Find the area of the parallelogram shown below.

Which is a stretch of an exponential decay function ?

sergiy2304 [10]

Using translation concepts, a stretch of a decay exponential function is given by:

$f(x) = 5\left(\frac{1}{5}\right)^x$

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

An exponential decay function is given by:

$y = ab^x$

In which |b| < 1.

A stretch means that the function is <u>multiplied by a factor with absolute value greater than 1</u>, hence the function would be given by:

$f(x) = 5\left(\frac{1}{5}\right)^x$

More can be learned about translation concepts at brainly.com/question/4521517

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7 0

2 years ago

Rewrite the function by completing the square.<br> f(x) = x2 – 10x + 44<br> +<br> f(x) = (x+

iVinArrow [24]

Answer:

$f(x)=(x-5)^{2}+19$

Step-by-step explanation:

we have

$f(x)=x^{2}-10x+44$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-44=x^{2}-10x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)-44+25=x^{2}-10x+25$

$f(x)-19=x^{2}-10x+25$

Rewrite as perfect squares

$f(x)-19=(x-5)^{2}$

$f(x)=(x-5)^{2}+19$

8 0

4 years ago

Amy loaned $5 to each of 20 people. She recorded each loan by writing -$5 in her bank book. What is the total changes in the amo

Bumek [7]

Answer:

$100

Step-by-step explanation:

multiply 5 times 20 because amy gave 5 dollars to 20 people. That would be how much she gave away in total.

5 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2

HACTEHA [7]

This question is incomplete, the complete question is;

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis

Answer:

V = π (512/15)

Step-by-step explanation:

Given that;

region of rotation

y² = 2x, x = 2y

Region is rotated about y-axis as shown in the image

for the point of intersection,

y²/2 = 2y

y² - 4y = 0

y(y-4) = 0

∴ y = 0, y = 4

so the region lies in 0 ≤ y ≤ 4

Now cross section area of washer is

A(y) = π(outer radius)² = π(inner radius)²

A(y) = π(2y)² - π(y²/2)²

A(y) = π(4y²) - π(y⁴/4)

A(y) = π(4y² - (y⁴/4))

now volume of the solid of revolution is

V = ⁴∫₀ A(y) dy

V = ⁴∫₀ π(4y² - (y⁴/4))dy

V = π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }

V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }

V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }

V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }

V = π { 256/3 - 1024/20 }

V = π { (5120 - 3072) / 60 }

V = π (512/15)

8 0

3 years ago

If y varies inversely with 2.5x, and y=5.6 and x=30, write an equation to represent this relationship

klasskru [66]

Let the constant of variation be c.
We are given that y varies inversely with 2.5x, this means that:
y = (c) / (2.5x)
This can be written as:
2.5xy = c

Now, we a re given that y = 5.6 at x = 30.
Substitute with these values in the equation to get the value of c as follows:
2.5xy = c
2.5(30)(5.6) = c
c = 420

Therefore, the equation that describes the relation is:
2.5xy = 420

3 0

4 years ago