40 points. Topic: Solving a word problem using a system of linear equations of the form y = mx + b A phone company offers two monthly plans. Plan A costs $8 plus an additional $0.17 for each minute of calls. Plan B costs $21 plus an additional $0.12 for each minute of calls. For what amount of calling do the two plans cost the same? ____minutes What is the cost when the two plans cost the same? $_____

Answer:

2y( 3x-1)(3x+1)

Step-by-step explanation:

18x^2y-2y

Factor out the greatest common factor 2y

2y( 9x^2 -1)

The term in the parentheses is the difference of squares

a^2 - b^2 = (a-b)(a+b)

2y( 3x-1)(3x+1)

Answer:

A. 8/1

Step-by-step explanation:

96/12=8

12/12=1

Therefore, the answer is 8/1. Have a good day!

8/1 is the unit rate of the fraction 96/12, option A is correct.

The given fraction is ninety six by twelve

96/12

Let us find the unit rate of 96/12

we can divide both the numerator and the denominator by their greatest common divisor, which in this case is 12.

96 divided by 12 is 8

and 12 divided by 12 is 1.

So 96/12 is equal to 8/1

Therefore, the simplified form of 96/12 is 8/1.

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Answer:

Step-by-step explanation:

The vertices (-2, -3) and (-2, 4) are on the same vertical line and are separated by 4 - (-3), or 7, units.  The vertices (-2, 4) and (5, 4) are on the same horizontal line (y = 4) and separated horizontally by 5 - (-2), or 7, units.  If you can picture this in your mind, you'll see a 45-45-90 isosceles triangle with leg lengths 7 (there are two such legs).

The next thing to do is to calculate the length of the hypotenuse of this triangle.  Using the Pythagorean Theorem, we get:

d = √(7² + 7²) = 7√2 ft.

The perimeter of this triangle is thus 7 ft by 7 ft by 7√2 ft, or approximately 23.9 feet, or 7.97 yd

and ...

The area of the triangular shape is A = (1/2)(base)(height), which here is

A = (1/2)(7)(7) = 49/2 ft^2, or 16.4 yd^2

Answer:

1. A

2. B

3. B

Step-by-step explanation:

1. 180+57-94= 29

2. 4x + 7 + 97 + 180 - 17x - 13 = 180

-13x = -91

x = 7

3. 180 - 64-38 = 78

180-78 =. 102

Answer:

A) 29°

B) 7°

B) 102°

Step-by-step explanation:

1. ------------------------

2.  ------------------------

3.  ------------------------

Answer:

48 =x

Step-by-step explanation:

3/4x + 12 = x

Subtract 3/4 x from each side

3/4x + 12-3/4x = x-3/4x

12 = 1/4x

Multiply each side by 4

12*4 =1/4x *4

48 =x

Answer:

x=48

Step-by-step explanation:

f(x) is basically just another way to write y.

If f(x)=x, then y=x.

x=3/4x+12 (Original Equation Substituting x for f(x), equal to y)

1/4x=12 (Subtract 3/4 from both sides of the linear equation)

x=48 (Multiply both sides by 4)

Answer:

explanation below

Step-by-step explanation:

(n - 2) * 180 = 8100

n - 2 = 8100/180

n - 2 = 45

n = 45 + 2

n = 47 sides <---answer

happy to help ya :)

The answer is 2

please see the attached picture for full solution

Hope it helps

Good luck on your assignment...

Answer:

x ≥ 2

Step-by-step explanation:

21 ≤ 3 + 9x

21 - 3 ≤ 9x

18 ≤ 9x

18 ÷ 9 ≤ x

2 ≤ x

x ≥ 2

The solution to the inequality 21 ≤ 3 + 9x by combining like terms and solving for x is, x ≥ 2.

Used the concept of inequality which states that,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that,

The inequality is,

21 ≤ 3 + 9x

Now, simplify the inequality by combining like terms and solving for x,

21 ≤ 3 + 9x

Subtract 3 on both sides,

21 - 3 ≤ 9x

18 ≤ 9x

It can be written as,

9x ≥ 18

9x - 18 ≥ 0

Take 9 as common,

9 (x - 2) ≥ 0

x - 2 ≥ 0

Therefore, the solution of expression is,

x  ≥ 0

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Answer:

t= -2

Step-by-step explanation:

9+4t=7t+15

Subtract 4t from both sides

9=3t+15

Subtract 15 from both sides

-6=3t

3t= -6

Divide both sides by 3

t= -2

Answer:

[tex]\£8:\£32[/tex]

Step-by-step explanation:

[tex]\frac{40}{1+4}[/tex]

[tex]\frac{40}{5}[/tex]

[tex]=8[/tex]

[tex]1:4[/tex]

[tex]1 \times 8:4 \times 8[/tex]

[tex]8:32[/tex]

Answer:

Tim gets £8

Sam gets £32

Step-by-step explanation:

Ratio is 1:4

So, Total parts are 1+4 = 5

Dividing it by total parts

= [tex]\frac{40}{5}[/tex]

= £ 8

So, Tim gets £8

But,

Sam gets 4(£8)

= Sam gets £32

Answer:

89

Step-by-step explanation:

I just multiplied 320 by 0.2 and then 250 by 0.1 and then added them  together. I hope it helps and I'm not sure what method you would use for this but that's mine.

Answer:

a, b, and d.

Step-by-step explanation:

They have a common angle = 25 deg.

The pair of sides created that common angle share the same ratio = 1/2

(6/12 = 3/6 = 8/16 = 1/2)

Hope this helps!

Answer:

The answer is B.

Step-by-step explanation:

You have to apply gradient formula by using coordinates :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Let (x1,y1) be (-14,-13),

L3t (x2,y2) be (7,0),

[tex]m = \frac{0 - ( - 13)}{7 - ( - 14)} [/tex]

[tex]m = \frac{13}{21} [/tex]

Answer:

B

Step-by-step explanation:

To find the answer we add to the fractions

5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 3/2 = 1 1/2

Answer:

1 1/2

Step-by-step explanation:

5/6 + 2/3

Get a common denominator

5/6 + 2/3 *2/2

5/6 + 4/6

9/6

Rewriting as a mixed number

1 3/6

1 1/2

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses.

-Shin ( and no need to thank me vote and give brainliest if you want, because i only wanna help! )

Answer:

$0.92

Step-by-step explanation:

Since only one ticket out of the 250 wins a 230 dollar prize, the expected payoff is 230/250=0.92. Hope this helps!

Answer:

Expected Payoff ⇒ $ 15.5 ; Type in 15.5

Step-by-step explanation:

Considering that all odd out of the 20 numbers will have a probability of winning a 31 dollar prize, take a proportionality into account;

[tex]20 - Total Number of Balls,\\1 - 20 - Numbering of Balls,\\Even = Odd, Between 1 - 20, Knowing 20 - Even,\\\\10 / 20 - Odd,\\10 / 20 - Even,\\1 / 2 - Probability of Choosing an Odd Ball,\\\\Proportionality - 1 / 2 = x / 31, where x = " Expected Payoff ",\\1 / 2 = x / 31 - Cross Multiply,\\2x = 31,\\\\Conclusion ; x = 15.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 15.5

Answer:

Step-by-step explanation:

Given the expression [tex]\frac{11}{12}/\frac{1}{3}[/tex], the equivalent expression can be gotten as shown;

[tex]= \frac{11}{12}/\frac{1}{3}\\= \frac{11}{12}*\frac{3}{1}\\ = \frac{11}{4} \\= 2+\frac{3}{4}\\ = 2\frac{3}{4}[/tex]

2 and three-fourth therefore gives the required expression

Answer:

2 and three-fourths

Step-by-step explanation:

Given the expression , the equivalent expression can be gotten as shown;

Step-by-step explanation:

Answer: 50 + m

Step-by-step explanation:

From the question, Erica and John are making brackets and Erica makes 25 bracelets while John makes m more bracelets than Erica. The total number of bracelets made will be:

Erica bracelet = 25

John bracelet = 25 + m

Total bracelet = 25 + 25 + m

= 50 + m

The expression that represents the total number of bracelets Erica and John made is 50 + m

Answer:

y = 6

Step-by-step explanation:

-3x + 9y = 18

-3(6) +6y = 18

-18 +6y = 18

Add 18 to each side

-18+18 +6y =18+18

6y = 36

Divide each side by 6

6y/6 = 36/6

y = 6

Answer:

see below

Step-by-step explanation:

Take the number of people surveyed and multiply by 30 %

8 * 30%

Change to decimal form

8 * .3

2.4

About 2.4 will purchase online

Answer:

1. x = -5 and x = 1

2. x = 5 and x = -1

3. no integral solutions

4. no integral solutions

Step-by-step explanation:

Answer:

1, 4, and –5

Step-by-step explanation:

on edge

Answer:

1) 752.9 m²    2) 2.68 ft

Step-by-step explanation:

1. 3.28 ft = 1 meter

90/3.28 = 27.44

27.44 x 27.44 = 752.9 m²

2. tan 15 = 10/x or x = 10/tan 15 = 2.68 ft

Profit = amount sold - expenses

Profit = 115,849 - 66,350

Profit = $49,499

Answer: 3y+6

Step-by-step explanation:

Answer:

total balls in the Machine = 7+5+4 = 16

Step-by-step explanation:

METHOD-1

Probability of First ball to be Blue = 7/(7+5+4) = 7/16

Probability of Second ball to be Green = 5/(15) = 5/15 [15 balls remaining after one being taken out in Step 1]

Probability of Third ball to be red = 4/(14) = 4/14 [14 balls remaining after Two being taken out in Step 1&2]

But this can happen in any order so the orders in which it can happen = 3!

i.e. Final Probability that machine dispenses one gumball of each color = (7/16)*(5/15)*(4/14)*3! = 1/4

Answer: Option E

METHOD-2

The total ways in which three balls can be Picked out of a total of 16 balls (with orders) = 16*15*14 = 840

The ways in which three balls of different colors can be taken out (with orders) = 7*5*4*3! = 3360

Probability = Favourable Outcome / Total Outcomes

i.e Probability = 840 / 3360 = 1/4

Answer: Option E

METHOD-3

The total ways in which three balls can be Picked out of a total of 16 balls (without orders) = 16C3 = 560

The ways in which three balls of different colors can be taken out (with orders) = 7C1 * 5C1 *4C1 = 140

Probability = Favourable Outcome / Total Outcomes

i.e Probability = 140 / 560 = 1/4

Answer: Option E

Answer:

[tex] a. = -35 \\ b. = 9a + 1 \\ c. = -35 [/tex]

Step-by-step explanation:

[tex]a. \\ = > \: 7a - 1 + 2a + 2 \\ \\ = > 7( - 4) - 1 + 2( - 4) + 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (a = - 4) \\ \\ = > - 28 - 1 - 8 + 2 \\ \\ = > - 37 + 2 \\ \\ = > - 35 \\ \\ \\ b. \\ = > 7a - 1 + 2a + 2 \\ \\ = > 7a + 2a - 1 + 2 \\ \\ = > 9a + 1 \\ \\ \\ c. \\ = > 9a + 1 \\ \\ = > 9( - 4) + 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (a = - 4) \\ \\ = > - 36 + 1 \\ \\ = > - 35[/tex]

Answer:

8 pencils for every 4 students or 2 pencils for every students

Step-by-step explanation:

Whatever you want to multiply or divide one from, you gotta do it to the other number so it can stay equivalent