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3 years ago

Write the equation of the line that is parallel to the line y = 2x + 2 and passes through the point (5, 3)?. .

1 answer:

6 0

The equation of the line given is 2 from the equation y = mx + b where m is the slope. For the lines to be parallel, their slopes should be equal. The equation of the line may also be expressed as,
y - y1 = m(x - x1)
Substituting the values,
y - 3 = 2(x - 5)
The simplified form of the equation is,
y = 2x - 7

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3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

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

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

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

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

3 years ago

Solve y=x+8 for x<br> can some one help me with this problem

IRINA_888 [86]

You have to plug in a random y value and use algebra to solve for x. It is impossible to do without at least one point for y.

7 0

3 years ago

I need to know the answer please…

Triss [41]

Answer is a= 51/7 or 7 2/7

Step by step

-2/3 (a + 3) = 5/3a - 19

Distribute to resolve parentheses

-2/3a -2 = 5/3a - 19

Now to move variables to one side
Add 2/3a to both sides

-2/3a + 2/3a -2 = 5/3a + 2/3a -19

Combine like terms

-2 = 7/3a -19

Add 19 to both sides to isolate variable

-2 +19 = 7/3a -19 + 19

17 = 7/3a

Divide both sides by 7/3 to solve for a
(Remember when you divide a fraction, flip it and multiply.)

17 * 3/7 = a

51/7 = a

Picture attached shows steps in order, I think that is what you also needed?

5 0

1 year ago

What is the surface area of a cylinder with a base radius of 3 ft and a height of 5ft

Solnce55 [7]

SA of a cylinder: 2 $\pi$ r² + 2 $\pi$ rh
r = radius of base
h = height of cylinder

Plug in 3 for r and 5 for h in the formula.
2 $\pi$ 3² + 2 $\pi$ (3)(5)
Use a calculator to solve.

2 $\pi$ 3² + 2 $\pi$ (3)(5) = 150.8 ft²

6 0

3 years ago

Please help ASAP (a lot of points ) show your work please

allsm [11]

Answer :-

1. value of x is 18

8 0

3 years ago