Simplify the expression. Explain each step (3y) x 9

the drawing of a building shown below has a scale of 1 inch and 30 feet. What is the actual hdight in feet of the building

34kurt

Given:
1 inch = 30 feet

The drawing of the building of this problem has the height of 1.25 inches and base of 0.75 inches.

Actual height:
1.25 inches * 30 feet/inch = 37.50 feet

Actual base:
0.75 inches * 30 feet/inch = 22.50 feet

5 0

3 years ago

A sector with a central angle measure of \purpleD{175\degree}175°start color #7854ab, 175, degree, end color #7854ab has a radiu

Alisiya [41]

Answer: $219.94\ cm^2$

Step-by-step explanation:

Given

The central angle of a sector measures $175^{\circ}$

The radius of the circle is $r=12\ cm$

The area of the sector is given by

$\Rightarrow A=\dfrac{\theta }{360^{\circ}}\pi r^2$

Insert the values

$\Rightarrow A=\dfrac{175^{\circ}}{360^{\circ}}\cdot \pi \times 12^2\\\\\Rightarrow A=219.94\ cm^2$

8 0

3 years ago

The explicit formula for a sequence is

Alexandra [31]

Answer:

28

Step-by-step explanation:

Let n = 21, and evaluate the expression.

$a_n = -2 + \dfrac{3}{2}(n - 1)$

$a_{21} = -2 + \dfrac{3}{2}(21 - 1)$

$a_{21} = -2 + \dfrac{3}{2}(20)$

$a_{21} = -2 + \dfrac{3}{1}(10)$

$a_{21} = -2 + 30$

$a_{21} = 28$

3 0

3 years ago

Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

3 0

3 years ago

X + 4y = 16 and 2x + 12y = 48 What is the value of x+y in the solution of the system?

likoan [24]

Answer:

x = − 4y + 16

x = − 6y + 24

Step-by-step explanation:

Let's solve for x.

x + 4y = 16

Step 1: Add -4y to both sides.

x + 4y + − 4y = 16 + − 4y

x = − 4y + 16

Answer:

x = − 4y + 16

Let's solve for x.

2x + 12y = 48

Step 1: Add -12y to both sides.

2x + 12y + − 12y = 48 + − 12y/2x= − 12y + 48

Step 2: Divide both sides by 2.

2x/2 = − 12y + 48/2x = − 6y + 24

Answer: x = − 6y + 24

( I hope this was helpful) >;D

8 0

3 years ago