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3 years ago

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Morgan is reupholstering an old chair with two circular cushions. Each cushion has a circumference of 7.85 feet. He will need tw

o pieces of fabric for each cushion. How many square feet of fabric will he need to cover the cushions? Use pie=3.14 and round to the nearest square foot.

2 answers:

arsen [322]3 years ago

8 0

Answer:

20 ft^2 is correct

Step-by-step explanation:

Have a great day

kramer3 years ago

3 0

Answer: He will need 20 feet of fabric .

Step-by-step explanation:

Given: circumference of cushion = 7.85 feet.

Since , circumference = $2\pi r$ , where r = radius.

$\Rightarrow\ 2\times3.14\times r=7.85\\\\\Rightarrow\ r=\dfrac{7.85}{6.28}\\\\\Rightarrow\ r=1.25$

Area of each piece = $\pi r^2$

$=3.14\times(1.25)^2=4.90625$\approx5\text{ feet}$

Area of 2 pieces = 2 x 5 feet = 10 feet

Area for 2 cushions = 2 x (Area of 2 pieces)

= 2 x 10 feet = 20 feet

He will need 20 feet of fabric .

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HELP ASAP (Geometry)

Andrei [34K]

1) Parallel line: $y=-2x-3$

2) Rectangle

3) Perpendicular line: $y = 0.5x + 2.5$

4) x-coordinate: 2.7

5) Distance: $d=\sqrt{(4-3)^2+(7-1)^2}$

6) 3/8

7) Perimeter: 12.4 units

8) Area: 8 square units

9) Two slopes of triangle ABC are opposite reciprocals

10) Perpendicular line: $y-5=-4(x-(-1))$

Step-by-step explanation:

1)

The equation of a line is in the form

$y=mx+q$

where m is the slope and q is the y-intercept.

Two lines are parallel to each other if they have same slope m.

The line given in this problem is

$y=-2x+7$

So its slope is $m=-2$ . Therefore, the only line parallel to this one is the line which have the same slope, which is:

$y=-2x-3$

Since it also has $m=-2$

2)

We can verify that this is a rectangle by checking that the two diagonals are congruent. We have:

- First diagonal: $d_1 = \sqrt{(-3-(-1))^2+(4-(-2))^2}=\sqrt{(-2)^2+(6)^2}=6.32$

- Second diagonal: $d_2 = \sqrt{(1-(-5))^2+(0-2)^2}=\sqrt{6^2+(-2)^2}=6.32$

The diagonals are congruent, so this is a rectangle.

3)

Given points A (0,1) and B (-2,5), the slope of the line is:

$m=\frac{5-1}{-2-0}=-2$

The slope of a line perpendicular to AB is equal to the inverse reciprocal of the slope of AB, so:

$m'=\frac{1}{2}$

And using the slope-intercept for,

$y-y_0 = m(x-x_0)$

Using the point $(x_0,y_0)=(7,1)$ we find:

$y-1=\frac{1}{2}(x-7)$

And re-arranging,

$y-1 = \frac{1}{2}x-\frac{7}{2}\\y=\frac{1}{2}x-\frac{5}{2}\\y=0.5x-2.5$

4)

The endpoints of the segment are X(1,2) and Y(6,7).

We have to divide the sgment into 1/3 and 2/3 parts from X to Y, so for the x-coordinate we get:

$x' = x_0 + \frac{1}{3}(x_1 - x_0) = 1+\frac{1}{3}(6-1)=2.7$

5)

The distance between two points $A(x_A,y_A)$ and $B(x_B,y_B)$ is given by

$d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

In this problem, the two points are

E(3,1)

F(4,7)

So the distance is given by

$d=\sqrt{(4-3)^2+(7-1)^2}$

6)

We have:

A(3,4)

B(11,3)

Point C divides the segment into two parts with 3:5 ratio.

The distance between the x-coordinates of A and B is 8 units: this means that the x-coordinate of C falls 3 units to the right of the x-coordinate of A and 5 units to the left of the x-coordinate of B, so overall, the x-coordinate of C falls at

$\frac{3}{3+5}=\frac{3}{8}$

of the distance between A and B.

7)

To find the perimeter, we have to calculate the length of each side:

$d_{EF}=\sqrt{(x_E-x_F)^2+(y_E-y_F)^2}=\sqrt{(-1-2)^2+(6-4)^2}=3.6$

$d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}=\sqrt{(-1-2)^2+(3-4)^2}=3.2$

$d_{GH}=\sqrt{(x_G-x_H)^2+(y_G-y_H)^2}=\sqrt{(-1-(-3))^2+(3-3)^2}=2$

$d_{EH}=\sqrt{(x_E-x_H)^2+(y_E-y_H)^2}=\sqrt{(-1-(-3))^2+(6-3)^2}=3.6$

So the perimeter is

p = 3.6 + 3.2 + 2 + 3.6 = 12.4

8)

The area of a triangle is

$A=\frac{1}{2}(base)(height)$

For this triangle,

Base = XW

Height = YZ

We calculate the length of the base and of the height:

$Base =XW=\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}=\sqrt{(6-2)^2+(3-(-1))^2}=5.7$

$Height =YZ=\sqrt{(x_Y-x_Z)^2+(y_Y-y_Z)^2}=\sqrt{(7-5)^2+(0-2)^2}=2.8$

So the area is

$A=\frac{1}{2}(XW)(YZ)=\frac{1}{2}(5.7)(2.8)=8$

9)

A triangle is a right triangle when there is one right angle. This means that two sides of the triangle are perpendicular to each other: however, two lines are perpendicular when their slopes are opposite reciprocals. Therefore, this means that the true statement is

"Two slopes of triangle ABC are opposite reciprocals"

10)

The initial line is

$y=\frac{1}{4}x-6$

A line perpendicular to this one must have a slope which is the opposite reciprocal, so

$m'=-4$

Using the slope-intercept form,

$y-y_0 = m'(x-x_0)$

And using the point

$(x_0,y_0)=(-1,5)$

we find:

$y-5=-4(x-(-1))$

Learn more about parallel and perpendicular lines:

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8 0

3 years ago

Distribute and simplify these radicals. square root of 60

PolarNik [594]

Answer:

2 sqrt(15)

Step-by-step explanation:

sqrt(60) = sqrt(4*15) = 2 sqrt(15)

4 0

3 years ago

I really need help with the last one if you could help it would be awesome! Tysm.

gladu [14]

it’s the second one..................

5 0

3 years ago

What is the solution to this equation -13x =25

abruzzese [7]

Answer:

-1 12⁄13

Step-by-step explanation:

-13x = 25 [Divide by -13]

x = -1 12⁄13

13 is your <em>divisor</em>, which will be your denominator, and the numerator is your <em>remainder</em><em>.</em><em> </em>Since 13 goes into 25 ONCE, 1 gets multiplied by 13 to get 13, then deduct that from 25 to get your remainder of 12. This is where you start putting the pieces together as a mixed number. Then attach the negative because whenever you divide a positive by a negative, you get a negative:

-25⁄13 = -1 12⁄13

I am joyous to assist you anytime.

3 0

3 years ago

Solve the inequality |x − 6| − 10 < 1 Write the answer as a compound inequality

Tju [1.3M]

|x-6| < 1 + 10 (move 10 to the right side)
|x-6| < 11

1)x-6 < 11 (here x >= 6)
2)-x+6 < 11 (here x < 6)

1)x<17
2)x>-5

so we get -5 < x < 17

the answer: (-5; 17)

5 0

3 years ago