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2 years ago

What is the distance between A(6, 2) and B(9, 12)? Round to the nearest tenth.

1 answer:

4 0

Use the distance formula:

d = $\sqrt{(x2-x1)^2+(y2-y1)^2}$
d = $\sqrt{(9-6)^2 + (12 - 2)^2}$
d = $\sqrt{(3)^2+ (10)^2}$
d = $\sqrt{9 + 100}$
d = $\sqrt{109}$
d = 10.4

Hope this helps :)

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A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

If 14 gallon of paint covers 13 of a wall in Luna's bedroom, how many gallons of paint does she need to cover 1 wall?

dimaraw [331]

Answer:

182 gallons tell me if im right

Step-by-step explanation:

14 times 13 = 182 gal

5 0

2 years ago

What is the value of a in simplest form?

devlian [24]

Answer:

$x^4$

Step-by-step explanation:

$\frac{x^{3} }{\sqrt[6]{x}}$

$((\sqrt{x})^{2})(x^{3} )$

$(x)(x^3)\\x^4$

6 0

2 years ago

Hi, can someone please help me? trying to graduate :(

inysia [295]

Slope intercept form is y=mx+b, therefore your answer is D.

Hope this helped :)

8 0

1 year ago

Tamira invests $5,000 in an account that pays 4% annual interest. How much will there be in the account after 3 years if the int

Talja [164]

Answer:

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

There will be $5636.359 in the account after 3 years if the interest is compounded monthly

Step-by-step explanation:

Tamira invests $5,000 in an account

Rate of interest = 4%

Time = 3 years

Case 1:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 1

Formula : $A=P(1+r)^t$

$A=5000(1+0.04)^3$

A=5624.32

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

Case 2:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 2

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{2})^{2 \times 3}$

A=5630.812

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

Case 3:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{4})^{4 \times 3}$

A=5634.125

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

Case 4:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{12})^{12 \times 3}$

A=5636.359

There will be $5636.359 in the account after 3 years if the interest is compounded monthly

8 0

3 years ago