Apollo Spas services 253 hot tubs. If each hot tub needs 115 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?

You would multiply each number by 20

Step-by-step explanation:

It says that right there

Answer:

Simplification is a method for solving a system of equations

Step-by-step explanation:

-Graphing is a real way to solve a System of Equations

-Substitution is a real way to Solve Systems of Equations

-Elimination is a real way to solve Systems of Equations

so, Simplifcation can't be one

Take 2x-4y=6 and 4x+2y=17 for example.

They are both in standard form, so you could change them to y=mx+b and graph it. The intersection is the correct answer.

You can also solve one of the equations for y or x, and substitute that into the other equation, and solve for both x and y

or, you could add the two equations together and solve for x and y.

You can't simplify them.

Answer:

[tex]f(10) = 173[/tex]

Step-by-step explanation:

Given

Exponential Function

[tex](x_1,y_1) = (3,10.125)[/tex]

[tex](x_2,y_2) = (6,34.2)[/tex]

Required

Determine f(10)

We have that

[tex]y = ab^x[/tex]

First, we need to solve for the values of a and b

For [tex](x_1,y_1) = (3,10.125)[/tex]

[tex]10.125 = ab^3[/tex] --- (1)

For [tex](x_2,y_2) = (6,34.2)[/tex]

[tex]34.2 = ab^6[/tex] ---- (2)

Divide (2) by (1)

[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]

[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]

[tex]3.38= b^{6-3}[/tex]

[tex]3.38= b^{3}[/tex]

Take cube root of both sides

[tex]b = \sqrt[3]{3.38}[/tex]

[tex]b = 1.5[/tex]

Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]

[tex]10.125 = a * 1.5^3[/tex]

[tex]10.125 = a * 3.375[/tex]

Solve for a

[tex]a = \frac{10.125}{3.375}[/tex]

[tex]a = 3[/tex]

To solve for f(10).

This implies that x = 10

So, we have:

[tex]y = ab^x[/tex] which becomes

[tex]y = 3 * 1.5^{10[/tex]

[tex]y = 3 * 57.6650390625[/tex]

[tex]y = 172.995117188[/tex]

[tex]y = 173[/tex] -- approximated

Hence:

[tex]f(10) = 173[/tex]

Answer:

Step-by-step explanation:

Given that:    

The equation of the damped vibrating spring is y" + by' +2y = 0

(a) To convert this 2nd order equation to a system of two first-order equations;

let y₁ = y

y'₁ = y' = y₂

So;

y'₂ = y"₁ = -2y₁ -by₂

Thus; the system of the two first-order equation is:

y₁' = y₂

y₂' = -2y₁ - by₂

(b)

The eigenvalue of the system in terms of b is:

[tex]\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0[/tex]

[tex]-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0[/tex]

[tex]\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}[/tex]

[tex]\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}[/tex]

(c)

Suppose [tex]b > 2\sqrt{2}[/tex], then  λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.

(d)

From λ² + λb + 2 = 0

If b = 3; we get

[tex]\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\[/tex]

Now, the eigenvector relating to λ = -1 be:

[tex]v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

[tex]\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

Let v₂ = 1, v₁ = -1

[tex]v = \left[\begin{array}{c}-1\\1\\\end{array}\right][/tex]

Let Eigenvector relating to  λ = -2 be:

[tex]m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

[tex]\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]

Let m₂ = 1, m₁ = -1/2

[tex]m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right][/tex]

∴

[tex]\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right][/tex]

So as t → ∞

[tex]\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }[/tex]

Answer:

-1.333333

Step-by-step explanation:

:)

have a very nice day

Answer:

0 cavities

minimum is 0 cavities. there are people having 0 cavities. see the graph.

hope it helps!

Answer:

0

Step-by-step explanation:

The minimum is the smallest value in the dataset. The smallest number of cavities is 0.

please give thanks by clicking the heart button! :)

Answer:

25 meters per second

Step-by-step explanation:

Divide to find m/s.

750 / 30 = 25

Check in necessary.

25 * 30 = 750

Answer:

25 per sec

Step-by-step explanation:

51.1 and 64.9

Step-by-step explanation:

Answer: 55.1 and 64.9

On edge.

Step-by-step explanation:

Answer:

70 I think but I'm not sure

Step-by-step explanation:

AC=70

Answer:

a. [tex](x - 3)^2 + 16[/tex]

b. [tex]8(x -7)^2[/tex]

c. [tex](a^2 - 1)(7x - 6)[/tex] or [tex](a+1)(a-1)(7x-6)[/tex]

d. [tex](x^2-4)(x^2+3)[/tex] or [tex](x-2)(x+2)(x^2+3)[/tex]

e. [tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]

Step-by-step explanation:

[tex]a.\ (x + 1)^2 - 8(x - 1) + 16[/tex]

Expand

[tex](x + 1)(x + 1) - 8(x - 1) + 16[/tex]

Open brackets

[tex]x^2 + x + x + 1 - 8x + 8 + 16[/tex]

[tex]x^2 + 2x + 1 - 8x + 24[/tex]

Collect Like Terms

[tex]x^2 + 2x - 8x+ 1 + 24[/tex]

[tex]x^2 - 6x+ 25[/tex]

Express 25 as 9 + 16

[tex]x^2 - 6x+ 9 + 16[/tex]

Factorize:

[tex]x^2 - 3x - 3x + 9 + 16[/tex]

[tex]x(x -3)-3(x - 3) + 16[/tex]

[tex](x - 3)(x - 3) + 16[/tex]

[tex](x - 3)^2 + 16[/tex]

[tex]b.\ 8(x - 3)^2 - 64(x-3) + 128[/tex]

Expand

[tex]8(x - 3)(x - 3) - 64(x-3) + 128[/tex]

[tex]8(x^2 - 6x+ 9) - 64(x-3) + 128[/tex]

Open Brackets

[tex]8x^2 - 48x+ 72 - 64x+192 + 128[/tex]

Collect Like Terms

[tex]8x^2 - 48x - 64x+192 + 128+ 72[/tex]

[tex]8x^2 -112x+392[/tex]

Factorize

[tex]8(x^2 -14x+49)[/tex]

Expand the expression in bracket

[tex]8(x^2 -7x-7x+49)[/tex]

Factorize:

[tex]8(x(x -7)-7(x-7))[/tex]

[tex]8((x -7)(x-7))[/tex]

[tex]8(x -7)^2[/tex]

[tex]c.\ 7a^2x - 6a^2 - 7x + 6[/tex]

Factorize

[tex]a^2(7x - 6) -1( 7x - 6)[/tex]

[tex](a^2 - 1)(7x - 6)[/tex]

The answer can be in this form of further expanded as follows:

[tex](a^2 - 1^2)(7x - 6)[/tex]

Apply difference of two squares

[tex](a+1)(a-1)(7x-6)[/tex]

[tex]d.\ x^4 - x^2 - 12[/tex]

Express [tex]x^4[/tex] as [tex]x^2[/tex]

[tex](x^2)^2 - x^2 - 12[/tex]

Expand

[tex](x^2)^2 +3x^2- 4x^2 - 12[/tex]

[tex]x^2(x^2+3) -4(x^2+3)[/tex]

[tex](x^2-4)(x^2+3)[/tex]

The answer can be in this form of further expanded as follows:

[tex](x^2-2^2)(x^2+3)[/tex]

Apply difference of two squares

[tex](x-2)(x+2)(x^2+3)[/tex]

[tex]e.\ a^{4n} -b^{4n}[/tex]

Represent as squares

[tex](a^{2n})^2 -(b^{2n})^2[/tex]

Apply difference of two squares

[tex](a^{2n} -b^{2n})(a^{2n} +b^{2n})[/tex]

Represent as squares

[tex]((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})[/tex]

Apply difference of two squares

[tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]

Answer:

-74+3i

Step-by-step explanation:

Answer:

Step-by-step explanation:

(5 + 3i) + (2 - 81)

5 + 3i + 2 - 81

74 + 3i

Answer:

i guess the answer is 680.

Answer:

2/5

Step-by-step explanation:

(2,2) and (7,4) 4-2/7-2=2/5

Answer:

2x-5y=-3

Slope=  2.000 /0.800

​x-intercept=-3/2=-1.50000

y-intercept=3/5=0.60000

y=16-4x

Slope=-8.0000/2.0000=-4.000

x-intercept=16/4=4

y-intercept=6/1=16.00000

Step-by-step explanation:

Answer:

Point C

Happy Holidays!

Step-by-step explanation:

ay

Answer:

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

Step-by-step explanation:

Given values of g and h are:

g = -7

h = 3

1. gh

The two numbers are being multiplied

Putting the values

[tex]gh = (-7)(3) = -21[/tex]

2. g^2-h

Putting the values

[tex]=(-7)^2-3\\=49-3\\=46[/tex]

3. g+h^2

Putting the values

[tex]= -7 + (3)^2\\=-7+9\\=2[/tex]

4. g+h

Putting the values

[tex]= -7+3\\=-4[/tex]

5. h-g

Putting the values

[tex]= 3 - (-7)\\=3+7\\=10[/tex]

6. g-h

Putting values

[tex]=-7-3\\=-10[/tex]

Hence,

The values of given expressions are:

1. gh = -21

2. g^2 - h = 46

3. g + h^2 = 2

4. g + h  = -4

5. h - g  = 10

6. g - h = -10

Answer:

1) - 21

2) 46

3) 2

4) -4

5) 10

6) -10

Step-by-step explanation:

[tex]1)gh = - 7(3) \\ \: \: \: \: \: \: = - 21[/tex]

[tex]2){g}^{2} - h = ( - 7 {)}^{2} - 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 49 - 3 \\ \: \: \: = 46[/tex]

[tex]3)g + {h}^{2} = - 7 + {3}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 7 + 9 \\ \: \: \: \: = 2[/tex]

[tex]4)g + h = - 7 + 3 \\ \: \: \: \: \: \: \: = - 4[/tex]

[tex]5)h - g = 3 - ( - 7) \\ \: \: = 10[/tex]

[tex]6)g - h = - 7 - 3 \\ \: \: \: \: \: \: \: \: \: \: = - 10[/tex]

Answer (least to greatest):

I hope this helps!

Answer:

1.6,- 11/5 ,2.25 , -2.4 15/10

Step-by-step explanation:

Answer:

(7,4)

Step-by-step explanation:

The x always goes first and the y goes second

Answer:

7,4

Step-by-step explanation:

x,y

Answer:

V = 167.55

Step-by-step explanation:

V = pir^2 h/3

V = pi(4)^2 (10/3)

The approximate volume of water in Anuj's cup is 42 cubic cm.

Volume is a measure of capacity that an object holds.

Formula for finding the volume of cone

volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]

where,

r is the radius of cone

h is the height of cone

π = 3.14

According to the given question

paper cups are of the shape of cone.

and,

diameter = 8cm

⇒ radius = [tex]\frac{8}{2}[/tex] = 4cm

the approximate volume  of water in cup = [tex]\frac{1}{3} \pi r^{2} h[/tex]

=[tex]\frac{1}{3}[/tex]×[tex]2^{2}[/tex]×π×10

=[tex]\frac{1}{3}[/tex]×4×3.14×10

= 41.86 = 42 cubic cm.

Hence, the approximate volume of water in Anuj's cup is 42 cubic cm.

Learn more about the volume of cone here:

https://brainly.com/question/1984638

#SPJ2

Answer:

Step-by-step explanation:

500×30=15000

Answer:

I believe the answer is 42 minutes :)

Step-by-step explanation:

B. 426 people per square. mile

Answer:

= −6x+10

Step-by-step explanation:

Answer:

-6x+10

Step-by-step explanation:

Multiply the 2 by each figure in the parenthesis. So, it becomes the sum of (2)-3x and 2(5), which is -6x+10.

Answer:

what is this......................

Answer:

y=(4/3)x-8

Step-by-step explanation:

Slope-intercept form: y=mx+b

4x-3y=24

3y=4x-24 (isolating the 3y)

y=(4/3)x-8 (dividing both sides by 3)

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

mark the answer below as brainliest x

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

The equation given is written in slope-intercept form (y = mx + b). In this form, 'm' represents the slope of a line and 'b' represents the y-intercept of the line. Since the equation asks for the slope, we can simply look at the value of 'm' in the equation. Then, we will find the slope.

slope - intercept form

y = mx + b

given equation

-y = -5x + 9

values

m = slope = -5

b = y-intercept = 9