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kakasveta [241]
2 years ago
14

Directions:Use the product rule to simplify the following monomials.

Mathematics
1 answer:
attashe74 [19]2 years ago
6 0

13) Answer: -3a^3b^2

\left(-6a^2b\right)\left(\frac{1}{2}ab\right)

=-6a^2b\frac{1}{2}ab

=-6a^2b^2\frac{1}{2}a

=-6a^3b^2\frac{1}{2}

=-3a^3b^2

14) Answer: 8y^5x

12y\left(\frac{2}{3}xy^4\right)

=12\cdot \frac{2}{3}xy^{1+4}

=12\cdot \frac{2}{3}xy^5

=\frac{2\cdot \:12xy^5}{3}

=\frac{24y^5x}{3}

=8y^5x

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The answer is Any Real Number
because  4(x + 1) = 4x + 4 for all value of x
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Write an absolute value equation to satisfy the given solution set shown on a number line.
aivan3 [116]

Answer: IX - 4I ≤ 4

Step-by-step explanation:

In the numer line we can see that our possible values of x are in the range:

0 ≤ x ≤ 8

And we want to find an absolute value equation such that this set is the set of possible solutions.

An example can be:

IX - 4I ≤ 4

To construct this, we first find the midpoint M of our set, in this case is 4.

Then we write:

Ix - MI  ≤ IMI

Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the <  > signs.

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Marizza181 [45]

Answer:

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Slope: 3

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y-3x=10    Add 3x to both sides. The y has to be isolated.

So it is y=10+3x     So we have to reorder it so y=3x+10

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A line goes through the points (5, -1) and (7, -5). What is a possible equation to a new line that is perpendicular?
Leya [2.2K]

<em>Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."  </em>

<em> </em>

<em> </em>

<em> </em>

<em>  5x+4y=2 </em>

<em> </em>

<em>-5x     -5x  (subtract 5x from both sides to move it to the right side of your equation) </em>

<em> </em>

<em>4y = 2 - 5x </em>

<em> </em>

<em>/4  /4  /4 (divide all the terms by 4 to get "y" by itself) </em>

<em> </em>

<em>y = (1/2) - (5/4)x  ... I suggest leaving your slope as a fraction. </em>

<em> </em>

<em> </em>

<em> </em>

<em>Now, we know that our slope, m , is going to be -(5/4).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know: </em>

<em> </em>

<em> </em>

<em> </em>

<em>y = 5 </em>

<em> </em>

<em>m = -(5/4) </em>

<em> </em>

<em>x = 7 </em>

<em> </em>

<em> </em>

<em> </em>

<em>y=mx+b </em>

<em> </em>

<em>5=(-5/4)(7) + b  -> I plugged in what we knew for y, m, and x.  </em>

<em> </em>

<em>5 = -(35/4) + b  -> I multiplied the numbers in the numerator (5 x 7) to get 35/4 </em>

<em> </em>

<em>20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4) </em>

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<em>+(35/4) +(35/4)  -> I add (35/4) to both sides to isolate b </em>

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<em>55/4 = b ... or b = 13.74 </em>

<em> </em>

<em> </em>

<em> </em>

<em>Answer:  </em>

<em> </em>

<em>m = -(5/4) </em>

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<em>b = 13.75</em>

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Find all x ∈ Z satisfying each of the following equations.3x = 2 (mod 7)
Vlada [557]

Answer:

7x−3=7k,x=7k+3,k∈ℤ

Step-by-step explanation:

3x ≡ 2 (mod 7)

3 is a solution, since 3×3−2=7.

All solutions are 3+7ℤ

y=3x−2/7=3(x−3)+7/7=3(x−3)/7+1

7x−3=7k,x=7k+3,k∈ℤ

5 0
2 years ago
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