , continuous , or the function has point discontinuity
X^3 + 7x^2 + 10x / x + 5
Answers
f(x) = x(x+5)(x+2) / (x+5)
f(x) = x(x+2)
The function is continuous everywhere/ in any domain.
The function x^3 + 7x^2 + 10x / (x + 5) is discontinuous at x = -5, where it has a jump discontinuity. The function is otherwise continuous and does not approach infinity, indicating no infinite discontinuity.
Explanation:The given function is x^3 + 7x^2 + 10x / (x + 5). To determine the continuity of the function, it's crucial to identify any values of x that would make the denominator zero since the function is undefined at these points.
In this case, if x is -5, the denominator will be zero, making the function undefined. Therefore, the function has a point of discontinuity or a jump discontinuity at x = -5.
The function does not have an infinite discontinuity because it never approaches infinity as x approaches any particular value. This function is continuous at every point except for x = -5. Therefore, "the function x^3 + 7x^2 + 10x / (x + 5) has one point of discontinuity at x = -5."
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if x>2, then x^2-a-6 / x^2-4=
Answers
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )
[tex] \frac{(x-3)(x+2)}{(x-2)(x+2)}= \frac{x-3}{x-2} [/tex]
Given than line a is parallel to line b and that line c is parallel to line d, if m<13=(12x-22) & m<14=(9x-29), find m<2.
a 65
b 70
c 85
d 110
Answers
12x-22+9x-29=180
21x-51=180
x=11
m<2=m<14
m<2=70°
The measure of ∠2 is 70° .
What is corresponding angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other and are equal in measure.
What is supplementary angles angles?When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.
According to the question
line a is parallel to line b and c and d are transversal for them
line c is parallel to line d and a and b are transversal for them
m∠13 = (12x - 22)°
m∠14 = (9x - 29)°
Now
As, ∠13 and ∠14 forms supplementary angles .
i.e
m∠13 + m∠14 = 180°
12x - 22° + 9x - 29° = 180°
21x - 51° = 180°
21x = 180° + 51 °
21x = 231 °
x = 11°
So,
m∠13 = 12*11 - 22° = 110°
m∠14 = 9*11 - 29° = 70°
Now,
according to corresponding angles
m∠14 = m∠6 = m∠2 = 70°
Hence, the measure of ∠2 is 70° .
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the form of a linear equation that shows the slope and one point is the...? ...?
Answers
Equations in point-slope form look like this: y - k = m(x - h) where m is the slope of the line and (h, k) is a point on the line (any point works). To write an equation in point-slope form, given a graph of that equation, first determine the slopeby picking two points.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
The form of a linear equation that shows the slope and one point is known as the point-slope form, which is written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
The form of a linear equation that shows the slope and one point is known as the point-slope form. Unlike the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, the point-slope form is typically written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
For example, if you are given a slope of 3 and a point (2, 5), the equation of the line in point-slope form would be y - 5 = 3(x - 2). To visualize this, consider a line graph with the x-axis as the horizontal axis and the y-axis as the vertical axis.
If this was plotted, the line would rise 3 units on the vertical axis for every 1 unit it rises on the horizontal axis, illustrating the concept of slope as the rise over run, which is consistent along the entire length of a straight line.
(Distribute , then simplify the remaining expression. Final answer must be in standard form) Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
Answers
[tex]4x^2(2x^2+x-5) - x(x^3+5x^2-3) + 17[/tex]
[tex]4x^2(2x^2)+4x^2(x)+4x^2(-5) - x(x^3)-x(5x^2)-x(-3) + 17[/tex]
[tex]8x^4+4x^3-20x^2 - x^4-5x^3+3x + 17[/tex]
[tex]7x^4-x^3-20x^2+3x + 17[/tex]
So the final simplified answer to problem 22 is
[tex]7x^4-x^3-20x^2+3x + 17[/tex]
--------------------------------
Problem 23
[tex]-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)[/tex]
[tex]-2x(x^3)-2x(-6x^2)-2x(6)+4x^3-(5x^4)-(10x)[/tex]
[tex]-2x^4+12x^3-12x+4x^3-5x^4-10x[/tex]
[tex]-7x^4+16x^3-22x[/tex]
So problem 23 simplifies to
[tex]-7x^4+16x^3-22x[/tex]
---------------------------------------------------------
Problem 24
[tex]4b[2a^2-5(3ab-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-5(3ab)-5(-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-15ab+10b^2]+29ab^2[/tex]
[tex]4b[2a^2]+4b[-15ab]+4b[10b^2]+29ab^2[/tex]
[tex]8a^2b-60ab^2+40b^3+29ab^2[/tex]
[tex]8a^2b-31ab^2+40b^3[/tex]
So problem 24 simplifies to
[tex]8a^2b-31ab^2+40b^3[/tex]
-------------------------------------------------
Problem 25
[tex]2y(6x-4x^2y)+13x^2y^2-6[/tex]
[tex]2y(6x)+2y(-4x^2y)+13x^2y^2-6[/tex]
[tex]12xy-8x^2y^2+13x^2y^2-6[/tex]
[tex]12xy+5x^2y^2-6[/tex]
The final answer for problem 25 is
[tex]12xy+5x^2y^2-6[/tex]
A number t multiplied by -4 is a least -2/5
Answers
The inequality -4t ≥ -2/5, where t is the variable in question, simplifies to t ≤ 1/10, indicating that t must be less than or equal to 0.1. Negative time values are a conceptual tool used in physics to discuss intervals before a chosen start time.
The student's question is about solving an inequality involving a variable t and understanding the concept of negative time. The inequality is given as a number t multiplied by -4 is at least -2/5. Mathematically, this can be written as -4t ≥ -2/5. To solve for t, we can divide both sides by -4 (remembering that dividing by a negative switches the inequality sign), so t ≤ 1/10 or t is less than or equal to 0.1. This condition must hold true for any value of t for the statement to be correct.
The concept of negative time is often used in physics to describe events that occurred before a certain reference point in time. The references to negative time values represent periods before some initial event, similar to counting backward. A negative t value does not imply 'backward' time travel in the literal sense, but rather a point in time before the designated start (t = 0).
WILL UPVOTE
what is the value of x in the following equation: 3x-15=4x+36
A.21
B.-51
C.-21
D.none of these
Answers
3x = 4x + 51
-x = 51
x = -51
________________________________________
Explanation:
________________________________________
Given: 3x − 15 = 4x + 36 ; Solve for "x" .
________________________________________
Let us subtract: "3x" from EACH side of the equation; AND
add: "15 to EACH side of the equation:
__________________________________________
→ 3x − 15 − 3x + 15 = 4x + 36 − 3x + 15 ;
__________________________________________
to get:
__________________________________________
→ 0 = x + 51 ;
___________________________________
→ Subtract "51" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;
___________________________________
→ 0 − 51 = x + 51 − 51 ;
__________________________
→ - 51 = x ; ↔ x = - 51 ; which is: "Answer choice: [B]: -51".
___________________________________
→ Now, let us check our answer, "x = -51 ; by plugging in "-51" for "x" in the original equation, and seeing in both sides of the equation hold true when x = - 51 ;
______________________________
→ Given: 3x − 15 = 4x + 36 ;
→ Substitute "- 51 for "x" ;
→ Start with the "left-hand side" of the equation:
→ 3x − 15 = (3*-51) − 15 = -153 − 15 = -168 ; when x = -51 ;
→ Then, let us examine the "right-hand side" of the equation:
__________________________________________
→ 4x + 36 ; Substitute "-51" for "x" ;
→ (4*-51) + 36 = -204 + 36 = -168
→ Does the "left hand side" of equation = the "right-hand side of the equation" when: x = -51???
______________________________
→ That is, when x = -51, does: - 168 =? -168 ?? Yes!
_________________________
Below are the functions of y = |x| and y = |x| – 3. How are the functions related?
a. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
b. The functions have the same shape.
c. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
d. The functions have the same y-intercept.
Answers
Hope this helps u!!!
Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function. Explain your response.
Answers
Ask yourself, Are there 2 or more x's that are the same value?
Yes) Continue to next step
No) It's a function :)
If there are 2 or more of the same x value, ask your self now if those x's have different y Values.
Yes) It is not a function, one x can not have more that 1 y value
No) Its a function :)
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
B. The cost of natural gas is $0.20 per unit.
C. The cost of electricity is $0.72 per unit.
D. The cost of natural gas is $0.83 per unit.
Answers
Answer:
The correct option is D. The cost of natural gas is $0.83 per unit.
Step-by-step explanation:
Consider the provided equation.
[tex]116y = 96.28[/tex]
We need to solve the above equation for y.
Divide both the sides by 116.
[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]
[tex]y=0.83[/tex]
Now consider the provided options.
Hence, the correct option is D. The cost of natural gas is $0.83 per unit.
An equation that sets two fractions equal to each other is called a ____.
Answers
Final answer:
An equation that sets two fractions equal to each other is known as a proportion, where equivalent ratios or fractions indicate the same value. This maintains the equality governed by the rules of algebra, important when performing operations on both sides of an equation.
Explanation:
An equation that sets two fractions equal to each other is called a proportion. This type of equation indicates that two ratios or fractions are equivalent. For example, if we have ½ on one side of the equation and 2/4 on the other, we have a proportion because both fractions represent the same amount.
When we have fractions with the same value in the numerator and the denominator, such as ¹¹/₁₀⁰ for micrometers to meters, we can simplify this to 1 because the quantities cancel each other out. This is true by the rules of algebra, specifically the property that if we perform the same operation on both sides of an equality, the equation remains balanced. This concept is crucial when working with proportions and equations involving fractions.
It's also important to remember that when adding fractions, they must have a common denominator. Ratios and percentages are other forms of expressing relative sizes or amounts which can also be related back to fraction and proportion concepts.
What decimal is represented by this expanded form? 5 x 10,000 3 x 1,000 2 x 10 8 x 1 6 1/1,000 4 x 1/,000?
Answers
water flows from a faucet at a rate of 5 liters every 25 seconds. At this rate, how much water will flow form the faucet in 45 seconds. Make a table.
Answers
Which ordered pairs are solutions to the inequality y − 4x ≤ −6?
Select each correct answer.
A.(1, 3)
B. (−2, −14)
C. (−1, −9)
D. (3, 5)
E. (0, −5)
Answers
The order pair given is (1, 3)
y-4x = 3-4(1) = -1
-1 is greater than -6
Therefore, this choice is wrong
Choice b:
The order pair given is (-2, -14)
y-4x = -14-4(-2) = -6
-6 is equal -6
Therefore, this choice is correct
Choice c:
The order pair given is (-1, -9)
y-4x = -9-4(-1) = -5
-5 is greater than -6
Therefore, this choice is wrong
Choice d:
The order pair given is (3, 5)
y-4x = 5-4(3) = -7
-7 is less than -6
Therefore, this choice is correct
Choice e:
The order pair given is (0, -5)
y-4x = -5-4(0) = -5
-5 is greater than -6
Therefore, this choice is wrong
Answer
b and d
Step-by-step explanation: