If the volume of a cubical room is 2700 cm^3 . Find its length

Answer:

4a^2

Step-by-step explanation:

GCF of 12 and 32 is 4.

GCF of a^3 and a^2 is a^2.

Therefore, the answer is 4a^2.

Answer:

320-7.500

Step-by-step explanation:

Answer: z=56

Step-by-step explanation:

Based on the figure, we can determine that 3y+8=68 and 4x=2z. With the knowledge that a trapezoid has 360°, we can first find the value of y to get the angle measures of the top angles. We can then subtract that from 360°.

3y+8=68        [subtract both sides by 8]

3y=60            [divide both sides by 3]

y=20

We now know the value of y is 20, but that is not relevant to solving this problem because we already know that the top angles are 68° each. So, we can subtract that from 360.

360-68-68=224

Now, we know that the bottom 2 angles have to add up to 224. Therefore, we can come up with 2 equations.

Equation 1: 4x=2z

Equation 2: 4x+2z=224

We can manipulate Equation 1 to be [tex]x=\frac{1}{2}z[/tex]. Once we plug that into Equation 2, we can find the value of z.

[tex]4(\frac{1}{2} z)+2z=224[/tex]         [multiply]

[tex]2z+2z=224[/tex]              [add]

[tex]4z=224[/tex]                      [divide both sides by 4]

[tex]z=56[/tex]

Now, we know that z=56.

Answer:

Step-by-step explanation:

Find the slope of QR. From that we can find the the slope of the line perpendicular to QR.

Q(-2, -5)   & R(8,1)

[tex]Slope \ = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-5]}{8-[-2]}\\\\=\frac{1+5}{8+2}\\\\=\frac{6}{10}\\\\=\frac{-3}{5}[/tex]

So, the slope of the line perpendicular to QR =  -1/m - 1÷ [tex]\frac{-5}{3} = -1*\frac{-3}{5}=\frac{3}{5}[/tex]

Bisector of QR divides the line QR to two half. We have find the midpoint of QR.

Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

               [tex]=(\frac{-2+8}{2},\frac{-5+1}{2})\\\\=(\frac{6}{2},\frac{-4}{2})\\\\=(3,-2)[/tex]

slope = 3/5  and the required line passes through (3 , -2)

y - y1 = m(x-x1)

[tex]y - [-2] = \frac{3}{5}(x - 3)\\\\y + 2 = \frac{3}{5}x-\frac{3}{5}*3\\\\y=\frac{3}{5}x-\frac{9}{5}-2\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{2*5}{1*5}\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{10}{5}\\\\y=\frac{3}{5}x-\frac{19}{5}[/tex]

Answer:

x=13

y= -9

(13, -9)

Step-by-step explanation:

If we are solving using the substitution method, we can take the first equation and set it to y so y=4-x.

Then, we can take that equation and plug it into the bottom one so

3x+4(4-x)=3

Simplify:

3x+16-4x=3

-x=-13

x=13

We can then plug 13 into any of the two given equations (I am just going to plug it into the top one)

So, 13+y=4 which y= -9

[tex]\displaystyle\bf \underbrace{19}_910{\underbrace{1}_9} \Longrightarrow This\: is \:an \:\:arithmetic\:\: progression[/tex]

Answer:

204g + 48

Step-by-step explanation:

simplifying the expression

Answer:

100

Step-by-step explanation:

5x4=20

20x5=100

Answer:

Falso.

Step-by-step explanation:

Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:

(a) El exponente es cero.

(b) El exponente es un negativo impar.

(c) El exponente es un negativo par.

(d) El exponente es un positivo impar.

(e) El exponente es un positivo par.

(a) El exponente es cero:

Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.

(b) El exponente es un negativo impar:

Considérese las siguientes expresiones:

[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]

Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:

[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]

[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]

Si [tex]n[/tex] es impar, entonces:

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]

Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.

(c) El exponente es un negativo par.

Si [tex]n[/tex] es par, entonces:

[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]

Puesto que [tex]d' = c'[/tex], la proposición es verdadera.

(d) El exponente es un positivo impar.

Considérese las siguientes expresiones:

[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]

[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]

Si [tex]n[/tex] es impar, entonces:

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]

(e) El exponente es un positivo par.

Considérese las siguientes expresiones:

[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]

Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.

Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.

Answer:

9. A. 2

Rectangle R:

Rectangle S:

Rectangle Area:

Rectangle R = L · W

Rectangle S = 2L · 2W = 2(L · W)

10.  A. (1, 3)

x + 2 = -2x + 5

x + 2x = 5 - 2

3x = 3

x = 1

y = x + 2 = 1 + 2 = 3

Answer:

You can choose between 10 different choices.

Step-by-step explanation:

Given that a lunch menu consists of 2 types of tortillas and 5 different fillings, to determine how many choices are there for ordering a burrito with one filling, the following calculation must be performed:

2 x 5 = X

10 = X

Therefore, you can choose between 10 different choices.

Answer:

x = 9

Step-by-step explanation:

When sum of two angles is 90, then they are known as complementary angles.

4x + 9  + 2x + 27 = 90

4x + 2x + 9 + 27 = 90

Combine like terms

6x + 36 = 90

Subtract 36 from both sides

6x = 90 - 36

6x = 54

Divide both sides by 6

x = 54/6

x = 9

Answer:

y = x + 4

Step-by-step explanation:

y = mx + b

y = 1x + b

5 = 1 + b

b = 4

y = x + 4

Step-by-step explanation:

hope it helps you...........

Answer:

A

Step-by-step explanation:

This is because when you do a the answer states, multipliying the top by 2, makes the top equation 6x-6y=12. When you subtract the second from the first you get:

 6x - 6y = 12

- 6x + (-)9y = (-)3

Which results in -15y = 9.

This results in an eliminated variable from the start of the system of equation.

The steps that will eliminate a variable in this system are:

Multiply the first equation by 2.

Then subtract the second equation from the first.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

[tex]3x - 3y = 6\\6x +9y = 3\\\\6x - 6y = 12\\6x +9y = 3\\\\15y = -9\\y = -3/5\\x= 2-3/5 = 7/5[/tex]

Learn more about method of elimination here

https://brainly.com/question/14619835

#SPJ2

( f ∘ g ) ( x ) is equivalent to f ( g ( x ) ) . We solve this problem just as we solve f ( x ) . But since it asks us to find out f ( g ( x ) ) , in f ( x ) , each time we encounter x, we replace it with g ( x ) . In the above problem, f ( x ) = x + 3 . Therefore, f ( g ( x ) ) = g ( x ) + 3 . ⇒ ( f ∘ g ) ( x ) = 2 x − 7 + 3 ⇒ ( f ∘ g ) ( x ) = 2 x − 4 Basically, write the g ( x ) equation where you see the x in the f ( x ) equation. f ∘ g ( x ) = ( g ( x ) ) + 3 Replace g ( x ) with the equation f ∘ g ( x ) = ( 2 x − 7 ) + 3 f ∘ g ( x ) = 2 x − 7 + 3 we just took away the parentheses f ∘ g ( x ) = 2 x − 4 Because the − 7 + 3 = 4 This is it g ∘ f ( x ) would be the other way around g ∘ f ( x ) = 2 ( x + 3 ) − 7 now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them. g ∘ f ( x ) = 2 x + 6 − 7 Next, + 6 − 7 = − 1 g ∘ f ( x ) = 2 x − 1

Hello,

[tex]f(x)=7x-3\\g(x)=x^2\\\\(fog)(x)=g(f(x))=g(7x-3)=(7x-3)^2=49x^2-42x+9\\\\(gof)(x)=f(g(x))=f(x^2)=7x^2-3\\\\(fog)(0)=g(f(0))=49*0^2-42*0+9=9\\\\(gof)(0)=f(g(0))=7*0^2-3=-3\\[/tex]

Since i don't know what is (g°O(1)  and you haven't correct your question ,

i has put the 2 possibles answsers.

Answer:

3 + 2k

Step-by-step explanation:

Given:

1/5(15 + 10k)

= (1/5 * 15) + (1/5 * 10k)

= (1 * 15)/5 + (1 * 10k)/5

= 15/5 + 10k/5

= 3 + 2k

Therefore,

1/5(15 + 10k) = 3 + 2k

The equivalent expression is 3 + 2k

Answer:

2+2 = 4

Step-by-step explanation:

Hope this helps.

Answer:

2 + 2 is 4 my guy

Step-by-step explanation:

thx for the points

Answer:

I hope this helps. There is a link

b

So what is that distance well we know that to get to negative 4 pi over 3 we took negative pi and travelled pi over 3.. So this is just pi over 3.. So our reference angle would be pi over 3.

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x=6[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3x + 15 = 33\\--------------\\\rightarrow 3x + 15 - 15 = 33 - 15\\\\\rightarrow 3x = 18\\\\\rightarrow \frac{3x=18}{3}\\\\\rightarrow \boxed{x = 6}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x=6

Step-by-step explanation:

3x+15=33

or as, 3x=33-15

or as, 3x=18

x=18/3=6

so we got 6 is the answer

Answer:

-8

Step-by-step explanation:

Answer:No

Step-by-step explanation:

Answer:

The weight of the package of chili powder is 181.44 g.

Step-by-step explanation:

Amount of chili powder = 4/10 pound

1 pound = 453.6 g

So,

4/10  pound = 4/10 x 453.6 = 181.44 g

The weight of the package of chili powder is 181.44 g.  

Answer:

20.6 m

Step-by-step explanation:

Hi there!

Assuming that the utility pole makes a 90-degree angle with the ground, this scenario creates a right triangle.

The 45 m-long cable is the hypotenuse and the 40 m between the base of the pole and the cable is one of the legs.

We must solve for the height of the utility pole, which is essentially the other leg of the right triangle.

We can use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the legs and c is the hypotenuse

Plug in the known information (leg=40, hyp=45)

[tex]40^2+b^2=45^2\\1600+b^2=2025\\b^2=2025-1600\\b^2=425\\b=20.6[/tex]

Therefore, when rounded to the nearest tenth, the height of the utility pole is 20.6 m.

I hope this helps!

Step-by-step explanation:

here is the answer to your question

Answer:

Step-by-step explanation:

I would start from the beginning and find the slope myself, just so I know what's going on (as opposed to being dropped in the middle of the problem). The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and for us:

[tex]m=\frac{5-3}{4-3}=2[/tex] so the slope is indeed 2. Now we need to write the equation in slope-intercept form. I find it easier to first write the equation in point-slope form and then solve it for y. Point-slope form is

[tex]y-y_1=m(x-x_1)[/tex] where m is the slope (2) and x1 and y 1 are from one of the coordinates (whichever one you want; as long as you do the math correctly, you will NOT get an incorrect answer. In other words, you can't pick the "wrong" point to use to write the equation.) I'm going to use (3, 3):

y - 3 = 2(x - 3) and

y - 3 = 2x - 6 and

y = 2x - 6 + 3 so

y = 2x - 3 and that's your equation. Of course, you will enter a (-3) in that box with the ? in it.

Answer:

See explanation

Step-by-step explanation:

Given:

5⁴/25 = 5²

25 = 5²

Then,

5⁴ / 25

= 5⁴/5²

Note:

• multiplication sign means addition in indices

• Division sign means subtraction in indices

Both numerator and denominator have the same base, so you'll pick one of the bases and subtract the powers

So,

5⁴/5²

= 5^(4 - 2)

= 5^(2)

= 5²

Therefore,

5⁴ / 25 = 5²

Step-by-step explanation:

100*77+72/4

100*77+18

7700+18

7718

Answer:

Step-by-step explanation:

54 ×100=5400

5400+77=5477

5477÷2 = 2738.5

Answer:

D

Step-by-step explanation:

dfjhygcftujnnbiijjhfsrfhhhuu

Answer:

x^5+8x^4+17x^3-14x^2-84x-72

Step-by-step explanation: