Meghan sells advertisements for a radio station. Each 30 second ad costs $20 per play, and each 60 second ad costs $35 per play. Meghan sold 12 ads for $315. She wrote the system below letting x represent the number of 30 second ads and y represent the number of 60 second ads. X y = 12. 20 x 35 y = 315. What is the solution to the system of equations? (3, 9) (6, 6) (7, 5) (11, 1).

Reproduce the proof. When n = 1, we have

n³ + 2n = 1³ + 2 = 3

which is clearly divisible by 3.

Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have

(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2

= n³ + 2n + 3 (n² + n + 1)

The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.

So the claim that 3 divides n³ + 2n is true for all natural numbers n.

Answer:

A) [tex]6x^8y^5[/tex]

B) [tex]4x^5z^8[/tex]

C) [tex]12a^9b^7[/tex]

D) [tex]6t^3s^9[/tex]

Step-by-step explanation:

A) [tex]3x^2y^4[/tex] ×[tex]2x^6y[/tex]

Multiply the numbers

[tex]6x^2y^4x^6y[/tex]

Combine exponents

[tex]6x^8y^4y[/tex]

Combine exponents

[tex]6x^8y^5[/tex]

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

B) [tex]xz^3x 4x^4z^5[/tex]

Step-by-step explanation:

[tex]xz^3[/tex] ×[tex]4x^4z^5[/tex]

[tex]4x^1^+^4z^3^+^5[/tex]

[tex]4x^5z^8[/tex]

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

C) [tex]4a^3b^2 X 3a^6b^5[/tex]

Multiply the numbers

[tex]12a^3b^2a^6b^5[/tex]

Combine exponents

[tex]12a^9b^2b^5[/tex]

Combine exponents

[tex]12a^9b^7[/tex]

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

D)

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

[tex]6s^9tt^2[/tex]

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

[tex]6s^9t^3[/tex]

Step-by-step explanation:

the rate of change is the slope of the line y/x. it is always the factor of x in the equation.

it indicates how many units y changes, when x changes a certain amount of units when going from one point to another.

we only need to look at 2 points.

to go from (0, 4) to (4, -3)

x changes by +4 (from 0 to 4),

y changes by -7 (from 4 to -3).

so the rate of change is -7/3

Answer:

tence there will be 6,00 insects abter 8 weeks.

Step-by-step explanation:

Answer:n = 20

Step-by-step explanatio

0.4 * n = 8

n = 8 / 0.4

n = 20

The equation represents 0.4n = 8 and the solution will be n = 20.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given,

Product of 0.4 and n is 8.

0.4n = 8

n = 8/0.4

n = 80/4 = 20

Hence "The answer will be n = 20 because the equation says that 0.4n = 8".

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Answer:

3.9X10^-4

Step-by-step explanation:

The value is increasing so your exponent increases

Answer:

-48, -96

Step-by-step explanation:

Pattern: The terms double as they go on.

Answer:

Tn=ar^(n-1)

a=first term

r=common ratio

Tn= term n

a= -6

r= -12÷-6 = 2

T4= -6(2)^(4-1) =48

T5= -6(2)^(5-1) =96

Based on the probability that the new vacuum cleaner has a fault, the probability that it does not have a fault is 0.987.

This refers to a mutually exclusive scenario in that the vacuum cleaner can either have a fault or will not have a fault.

When that happens, the probability of one occurring can be found by deducting the probability of the other occurring from 1.

The probability of the cleaner not having a fault is therefore:

= 1 - 0.013

= 0.987

In conclusion, the probability that the cleaner does not have a fault is 0.987.

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Answer:

275mm = 27.5cm

1,000L = 1 kL

Hope this helps :)

275mm= 27.5cm and 1000L= 1KL

Step-by-step explanation:

For 257mm to get to 27.5cm, you have to divide the length value by 10 and so it becomes 27.5. Also for 1000L to become to 1KL you have to divide the volume value by 1000.

Answer:

x = 11

Step-by-step explanation:

∠ EAB = ∠ AED = 4x ( alternate angles )

∠ AEB and ∠  GEB are adjacent angles on a straight line and sum to 180° , so

∠ AEB + 125° = 180° ( subtract 125° from both sides )

∠ AEB = 55°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ EBC is an exterior angle of the triangle , then

∠ EBC = ∠ AEB + ∠EAB , that is

9x = 55 + 4x ( subtract 4x from both sides )

5x = 55 ( divide both sides by 5 )

x = 11

Answer:

y=0.2x+1

Step-by-step explanation:

2=5a+b

1.2=1a+b

0=-5a+b

we get that a=0.2, b=1

The required equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

A linear equation is defined as an equation in which the highest power of the variable is always one.

According to the given graph,

We can see two points are (-5, 0) and (5, 2)

The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Here

x₁ = -5, y₁ = 0

x₂ = 5, y₂ = 2

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

Substitute values in the equation, we get

⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))

⇒ y - 30 = (2)/(-4)(x + 5)

⇒ y - 30 = -1/2(x + 5)

⇒ y = (-1/2)x - 5/2 + 30

⇒ y = -0.5x + 27.5

Thus, the required equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

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Answer:

7375

24

Step-by-step explanation:

c=5500+125(15)

c=7375

8500=5500+125n

Answer:

x = 7

Step-by-step explanation:

If u // v, then

19x - 3 = 130   {Corresponding angles are congruent}

19x = 130 + 3

19x = 133

x = 133/19

x = 7

Answer: 2

Step-by-step explanation:

A is the scale or vertical stretch

H is what makes it move right or left.

K is what makes it move up or down.

a = 1

h = -2

k = -7

y = (1) (x-(-2))² + (-7)

y= (x + 2)² -7

(Also, you will learn b in the equation. The equation would be a(b(x-h))² + k. B would be about horizontal compression.)

Answer:

$875.00

Step-by-step explanation:

Step-by-step explanation:

[tex]\displaystyle \rm -2z+3-z=-4z+2 \\\\ -3z+3=-4z+2 \\\\ 4z-3z=-3+2 \\\\ \underline{z=-1 \ \ \ \ } \\\\[/tex]

[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]

Given to solve: -2z+3-z = -4z+2

⇛ -3z + 3 = -4z + 2

⇛ -3z + 4z = 2 - 3

⇛ z = -1

Required value of z is -1. The steps we followed are: We shifted z to a single side and other numbers to other side. Then we equated to get the result.

Answer:

The answer to your question is y=1/2×13/2

Answer:

6 full days

Step-by-step explanation:

550-40=510

510/85=6

Answer:

you could rent the car for 6 full days.

Step-by-step explanation:

first you would do 85x5=425 and you know that gets you close so then you would do 85x6=510+40=550

Answer:

x = 7

Step-by-step explanation:

The sum of exterior angles in a polygon is 360°.

( 11x - 5 )° + ( 4x + 29 )° + ( 6x + 13 )° + ( 9x - 15 )° + 67° + 61° = 360°

30x + 22 + 128 = 360

30x = 210

x = 7

Answer:

a. [tex]\boxed{y=-3x+16}[/tex]

b.[tex]\boxed{y=\frac{1}{3}x+1}[/tex]

Step-by-step explanation:

a.[tex]y-10=-3(x-2)[/tex]

[tex]\rightarrow y=-3x+6+10\\\rightarrow \boxed{y=-3x+16}[/tex]

b. [tex]y-2=\frac{1}{3}(x-3)\\\rightarrow y=\frac{1}{3}x-1+2\\\rightarrow \boxed{y=\frac{1}{3}x+1}[/tex]

Answer:

The three dollar

Step-by-step explanation:

for the three dollar one its 25% off and the 5 dollar one is 20% off

Answer:

B and C

Step-by-step explanation:

I hope you find this helpful

Step-by-step explanation:

Answer: The filled out chart is shown below.

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

Explanation:

For each row, we divide the number of locations over the population count. Treat the population values in millions. Something like 35.2 million means 35,200,000 which is the same as writing 35.2*10^6 when using scientific notation. I prefer to stick to scientific notation.

In the first row, they computed 1460/(35.2*10^6) = 0.0000415 = 4.15*10^(-5); the last entry of 4.15 for this row represents having 4.15 stores for 100,000 people. In other words, we chop off the 10^(-5) portion in 4.15*10^(-5). This is because the 10^(-5) portion represents "1 out of 100,000".

The other remaining rows are handled the same way. I'll show the steps for the second row

Like the previous row, each value is approximate.

Check out the table below. The stuff in gray represents the new entries that were previously blank.