Under his cell phone plan, Josiah pays a flat cost of $37 per month and $3 per gigabyte. He wants to keep his bill at $43.60 per month. Write and solve an equation which can be used to determine xx, the number of gigabytes of data Josiah can use while staying within his budget.

Answer:

Step-by-step explanation:

1.)  [tex]c = \sqrt{a^{2} +b^{2} }[/tex]

a = 10, b = 7, c = x?

10+7= x

[tex]10^{2} + 7^{2} =x^{2}[/tex]

100 + 49 = [tex]x^{2}[/tex]

149 = [tex]x^{2}[/tex]

[tex]\sqrt{149} =[/tex] 12.206...

x = 12.2

2.) x + 19 = 21

[tex]x^{2} + 19^{2} =21^{2}\\21^{2}-19^{2} = x^{2}[/tex]

441 - 361 = [tex]x^{2}[/tex]

80 = [tex]x^{2}[/tex]

[tex]\sqrt{80}[/tex] = 8.94

x = 9

3.) x + 16 = 27

[tex]x^{2} + 16^{2}= 27^{2} \\27^{2} -16^{2} =x^{2}[/tex]

729 - 256 = [tex]x^{2}[/tex]

473 = [tex]x^{2}[/tex]

[tex]\sqrt{473}[/tex] = 21.74

x = 21.7

4.) 12.8 + 5.3 = x

[tex]12.8^{2} + 5.3^{2} =x^{2} \\163.84 + 28.09 = x^{2}\\191.93 = x^{2} \\\sqrt{191.93} = 13.85\\x = 13.9[/tex]

8.) x = 11.48 ft

a = 3.5 ft , b = x=? , c = 12 ft

[tex]3.5^{2} + x^{2} =12^{2} \\12.25 +x^{2} =144\\144-12.25=x^{2} \\131.75 = x^{2} \\\sqrt{131.75} =11.48\\x = 11.48[/tex]

9.) x = 32.078 feet

[tex]14^{2} +x^{2} =35^{2}\\196 + x^{2} =1225\\1029 = x^{2} \\\sqrt{1029} = 32.078 ft\\x = 32.078 ft\\[/tex]

10.) perimeter = 31.96

hope this helped a lot

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’creating a system linear equation, the number of possible gallons of gasoline that can be purchased is 60 gallons

Given the Parameters :

Hence, we have :

1170 + 2.80g = 1338

2.80g = 1338 - 1170

2.80g = 168

g = 168/2.80

g = 60

Therefore, only 60 gallons of gasoline can be purchased.

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Answer: It all depends on what type of number line you're doing.

Step-by-step explanation:

Answer:

20000

Step-by-step explanation:

Answer:

20000

Step-by-step explanation:

Step-by-step explanation:

y = 4x + 3

subtract 3 on both sides of equation

y - 3 = 4x + 3 - 3

y - 3 = 4x

divide the equation by 4 on both sides

\frac{y - 3}{4} = \frac{4x}{4}4y−3=44x

x = \frac{y - 3}{4}4y−3

DONE.

Answer:

3

Step-by-step explanation:

Not sure, but let's take 32 to be the answer

4(5+x)=32

4×5= 20

4×x= 4x

20-4x=32

4x=32-20

4x=12

12÷4

x=3

Answer:

4n - 5

Step-by-step explanation:

let the number be n then the product of 4 and this number is 4n

Subtract 5 from 4n gives

4n - 5

Answer:

1/6

0.95833333333

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

1/6 (1/4) + 17/24 = 1/24 + 17/24

=3/4

Answer:

thats as simple as it gets unless you meant to write 3x=-20, then it would be x = 20/3

Answer:

This cannot be simplified

Step-by-step explanation:

3x-20 is the answer

Answer:

  £225

Step-by-step explanation:

The relationship between the cost price (cp) and the selling price (sp) is ...

  cp + 5% × cp = sp

  cp(1.05) = sp . . . . . . collect terms

  cp = sp/1.05 . . . . . . divide by 1.05

  cp = £236.25/1.05 = £225

The original wholesale price was £225.

Step-by-step explanation:

due to the laws of symmetry of the angles of 2 crossing lines (and parallel lines are simply repeating and mirroring these angles), both angles must be equal.

5x - 5 = 6x - 27

-5 = x - 27

x = 22

Answer:

if a joke i dont know

The Triangles are congruent by SAS Criteria.

The step by step explanation is there in the image I attached.

Hope it helps you....

Please mark as brainlliest!!!

Answer:

Step-by-step explanation:

what is the question

Answer:

x=16

Step-by-step explanation:

Heres the work below

Hope this Helps

Answer:

A. The reciprocal of 9/10 is 10/9

B.2/3

Step-by-step explanation:

A. A reciprocal is the inverse of a number

B. 3/5*10/9=

30/45 or 2/3

Answer:

-1

Step-by-step explanation:

They already did the opposite reciprocal for you.

They have it in the form  now.

To find b you just enter (x,y)=(8,1).

Let's do that.

Subtract 2 on both sides:

b=-1

Answer:

8(3x + 1)

Step-by-step explanation:

8 and 24 are multiples of 8

(8/8) + (24x/8) = 1 + 3x

The equation with distributive property is 8(1 + 3x)

-Chetan K

Answer:

Step-by-step explanation:

[tex](-1)^{n} = -1 , if \ n \ is \ a \ odd \ integer\\\\\\\\(-1)^{2003} =-1 \\\\(\dfrac{-3}{4)}^{2}=\dfrac{3}{4}, \ as \ 2 \ is \ even \ number.\\\\(\dfrac{2}{3})^{3}*(\dfrac{-3}{4})^{2}*(-1)^{2003}=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{4^{2}}*(-1)\\\\\\=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{2^{4}}*(-1)\\\\\\=\dfrac{-1}{3^{3-2}*2^{4-3}}\\\\\\=\dfrac{-1}{3^{1}*2^{1}}\\\\=\dfrac{-1}{6}[/tex]

[tex](\dfrac{2}{5})^{2}*(\dfrac{-5}{12})^{3}=\dfrac{2^{2}}{5^{2}}*\dfrac{(-5)^{3}}{(2^{2}*3)^{3}}\\\\\\=\dfrac{2^{2}}{5^{2}}*\dfrac{- 5^{3}}{2^{6}*3^{3}}\\\\\\= -\dfrac{5^{3-2}}{2^{6-2}*3^{3}}\\\\\\= -\dfrac{5}{2^{4}3^{3}}\\\\= -\dfrac{5}{16*3}\\\\\\= \dfrac{-5}{48}[/tex][tex]HINT: \dfrac{a^{m}}{a^{n}}=a^{m-n}, m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}}, n >m\\\\\\(a^{m})^{n}=a^{m*n}[/tex]

Answer:

14.28

Step-by-step explanation:

Answer:

F because you cannot prove that any of the angles are the same with only one set of parallel lines

Answer:

See below:

Step-by-step explanation:

So we want to know what 9 to the -8th exponent will be if I understand your question right.

To solve for [tex]9^{-8}[/tex] we first have to solve for [tex]9^{8}[/tex] which would be 43046721.

Now, if we have a negative number, the answer would be 1 divided by that number, so therefore, we get [tex]9^{-8} =\frac{1}{43046721}[/tex]

Cheers!

Answer:

-11/16

Step-by-step explanation:

1) Find the Least Common Denominator (LCD) of [tex]\frac{15}{32} ,\frac{7}{31}[/tex] In other words, find the Least Common Multiple (LCM) of 32,31.

Method 1: By Listing Multiples

1. List the multiples of each number.

Multiples of 32: 31,64,96,... 928, 960 ,992,...

Multiples of 31: 31, 62, 93 , ... , 930, 961 , 992, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 992

Method 2: By Prime Factors

1. List the prime factors of each number.

Prime Factors of 32: 2,2,2,2,2

Prime Factors of 31: 31

2.  Find the union of these primes.

2,2,2,2,2,31

3. Multiply these numbers: 2 * 2 * 2 * 2 * 2 * 31 = 992. This is the LCM.

LCM = 992

2) Make the denominators the same as the LCD.

[tex]-\frac{15*31}{32*31} +\frac{7*32}{31*32}[/tex]

3) Simplify. Denominators are now the same.

[tex]-\frac{465}{992} +\frac{224}{992}[/tex]

4) Join the denominators.

[tex]\frac{-465+224}{992}[/tex]

5) Simplify

[tex]-\frac{241}{992}[/tex]

Decimal Form: -0.242944

Answer:

yes

Step-by-step explanation:

3(x - 6) = [tex]\frac{3x}{4}[/tex] ( multiply both sides by 4 to clear the fraction )

12(x - 6) = 3x , distribute left side

12x - 72 = 3x ( subtract 3x from both sides )

9x - 72 = 0 ( add 72 to both sides )

9x = 72 ( divide both sides by 9 )

x = 8

x = 8 is the only solution and is therefore unique

Answer:

8

Step-by-step explanation:

Answer:

170 kg. of parsnips are left

Step-by-step explanation:

Given:

850 kg. of parsnips

30 % to the local market

50 % to a local supermarket

Solution:

First, add the two percentages.

30 + 50 = 80%

That means 80 % of parsnips mass go to the markets.

Now let's find the mass of delivered parsnips.

Change 80% to decimal form.

80% = 0.8

Now multiply it by 850 kg.

850 x 0.8 = 680

The delivered parsnips mass is 680 kg.

Now to find the mass of parsnips left, subtract 680 to 850

850 - 680 = 170 kg.

170kg. of parsnips are left.

Answer:

1 stamp = $0.51

Step-by-step explanation:

20 stamps = $10.20

=> 1 stamp = 10.20/20

=> 1 stamp = $0.51

Hoped this helped.

Answer:

x = - 10, x = - 6

Step-by-step explanation:

x² + 16x + 60 = 0

Consider the factors of the constant term (+ 60) which sum to give the coefficient of the x- ter (+ 16)

The factors are + 10 and + 6 , since

10 × 6 = 60 and 10 + 6 = 16 , then

(x + 10)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 10 = 0 ⇒ x = - 10

x + 6 = 0 ⇒ x = - 6

Answer:

15 very simple

Step-by-step explanation:

im always right