20) A gas station charges $4.09 for a gallon of premium unleaded. The gas station charges
$.20 less per gallon of gasoline if a customer also gets a car wash. A car wash cost $10.
Write an inequality and solve to find the possible amounts (in gallons round to the nearest
hundredth) of gasoline that you can buy if you also get a car wash and can spend at most
$30?

The most appropriate choice for linear equation will be given by-

The cost of bench is $375

What is linear equation?

A one degree equation is called a linear equation.

Here,

Let the cost of the bench be $x

cost of garden table = $(x + 80)

Total cost of bench and garden table= $(x + x + 80)

                                                              = $(2x + 80)

By the problem,

                           2x + 80 = 830

                            2x = 830 - 80

                             2x = 750

                                x = [tex]\frac{750}{2}[/tex]

                                x  = $375
So,

The cost of bench is $375

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Answer:

[tex]y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]

Step-by-step explanation:

Intercept form of a quadratic equation

[tex]y=a(x-p)(x-q)[/tex]  

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies-6&=a(5-(-7))(5-3)\\-6&=a(12)(2)\\-6&=24a\\a&=\dfrac{-6}{24}\\\implies a&=-\dfrac{1}{4}\end{aligned}[/tex]

Substitute the given x-intercepts and the found value of a into the formula:

[tex]\implies y=-\dfrac{1}{4}(x+7)(x-3)[/tex]

Expand to standard form:

[tex]\implies y=-\dfrac{1}{4}(x^2-3x+7x-21)[/tex]

[tex]\implies y=-\dfrac{1}{4}(x^2+4x-21)[/tex]

[tex]\implies y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

(-4,5)

4 to the left on the axis is neg. 5 units up on the y axis makes it positive.

The given expression is

3.4 - 2.8d + 2.8d - 1.3

By collecting like terms, we have

- 2.8d + 2.8d + 3.4 - 1.3

= 0 + 2.1

= 2.1

Answer:

26, 27, 28

Step-by-step explanation:

Let the 3 integers be: x, x+1, x+2

x+x+1+x+2 = 81

3x+3 = 81

3x = 78

x = 26

x+1 = 27

x+2 = 28

Check the picture below.

let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.

The diagram of the number line is shown below

Thus, the distance CD which is the distance between point D and point C is

13 - 11 = 2

CD = 2

Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.

A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.

The credit card balance consists of purchases, finance charges, and repayments.

Credit card's APR = 11.99%

Credit limit = $1,800

Minimum monthly payment = 6.5%

Purchase at the beginning of the month = $550

Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)

New balance = $555.50

Minimum payment = $36.11 ($555.50 x 6.5%)

Balance after the minimum payment = $519.39 ($555.50 - $36.11)

Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.

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The difference between the depths in February and July is D. 13 feet.

From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.

Therefore, it should be noted that the depth in July is -18.

Therefore, the difference between the depths in February and July will be:

= -5 - (-18)

= -5 + 18

= 13

Therefore, the difference is 13 feet.

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Answer:2 choice

Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2

Answer:

Step-by-step explanation:

1) Let's solve that exponential equation

Converting the bases:

2) Since we are on the same base let's just calculate the exponents.

3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.

When He started operating the exponents.

The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Here, we are given a circle with center D and equation as-

[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]

Comparing this to the general form of equation of a circle which is  [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-

g = 1, f = -4 and c = 8

thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3

Now, since PT is a tangent to the circle, DP will e perpendicular to PT.

We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)

= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]

= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]

= [tex]\sqrt{25 +4 }[/tex]

=[tex]\sqrt{29}[/tex]

Thus, in triangle, PDT by using Pythagoras theorem, we will have-

[tex]PT^{2} + DT^{2} = PD^{2}[/tex]

since DT is the radius of the circle, DT = 3

⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]

[tex]PT^{2} + 9 = 29[/tex]

[tex]PT^{2} = 29 - 9[/tex]

[tex]PT^{2} = 20[/tex]

[tex]PT = \sqrt{20}[/tex]

Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.

Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]

so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)

Thus, the equation of the circle will be-

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

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The three Points that  lie on the given line 2x=6y+4 are  (5,1) , (8,2) and (11,3).

The given equation of line is given below,

2x=6y+4                              equation 1

We need to find the points that lie on the given line.

Point 1 :

Put x = 5 in equation 1

2(5) = 6y + 4

6y = 6

y=1

So, Point (5,1) lie on the given line.

Point2:

Put x = 8 in equation 1

2(8) = 6y + 4

6y = 12

y=2

So, Point (8,2) lie on the given line.

Point 3 :

Put x = 11 in equation 1

2(11) = 6y + 4

6y = 18

y=3

So, Point (11,3) lie on the given line.

Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .    

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Answer: B. (5√3)

Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.

Step 1: Concept

To convert km to meters you will multiply with 1000.

To convert minute to hour you will divide by 60

Step 2: Convert

Step 3: Final answer

Option B and D

The cost of the present is $20.67

Given,

The cost of the present = x

Amount given by cousin = $13.78

Amount given by cousin is 2/3 of x.

That is,

13.78 = 2/3 of x

Lets find x

13.78 = 2/3 × x

13.28 = 2x/3

Multiply with 3 on both sides

13.78 × 3 = (2x/3) × 3

We get,

41.34 = 2x

Divide 2 on both sides

That is,

41.34/2 = 2x/2

We get,

x = 20.67

Here, x is the cost of the present

Therefore, the cost of the present is $20.67

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Answer:900

Step-by-step explanation: 1. set up an equation

x= (p * n)/100 when x= the answer p= the percentage and n= the total number

2. plug in the numbers

x= (30 * 3000)/100

3.solve

x= (30*3000)/100

x= (90000)/100

x= 900

Answer:

eywgw6 the car is in the car is in the car is in

Step-by-step explanation:

Wu and I will be in the car is in the car is in the car is in the car is here and we can 4

Answer:

Safe fund = $24,000

Risky fund = $6,000

Step-by-step explanation:

Definition of variables:

Given information:

Convert the percentages into decimal form:

[tex]\implies 2.5\%=\dfrac{2.5}{100}=0.025[/tex]

[tex]\implies 8\%=\dfrac{8}{100}=0.08[/tex]

Create a system of equations from the given information and defined variables:

[tex]\begin{cases}0.025x+0.08y=1080\\x=4y\end{cases}[/tex]

Substitute the second equation into the first equation and solve for y:

[tex]\implies 0.025(4y)+0.08y=1080[/tex]

[tex]\implies 0.1y+0.08y=1080[/tex]

[tex]\implies 0.18y=1080[/tex]

[tex]\implies \dfrac{0.18y}{0.18}=\dfrac{1080}{0.18}[/tex]

[tex]\implies y=6000[/tex]

Substitute the found value of y into the second equation and solve for x:

[tex]\implies x=4(6000)[/tex]

[tex]\implies x=24000[/tex]

Therefore, the amount invested in each fund was:

Answer:

-1, 1

Step-by-step explanation:

The translation is 1 unit left and 1 unit up.

Answer:

A. 1 1/2 cubic inches

Explanation:

We are told that the side length of the cube is 1/8 of an inch. Furthermore, we are also told that the rectangular prism fits 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height. This means the measures of the dimensions of the prism are

Therefore, the volume of the prism is

Hence, the volume of the prism is 1 1/2 cubic inches

There are 38,936,000 people over the age of 64 were in the U.S.

Option 2 is true.

What is Percentage?

A relative value indicating hundredth part of any quantity is called percentage.

Given that;

In 2012, the U.S. population was about 314 million.

Now,

Total population = 314,000,000

In the pie chart, The percent of people over the age of 64 were in the U.S will be 12.4%

Hence, Solve as;

Number of people over the age of 64 = 314,000,000 × 12.4%

                                                           = 314,000,000 × 12.4 / 100

                                                           = 31,400,00 × 12.4

                                                           = 38,936,000

Thus,

There are 38,936,000 people over the age of 64 were in the U.S.

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[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]

when you divide or multiply by a negative number the signs <> change directions.

The value of k given that both points lie on a line passing through the origin is 48.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since both points lie on a line which passes through the origin, we can logically deduce the following points:

Point (x, y) = (0, 0)

Substituting the given points into the formula, we have;

Slope, m = Δy/Δx

Slope, m = (-2 - 0)/(-12 - 0)

Slope, m = -2/-12

Slope, m = 1/6

At point (-12, -2) and (k, 8), we have:

1/6 = (8 - (-2))/(k - (-12))

1/6 = (8 + 2)/(k + 12)

1/6 = 10/(k + 12)

k + 12 = 10(6)

k + 12 = 60

k = 60 - 12

k = 48

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