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3 years ago

Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem.

Mathematics

1 answer:

Drupady [299]3 years ago

5 0

Answer:

1/5

Step-by-step explanation:

Use Pythagoras theorem

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(Multiying by a unit fraction. Find the product mentally. (5.6) × 1/8=

Ipatiy [6.2K]

Step-by-step explanation:

(5.6) × 1/8

$(5.6) \cdot \frac{1}{8}$

Here the unit fraction is 1/8

multiply 5.6 times 1

so its 5.6. then divide the decimal by 8

we know that 8 times 7 is 56

so 56 divide by 8 is 7

we have decimal point 1 number to the left

so we move decimal point 2 place left

Hence 5.6 divide by 8 is 0.7

$(5.6) \cdot \frac{1}{8}=0.7$

Answer: 0.7

6 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

Using the volume formula of a cylinder

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

A rectangular room’s length is 2 feet less than its’ width and the area of the room is 120 ft^2

julia-pushkina [17]

Answer:

a. 120/w = l

120/l = w

b. l times w = 120

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Riley and Erik have earned a total of 135 tokens to buy items in the school store. The ratio of the number of tokens that Riley

lisabon 2012 [21]

Answer:

Riley has 72 tokens

Step-by-step explanation:

System of Equations

We have two conditions for the tokens Riley and Erik have earned. Let's call x and y to the number of tokens of Riley and Erik respectively. The first condition states that

$x+y=135$

Solving for y

$y=135-x$

The second condition is that the ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. It's written as

$\displaystyle \frac{x}{y}=\frac{8}{7}$

Or equivalently

$7x=8y$

Replacing y from the first equation

$7x=8(135-x)$

Operating

$7x=1080-8x$

Simplifying

$15x=1080$

$\boxed{x=72}$

Riley has 72 tokens

3 0

3 years ago

At a sale this week, a suit is being sold for $663. This is a 15% discount from the original price.

nignag [31]

Answer:

563.55

Step-by-step explanation:

85/100*663=563.55

6 0

3 years ago

Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem. ​

Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem.