Use a factor tree to find the prime factorization of each number

The coordinates of parallelogram PVWZ are P(0, 0), V(-p, q), and W(-p - r, q). Find the coordinates of Z without using any new v

Drupady [299]

For the answer to the question above asking to f<span>ind the coordinates of Z without using any new variables.
</span>

Vector WZ equals vector VP, which is (p, -q)
So Z is (-p - r + p, q - q) which is (-r, 0)
I hope my answer helped you.

3 0

3 years ago

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Mr.Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below. Based

julia-pushkina [17]

Answer:

infinitely many solutions

Step-by-step explanation:

0 = 0 ← is a true statement.

Indicates that the 2 lines are the same line, that is one lying on top of the other.

Thus the system has an infinite number of solutions

4 0

3 years ago

Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

4 years ago

The absolute value function, f(x) = –|x| – 3, is shown. What is the range of the function? all real numbers all real numbers les

Harman [31]

Answer:

all real numbers less than or equal to –3

Step-by-step explanation:

Look at the y-values that the graph shows. There are none greater than -3. Any value of -3 or less is possible.

5 0

3 years ago

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What is minutes spent on homework

Eduardwww [97]

It appears that you have here a list of the # of minutes spent each day on HW, and that y ou need to sum up this list to answer the question. Unfortunately I cannot read the last numeral.

The answer (assuming that my guess is correct) would be found as follows:

Total hours spent on HW in one week = (18+20+22+11+19+18+ ?? )

3 0

3 years ago