For the holidays, Antonio is driving to visit his grandparents who live 441 miles away. Antonio's car gets 31.5 miles per gallon of gas when he is driving on the highway. In order to budget for his trip, Antonio wants to know how much gas he will need.
Use an equation to find how much gas Antonio needs for the drive.
Antonio needs
gallons of gas.

Answer:

5x + 7x = 180

x = 15

Step-by-step explanation:

5x + 7x = 12x

180/12 = 15

The constant of variation of the data point is 8.

An equation is an expression that shows the relationship between two or more variables and numbers.

If two variables are proportional, they can be represented by:

y ∝ x

y = kx

k  is the constant of variation.

For the point (9, 72):

72 = 9k

k = 8

For the point (4, 32):

32 = 4k

k = 8

For the point (7, 56):

56 = 7k

k = 8

The constant of variation of the data point is 8.

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[tex]\mathfrak{( \frac { 6 x } { y } ) ( \frac { y } { 3 x - 3 } ) } [/tex]

[tex]\mathfrak{ \frac{6xy}{y\left(3x-3\right)} } [/tex]

[tex]\mathfrak{ \frac{6x}{3x-3} } [/tex][tex]\mathfrak{ \frac{6x}{3\left(x-1\right)} } [/tex]

[tex]=\boxed{\mathfrak{\frac{2x}{x-1} } }[/tex]

☆ Option 3 is correct.

[tex]\mathbb{MIREU} [/tex]

Answer:

The first graph is correct.

Step-by-step explanation:

Note that the equation states x ≥ 2.  It includes the "equals" sign, so the graph line should include 2.  This is indicated by the solid line, as opposed to the 4th graph, which shows it as a dashed line.  The dashed line is correct for x>2, but not for x ≥ 2.

Answer:

If x = -3,

then y might equal -6

If y = -20,

then x might equal -13

Step-by-step explanation:

I have used a graph to estimate these answers. See image. If you are learning how to find the line of best fit for a data set, you might be expected to do those calculations, depending on the level of your math class. Many upper level math classes would use technology to find a line of best fit.

See image to see the data set given on an xy-axis in red. The circled areas are where the estimated numbers would lie, where

x = -3 (in blue) and where

y = -20 (in green)

The directions say estimate, so a graph is a good justification for several answers in the general area.

Answer:

1: 3)

2: 2)

4: 3)

5: 4)

6: 4)

Step-by-step explanation:

they way it is written, she has one of the best paying jobs in the world : $1470 per hour ...

but I guess it is really $14.70 per hour, right ?

that is then her basic wage : $14.70 per hour for 40 hours = 14.7 × 40 = $588.

her overtime rate is then 14.7×1.25 (one time and a quarter) = 18.375 ≈ $18.38

and she gets that rate for all hours beyond the basic 40 hours, so, 52-40 = 12 hours.

12×18.38 = $220.56

or if you need it totally precise

12×18.375 = $220.50

in total, her gross wage for that week is then

588 + 220.56 = $808.56

or totally precise with unrounded hourly rates

588 + 220.5 = $808.50

which would create a mean hourly rate

808.56/52 = $15.54923077... per hour ≈ $15.55 per hour

or

808.5/52 = $15.54807692... per hour ≈ $15.55 per hour

many payroll systems do the rounding of the hourly rates and then calculate the total amount (as the first option here). some others keep the full decimal positions in the calculation and then only round the total (as the second option here).

so, it is the question what your teacher expects here. I cannot tell from the description.

Answer: just add 75 and 45 + x and do division for 69 ok  but times the 45 with 69 ok good luck

Step-by-step explanation:

X/12 = -8

Solve for x by multiplying both sides by 12

X = -96

Answer:

X=12*-8-----> X= -96. multiply 12 by -8

Answer:

y = 3/4x

Step-by-step explanation:

Given:

x1 = -4

y1 = -3

slope (m) = 3/4

Solution:

y - y1 = m ( x - x1 )

y - (-3) = 3/4 ( x - (-4) )

y + 3 = 3/4 ( x + 4 )

y + 3 = 3/4x + 3

y = 3/4x + 3 - 3

y = 3/4x

Answer:

Well a triangle itself is worth 180 degrees (Inteirior angles)

your given “a” “b” and you need to find c.

So you can subtract

A is 50

B is 55

So

<BCA= 180- 55-50

Is the answer (b)

Answer:

B

Step-by-step explanation:

A triangle's angles all add up to 180 degrees. If m∠A is 50 and m∠B is 55 then m∠C is 75.

m∠C = 180 - (m∠A - m∠B); which is 180 - 105

180 - 105 is 75; Therefore, m∠C is 75 degrees

Proof: 50 + 55 + 75 = 180

The number of bacterial population after 5 hours is; 816

N(t) = N_o(1 + r)^(t)

Where;

N(t) is number of bacteria after t hours

N_o is number of bacteria initially

r is growth rate

t is time

N_o = 480

r = 11.2% = 0.112

t = 5

N(5) = 480(1 + 0.112)^(5)

N(5) = 816.14

Read more about exponential growth at; https://brainly.com/question/15316908

Answer:

Step-by-step explanation

Answer:

69

Step-by-step explanation:

The number 75 decreased by 8% means that you are looking for 92% of 75. To find a percent of the number you can multiply a number by the percent in decimal form. So, to find 92% of 75, multiply 75*0.92. This gives you 69. Doing this is the same as finding 8% of 75 and then subtracting.

Answer:

The lines will cross at (-5,1)

Step-by-step explanation:

I graphed it

why you copy my profile picture hello.....

Answer:

97

Step-by-step explanation:

A straight horizonal line is 180 degrees, so you subtract 83 from 180 to get 97, which is the measure of angle JKL

Answer:

5.6

Step-by-step explanation:

if x is -1. multiply -0.6 * -1. Which is -0.6.

Then add -0.6 and 6.2 and the answer you would get is 5.6.

Answer:

h⁰ = 84⁰

f⁰ = 132⁰

g⁰ = 28⁰

Step-by-step explanation:

As we know that sum of all the angles in a triangle is 180⁰, so,

h⁰ + 48⁰ + 48⁰ = 180⁰

h⁰ = 84⁰

Now, we can find f⁰ by Linear Pair theorem, which states that the angles sum will equal to 180⁰.

48⁰ + f⁰ = 180⁰

f⁰ = 132⁰

Again, g⁰ can be founded the same way as h⁰.

20⁰ + 132⁰ + g⁰ = 180⁰

g⁰ = 28⁰

HOPE IT HELPS :)

Answer:

8

Step-by-step explanation:

Answer:

85 degrees

Step-by-step explanation:

the inside of a triangle is always 180 degrees.

180-45-59=85

Answer:

7.52

Step-by-step explanation:

5.37 + x = 12.89

In order to solve this equation, we must isolate the variable, x.

1.) To do this, subtract 5.37 on both sides of the equation.

5.37 + x = 12.89

-5.37         -5.37

x = 7.52

Therefore, x = 7.52

Answer:

Answers of given questions are written below :

Step-by-step explanation:

[tex]\large{\tt{\underline{\underline{\purple{SOLUTION : - }}}}}[/tex]

5.37 + x = 12.89

[tex] \implies{\tt{5.37 + x = 12.89}}[/tex]

[tex] \implies{\tt{ x = 12.89 - 5.37}}[/tex]

[tex] \implies{\tt{ x = 7.52}}[/tex]

[tex]\star{\underline{\boxed{\sf{\red{ x = 7.52}}}}}[/tex]

Hence, the value of x is 7.52

[tex]\begin{gathered}\end{gathered}[/tex]

42 = 6x - 24

[tex] \longmapsto{\sf{42 = 6x - 24}}[/tex]

[tex] \longmapsto{\sf{ 6x = 42 + 24}}[/tex]

[tex] \longmapsto{\sf{ 6x = 66}}[/tex]

[tex] \longmapsto{\sf{x = \dfrac{66}{3}}}[/tex]

[tex] \longmapsto{\sf{x = 11}}[/tex]

[tex]\star{\underline{\boxed{\sf{\red{ x = 11}}}}}[/tex]

Hence, the value of x is 11.

[tex]\begin{gathered}\end{gathered}[/tex]

10x + 25 = 50

[tex]{\longrightarrow{\rm{10x + 25 = 50}}}[/tex]

[tex]{\longrightarrow{\rm{10x= 50 - 25}}}[/tex]

[tex]{\longrightarrow{\rm{10x= 25}}}[/tex]

[tex]{\longrightarrow{\rm{x= \dfrac{25}{10}}}}[/tex]

[tex]{\longrightarrow{\rm{x=2.5}}}[/tex]

Hence, the value of x is 2.5.

[tex]\rule{300}{2.5}[/tex]

Corry's conjecture is right, and the volume follows a pattern

The volume of a cube of side length l is:

[tex]V = l^3[/tex]

For the first cube of length 1 in, the volume is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

For the second cube of length 2 in, the volume is:

[tex]V = 2^3[/tex]

[tex]V = 8[/tex]

For the third cube of length 1 in, the volume is:

[tex]V = 3^3[/tex]

[tex]V = 27[/tex]

So, the total volume is:

[tex]Total =1 + 8 + 27[/tex]

[tex]Total =36[/tex]

The volume of a rectangular prism of base lengths 6 in and height 1 in is:

[tex]Volume = 6^2 \times 1[/tex]

[tex]Volume = 36[/tex]

Assume, he adds a cube of side length 4 in, the volume is:

[tex]V = 4^3[/tex]

[tex]V = 64[/tex]

The total volume would be:

[tex]V =36 + 64[/tex]

[tex]V =100[/tex]

The base length of the rectangular prism would be:

[tex]Length =1+2+3+4[/tex]

[tex]Length =10[/tex]

The volume of the rectangular prism would be:

[tex]Volume = 10^2 \times 1[/tex]

[tex]Volume = 100[/tex]

So, the pattern is:

Cubes                Volumes

1, 2, 3                    36

1, 2, 3,4                  100

Corry's conjecture is right, and the volume follows a pattern

Read more about conjectures at:

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Answer:

Step-by-step explanation:

AND REMEMBER DO ALWAYS READ AND WRITE

Answer:

Y = X times 0.28

Step-by-step explanation:

1. You set it up as a proportionality

12/1 and 3.36/x

The x stands for how much money it takes to get 1 ounce

2. You do the old man line.

12 times x = 3.36 times 1

12x = 3.36

3. Now you divide 3.36 by 12

3.36 divided by 12

.28

4. You insert 0.28 into the problem

12 times 0.28 = 3.36

X = 0.28

So 1 ounce costs $0.28

So Y = X times 0.28

Answer:

Step-by-step explanation:

Answer:(-4,3)

Step-by-step explanation:

Here, Every equation has same slope (-4) and same y-intercept (3), so we don't need to calculate those.

Now, as coordinates are in left-portion, and also touches the line, it would be: y ≥ -4x + 3

Answer:

15 in the correct answer

Answer:

x = 2

y = 3

Explanation:

Answer:

S (2, - 15 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Using (x₁, y₁ ) = T (0, 3 ) and (x₂, y₂ ) = S (x, y )

Calculate the midpoint using above and equate to coordinates of (1, - 6 )

[tex]\frac{x+0}{2}[/tex] = 1 ( multiply both sides by 2 )

x = 2

[tex]\frac{y+3}{2}[/tex] = - 6 ( multiply both sides by 2 )

y + 3 = - 12 ( subtract 3 from both sides )

y = - 15

S has coordinates (x, y ) = (2, - 15 )

Answer:

Point S is at the ordered pair (2,-15)

Step-by-step explanation:

midpoint formula : midpoint ordered pair (x,y) = ( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

midpoint x = [tex]\frac{x1+x2}{2}[/tex] ; midpoint y = [tex]\frac{y1+y2}{2}[/tex]

midpoint x = 1 x1 = 0 midpoint y = -6 y1=3

Solve each equation for x2 and y2 to get the points for S.

x = [tex]\frac{x1+x2}{2}[/tex]

1 = (0) +x2 / 2

2 = x2

y = [tex]\frac{y1+y2}{2}[/tex]

-6 = 3 + y2 / 2

-12 = 3 + y2

-15 = y2

(2,-15) are the coordinates to point S.

Answer:

16^2

Step-by-step explanation:

All you have to do is do 64 *.25 and you get 16

The area of the smaller pentagon is 4 in². thus option B is correct.

The ratio of the side lengths are given:

Small : Large = 3.5 : 14

The area of the larger pentagon is given;

Area = 64 in²

By Using the given parameters, the area of the small pentagon:

Area = (Small/Large)² * Area of Large

Area = (3.5/14)² * 64

Area = 4

Hence, the area of the smaller pentagon is 4 in². thus option B is correct.

Read more about areas:

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