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3 years ago

I need help with #4 asap plsss

Mathematics

1 answer:

V125BC [204]3 years ago

8 0

Answer:

5 and 8 are supplementary

3=8 (vertically opposite)

so 5 and 3 are supplementary

also 5 and 6 are supplementary (linear pair)

now we've got

5+3=180°

5+6=180°

3=6

Statement: 5 and 3 are supplementary as 3=8

reason: vertically opposite

statement: 5 and 6 are supplementary

reason: linear pair

statement: 3=6

reason: both are supplementary to a same angle

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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

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

Find the area of the rectangular playground

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

25. An apple is launched directly upward at 64 feet per second from a platform 80 feet high. The equation for this

Viktor [21]

Answer:

a. 144 ft

b. 5 s

Step-by-step explanation:

h = -16t² + 64t + 80

a. This is a parabola, so the maximum height is at the vertex.

t = -64 / (2 × -16)

t = 2

h = -16(2)² + 64(2) + 80

h = 144

The apple reaches a maximum height of 144 ft.

b. 0 = -16t² + 64t + 80

0 = t² − 4t − 5

0 = (t + 1) (t − 5)

t = -1 or 5

t must be positive, so it takes 5 seconds to reach the ground.

3 0

2 years ago

Abraham is installing carpet in his bedroom. On the blueprints, Abraham's bedroom is 6 inches wide and 10 inches long. If the sc

erma4kov [3.2K]

Answer:

240 square feet

Step-by-step explanation:

Hello, I can help you with this

Step one

find the real scale

According to the data

scale is 1 in : 2 ft

also remember 1ft=12 inches

scale is 1in: 2(12 inches)

scale is 1 in :24 in

the purpose of use inches a unit in both sides is to eliminate the, the scale must be adimensional

so escales is

1:24 , this means, that a measure on the blueprint must be multiplied by 24 to know its real value

Step 2

with the escale find the real dimensions, you can use a rule of three

Abraham's bedroom is 6 inches wide

blueprint ⇔ bedroom

1 in ⇔ 24 in

6 in ⇔x

x=(6*24)/1

x=144 inches=12 ft

Abraham's bedroom is 10 inches long

1 in ⇔ 24 in

10 in ⇔y

y=(10*24)/1

x=240 inches=20 ft

Step 3

find the area

the area is wide *long

area=x*y

area=12ft*20ft

area=240 square feet.

Have a good day

5 0

3 years ago

D = 8a The variable a represents the number of attendees, and the variable d represents the cost in dollars. At most how many at

suter [353]

Answer: At most 9 attendees can be there.

Step-by-step explanation:

Given equation: d = 8a , where a represents the number of attendees, and the variable d represents the cost in dollars.

To find : the number of attendees, if Will budgets a total of $72 for his graduation picnic.

72=8a

⇒ 9 = a [divide both sides by 8]

∴ a= 9

Hence, at most 9 attendees can be there.

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2 years ago

Lori entered a 100 km race. A Kilometer is about of a mile. About how many miles ling is the race?

djverab [1.8K]

Answer:

About 62.1371

Step-by-step explanation:

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3 years ago