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3 years ago

if you horizontally strech the quadratic parent function, f(x)=x^2, by a factor of 4, what is the equation of the new function?

Mathematics

1 answer:

max2010maxim [7]3 years ago

8 0

Answer:

g(x) = x^2/16

Step-by-step explanation:

To stretch a function horizontally by a factor of k, replace x with x/k.

You want a stretch factor of 4, so your function is ...

g(x) = f(x/4) = (x/4)^2

g(x) = x^2/16

The attached graph shows the horizontal stretch.

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What is −4(−5x+2)−3x−5= -30

alexandr1967 [171]

Answer:

x = -1

Step-by-step explanation:

Step 1: Write equation

-4(-5x + 2) - 3x - 5 = -30

Step 2: Solve for x

Distribute -4: 20x - 8 - 3x - 5 = -30

Combine like terms: 17x - 13 = -30

Add 13 on both sides: 17x = -17

Divide both sides by 17: x = -1

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3 years ago

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A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the teams change in field posit

patriot [66]

Subtract 5 each play so go backwards from zero and you should finish at -15

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3 years ago

Find the indicated values, where g(t) = t^2 - t and f(x) = 1 + x g(f(3)-2f(1))

VashaNatasha [74]

Answer:

B. 0

Step-by-step explanation:

Given

g(t) = t² - t

f(x) = 1 + x

Required

Find g(f(3) - 2f(1))

First, we'll solve for f(3)

Given that f(x) = 1 + x

f(3) = 1 + 3

f(3) = 4

Then, we'll solve for 2f(1)

2f(1) = 2 * f(1)

2f(1) = 2 * (1 + 1)

2f(1) = 2 * 2

2f(1) = 4

Substitute the values of f(3) and 2f(1) in g(f(3) - 2f(1))

g(f(3) - 2f(1)) = g(4 - 4)

g(f(3) - 2f(1)) = g(0)

Now, we'll solve for g(0)

Given that g(t) = t² - t

g(0) = 0² - 0

g(0) = 0 - 0

g(0) = 0

Hence, g(f(3) - 2f(1)) = 0

From the list of given options, the correct answer is B. 0

5 0

3 years ago

A chemist has 100 g of a 15% saline solution that she wants to strengthen to 29%. The percentage P of salt in the solution by ma

Vinil7 [7]

Answer:

D., x= 19.7 or ≈20. g

Step-by-step explanation:

P(x) = [100(15+x)]/(100+x)

When 0 g additional salt is added, x=0. we have

P(0) = [100(15+0)]/(100+0)= 15

x=0, P=15

We can see this point only on the graph D.

P(x) =29 = [100(15+x)]/(100+x)

29 = [100(15+x)]/(100+x)

29(100+x) = 100(15+x)

2900+29x = 1500+100x

2900-1500=100x-29x

1400 = 71x

x ≈ 19.7 g or ≈20. g

From the graph D, we can see that to get 29% we need to add ≈ 20 g of salt.

4 0

3 years ago

Review the graph of function g(x). On a coordinate plane, y = g (x) has a straight line connecting point (negative 5, 4) and (ne

Step2247 [10]

Answer:

Option (1)

Step-by-step explanation:

From the graph attached,

Points connecting the graph 'g' are (-5, 4), (-2, 1), (0, -1), (4, -2).

Since, rule to get the points lying on the graph of the inverse of the given function is,

(x, y) → (y, x)

If (x, y) is a point on function 'g' then (y, x) will lie on the inverse of the given function.

By the given rule, points on $g^{-1}(x)$ will be,

(4, -5), (1, -2), (-1, 0), (-2, 4)

Therefore, value of the inverse function at x = 4 will be,

y = $g^{-1}(4)$ = -5

Option (1) will be the correct option.

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3 years ago

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