Triangle ABC maps to triangle A′B′C′ by a 90∘ rotation counterclockwise about the origin.

Amy is helping plan her school's new basketball court. The west edge of the basketball court is located on the line y = 2x + 5.

ipn [44]

Answer:

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

Step-by-step explanation:

The east edge cannot intersect with the west edge means that two lines are parallel.

If the two lines are parallel then they have same slope. We need to find the slopes of given lines and check which line has slope same as slope of west edge.

Slope of west edge.

y = 2x + 5

The standard equation for slope intercept form is:

y = mx+b

where m is the slope. So, m= 2

Now finding line for east edge.

Option 1.

Convert each given equation to standard slope intercept form and find the slope.

2x -y =96

-y = -2x +96

Multiply with -1

y = 2x -96

m = 2

Option 2.

-2x -y = 96

-y = 2x +96

y = -2x-96

m = -2

Option 3

-y-2x =48

-y = 2x +48

y = -2x -48

m = -2

Option 4.

y+2x = 48

y = -2x+48

m = -2

So, only line of Option 1 has slope = 2 which is equal to the slope of west edge.

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

7 0

3 years ago

4 in.

sleet_krkn [62]

Answer:

305.12 square inches

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The area of the window is equal to the area of a rectangle, plus the area of two quarter circles plus the area of the smaller square between the two upper corners

so

Find the area of rectangle

$A=(12)(26-4)=264\ in^2$

Find the area of the two quarter circle

$A=2[\frac{1}{4}(3.14)(4^2)]$

$A=25.12\ in^2$

Find the area of the smaller square between the two upper corners

$A=(12-8)(4)=4^2=16\ in^2$

The total area is equal to

$A=264+25.12+16=305.12\ in^2$

4 0

3 years ago

Plz help.. plzz if you can

Mazyrski [523]

Answer:

C is a function

Step-by-step explanation:

We can use the vertical line test. If a vertical straight lines passes through the graph more than one, it is not a function

A and B are not functions

C is a function

5 0

3 years ago

The cost for renting a weed trimmer varies directly with the number of hours used. A weed trimmer rented for 5 hours costs $32.5

wlad13 [49]

Let the cost for renting be y and the number of hours be x
then:
y=kx
where:
k is the constant of proportionality
k=y/x
y=$32.5 when x=5 hours
thus;
k=32.5/5
k=6.5
hence the equation is:
y=6.5x
thus the value of y when x=8 hours will be:
y=6.5(8)=$52
Answer:'

<span>A y = $6.5x, y = $52.00</span>

4 0

3 years ago

A weather report stated that the monthly rain amounts for the past three months were 15.82 inches, 17.4 inches, and 9.56 inches.

HACTEHA [7]

Answer:

42.78 inches

Step-by-step explanation:

The anount of rainfall for the past three months are

15.82 inches

17.4 inches

9.56 inches

Therefore the total amount of rainfall for the three months can be calculated as follows

= 15.82+17.4+9.56

= 42.78

Hence the total rainfall for three months 42.78 inches

8 0

2 years ago