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3 years ago

Find the values of x and y. (image below)

Mathematics

1 answer:

DanielleElmas [232]3 years ago

5 0

Opposite angles have the same measures. This allows you to set and solve the following equations:

$\begin{cases} 26-6x = 20-8x \\ 5y = 9y-76 \end{cases}$

To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:

$\begin{cases} -6x+8x = 20-26 \\ 5y-9y = -76 \end{cases}$

Sum like terms:

$\begin{cases} 2x = -6 \\ -4y = -76 \end{cases}$

Divide the first equation by 2 and the second by -4:

$\begin{cases} x = -3 \\ y = 19 \end{cases}$

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“An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and wor

Artist 52 [7]

Answer:

Part 1) The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Part 2) The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

Step-by-step explanation:

Step 1

Find the radius of each sphere

we know that

The circumference of a circle is equal to

$C=2\pi r$

Find the radius of the sphere with a 5.50-meter circumference

For $C=5.50\ m$

assume

$\pi =3.14$

substitute and solve for r

$5.50=2(3.14)r$

$r=5.50/[2(3.14)]=0.88\ m$

Find the radius of the sphere with a 7.85-meter circumference

For $C=7.85\ m$

assume

$\pi =3.14$

substitute and solve for r

$7.85=2(3.14)r$

$r=7.85/[2(3.14)]=1.25\ m$

step 2

Find the surface area of each sphere

The surface area of sphere is equal to

$SA=4\pi r^{2}$

Find the surface area of sphere with a 5.50-meter circumference

For $r=0.88\ m$

assume

$\pi =3.14$

substitute

$SA=4(3.14)(0.88)^{2}$

$SA=9.73\ m^{2}$

Find the surface area of sphere with a 7.85-meter circumference

For $r=1.25\ m$

assume

$\pi =3.14$

substitute

$SA=4(3.14)(1.25)^{2}$

$SA=19.63\ m^{2}$

step 3

Find the cost of finishing each sphere

we know that

To find out the cost , multiply the surface area by $92 per square meter

Find the cost of sphere with a 5.50-meter circumference

$9.73*(92)=\$895.16$

therefore

The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Find the cost of sphere with a 7.85-meter circumference

$19.63*(92)=\$1,805.96$

therefore

The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

6 0

3 years ago

What is the area of a rectangles with the side lengths 5 inches and 1/3 inches?

sveticcg [70]

Answer:

area of a rectangle is length multiplied by breath, which is the multiplication of 5 an 1/3

3 0

3 years ago

1. What is an equation of a line, in point-slope form, that passes through (1,-7) and has a slope of -2/3?

Nookie1986 [14]

1. What is an equation of a line, in point-slope form, that passes through (1,-7) and has a slope of -2/3?

Point Slope form y − y1 = m(x − x1)

Y1: -7 x1:1 slope :-2/3

Y-(-7)=-2/3(x-1)

Y+7=-2/3(x-1)

2. What is the equation of a line, in point-slope form, that passes through (-2,-6) and had a slope of 1/3?

Y-(-6)=1/3(x-(-2))

Y+6=1/3(x+2)

3.What is an equation in point-slope form of the line that passes through the points (4,5) and (-3,-1)

SlopeM: =change in y/change in x

M= -1-5/-3-4

M= -6/-7

M=6/7

So now slope:6/7, point (4,5)

Y-y1=m(x-x1)

Equation in point slope

Y-5=6/7(x-4)

6 0

4 years ago

Cone A has a radius of 2 inches and a height of 3 inches. In cone B, the height is the same, but the radius is doubled. Calculat

wlad13 [49]

Answer: Option C.

Step-by-step explanation:

Use the formula for calculate the volume of a cone:

$V=\frac{1}{3}\pi r^2h$

Where r is the radius and h is the height.

Volume of the cone A:

$V_A=\frac{1}{3}\pi (2in)^2(3in)=12.56in^3$

Volume of the cone B:

If the height of the cone B and the height of the cone A are the same , but the radius of the cone B is doubled, then its radius is:

$r_B=2r_A\\r_B=2*2in\\r_B=4in$

Then:

$V_B=\frac{1}{3}\pi (4in)^2(3in)=50.26in^3$

Divide $V_B$ by $V_A$ :

$\frac{V_B}{V_A}=\frac{50.26in^3}{12.56in^3}=4$

Therefore: When the radius is doubled, the resulting volume is 4 times that of the original cone.

5 0

3 years ago

Read 2 more answers

PLZ HELP ASAP!!!! Solve for X: 2X^3 = 54

mariarad [96]

X=3

Divide both sides of the equation by 2
X^3 =27

Write the number in exponential form with an exponent of 3
X^3=3^3

Since the exponents are the same, set the bases equal
X=3

6 0

3 years ago