On a recent trip to the movies , you see a advertisement for 2 adult tickets and 6 child tickets for $60. Write and equation using A to represent the cost of an adult ticket and C to represent the cost of a child ticket

Answer: a = 12, b = 2, c = 11

Step-by-step explanation:

Using exponent rules we can distribute the exponent of 3 to the xyz.

This results in the numerator now being. [tex]x^{5*3}+y^{1*3}+z^{4*3}\\[/tex] This can be simplified to, [tex]x^{15}y^{3}z^{12}\\[/tex].

Now divide the numerator by the denominator subtracting the exponents.

Which equals, [tex]x^{12}y^{2}z^{11}[/tex]

So a = 12

b = 2

and

c = 11

The values of [tex]a, \ b,\ c[/tex] are  [tex]12,\ 2,\ 11[/tex] .

Exponent indicates that the base is to be raised to a certain power. So, it is the power of the base.

We have,

[tex]\frac{(x^5yz^4)^3}{x^3yz}=x^ay^bz^c[/tex]

Now simplify the above given equation;

[tex]\frac{(x^5*3y^1*3z^4*3)}{x^3yz}=x^ay^bz^c[/tex]

[tex]\frac{(x^{15}y^3z^{12})}{x^3yz}=x^ay^bz^c[/tex]

Now, Using the exponent rule;

[tex]\frac{a^n}{a^m} = a^{n-m}[/tex]

So,

[tex](x^{15-3}y^{3-1}z^{12-1})=x^ay^bz^c[/tex]

[tex](x^{12}y^{2}z^{11})=x^ay^bz^c[/tex]

Now,

As we see variables on both sides of equation are same (i.e. bases of powers are same), so now compare the powers of sides of variables;

⇒    [tex]x^{12}=x^a[/tex]

       [tex]a=12[/tex],

And, [tex]y^2=y^b[/tex]

         [tex]b=2[/tex]

And, [tex]z^{11}=z^c[/tex]

         [tex]c=11[/tex]

So, the values of [tex]a, \ b,\ c[/tex] are [tex]12,\ 2,\ 11[/tex] which are find out using the  exponent rule.

Hence, we can say that the values of [tex]a, \ b,\ c[/tex] are [tex]12,\ 2,\ 11[/tex] .

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Answer:

5 years old

Step-by-step explanation:

Kevin= k

Daniel= d

Answer:

Kevin is 6 now

Step-by-step explanation:

K= D+3

2 years ago K-2 =4 (D-2) plug in D+3 for K

D+3-2=4D-8

D+1 =4D-8 rearrange equation by subtracting D and adding 8

9 = 3D

D =3 so K =6

Answer:5 milllion

And the minimum is 25

Step-by-step explanation:

Answer:

a = 17 sqrt(2)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite / hypotenuse

sin 45 = 17/a

Multiply each side by a

a sin 45 = 17

Divide each side by sin 45

a = 17 / sin 45

a = 17 / ( 1 / sqrt(2))

a = 17 sqrt(2)

Answer:

108

Step-by-step explanation:

Mike's current age, be M

Then Brandon's is: M - 27

Also, M = 4(M - 27)

M = 4M - 108

M - 4M = - 108

- 3M = - 108

Answer:

250.5 - 35m = 300 - 45.25m

Complete question:

Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

250.5 + 35m = 300 + 45.25m

250.5 – 35m = 300 – 45.25m

250.5m – 35 = 300m – 45.25

250.5m + 35 = 300m + 45.25

Step-by-step explanation:

For The International Business Club: y = 250.50 - 35m,  

For The Future Agricultural Leaders Club: y = 300 - 45.25m.

So the answer is 250.5 - 35m = 300 - 45.25m

250.5 – 35m = 300 – 45.25m

Explanation:
It's this one because the initial for international Business Club is $250.50 and their monthly spending is $35, and for Future Agricultural Leaders Club their initial is $300 and their monthly spending is $45.25

So, the equation would be 250.5 – 35m = 300 – 45.25m

Answer:

x=16

Step-by-step explanation:

37+(3x+5)=90 (because its a right angle)

3x+5=90-37=53

3x=53-5=48

x=48/3

=16

Answer:

Step-by-step explanation:

Identify the opposite of 2 on the number line.

✔ –2

Identify the opposite of 5 on the number line.

✔ –5

Using your results, which statement is true?

Since –2 is further

✔ right on the number line, –2 > –5

.

this is the answer

The correct state would be negative 2 is greater than negative 5.

The opposite of the numbers can be obtained changing the positive numbers to negative equivalent of the number as follows;

From the initial given expression, 2 < 5, that is 2 is less than 5.

From the opposite numbers, -2 > - 5, that is negative 2 is greater than negative 5.

Thus, the correct state would be negative 2 is greater than negative 5.

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Answer: 4

Step-by-step explanation:

6 times 2 = 12 on the bottom so on the top you do the same thing. 2 times 2 is 4.

Answer:

2/12

Step-by-step explanation:

because when u multiple 2×6=12

so when u get 12 u think of multiplying it by 2 ,

2×2=4

Answer:

x = [tex]\frac{-1}{4} + \frac{1}{4} \sqrt{29}[/tex]

Step-by-step explanation:

For this equation: a=4, b=2, c=-7

4x²+2x+−7=0

Step 1: Use quadratic formula with a=4, b=2, c=-7.

x=  [tex]\frac{-b + \sqrt{bx^{2}-4ac } }{2a}[/tex]

x = −(2)±√(2)2−4(4)(−7)  ÷ 2(4)

x = −2±√116   ÷ 8

x = [tex]\frac{-1}{4} + \frac{1}{4} \sqrt{29}[/tex]

Answer:

She invested $30,000 at 9%

Step-by-step explanation:

Let the amount invested per percentage be $x and $y respectively

Total investment is 40,000

This means that;

x + y = 40,000 ••••••••••(i)

Now for her income;

9/100 * x = 9x/100

for the 12% = 12/100 * y = 12y/100

Now;

9x/100 + 12y/100 = 3,900

9x + 12y = 390000 •••••••••(ii)

we solve both simultaneously

From i, y = 40,000-x

Substitute this into ii

9x + 12(40,000-x) = 390,000

9x + 480,000-12x = 390,000

3x = 480,000-390,0000

3x = 90,000

x = 90,000/3

x = $30,000

The input value for which f(x) = g(x) is true is -1

The formula for calculating the equation of a line is expressed as:

[tex]y=mx+b[/tex]

m is the slope

b is the y-intercept

For table 1,

Get the slope:

[tex]Slope=\frac{3-3}{3-2}\\Slope =\frac{0}{1} \\Slope =0[/tex]

Use the coordinate (-2, 3) and m = 0 to get the value of "b"

[tex]y=mx+b\\3 = 0(-2) + b\\b = 3[/tex]

The required function for table 1 is f(x) = 3

For table 2:

Get the slope:

[tex]Slope=\frac{0-1}{3-2}\\Slope =\frac{-1}{1} \\Slope =-1[/tex]

Use the coordinate (-2, 4) and m = -1 to get the value of "b"

[tex]y=mx+b\\4 = -1(-2) + b\\b = 4-2\\b=2[/tex]

The required function for table 2 is g(x) = -x + 2

If the function f(x) = g(x), hence:

-x + 2 = 3

-x = 3 - 2

-x = 1

x = -1

Hence the input value for which f(x) = g(x) is true is -1

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Answer: -1

Step-by-step explanation:

Answer:

g(-3)=10

Step-by-step explanation:

We want to find what g(x), or y is, when x is equal to -3.

g(x)== x² + 1

x= -3

Substitute -3 in for x.

g(-3)=(-3)²+1

Evaluate the exponent first. -3² is equivalent to -3*-3, which is equal to 9.

g(-3)=9+1

Add 9 and 1

g(-3)=10

Answer:

Step-by-step explanation:

g(x)=x^2+1

at g(-3) = (-3)^2+1

=9+1=10

Answer:

0 degrees?

Step-by-step explanation:

It looks perfectly even to me

Answer:

13

Step-by-step explanation:

We were already given the formula and were left with [tex]169 = c^2[/tex].

To find c we would find what by itself equals 169.

We know [tex]12 * 12[/tex] is 144

so its greater than 12

we also know that 13 * 13 is 169

so c would be equal to 169

Answer:

x(3+4)=4(x+3), (x+2)+5(x-1)=3(x+3)

Step-by-step explanation:

x(3+4)=4(x+3)

3x+4x=4x+12

7x=4x+12

Subtract 4x by both sides

3x=12

Divide 3 by both sides to get x=4

4x+5=3(x+2)

4x+5=3x+6

Combine Like terms

1x+5=6

Subtract 5 from both sides

x=1

(x+2)+5(x-1)=3(x+3)

x=4

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

A pentagon has n = 5, thus

sum = 180° × 3 = 540°

Answer:

The principal, real, root of:

²√7.937005259841 = 2.81726911

All roots:

2.81726911

−2.81726911

7.937005259841 is not a perfect square

Step-by-step explanation:

side length a = 7.937005259841 ft

face diagonal f = 11.224620483094 ft

solid diagonal d = 13.747296369986 ft

surface area S = 377.97631496846 ft2

volume V = 500 ft^3

Answer:

3x = 14

Step-by-step explanation:

5x - y = 6

-2x +y = 8

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

3x+0y = 14

3x = 14

Answer:

3x = 14

Step-by-step explanation:

5x - y = 6

-2x +y = 8

3x+0y = 14

3x = 14

Answer:

a≤39/5

Step-by-step explanation:

60a - 80a ≥ -64 -92

-20a≥-156

a≤156/20

a≤39/5

Answer:

The answer is 4:21

Step-by-step explanation:

Answer:

[tex] 30\: m^2 [/tex]

Step-by-step explanation:

For triangle:

Base = (4 + 3 +1) m = 8 m

Height = 9 m

For rectangle:

Length = 3 m

width = 2 m

Area of shaded region = Area of triangle - Area of rectangle

[tex]= \frac{1}{2}\times base\times height-length \times width \\\\= \frac{1}{2} \times (4 + 3 + 1) \times 9 - 3 \times 2 \\ \\ = \frac{1}{2} \times 8 \times 9 - 6 \\ \\ = 4 \times 9 - 6 \\ = 36 - 6 \\ = 30 \: {m}^{2} [/tex]

Answer:

Its Las sillas son nuestras

Step-by-step explanation:

On Edge 2021

Answer:

nuestras

Step-by-step explanation:

Answer:

it's 2 because it's the smallest number

Answer:

(10, - 20 )

Step-by-step explanation:

Given the 2 equations

y = - 5x + 30 → (1)

x = 10 → (2)

Since the value of x is given substitute x = 10 into (1) for y

y = - 5(10) + 30 = - 50 + 30 = - 20

Solution is (10, - 20 )

Answer:

(10, -20)

Step-by-step explanation:

y = –5x + 30

x = 10

------

x=10 ⇒ y= -5*10+30= -20

Then solution is (10, -20)

Answer:

A

Step-by-step explanation:

18%=18/100=0.18

0.18*30.80=5.544 or about $5.50. Hope this helps!