In 2012, the population of a city was million. The exponential growth rate was % per year.

What is y=x by a vertcal stretch of 5

kakasveta [241]

Answer: The vertical stretch of 5 in the equation y = x is defined by $y=5x$ .

Explanation:

The given equation is,

$y=x$

It can be written as,

$f(x)=x$

The function is defined as $S\cdot f(x)$ .

If $S\geq 1$ , then the function has a vertical stretch by a factor of S units.

If $0$ , then the function has a vertical shrink by a factor of S units.

Since we have to find the vertical stretch of 5 in the equation y = x.

$y=5f(x)$

$y=5x$

The below figure shows the graph of y = x and $y=5x$ .

7 0

2 years ago

Can someone help me find the measure of each angle in the triangle?

Cerrena [4.2K]

Answer:Remember -- the sum of the degree measures of angles in any triangle equals 180 degrees. ... So, the measure of angle A + angle B + angle C = 180 degrees. ... If a triangle is equilateral, what is the degree measure of each of its angles?

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Amira has 3/4 of a bag of cat food. her cat eats 3/4 lbs of a bag per week

Stels [109]

Answer:

1 week

Step-by-step explanation:

<u><em>The correct question is</em></u>

Amira has 3/4 of a bag of cat food .Her cat eats 3/4 of a bag per week . How many weeks will the food last ?

we know that

To determine how many weeks her food will last, we take the amount of food and divide by how much she feeds her cats.

3/4 bag ÷ 3/4 bag per week

$\frac{3}{4}: \frac{3}{4}$

Multiply in cross

$\frac{3*4}{4*3}=1\ week$

8 0

3 years ago

A. [4 marks]

storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is $u_{n}=u_{1}+(n-1)d$ , where

$u_{1}$ is the first term
d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is $u_{n}=u_{1}r^{n-1}$ , where

$u_{1}$ is the first term
r is the common ratio between each two consecutive terms $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∵ $u_{1}$ of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ $u_{2}$ , $u_{3}$ , $u_{6}$ are the first 3 terms of a geometric sequence

∵ $u_{2}$ = 1 + (2 - 1)d

∴ $u_{2}$ = 1 + d

∵ $u_{3}$ = 1 + (3 - 1)d

∴ $u_{2}$ = 1 + 2d

∵ $u_{6}$ = 1 + (6 - 1)d

∴ $u_{2}$ = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

(1 + 5d)

∵ The common ratio in the geometric sequence is $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∴ $r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

- Use cross multiplication with the equal fractions

∵ $\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

7 0

3 years ago

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of pape

Mashutka [201]

Answer:

Option C. is the correct option.

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each hat.

Cone with diameter six inches and slant height eight inches.

What is the correct amount of paper Aubrey will need per hat? Explain Aubrey’s mistake. Use 3.14 for π and round to the nearest inch.

A. About 70 in2; Aubrey found the surface area of the cone, but did not include the base.

B. About 70 in2; Aubrey used the diameter instead of the radius to find the surface area of a cone.

C. About 75 in2; Aubrey found the surface area of the cone and included the base.

D. About 75 in2; Aubrey found the volume of the cone instead of the surface area.

Lateral surface area of a cone = Paper required to for each hat

Lateral surface area = πrl

Here r = radius of the cone

l = lateral height of the cone

Lateral surface area = π(3)(8)

= 75.36 square inches

≈ 75 square inches

Therefore, total paper required for each cap is about 75 square inches.

Total surface area of the cone (Lateral area + Area of the base)

= πr(r + l)

= 3.14(3)(3 + 8)

= 103.62

≈ 104 square inches.

Aubrey did a mistake by finding the total surface area (including base area) of the cone instead of lateral surface area.

Therefore, option C. is the correct option.

7 0

2 years ago

In​ 2012, the population of a city was million. The exponential growth rate was ​% per year.

In 2012, the population of a city was million. The exponential growth rate was % per year.