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You had to take your car to the shop for a weird noise. The mechanic charges a flat rate of $100 for looking at your car and $50 an hour to fix the problem. Write an algebraic expression (equation) where P represents how much you will
have to pay and his the number of hours it takes to get your car foxed.

By means of weighted averages, we conclude that an amount of 285 gallons are needed to prepare a 70 % salt solution.

In this problem we find two salt solutions with distinct concentrations, one with 80 % and another with 13 %, the latter in a quantity of 50 gallons. The required quantity of 80 % salt solution is determined by using weighted averages:

(80 / 100) · x + (13 / 100) · 50 = (70 / 100) · (x + 50)

0.8 · x + 13 / 2 = 0.7 · x + 35

0.1 · x = 57 / 2

0.2 · x = 57

x = 285

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The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a

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

Given the equation:

3a(15 + 3 - 3²) + 7a(8/4)

Simplifying the exponents:

3a(15 + 3 - 9) + 7a(8/4)

Simplifying the terms in the bracket:

3a(9) + 7a(2)

Opening the parenthesis:

27a + 14a

Adding:

= 41a

The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a

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Answer:

Step-by-step explanation:

330-250 =80

The equation of the composite function h(x) is h(x) = -10x^2 + 40x

The functions are given as

f(x) = 2x – 8

g(x) = –5x

The equation of the composite function is given as

h(x) = f(x)g(x)

Substitute f(x) = 2x – 8 and g(x) = –5x in the equation h(x) = f(x)g(x)

So, we have

h(x) = (2x - 8) x (-5x)

Evaluate the product

h(x) = -10x^2 + 40x

Hence, the equation of the composite function h(x) is h(x) = -10x^2 + 40x

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The equation of a straight line that is parallel to y = 2x -8 and passes through the point (0,-3) is  y=2x-3 .

The general equation of straight line is of the form y=mx+c where m is the slope of the equation and c is the y-intercept of the equation.

The slope is defined as the tangent of the angle made by the line with the positive direction of x axis.

he y-intercept of a straight line is the point where the graph passes the y-axis.

The given equation of the line is y=2x-8. Comparing the given equation with the general equation of a straight line we can conclude that the slope of the line is 2.

Two parallel lines have the same slope . Therefore the slope of the line parallel to y = 2x -8 is also 2.

We know that if a line with slope m passes through(x₁, y₁) then the equation of the line is given by

y-y₁=m(x-x₁)

The required line passes through (0,-3)

∴putting the values we get:

y-(-3)=2(x-0)

or, y+3=2x

or, y=2x-3

Therefore the line parallel to  y = 2x -8 and passing through the point (0,-3) is y=2x-3.

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Answer:

  e^6 ≈ 403

Step-by-step explanation:

You want the value of e^(4x-2) when x = 2.

Put 2 where x is in the expression and do the arithmetic.

  e^(4·2 -2) = e^6 ≈ 403.429

The value of the expression is about 403.

Answer: The answer is  6x^4-4x

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

B lost the election by 15,840 votes.

Since A got 132000+12% of 132000 votes=147840 votes.

2400mL is the amount of 60%acid solution to mix.

Let the amount of acid be mixed be x.

From the question, we get an equation that,

60%x + 35% × 600/ x + 600 = 55%

(Here x ≠ -600, as the denominator can never be 0.)

60%× x + 35% ×600 = 55%(x + 600)

Now we have to find the value of x to know the amount of acid that is mixed in a solution.

0.60x + 0.35 × 600 = 0.55(x+600)

0.60x + 210 = 0.55 + 330

0.05x = 120

x = 120/0.05

  = 2400

Therefore we get an amount of acid to be mixed is 2400mL.

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The total capacity will be 8 2/5 liters.

From the information, the bottles wee filled with 6/5 liters each.

Therefore, the capacity will be:

= Number of drums × Quantity

= 7 × 6/5

= 42/5..

= 8 2/5 liters.

Therefore, the total capacity will be 8 2/5 liters.

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Samuel's test score if he got 9 questions wrong=55

Samuel's test score if he got x questions wrong=45

Mean score: A mean scale score is the average performance of a group of students on an assessment. Specifically, a mean scale score is calculated by adding all individual student scores and dividing by the number of total scores. It can also be referred to as an average.

let y equal the number of questions

let's find how many total questions are there,

100=5y

divide by the coefficient of y which in the case is 5

20=y

so we have total of 20 questions each are worth 5 points

now, Samuel got 9 questions wrong and if we know they are 20 total questions

20-9=11

so, we know Samuel got 11 questions correct

let's use an expression to figure out his score

let x be the number of questions

5x

substitute

5(11)=55

his score if he got x questions wrong

20-11=9

9(5)=45

Samuel's test score if he got 9 questions wrong=55

Samuel's test score if he got x questions wrong=45

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The mean of the set of numbers is 4362.92

The median is 4164.5

The mode is 0.

It should be noted that the mean is the average sat of numbers. The addition of the numbers is 52355 and there are 12 numbers.

The mean will be:

= 51355 / 12

= 4362.92

The median is the number in the middle. This will be:

= (3838 + 4491)/2

= 4164.5

The mode is 0 since the observations were only once.

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Answer:

4 - 3x

Step-by-step explanation:

please mark me as brainliest

Answer:

3x-4= Y

Y= her dad's age.

Answer:

a > 6

Step-by-step explanation:

[tex]a-2 > 4\\=a-2+2 > 4+2\\a > 6[/tex]

Answer:

1) 60

2) 90

Step-by-step explanation:

Evaluate (f+2) (g+8), when f = 4 and g = 2

Solution

(f+2) (g+8)

Evaluate for f=4,g=2

(4+2)(2+8)

(4+2)(2+8)

=60

Evaluate 2Tu, when T = 5 and u = 9

Solution

2tu

Evaluate for t=5,u=9

(2)(5)(9)

(2)(5)(9)

=90

Answer:

Step-by-step explanation:

replace f and g for their values

(4+2)(2+8)

= 6*10

= 60

replace t and u for their values

2*5*9

= 10*9

= 90

The number of times that the spaceship can trave is 7.6 times

From the information, light travels at the speed of about 1.9×10^6 miles per second. Suppose a spaceship is able to travel at the speed of light. If the distance around Earth along the Equator is about 2.5×10^5 miles.

Therefore, the number of times that the spaceship can travel will be:

= 1.9 × 10^6 / 2.5 × 10^5

= 7.6

It can travel 7.6 times.

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Answer: 8 Remainder 4

Step-by-step explanation: Sum is the answer to addition so 5 plus 2 is 7 and 60 divided by 7 is 8 with a Remainder of 4

[tex]distance = |x-y| \\ where \: x \: and \: y \: are \: any \: two \: numbers[/tex]

It doesn't matter which number you put first as long as you don't forget your absolute value.

If you don't want to put the absolute value, the equation becomes:

[tex]distance = x-y \\ where \: x \: and \: y \: are \: any \: two \: numbers \\ under \: condition \: that \: x > y[/tex]

[tex]distance = 16 - ( - 8) = 16 + 8 = 24 \\ distance = |16-(-8)|=|16+8|=|24|=24 \\ or \\distance = | - 8-(16)|=| - 8 - 16|=| - 24|=24[/tex]

The function which passes from (1,4) and (5,1) is y= -7/20x² + 27/20x   +3

and the net change between the indicated points is -3, whereas the average rate change is -3/4.

Given, from the graph, the function passes (1,4) and (5,1).

Let y = ax² + bx + 3

from point 1.

the equation is: a + b+ 3 = 4 eq(1)

from point 2.

the equation is 25a + 5b + 3 = 1 eq(2)

solving equation 1 and equation 2.

we get, 20b = 99-72

20b = 27

b = 27/20

substitute b value in equation 1.

a + 27/20 + 3 = 4

20a = -7

a = -7/20

hence y = -7/20x² + 27/20x +3

(a) net change = change in y coordinates.

net change = y₂ - y₁

net change = 1 - 4

= -3

(b) Average rate = change in y coordinates / change in x coordinates

= 1 - 4/5-1

= -3/4

hence  we get the required answers.

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Answer:

Step-by-step explanation:

v = √(2e / m)

I stitched a photo of the solution.

Answer:

about 4.89% is the percentage of population under 20 in Japan 2018

Answer:

5 x 10^-5

2.5 x 10^-3

0.02

0.0016

Step-by-step explanation:

√80 on the number line would be marked at (8.94, 0) on the number line.

Hope this graph helps!

The value of x is 13

From the diagram shown, we have that the line segments as;

NK = NM + ML + LK

Where;

Substitute the values into the equation

(x - 6) + 9 + 2x - 19 = 23

collect like terms

x + 2x -6 + 9 - 19 = 23

Add like terms

3x - 16 = 23

3x = 23 + 16

3x = 39

Divide both sides by 3

x = 39/ 3

x = 13

Thus, the value of x is 13

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Answer:

Slope = (-7/4)

Step-by-step explanation:

Point 1: (-3, 4); Point 2: (1, -3)

            (x₁, y₁)               (x₂, y₂)

       y₂ - y₁        -3 - 4           -7           -7

m = ----------- = ----------- = ----------- = ------

       x₂ - x₁         1 - (-3)         1 + 3        4

I hope this helps!