For a basic subscription, a cable television provider charges an activation fee of $60, plus $125 per month. What linear function represents the total cost of a basic cable subscription for t months? What is the total cost for two years of service?

Answer:

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Answer:

x=6,x=-7

Step-by-step explanation:

x^2+x-42=0

x^2-6x+7x-42=0

x(x-6)7(x-6)=0

(x-6)(x+7)=0

Answer: 5x^3 + 3x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

           6x2 - 8x - 2

Simplify   ————————————

              x - 1    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  6x2 - 8x - 2  =   2 • (3x2 - 4x - 1)

Trying to factor by splitting the middle term

3.2     Factoring  3x2 - 4x - 1

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -1

Step-1 : Multiply the coefficient of the first term by the constant   3 • -1 = -3

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -4 .

     -3    +    1    =    -2

     -1    +    3    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Polynomial Long Division :

3.3    Polynomial Long Division

Dividing :  3x2-4x-1

                             ("Dividend")

By         :    x-1    ("Divisor")

dividend     3x2  -  4x  -  1

- divisor  * 3x1     3x2  -  3x    

remainder      -  x  -  1

- divisor  * -x0      -  x  +  1

remainder          -  2

Quotient :  3x-1

Remainder :  -2

Final result :

 2 • (3x2 - 4x - 1)

 ——————————————————

       x - 1      

See results of polynomial long division:

1. In step #03.03

[tex]\qquad[/tex]_________________________

[tex]\bf Multiplying\:by\:\: \purple{ \dfrac{5+\sqrt{3}}{5+\sqrt{3}}}\\[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \bf \dfrac{1}{5 - 2\sqrt{3} } \times \dfrac{5 + 2\sqrt{3} }{5 + 2\sqrt{3} }\\ [/tex]

[tex]\qquad[/tex][tex]\longrightarrow \sf \dfrac{1(5 + 2\sqrt{3}) }{(5 - 2\sqrt{3})(5 + 2\sqrt{3}) } [/tex]

[tex]\qquad[/tex][tex]\longrightarrow \sf \dfrac{5 + 2\sqrt{3} }{ {(5)}^{2} - (2 \sqrt{3})^{2} } [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(5 \times 5) - (2 \times 2 \times \sqrt{3} \times \sqrt{3} )} [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(25) - (12)} [/tex]

[tex]\qquad[/tex][tex] \purple{ \longrightarrow \bf \dfrac{5 + 2 \sqrt{3} }{13} } [/tex]

[tex]\qquad[/tex]_________________________

Answer is 2/(5+√13)

Rationalize the denominator 1/ (5-2√3)

Answer:

Step-by-step explanation:

The speed of the plane was 291.13mph.

Speed is distance travelled per unit time. It is scalar quantity

Given

The difference in distances was 600 miles; the difference in speeds was 190mph. That means the time was 600/190 = 3.16 hours.

Since the plane flew 920 miles in that time, its speed was 920/3.16 = 291.13mph.

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[tex]2(4x+1)<3(2x-3)\\\\\implies 8x +2 < 6x -9\\\\\implies 8x <6x -9 -2\\\\\implies 8x -6x < -11\\\\\implies 2x<-11\\\\\implies x< -\dfrac{11}2\\\\\\\text{Interval,} ~ \left(-\infty, -\dfrac{11}2 \right)[/tex]

Answer:

x<3.5

Step-by-step explanation:

multiply 2 with 4x and 1 to get 8x + 2 < 3(2x-3). Then multiply 3 by 2x and -3 to get 8x + 2 < 6x- 9. Then subtract -6x on both sides to get 2x + 2< -9. Next subtract 2 from -9 so x is by itself and then you get 2x < 7. Finally divide 2 on each side so you leave x byitself completely. You get x > 3.5

I hope u get it right!

Answer:

Rate of sales tax = 6% of $60

Sales tax = [tex]\frac{6}{100}[/tex] × 60

               = $3.60

Answer:

10/12 i took the test

Step-by-step explanation:

Answer:

18/4  ,  27/6   ,   36/8

Step-by-step explanation:

9 to 2 x 2 = 18 to 4

9 to 2 x 3 = 27 to 6

9 to 2 x 4 = 36 to 8

Answer:

Cos C = adjecent/hypotenuse

Cos C = 14/50

divide the numerator and the denominator by 2

Cos C = 7/25

The answer is C

Answer:

44 dollars

Step-by-step explanation:

Since we need to find the total sales, we do 152 * .29, but we are estimating, therefore, instead we can do 150 * .29, which is 43.5. Rounding up we get 44, thus 44 is our answer

The system of equations representing the number of Blue-ray discs and DVD's after t months are:

507 + 26t

925 - 12t

Each month, the number of DVD's sold decreases by 12, this can be modelled as:

number of DVD in opening month - (monthly decrease x number of months)

Number of DVD's in t months = 925 - 12t

Each month, the number of Blue-ray discs sold increases by 26, this can be modelled as:

number of blue-ray discs in opening month + (monthly increase x number of months)

Number of Blue-ray discs in t months = 507 + 26t

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Answer:

[tex]c=\frac{81}{4}[/tex]

I hope this is the right answer and I hope this helps

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.

The expression is given below.

⇒ x² + 9x + c

The value of the variable 'c' to convert the expression as the square of a binomial will be given as,

c = (9/2)²

c = 81 / 4

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

More about the perfect square trinomial link is given below.

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Step-by-step explanation:

I think the answer is like this

Answer:

160

Step-by-step explanation:

4th square number: 16

12th square number: 144

16 + 144 = 160

The price of the one notebook will be Rs. 10.6

If Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store, with a total of Rs. 95 paid in all, then;

1x + 4x + 4x = 95

9x = 95

x = 95/9

x = 10. 6

Hence the price of the one notebook will be Rs. 10.6

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Answer:

Step-by-step explanation:

Circumscribed means written around the outside. -scribe means writing and

think of how circumference is the distance around the outside of a circle. It is a little more special and specific...all the segments that make the triangle are tangents to the circle, that is, they only touch the circle at one point.

So the circle is inscribed-- that is, written inside of the triangle (in the same, special specific way).

Circle A is inscribed in triangle RST.

Answer:

Inscribed

Step-by-step explanation:

What is polygon inscribe?

Answer:

Step-by-step explanation:

Let the required distance be x.

We have a right triangle with vertical leg of 70 feet and the acute angle opposite to this leg is 22 degrees.

Use trigonometry:

Answer:

60 have 12 factors :1,2,3,4,5,6,10,12,15,20,30,60

Answer:

6

Step-by-step explanation:

5% of 120 were late

= [tex]\frac{5}{100}[/tex] × 120

= 0.05 × 120

= 6

Answer:

22.5

Step-by-step explanation:

since 2.25 divided by 0.10 is 22.5 so she can message 22.5 friends

Answer:

You would count another table for the remainder. Therefore, 8 tables are needed to seat 63 people. It does not matter whether all seats are filled on the 8th table.

Answer:

SAS is the answer

Step-by-step explanation:

Answer:

HL.

Step-by-step explanation:

Right triangles with the hypotenuse and one leg congruent

Answer: we need to know what the equation is

Step-by-step explanation:

Step-by-step explanation:

1B.) Zero power rule

C.) 1

2B.) Product of powers rule

C.) y^(7+11) = y^18

3B.) Quotient of powers rule

C.) b^(18-5) =b^13

4B.) Power of a power rule

C.) 3^(2×2) =3^4= 81

5B.) None

C.) 729

Answer:

V=TTr²h

Step-by-step explanation:

Why?

Because you will v=TT r² h/3

so the answer is

v=TT r² h/3,r É R,h É R

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Answer:

x = 1.125 AKA x = 1 1/8 AKA x = 9/8

Step-by-step explanation:

CB to ED = 1 : 9

Scale Factor = 1/9

[tex]\frac{1}{9} = \frac{x}{x+9}[/tex] -> cross multiply

9x = x + 9

-x     -x

8x = 9

[tex]\frac{8x}{8} =\frac{9}{8}[/tex]

x = 9/8

Answer:

A, B, D

Step-by-step explanation:

from this function, we can see that 2x is being subtracted from 100. x is the number of incorrect problems, so this can not be a negative value. therefore, the maximum score you can get is 100. y is equal to your final grade as calculating the right side of the equation results in the grade you receive based on the number of incorrect answers. this is a linear function since its highest power is 1. each question is worth 2 points as 2 is being multiplied by the number of incorrect questions (x).

The function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

The points on the graph are given as:

[tex](x,y) = (-3,3)[/tex] --- the inflection point

[tex](x,y) = (0,4.5)[/tex] --- the y-intercept

The function that satisfy the above points is:

[tex]y = \sqrt[3]{x+3} + 3[/tex]

The proof is as follows:

At the inflection point, we have the x value to be -3.

So, the function becomes

[tex]y = \sqrt[3]{x+3} + 3[/tex]

[tex]y = \sqrt[3]{-3+3} + 3[/tex]

[tex]y = \sqrt[3]{0} + 3[/tex]

[tex]y = 0+ 3[/tex]

[tex]y = 3[/tex] ---- the y-value at the inflection point is true for x = -3

Also, at the y-intercept, we have the x-value to be 0

So, the function becomes

[tex]y = \sqrt[3]{x+3} + 3[/tex]

[tex]y = \sqrt[3]{0+3} + 3[/tex]

[tex]y = \sqrt[3]{3} + 3[/tex]

[tex]y = 1.45+ 3[/tex]

[tex]y = 4.45[/tex] ---- the y-value at the y-intercept is true for x = 0

Hence, the function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

Read more about graphs and functions at:

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Answer:

D

Step-by-step explanation: