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3 years ago

Is the line through points P(–3, –2) and Q(2, 3) perpendicular to the line through points R(10, –1) and S(15, –6)? Explain.

Mathematics

1 answer:

pychu [463]3 years ago

5 0

Answer:y = mx + b

(–6) = (4)(–1) + b

–6 = –4 + b

–2 = b

Step-by-step explanation:

You might be interested in

From the set {20, 38, 47}, use substitution to determine which value of x makes the inequality true.

vredina [299]

One way is to solve (it's easier)

x-9>29
add 9
x+9-9>29+9
x+0>38
x>38
just pick the numbers bigger than 38 as answer

47 is only number (38>38 is false)

answer is A

7 0

3 years ago

The volume of a sphere whose diameter is 18 centimeters is _ cubic centimeters. If it’s diameter we’re reduced by half, it’s vol

kaheart [24]

<h2>Answer:</h2>

<u>First Part</u>

Given that

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

We have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}$

<u>Second Part</u>

Given that

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

If the Diameter were reduced by half we have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}$

This shows that the volume would be $\frac{1}{8}$ of its original volume

<h2>Step-by-step explanation:</h2>

<u>First Part</u>

Gather Information

$Diameter = 18cm$

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

Calculate Radius from Diameter

$Radius = \frac{Diameter}{2} = \frac{18}{2} = 9$

Use the Radius on the Volume formula

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}$

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

$Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3$

We can see now that one of the 3s can be already divided by the 3 in the denominator

$Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3$

Finally, since we can't simplify anymore we just calculate it's volume

$Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}$

$Volume \approx 3053.63 cm^{3}$

<u>Second Part</u>

Understanding how the Diameter reduced by half would change the Radius

$Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}$

Understanding how the Radius now changes the Volume

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

With the original Diameter, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\$

If the Diameter were reduced by half, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}$

But we can see that the numerator is exactly the original Volume!

This shows us that the Volume would be $\frac{1}{8}$ of the original Volume if the Diameter were reduced by half.

3 0

2 years ago

Which pair of numbers below have 4 and 6 as common factors?

stepan [7]

24 and 12.
explanations
24:
$6 \times 4 = 24$

12:
$4 \times 3 = 12$
12:
$6 \times 2 = 12$

3 0

2 years ago

Two numbers are in the ratio 3:8.<br> The larger number is 96, find the<br> sum of the numbers

zloy xaker [14]

Answer:

The sum of the numbers is <em>132</em>

Step-by-step explanation:

First find the smallest number

3/8=x/96
2(96)=8x
288=8x
x=36

Thus, you found the smallest number

then there sum given as 96+36=132

6 0

1 year ago

1) A right triangle has a side that measures 4 m and a hypotenuse that measures8.5 m. What is the measure of the other side of t

hammer [34]

1) Use the pathagreom theorem; a^2+b^2=c^2
(The hypotenuse is always c. The other two legs can be either a or b.)
*use x for the unknown side*
1. Plug in the measurements
4^2+x^2=8.5^2
2. Solve
16+x^2=72.25
RADICAL(56.25)=> 7.5
The measure of the other side of the triangle (x) is= 7.5 m

2) Draw a square with the measure of 20 cm on each side.
Draw a diagonal line across the square.
(Use the pathagroeam theorem)
We know that the legs are 20, and 20. The hypotenuse is what we are trying to find (x).
1. Plug in the measurements
20^2+20^2=x^2
2. Solve
800= x^2
20 RADICAL(2)=> 28.28
The measure of the other side of the triangle (x) is= 28.3 cm

3 0

3 years ago