How do you write -4i as a complex number?

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

3 years ago

3.Solve for the the values of x by factoring

k0ka [10]

Answer:

x = 8 ; x = -3

Step-by-step explanation:

Sum = -5

Product = - 24

Factors = 3 , (-8)

x² - 5x - 24 = 0

x² - 8x + 3x - 3 * 8 = 0

x(x - 8) + 3(x - 8)= 0

(x - 8)(x + 3) = 0

x - 8 = 0 ; x + 3 = 0

x = 8 ; x = -3

3 0

3 years ago

Read 2 more answers

The point A = (7,4) is dilated from the origin by a scale factor r = 3. What are the coordinates of A' ?

fomenos

Given:

The coordinates of point A are (7,4).

It is dilated from the origin by a scale factor r = 3.

To find:

The coordinates of A'.

Solution:

If a figure is dilated from the origin by a scale factor k, then

$(x,y)\to (kx,ky)$

Here, the figure is dilated from the origin by a scale factor 3, so the rule of dilation is given by:

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(7,4)\to A'(3(7),3(4))$

$A(7,4)\to A'(21,12)$

Therefore, the coordinates of point A' are (21,12).

6 0

3 years ago

If you have to figures - Figure A and Figure B, and their linear scale factor is 2/5, then does that mean Figure B's sides are 2

zysi [14]

Answer:

Correct answer: Figure A's sides are 2/5 of figure B.

Step-by-step explanation:

In the order the figures are given the proportion will be:

A : B = 2 : 5

By multiplying the outer and inner members of the proportion we get:

5 · A = 2 · B ⇒ A = (2/5) · B

That mean figure A's sides are 2/5 of figure B.

This means that the two units of figure A are referred to as the five units of figure B.

God is with you!!!

3 0

3 years ago

Suppose that a random sample of size 36 is to be selected from a population with mean 43 and standard deviation 6. What is the a

lana66690 [7]

Answer:

61.70% approximate probability that X will be more than 0.5 away from the population mean

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$