Let f(x)=25x2−2 . The function g(x) is a vertical stretch of f(x) by a factor of 2. What is the equation of g(x)?
When the function f(x)=25[tex]x^2[/tex]−2 is vertically stretched by a factor of 2 to create the function g(x), the resulting equation is g(x) = 50[tex]x^2[/tex]−4.
Explanation:The equation of g(x) can be found by vertically stretching f(x) by a factor of 2. Since f(x) = 25[tex]x^2[/tex] - 2, we can multiply the function by 2 to get g(x) the equation:
The function g(x) is described as a vertical stretch of the function f(x) by a factor of 2. If f(x)=25[tex]x^2[/tex]−2, a vertical stretch implies that we multiply all y-coordinates by the given factor, which is 2 in this case. Therefore, g(x) will be 2*f(x).
This gives us:
g(x) = 2*(25[tex]x^2[/tex] −2)
Expand this:
g(x) = 50[tex]x^2[/tex]−4
So, the equation of g(x) after the vertical stretch of f(x) by a factor of 2 is g(x) = 50[tex]x^2[/tex] −4.
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The equation of g(x), which is a vertical stretch of f(x) = 25x² - 2 by a factor of 2, is g(x) = 50x² - 4.
To solve this, we need to apply a vertical stretch to the function f(x).
A vertical stretch by a factor of 2 means multiplying the entire function f(x) by 2.
Given :
f(x) = 25x² - 2
we multiply it by 2:
g(x) = 2 * (25x² - 2)
g(x) = 50x² - 4
So, the equation of g(x) is g(x) = 50x² - 4.
A retail store marks up its OTC (over-the-counter) merchandise 50% based on acquisition cost. What's the retail price of an item that costs $2?
A toy rocket was shot into the air. The graph below represents the height over the time of the rocket. Which of the following are true? Select all that apply.
A. The rocket was launched from a platform 4.9 feet above the ground
B. The rocket reached a maximum height of 59 feet
C. It took the rocket 3.5 seconds to reach its maximum height
D. The rocket landed after 34 seconds
E. The equation that represents the rocket’s height over time has two solutions
The correct statements are:
- B. The rocket reached a maximum height of 59 feet.
- C. It took the rocket 3.5 seconds to reach its maximum height.
- E. The equation that represents the rocket’s height over time has two solutions.
To determine which statements about the rocket's flight are true, analyze the given graph.
1. Statement B: The rocket reached a maximum height of 59 feet.
- This statement is true. The highest point on the graph is marked as (3.5, 59), indicating that the maximum height of the rocket was 59 feet.
2. Statement C: It took the rocket 3.5 seconds to reach its maximum height.
- This statement is true. The coordinates (3.5, 59) show that the rocket reached its maximum height at 3.5 seconds.
3. Statement E: The equation that represents the rocket’s height over time has two solutions.
- This statement is true. The parabolic path of the rocket implies a quadratic equation. A quadratic equation typically has two solutions, which correspond to the times when the rocket is at ground level (height = 0). From the graph, we see the rocket starts at (0, 0) and lands at (6.9, 0), confirming two solutions.
Verifying the incorrect statements:
1. Statement A: The rocket was launched from a platform 4.9 feet above the ground.
- This statement is false. The graph shows that the rocket was launched from the origin point (0, 0), meaning it was launched from ground level, not 4.9 feet above the ground.
2. Statement D: The rocket landed after 34 seconds.
- This statement is false. The graph indicates the rocket landed at 6.9 seconds, not 34 seconds.
The correct options are:
A. The rocket was launched from a platform 4.9 feet above the ground.
B. The rocket reached a maximum height of 59 feet.
C. It took the rocket 3.5 seconds to reach its maximum height.
D. The rocket landed after 34 seconds.
E. The equation that represents the rocket's height over time has two solutions.
To determine the validity of each statement, we must analyze the graph of the rocket's height over time. Here is the logical reasoning behind each option:
A. The rocket was launched from a platform 4.9 feet above the ground.
This statement is true if the graph's vertical intercept (the height at time zero) is 4.9 feet. The vertical intercept is the starting height of the rocket before it is launched.
B. The rocket reached a maximum height of 59 feet.
This statement is true if the graph reaches a maximum value of 59 feet at some point in time. This would be the peak of the graph, where the height is greatest.
C. It took the rocket 3.5 seconds to reach its maximum height.
This statement is true if the time at which the graph reaches its maximum height is 3.5 seconds. This is the horizontal coordinate of the peak of the graph.
D. The rocket landed after 34 seconds.
This statement is true if the graph returns to the horizontal axis (height of zero) at 34 seconds. This would indicate that the rocket has returned to the ground.
E. The equation that represents the rocket's height over time has two solutions.
This statement is true if the graph intersects the horizontal axis at two distinct points. The first intersection represents the launch point (time zero), and the second intersection represents the landing point. The fact that there are two intersections implies that the equation has two solutions.
I have 10 minutes, Help! Joani has some stuffed animals. She has 2 times as many as Lily. Lily has 6 stuffed animals. Joanie gave 2 away and bought 4 more. How many stuffed animals does Joani have now?
Students's solution: Lily has 6 stuffed animals, so Joani had 6 × 2 to begin with. So Joani had 12 stuffed animals. She gave away 2, so 12 – 2 = 10. She bought 4, so 10 + 4 = 14. So Joani has 14 stuffed animals.
Here is another problem that can also be solved by working backwards.
Wyatt has 3 times as many baseballs as golf balls. He has 5 fewer tennis balls than baseballs. Wyatt has 4 golf balls.
How many tennis balls does Wyatt have?
Which of the following values are needed to determine the area of the trapezoid choose all that apply
find cos^-1 0.9455 to the nearest degree.
A.26 degrees
B.71 degrees
C.19 degrees
D.41 degrees
Answer:
[tex]Cos^{-1}(0.9455)[/tex] = 19 degree.
Step-by-step explanation:
Given: [tex]Cos^{-1}(0.9455)[/tex].
To find : values of [tex]Cos^{-1}(0.9455)[/tex].
Solution : We have given that [tex]Cos^{-1}(0.9455)[/tex].
[tex]Cos^{-1}(0.9455)[/tex]. =0.33166 radians
In form of degree
0.33166 radians = 19 degree.
Therefore, [tex]Cos^{-1}(0.9455)[/tex] = 19 degree.
A person sold 100 shares of stock at a loss of 40%. If the selling price for the 100 shares was 3000 which of the following comes closest to what was paid for the stock
what happens in the last part if it is 2/8 + 1
Solve -12>3x then graph on a number line that you create and please please show all of your work step by step.
Solve the equation and show all work please show steps!!
4f + 11 = 29
Annabel went to the beach for the day and rented a surfboard. The surfboard rental was $7.00 per hour, plus a rental fee of $12.00 which equation could Annabel use to find the total cost (c) if renting a surfboard for x amount of hours?
a $58 camera is on sale for 20% off find the sale price
The sales price of the camera is $46.4
How to determine the sales price?The given parameters are:
Discount = 20%
Price = $58
The sales price is calculated using:
Sales price = Price * (1 - discount)
This gives
Sales price = $58* (1 - 20%)
Evaluate
Sales price = $46.4
Hence, the sales price of the camera is $46.4
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HELPP ME PLZZZZ
Which of the four images was formed by a reflection of the letter T?
A
B
C
D
The answer is not A because T would be flipped, the answer is not D because T can not be reflected in that area without translations, and the answer is not B because T cannot (once again) be reflected in such locations without translations, Therefore, that leaves us with our best bet being the answer C.
original price 75$ markdown 15%
5.7x=5.64
what is x?
Find the area of the regular polygon.
Please explain how you got your answer!
What is the volume of a cube with a side length of 5 cm?
A)
10 cm3
B)
15 cm3
C)
25 cm3
Eliminate
D)
125 cm3
Which expression is equivalent to the expression below? Select all that apply. –25(15 – 20d + 5c) A. –30 + 40d – 10c B. –6 + 8d – 2c C. –2c + 8d – 6 D. 6 – 8d + 2c
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. So, the correct options are B and C.
Given:
The given expression is:
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
To find:
The equivalent expressions.
Explanation:
We have,
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
Using the distributive property, we get
[tex]=-\dfrac{2}{5}(15)-\dfrac{2}{5}(-20d)-\dfrac{2}{5}(5c)[/tex]
[tex]=-6+8d-2c[/tex]
It can be rewritten as:
[tex]=-2c+8d-6[/tex]
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. Therefore, the correct options are B and C.
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Upon applying the distributive property, the given expression, –25(15 – 20d + 5c), simplifies to –375 + 500d – 125c. None of the options provided match this expression, making the correct answer 'None of the above'.
Explanation:The student is asked to find an expression equivalent to –25(15 – 20d + 5c). To do this, we will apply the distributive property to multiply –25 by each term inside the brackets. This gives us:
–25 × 15 = –375–25 × (–20d) = 500d–25 × 5c = –125cCombining these we get the expression –375 + 500d – 125c. When we look at the options provided, none are equivalent to the expression we derived. Therefore, the correct answer is:
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Nicole uses 3 cups of vinegar and her salad dressing recipe how much vinegar with Nicole used to make 3/4 of recipe
Final answer:
Nicole will need 2 1/4 cups of vinegar to make 3/4 of her salad dressing recipe, as you multiply the total amount (3 cups) by 3/4.
Explanation:
Nicole uses 3 cups of vinegar for her full salad dressing recipe. To make 3/4 of the recipe, you would calculate three-quarters of the total amount of vinegar used. Simply multiply 3 cups by 3/4 to find out how much vinegar Nicole would need.
The calculation is as follows:
3 cups × 3/4 = 9/4 cups9/4 cups can be simplified to 2 1/4 cupsThus, Nicole will need 2 1/4 cups of vinegar to make three-quarters of her salad dressing recipe.
Write and solve a real-world problem that represents the following one-variable inequality. Then solve the inequality, showing all steps.
200 + 0.75x ≤100 + 2.50x
helppppppppppppp meeeeeeeeeeeeeeeee
You are collecting email addresses from 74 customers per day, which is about 90% of the daily goal of __________ emails per day."
What is greater 2.159 or 2.259
what is 64/25 as a mixed number?
Use tens to solve 13-7
Draw 4 circle shade 2 circle
Could someone explain me question 9 thank you
Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16
Answer:
Step-by-step explanation:
To obtain the graph of a parabola, three data are necessary: the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values of x for which the expression is 0. Graphically, the roots correspond to the abscissa of the points where the parabola cuts the x-axis.) and the concavity.
Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:
Vertex= for your calculation, [tex]xv=\frac{-b}{2*a}=\frac{-12}{2*2}[/tex], so xv=-3. Now that you know x, all you have to do is enter its numerical value into the original formula to find yv. yv=2*(-3)²+12*(-3)+16. Then yv=-2Roots: The roots are calculated using the expression: [tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]. Replacing the values that you have:[tex]x1,x2=\frac{-12+-\sqrt{12^{2}-4*2*16 } }{2*2}[/tex] Solving, you obtain x1=-2 and x2=-4Concavity: If a> 0 (positive) the parabola is concave or pointed upwards, while if a <0 (negative) the parabola is convex or pointed downwards. In this case a = 2, so the parabola opens upward, being concave.In this way, the graph shown in the attached image is obtained.
A cylinder shaped juice pitcher has a diameter of 12 cm and a height of 25 cm. What volume of juice does the pitcher contain when it is 25% full? Use 3.14 to approximate pi. Enter your answer as a decimal to the tenths place in the box
Answer:
706.5
Step-by-step explanation:
Zoe's Fish tank holds 27 L of water she uses a 3L container to fill the tank how many times does she have to fill the three litter container in order to fill the fish tank
Zoe's Fish tank holds 27 L of water, so this is the capacity of the tank. On the other hand, Zoe uses a 3L container in order to fill the tank, so the question is how many times does she have to fill the three litter container in order to fill the fish tank? Let's solve this as follows:
First time:
She pours 3L
Second time:
She pours another 3L, but she previously poured 3L, so she has poured 6L
Third time:
She pours another 3L, but she previously poured 6L, so she has poured 9L
Fourth time:
She pours another 3L, but she previously poured 9L, so she has poured 12L
Fifth time:
She pours another 3L, but she previously poured 12L, so she has poured 15L
Sixth time:
She pours another 3L, but she previously poured 15L, so she has poured 18L
Seventh time:
She pours another 3L, but she previously poured 18L, so she has poured 21L
Eighth time:
She pours another 3L, but she previously poured 21L, so she has poured 24L
Ninth time:
She pours another 3L, but she previously poured 24L, so she has poured 27L
According to this, she needs to pours the 3L container nine times in order to fill the fish tank. This can also be solved dividing 27L/3L= 9