What is the following product?

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

All the exponents inside the parenthesis are multiplied by the exponent outside the parenthesis.

Then

[tex]\frac{m^{-7}n^{14} }{m^{-25}n^{40} }[/tex] ÷ [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]

[ Using the rule [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] ]

= [tex]m^{(-7-14)}[/tex] [tex]n^{(14-(-28)}[/tex] ÷ [tex]m^{(-15-10)}[/tex] [tex]n^{(25-(-15)}[/tex]

= [tex]m^{-21}[/tex] [tex]n^{14+28}[/tex] ÷ [tex]m^{-25}[/tex] [tex]n^{25+15}[/tex]

= [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]

= [tex]m^{(-21-(-25))}[/tex] [tex]n^{(42-40)}[/tex]

= [tex]m^{(-21+25)}[/tex] n²

= [tex]m^{4}[/tex] n² = [tex]m^{x}[/tex] [tex]n^{y}[/tex] , so x = 4 and y = 2

Then

[tex]m^{x-2y}[/tex] = [tex]m^{4-2(2)}[/tex] = [tex]m^{4-4}[/tex] = [tex]m^{0}[/tex] = 1 ← as required

Answer:

L=7 units and B=3 units

Step-by-step explanation:

L=B+4 ... Equation 1

P = 20

P=2(B+L)... Equation 2

20=2(B+B+4)... Substituting equation 1 to equation 2

20=2(2B+4)

20=4B+8

20-8=4B

12=4B

12/4=4B/4

B=3... Solve for B

L=B+4

L=3+4

L=7... Solve for L

Answer:

These two triangles are similar triangles. This means that their side lengths are proportional to each other.

Thus, making line segment EC equal to "x", and BC equal to "y" we can write:

8/y = 28/(10+y)

The next step is to get rid of the fractions, which can be done by cross multiplying.

So we have:

8(10+y) = 28(y)

After distribution and some simplification, you should get the value of y.

80+8y = 28y

80 = 20y

80/20 = 20y/20

4 = y

y = 4

Knowing that y = BC, and y = 4, it is clear that BC = 4.

Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.

Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)

In our case, a and  b are 8 and 4 (the order doesn't really matter here).

So we have: 8^2 + 4^2 = c^2

64 + 16 = c^2

80 = c^2

c = sqrt 80

c  = 4 sqrt 5

And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.

Hope this helps!

Answer:

26297.4 weeks

Step-by-step explanation:

hope it will help u

please mark me brillient

Answer:

Step-by-step explanation:

Begin by combining like terms and then factoring. Combining like terms will give you

[tex]10p^2-17p-20=0[/tex] Using the "old-fashioned" way of factoring, the a times c method, our a = 10, b = -17 and c = -20.

a * c = 10(-20) = -200 and now we need the factors of 200 (don't worry about the negative) that combine to give us that middle term, -17p (here is where the negative matters). The factors of 200 are:

1. 200;  2, 100;  4. 50;  5, 40;  8, 25;  10, 20

The combination of those numbers that can be manipulated to give us a -17p is the 8, 25 as long as we say that the 25 is negative and the 8 is positive. Rewrite the original polynomial to reflect those factors:

[tex]10p^2-25p+8p-20=0[/tex] and then factor by grouping:

[tex](10p^2-25p)+(8p-20)=0[/tex] and factor out from each set of parenthesis what is common:

[tex]5p(2p-5)+4(2p-5)=0[/tex] again factor out what is common:

(2p - 5)(5p+ 4) = 0. These are the factors; therefore the solutions are

2p - 5 = 0 so

2p = 5 and

p = 5/2  and

5p + 4 = 0 and

5p = -4 so

p = -4/5

Answer:

the answer is correct

Step-by-step explanation:

hope u like

Step-by-step explanation:

Hey there!

Please see your required answer in picture.

Hope it helps!

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

Answer:

As you may already know, water drops that fall from the cloud are considered "rain".

The Sun's heat turns the moisture or water from leaves, plants, rivers, lakes, and oceans - and turns it into gas or also called, vapor. This water vapor then turns into gas and disappears into the air. When it gets mixed with the air, it cools down. When it cools down, it changes into small water drops, which then form a cloud. These small water drops join together with other water drops to create larger and bigger water drops.

You may know this now because this is the easiest part. What happens when something gets heavy or is over-filled? It falls down, right?

So, the large drops from water fall down as they get too heavy for the cloud to carry. These big droplets falling down on us are called Rain.

Answer:

seven and eight tenths is greater than three and four tenths

Answer: 109m^2

Step-by-step explanation:

(5)(8.4)/2 = 21 m^2

(4 ) (21) = 84 m^2

Base = 5^2 = 25 m^2

84 + 25 = 109 m^2

Answer:

The answer for this question is A

Answer:

A. Town A and Town B had the same low temperatures.

Step-by-step explanation:

The towns both A and B had low temperatures is shown by the same rate of low temperatures.

Answer:

16 a*a

Step-by-step explanation:

(4a)^2

(4a) (4a)

16 a*a

Answer:

16a²

Step-by-step explanation:

(4a)²

=>(4)² x (a)²

=> 16 x a²

=>16a²

Step-by-step explanation:

[tex]3)b \: c \ \: d \: e \\ \\ 4)bc \: nd \: de \\ 5)s \\ 6)t \\ thank \: you[/tex]

Answer:

Greatest common factor (GCF) of 36 and 210 is 6.

Step-by-step explanation:

Answer:

6

Brainliest, please! (Almost an Ace!)

Step-by-step explanation:

Look at the smallest factor, 36. Find its factors.

36: 1, 2, 3, 6, 12, 18, 36

Out of all of them, which is the biggest one that 126 and 210 are also divisible by?

We see that they're divisible by 1, 2, 3, and 6.

Our answer is 6.

Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3

Answer:

Step-by-step explanation:

-14 1/9 is close to - 14

-2 and 9/10 is close to - 3

The best estimate would be 42 (14 * 3)

Estimate means you put your calculator on the kitchen counter until you've done this question.

Let's see what the actual answer is. 40.92222 which is close to 41.

42 is a pretty good estimate.

3 Answers:

==========================================================

Explanation:

Let's go through the answer choices one by one.

In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.

The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

Sides are equal

Now,

Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:

A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.

B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.

Therefore, by the  congruent triangles the answer will be LL (Side-Side-Side).

Learn more about congruent triangles here:

https://brainly.com/question/16921692

#SPJ7

value of x should be 3.2 units

Answered by Gauthmath must click thanks and mark brainliest

Answer: C

Step-by-step explanation:

To solve for 12, we can use eliminate or substituion to solve our system of equations. Let's use elimination method.

[tex]\left \{ {{3f-2k=10} \atop {-3f-2k=14}} \right.[/tex]

Let's add the equations together. This way, 3f+(-3f)=0

[tex]-4k=24[/tex]                   [divide both sides by -4]

[tex]k=-6[/tex]

Now that we know k, we can plug it into either equation to find f.

[tex]3f-2(-6)=10[/tex]        [multiply]

[tex]3f+12=10[/tex]             [subtract both sides by 12]

[tex]3f=-2[/tex]                    [divide both sides by 3]

[tex]f=-\frac{2}{3}[/tex]

Now that we have f and k, we know that C is the correct answer.

Answer:

Yes

Step-by-step explanation:

This equation does not factorise, so quadratic equation will be useful. It is easier than other methods that can be applied to this equation.

Answer:

The coordinate of b = (2, 2)

Step-by-step explanation:

The details of the quadrilateral abcd are;

The quadrilateral is symmetric about the y-axis (the line x = 0)

The coordinates of the vertices are; a(-2, 2), c(2, 1)

The location of the vertex, b = The first quadrant

We have;

The line [tex]\overline {ab}[/tex] is perpendicular to the line [tex]\overline {bc}[/tex]

Let (x, y) represent the coordinate of the vertex b, we have;

(y - 2)/(x - (-2)) = (y - 2)/(x + 2) = -1/(y - 1)/(x - 2) = - (x - 2)/(y - 1)

(y - 2)·(y - 1) = -(x + 2)·(x - 2)

y² + x² - 3·y - 2 = 0...(1)

y² + x² = 3·y + 2

Also we have;

(y - 2)² + (x - 1)² + (y - 2)² + (x - (-2))² = (2 - 1)² + (2 - (-2))² = 17

Therefore;

2·y² + 2·x² - 8·y + 2·x + 13 = 17

2·(3·y + 2) - 8·y + 2·x + 13 = 17

Using an online tool, we have;

x = y

From equation (1), we have;

2·y² - 3·y - 2 = 0

∴ y = 2, or y = -1/2

Where y = 2, we have;

x = y = 2

Therefore, the point b = (2, 2).

Answer:

i think its 58,660

Step-by-step explanation:

Answer:

58,660

Step-by-step explanation:

Answer:

a3+13a

Step-by-step explanation:

sorry I don't know how to solve this

Answer:+-3

Explanation:

I added 4 on both side so that a^2+1/a^2-2 becomes a^2+1/a^2+2 which is Special products of (a^2+1/a^2).

Answer:

y = 10

Step-by-step explanation:

6y−3=57

6y = 60

y = 10

Answer:

IN MY OPINION D NO IS THE CORRECT ANSWER OF YOUR QUESTION.

Answer:

in my opinion d is the correct answer of your questions.

Step-by-step explanation:

Because subtract subtract sign is always add.

hope this will help you

thanks

Answer:

Well this question is actually a piece of cake. Just pick your favorite number. Multiply it by 10. Then do whatever operation you want with the 2,300. For the exponent part of this. Lets say we do it this way y times z equals 2,300. Exponents are letters used in mathematical terms. So any letter can be used to represent any number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a^1=-2

a^n=a×a^n-1

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: \: of \: \: cylinder \: = \: \pi \: {r}^{2} \: h }}}}}\end{gathered}[/tex]

⇥Volume of the cylinder = π r² h

⇥Volume of the cylinder = 3.14 × 36 × 16

⇥Volume of the cylinder = 113.04 × 16

⇥Volume of the cylinder = 1808.64

Hence , the volume of cylinder is 1808.64 cm²