T-Mobile has a family plan of four lines for $120 and additional lines are $10 each per month. If Jason wants to spend at most $175 per month on a cell phone expenses, what is the correct inequality that represents the amount of additional lines he can afford?

[tex]\sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]      or     [tex]\sf \dfrac{54a-52}{24}[/tex]

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[tex]\sf \rightarrow 7\left(\dfrac{5}{14}a-\dfrac{5}{21}\right)-\dfrac{1}{12}\left(3a+6\right)[/tex]

use distributive method

[tex]\sf \rightarrow \dfrac{5a}{2}-\dfrac{5}{3}-\dfrac{a}{4}-\dfrac{1}{2}[/tex]

group terms

[tex]\rightarrow \sf \rigtharrow \dfrac{5a}{2}-\dfrac{a}{4}-\dfrac{5}{3}-\dfrac{1}{2}[/tex]

make the denominators same

[tex]\rightarrow \sf \rigtharrow \dfrac{2(5a)}{4}-\dfrac{a}{4}-\dfrac{2(5)}{6}-\dfrac{3(1)}{6}[/tex]

simplify

[tex]\rightarrow \sf \rigtharrow \dfrac{10a-a}{4}-\dfrac{10+3}{6}[/tex]

answer in separate constants

[tex]\rightarrow \sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]

make the denominators same

[tex]\rightarrow \sf \dfrac{6(9a)}{24}-\dfrac{4(13)}{24}[/tex]

simplify

[tex]\rightarrow \sf \dfrac{54a}{24}-\dfrac{52}{24}[/tex]

join both fractions

[tex]\rightarrow \sf \dfrac{54a-52}{24}[/tex]

Answer:

 [tex]\boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

Step-by-step explanation:

[tex]7(\dfrac{5a}{14} - \dfrac{5}{21} ) - \dfrac{(3a + 6)}{12}[/tex]

Step-1: Simplify the distributive property

⇒ [tex]\dfrac{35a}{14} - \dfrac{35}{21} - \dfrac{(3a + 6)}{12}[/tex]

Step-2: Make common denominators

⇒ [tex]\dfrac{35a \times 3}{14 \times 3} - \dfrac{35 \times 2}{21 \times 2} - \dfrac{7 \times (3a + 6)}{12 \times 7}[/tex]

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{7 \times (3a + 6)}{84}[/tex]

Step-3: Simplify the distributive property

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a + 42}{84}[/tex]

Step-4: Rewrite (21a + 42)/84 in a different way

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a}{84} + \dfrac{42}{84}[/tex]

Step-5: Add/Subtract if necessary

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}}[/tex]

Step-6: Simplify the fractions

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}} = {\dfrac{9a}{4} - \dfrac{49}{42}} = \boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

cos θ = Adjacent/ hypotenuse

cosθ= 5/13

a²+b²= c²

a² + 5² = 13²

a² = 13² - 5²

a² = 144

a=√144

a= 12

a is the opposite = 12

b is the Adjacent = 5

c is the hypotenuse = 13

a) tan θ= opposite/Adjacent

tan θ = 12/5

b) sin θ= opposite/ hypotenuse

sinθ= 12/13

C) sec θ= hypotenuse / Adjacent

sec θ= 13/5

d) cscθ= hypotenuse /opposite

cscθ= 13/12

e) cotθ=Adjacent/ opposite

cotθ= 5/12

Answer:

5x-9

Step-by-step explanation:

Add 2x and 3x since they're like terms

5x-9

Answer:

28.26 ft squared

Step-by-step explanation:

Area is pi*r^2

3.14*(3)^2

3.14*9

28.26

Step-by-step explanation:

The graphs are not give but the graph looks like the above picture.

The market share of the companies is an illustration of fractions.

The market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

The current market shares are:

After 6 months, we have:

Company A:

Company B:

Company C:

The amount of customers lost by each company is

Lost = Market share * [Share retained - Share lost to the other two companies].

So, we have:

A = 2/9 * [3/4 - 1/6 - 1/12] = 1/9

B = 4/9 * [1/2 - 1/3 - 1/6] = 0

C = 1/3 * [3/8 - 1/4 - 3/8] = -1/12

The amount of customers gained by each company is

Gain = Market share of company gained from * Share gained

So, we have:

A = 1/3 * 4/9 + 1/4 * 1/3 = 25/108

B = 1/6 * 2/9 + 3/8 * 1/3 = 35/216

C = 1/12 * 2/9 + 1/6 * 4/9 = 5/54

The total gain in 6 months is:

Total Gain = Gain + Loss.

This gives

A = 25/108 + 1/9 = 37/108

B = 35/216 + 0 = 35/216

C = 5/54 - 1/12 = 1/108

Hence, the market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

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Answer:

314 miles

Step-by-step explanation:

Area of circle: 3.14(r^2)

Now lets solve!

3.14(10^2)

3.14(100)

314

Have an amazing day!!!

Please rate and mark brainliest!!

The area of the circle formula --> [tex]\pi r^2[/tex]

 [tex]Area = \pi r^2=\pi (10mi^2) = (100\pi) mi^2= 314 mi^2[/tex]

Hope that helps!

Answer:

The function h(x) is increasing on the interval (-2, ∞)

Step-by-step explanation:

Given function:  [tex]h(x)=3 \sqrt{x+2}[/tex]

We cannot square root a negative number, therefore the domain (x-values) is restricted:

[tex]x+2\geq 0 \implies x\geq -2[/tex]

Therefore, [tex]h(x)\geq 0[/tex]

⇒ The function h(x) is increasing on the interval (-2, ∞)

Answer:

FLVS ANSWER D-  The function h(x) is increasing on the interval (–2, ∞).

Step-by-step explanation:

you dont need one

Answer:

Step-by-step explanation:

Answer:

-509

Step-by-step explanation:

1. Subsitute 5 for a in the expression.  -6(5)^3+8(5)^2+8(5)+1

2. -6(125)+8(25)+40+1

3. -750+200+41

4. -509

Answer:

22.5

Step-by-step explanation:

8 pieces is 180 calories to find the calorie of one piece :

180/8 to get 22.5

Step-by-step explanation:

[tex]( \sqrt{2 + i} ) {}^{8} [/tex]

Notice that

[tex] \sqrt{a} = a {}^{ \frac{1}{2} } [/tex]

So

Answer:

C. (2,7)

Step-by-step explanation:

2x+3 = 3x+1

x=2

y= 2×2+3

y=7

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The given function is :

[tex]\qquad \tt \dashrightarrow \:f(x) = \frac{1}{x} [/tex]

here, for each value of x there is an unique value of f(x), so we can infer that it's a " one - one " function.

but it isn't an onto function because for value of x as 0, we have no value of f(x) [ undefined ]

Answer:

[tex]x=-7,-3[/tex]

Step-by-step explanation:

Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:

[tex]x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3[/tex]

As you can see, because we change [tex]x^2+10x+21[/tex] to [tex]x^2+10x+25[/tex] by adding 4 to both sides, we were able to reduce it to [tex](x+5)^2[/tex], a perfect square, and solve the rest of the problem.

By dividing the figure into a rectangular prism and a pyramid, we will see that the total volume is 2,400 ft^3

We can divide the given figure into two simpler ones.

A rectangular prism of 20 ft by 10 ft by 10 ft, whose volume is the product of these dimensions:

V = 20ft*10ft*10ft = 2,000 ft^3

And a pyramid of 4 sides, with a height of 6ft and a base of 20ft by 10ft, and we know that the volume of the pyramid is one-third of the product between the base and the height.

V' = (1/3)*6ft*(20ft*10ft) = 400ft^3

Then the total volume of the given figure is:

volume = V + V' = 2,000ft^3 + 400ft^3 = 2,400 ft^3

If you want to learn more about volumes, you can read:

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Answer:

B

Step-by-step explanation:

Combine like terms

8x + x = 9x

Put the numbers in the correct format

x³ + 9x + 5

This type of equation is a cubic trinomial because it has 3 terms and the first term is x cubed.

I hope this helps and please mark me as brainliest!

Answer:

The answer is B

Step-by-step explanation:

It is a cubic and a trinomial

Answer:

48×4.3=184 and that is the easy way how to do it

Answer:

answer is 40

hope it helps

Using proportions, it is found that the total cost of gasoline and rental for the trip is of $253.

A proportion is a fraction of a total amount.

In this problem, the total cost is composed by:

Hence, the total cost is given by:

C = $3.85 x 40 + $99 = $253.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

C = $3.85 x 40 + $99 = $253.

Step-by-step explanation:

I took the test

Answer:

coke red

Step-by-step explanation:

correct me if im wrong

Answer:

P(M &C) = 0.24

Step-by-step explanation:

Chemistry book will be denoted by C

Mathematics book will be denoted by M

5C2 = 10

There are 10 possible ways in which she can choose two books from the 5 books.

The probability of choosing a chemistry book:

P(C) = 2/5

The probability of choosing a mathematics book:

P(M) = 3/5

Probability of choosing a chemistry book and a mathematics book:

P(M &C) = (2/5) × (3/5)

P(M &C) = 0.24 or 24%

The probability that she pulls out a math book and a chemistry book will be 0.24.

The term probability refers to the likelihood of an event occurring

Given that;

Julia has 2 chemistry books and 3 math books.

Now,

Since, Julia has 2 chemistry books and 3 math books.

Hence, Total number of books = 2 + 3 = 5

So, The probability to choosing a chemistry book = 2/5

And, The probability to choosing a math book = 3/5

Thus, The probability that she pulls out a math book and a chemistry book is,

⇒ 2/5 × 3/5

⇒ 6/25

⇒ 0.24

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Answer:

-4

Step-by-step explanation:

y=2-9×(2/3)=2-6= -4

Answer:

25.86

Step-by-step explanation:

22 * 5 = 110

50 * 3 = 150

17 * 6 = 102

110 + 150 + 102 = 362

362 / 14 = 25.86

The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

A function assigns the value of each element of one set to the other specific element of another set.

Function g is represented by the table.

The line plotted with these data is shown below where y represent the g(x).

In this line,

Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

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Answer:

3

Step-by-step explanation:

3/10 = .3

Answer:

cos θ = 4/5

Explanation given below in the image,

I hope my answer helps you.

Answer:

  -∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞

Step-by-step explanation:

The domain of any polynomial is "all real numbers." The domain of any rational function excludes any values of the variable that result in the denominator being 0. The function is "undefined" there.

__

  [tex]v(x)=\dfrac{x^2-25}{2x^2+13x+15}=\dfrac{(x+5)(x-5)}{(x+5)(2x+3)}\qquad x\notin \{-5,-\dfrac{3}{2}\}[/tex]

The values x=-5 and x=-3/2 make the denominator of v(x) become 0, so those values are excluded from the domain of v(x). The function is "undefined" when its denominator is zero.

  -∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞

_____

Additional comment

The numerator and denominator factors (x+5) cancel each other, so there is no vertical asymptote at x=-5. Rather, the function has a "hole" there, where it is undefined. The limit as the function approaches x=-5 from either direction is v(x) = 10/7.

Answer:

Step-by-step explanation:

First what we must do is rewrite the table to find a solution:

0.25^x −0.75x+1

   64     3.25

   16     2.5

    4      1.75

    1      1

 0.25     0.25

 0.0625 −0.5  

 0.015625  −1.25

We see where the values of the function are the same:

x = 0 (1)

x = 1 (0.25)

answer:

x = 0

x = 1

Answers: