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2 years ago

Fill in the blanks below.

Mathematics

1 answer:

alexira [117]2 years ago

6 0

Answer:

-4/0, and 0/9

Step-by-step explanation:

slope formula

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Find the lengths of the sides of the triangle PQR. P(2, −3, −4), Q(8, 0, 2), R(11, −6, −4) |PQ| = Incorrect: Your answer is inco

Aloiza [94]

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If you know two points, the distance between then its given by:

$P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}+(z_{2}-z_{1} )^{2} }$

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

$d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\$

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}} \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\$

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

$d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}} \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\$

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

$side^{2} +side^{2}=hypotenuse ^{2}$

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

$9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false$

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

3 0

2 years ago

What is the square root of 9

Mariulka [41]

The square root of 9 is 3. ✌️

7 0

3 years ago

Read 2 more answers

A speed walker covered 4 1/2 mi in 3/4 hour. How far will he walk in 3/4 hour if he walks?

Nezavi [6.7K]

Given:

Consider the complete question is "A speed walker covered $4\dfrac{1}{4}$ mi in $\dfrac{3}{4}$ hour. How far will he walk in 3/4 hours if he walks twice as fast?"

A speed walker covered $4\dfrac{1}{4}$ mi in $\dfrac{3}{4}$ hour.

To find:

Distance covered by him if in 3/4 hour if he walks twice as fast.

Solution:

We have,

$Distance=4\dfrac{1}{2}=\dfrac{9}{2}$

It means a speed walker covered $\dfrac{9}{2}$ mi in $\dfrac{3}{4}$ hour.

If the speed is twice then he can cover double distance is same time.

Distance covered by him if in 3/4 hour if he walks twice as fast is

$2\times \dfrac{9}{2}=9$

Therefore, distance covered by him is 9 mi.

7 0

2 years ago

One more: even more points xd

Reil [10]

I want points too hahah

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2 years ago

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Factorise 21x-14y<br> Pls try answer its for my homework thx

prohojiy [21]

$21x-14y \\ \\ GCF = 7 \\ \\ 7( \frac{21x}{7} + \frac{-14y}{7} ) \ / \ factor \ out \ gcf \\ \\ 7(3x - 2y) \ / \ simplify \\ \\ Answer: \fbox {7 (3x - 2y)}$

4 0

2 years ago