Two mechanics worked on a car. The first mechanic to work for 5 Hours in the second mechanic work for 15 Hours. Together they charged a total of $2000. What was the rate charge per hour by each mechanic if the sum of the two rates was $170 Per hour ?

Replace x in each equation with 4:

f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21

g(x) = x^2-9 = 4^2 -9 = 16-9 =7

Now you have values for f(x) and g(x) now you can solve for f/g and f+g:

f/g = 21 / 7 = 3

f+g = 21 + 7 = 28

For this case, we have that by definition:

[tex](f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}[/tex]

We have the following functions:

[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]

So:

[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]

On the other hand:

[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]

[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]

Answer:

[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]

Answer: [tex]y=-2x-3[/tex]

Step-by-step explanation:

The equation of the line in slope-intercept form, is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

By definition, parallel lines have the same slope.

Then:

- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]

- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:

[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]

Then, the equation for the line containing the side opposite the side containing the first two vertices is:

[tex]y=-2x-3[/tex]

Answer:

kayla will earn $26

She will earn $36.00 in 4 hours.

27 divided by 3 = 9

9 x 4 = 36

Hope this makes sense and helps.

Answer:

the answer is c

Step-by-step explanation:

Final answer:

To subtract 6 ounces from 3 pounds, convert 3 pounds to ounces (3 x 16 = 48 ounces), subtract 6 ounces (48 - 6 = 42 ounces), then convert back to pounds and ounces (42 ounces = 2 pounds and 10 ounces). The answer is 2 pounds, 10 ounces.

Explanation:

Subtracting Ounces from Pounds

The question asks to subtract 6 ounces from 3 pounds. In order to compare or subtract different units of weight, it is essential to convert them to the same unit. Firstly, we must remember the unit equivalence where 1 pound = 16 ounces. Now, to start the conversion, we multiply the number of pounds by 16 to get the total number of ounces, which is a step in solving these types of conversion problems.

Therefore, for 3 pounds:

3 pounds × 16 ounces/pound = 48 ounces.

Now subtract the given ounces: 48 ounces - 6 ounces = 42 ounces.

Since we know there are 16 ounces in a pound, we divide the total ounces by 16 to convert back to pounds and ounces.
42 ounces ÷ 16 ounces/pound = 2 pounds with a remainder of 10 ounces.

Hence, subtracting 6 ounces from 3 pounds gives us 2 pounds, 10 ounces.

Answer:

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = [tex]\sqrt{85}[/tex]/7

tan θ = 6/7

Step-by-step explanation:

The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;

6^2 +7^2 = hypotenuse^2

hypotenuse = [tex]\sqrt{85}[/tex]

csc θ = 1/sinθ

sinθ = opposite side/hypotenuse

       = 6/[tex]\sqrt{85}[/tex]

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = 1/cosθ

cosθ = adjacent side/hypotenuse

sec θ = hypotenuse/adjacent side

         = [tex]\sqrt{85}[/tex]/7

tan θ = Opposite side/adjacent side

         = 6/7

Answer:

A and B

Step-by-step explanation:

When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.

Hope this helped ^-^

The lengths of the legs of each triangle are:

1) Leg = √19

2) Leg = √105

3) Leg = √60

How to use Pythagoras Theorem?

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

a = √(c² - b²)

1) We are given that:

Hypotenuse = 10

Opposite side = 9

Thus, using Pythagoras Theorem, we have:

Leg = √(10²- 9²)

Leg = √19

2) We are given that:

Hypotenuse = 19

Opposite side = 16

Thus, using Pythagoras Theorem, we have:

Leg = √(19²- 16²)

Leg = √105

3) We are given that:

Hypotenuse = 8

Opposite side = 2

Using Pythagoras Theorem, we have:

Leg = √(8²- 2²)

Leg = √60

X+Y = 21 ---> Y = 21-x

X-y = 5

x - (21-x) = 5

2x - 21 = 5

2x = 26

x = 13

13 and 8

The two numbers are 13 and 8.

13 + 8 = 21

The difference (13 - 8) is 5.

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+2}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation of a line:

[tex]y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}[/tex]

and the point (0, 2) → b = 2.

Substitute:

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

Answer:

Step-by-step explanation:

DDD

Answer:

the first one i believe

Step-by-step explanation:

hope this helps

Answer:

3√4

Step-by-step explanation:

Answer:

5 cups 39 fl oz

Step-by-step explanation:

There are 2 cups to a pint, so 2pt 4 fl oz becomes 4 cups 4 fl oz, which is less than 5 cups 39 fl oz

Answer:

−2sin(2θ)cos(4θ)

Step-by-step explanation:

sin(2∅)-sin(6∅)

Sum product Identity

sinα  - sinβ  = 2cos((α+β)/2)sin((α-β)/2)

Putting α= 2∅ and β= 6∅ in the identity we get

sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)

                        =2cos(8∅/2)sin(-4∅/2)

                        =2cos(4∅)sin(-2∅)

                         = -2sin(2∅)cos(4∅)

Answer:

$3116

Step-by-step explanation:

First off, we need to find the value of the appliance after the down payment.

$2450 - $600 = $1850

This then makes our principal $1850.

P = $1850

r = 9% or 0.09

t = 4 years

To find the total cost of the appliance plus interest, we need to look for our accrued amount first.

A = P + Prt

A = $1850 + $1850(0.09)(4)

A = $1850 + $666

A = $2516

Now that we know our accrued amount, we then add our down payment to find the total cost.

Total cost = $2516 + $600

Total cost = $3116

To calculate the cost of an appliance with added interest, subtract the down payment from the purchase price to determine the amount of the loan. This is followed by the calculation of the total interest over the length of the loan. Adding these two amounts provides the total cost of the appliance plus interest, which in this case is $2516.

The total cost of the appliance plus interest can be calculated by first determining the amount of the loan made, which is the cost of the appliance minus the down payment. This comes out to $2450 - $600 = $1850.

Then, the add-on interest over 4 years is calculated by multiplying the amount of the loan by the annual interest rate and by the number of years. For this question, that is $1850 * 0.09 * 4 = $666.

So, the total cost of the appliance with interest added is the sum of the amount of the loan and the amount of the interest. Therefore, $1850 + $666 = $2516 is the total cost for the appliance plus interest.

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My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.

Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.

Answer:

1,350 students

Step-by-step explanation:

The number of students this year is 90% of the number from last year.  Find 90% of 1500....

90% is 0.9 as a decimal,

0.9(1500) = 1,350 students

Answer: 2i50 students

Step-by-step explanation:

Do 90% of 1,500

10% = 150

150 x 9 = 1350

We need the total amount of students

So do 1350 + 1500 = 2850 students

Answer:

The means is 8.5 The Median is 6

Step-by-step explanation:

1) to find the mean just Simply add all the numbers together and divided by how many numbers that is giving. (Because you are simply finding the average)

9+6+5+3+28+6+4+7=68

68 divided by 8 = 8.5

2) to find the median simply organize the numbers from least to greatest Like this: (3,4,5,6,6,7,9,28) Then keep crossing out from both sides teal you find the middle Number.

If there a odd amount of number the median will be one Number, if even 2 numbers ( if 2 numbers just add them both and divide by 2)

In This Case the Median is 6,6 but Its actually 6 Why (6+6=12) and (12/2=6) so your median is 6.

Hopes This helps!

The mean of the given data 9, 6, 5, 3, 28, 6, 4, 7 is 8.5 and the median is 6.

The mean is defined as the average of all the values or the mean can be defined as the sum of all observations by the total number of observations.

[tex]Mean =\dfrac {\ Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]

[tex]Mean = \dfrac{9 + 6 + 5 + 3 + 28 + 6 + 4 + 7}{8}[/tex]

Mean = [tex]\dfrac{68}{8}[/tex]

Mean  = 8.5

Therefore, the mean of the data set is 8.5.

The median is defined as:

The median is the middle value when the data set is arranged in ascending or descending order.

If there are two middle values, the median is the average of those two values.

Arrange the data set in ascending order: 3, 4, 5, 6, 6, 7, 9, 28.

Here n = 8, since n is even so the median is calculated as:

Median = [tex]\dfrac{(\dfrac{n}{2}) \ th \ observation + (\dfrac{n}{2}+1) \ th \ observation}{2}[/tex]

Median =[tex]\dfrac{( 4 \ th \ observation + 5 \ th \ observation)}{2}[/tex]

The 4th observation is 6 and the 5th observation is 6.

So, this mean will be 6.

Therefore, the median of the data set is 6.

The Mean is  8.5 and the median is  6.

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Answer:

1,2,4

Step-by-step explanation:

Factors are the numbers that we can multiply together to make 4

1*4 = 4

2*2 = 4

The factors are 1,2 and 4

Answer:

Step-by-step explanation:

[tex]Factors\ of\ 4:\ 1,\ 2,\ 4\\\\4=4\cdot\boxed{1}\\4=2\cdot\boxed2\\4=1\cdot\boxed4[/tex]

Answer:

Start by moving the decimal place in the number until you have a coefficient between 1 and 10. The number of places to the left that you had to move the decimal point is the exponent. so for example, 0.000345 would be 3.45(10)^4

Step-by-step explanation:

Hope that helps!

Answer:

The final solution is all the values that make  

( x 4  +  5  x 2  −  36 ) ( 2  x 2  +  9 x  −  5 )  =  0  true.  x  =  − 2 ,  2  ,  3  i  ,  −  3  i  , 1  2 ,  −  5

Step-by-step explanation:

x 4  +  5  x 2  −  36  =  0  2  x 2  +  9 x  −  5  =  0

Answer:

1,2,2,5,3

Step-by-step explanation:

it's right you idiots

Answer:

Step-by-step explanation:

If Lina supposedly bought 10 rolls, we would show it by the following equation,5*10=50, and since 25 is half of 50, we would have 5 as our solution.

25/5=5

5 rolls of films is our solution

Answer:

B

Step-by-step explanation:

D: You will not get a cubic function. Nothing adds to give a term with x^3 in it.

C: A rational function is of the form (x^2 + 3x + 2) / (x^2). In other words it has a numerator and a denominator that are polynomials. Unless one or both started out like that, the answer is not a rations function.

A: It can't be linear. The x^2 term will carry over after addition.

The answer is B. One of the polynomials started out as a quadratic. It will remain that way.

It’s the forth one

The answer is -|x-4|.

Answer:y=-|x-4|

Step-by-step explanation:

we know the graph of y=|x| touches at x=0 and opens upward towards y axis

but this graph is facing downwards therefore it should be of form

y=-|x|

but it touches the x axis at x=4

therefore the graph is represented by

y=-|x-4|

4 is added inside the mod because it intersect x axis at x=4

The graph would be y=-|x-4|+1 if it shifts 1 unit upwards.

Answer:

1320 ways

Step-by-step explanation:

Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.

The permutation formula is:

[tex]_{n}P_{k}=\dfrac{n!}{(n-k)!}[/tex]

n = 12

k = 3

Now that we have our variables, let's plug them into the formula.

[tex]_{12}P_{3}=\dfrac{12!}{(12-3)!}[/tex]

[tex]_{12}P_{3}=\dfrac{12!}{9!}[/tex]

[tex]_{12}P_{3}=1320[/tex]

So there are 1320 different ways that the contestants will be awarded.

3 1/2 pints - 3/4 pints

3 1/2 = 3 2/4

3 2/4 = 2 6/4

2 6/4 - 3/4

2 3/4

Answer: 2 3/4 pints of berries

Sasha bought 3 and 1/2 pints of blueberries, ate 3/4 of a pint, and after calculating, she has 2 and 3/4 pints left for making jelly.

The student, Sasha, initially bought 3 and 1/2 pints of blueberries and then ate 3/4 of a pint. To find out how many pints of berries she has left, we need to subtract the amount eaten from the amount bought.

We calculate:

Converting 11/4 pints back to a mixed number, we get 2 and 3/4 pints. Therefore, Sasha has 2 and 3/4 pints of blueberries left to make jelly.

The error is the way she wrote 3%

3% = 0.03

The correct equation should be y = 78,000(0.03)^x

Cameron - х years

Josephina is five years older than Cameron = х+5 years

sum of their ages is 31

х+х+5=31

2х=31-5

2х=26

х=13 Cameron

13+5=18 Josephina

The age of Josephina and Cameron is 13 and 18.

here Cameron be х years

And, Josephina is five years older than Cameron so х+5 years

Also,

The sum of their ages is 31

Now

х+х+5=31

2х=31-5

2х=26

х=13 Cameron

13+5=18 Josephina

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Answer:

Asa has $13 and owes $39

Step-by-step explanation:

25 + 14 = 39$ (amount of money he owes)

25 - 12 = 13$ (amount of money he has)

Answer:

[tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

We are given that Jack rolls two standard number cubes and we are to find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd.

A sum of two from two rolls would always be one even and one odd, whatsoever is the case.

To have a sum of five, we can have (1, 4), (2,3), (3,2) or (4,1) out of a sample space of 36 so the probability will be [tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex].

Answer:

C

Step-by-step explanation:

From the given coordinates

A(6, 0), B(0, 0) then AB = 6 - 0 = 6

B(0, 0), C(0, 8) then BC = 8 - 0 = 8

To calculate AC use Pythagoras' theorem on the right triangle formed

AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100

Take the square root of both sides, hence

AC = [tex]\sqrt{100}[/tex] = 10

Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C

Answer:

[tex]x<8\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]-4x+35>2\\-4x>-33\\x<\frac{33}{4} \\x<8\frac{1}{4}[/tex]

Remember to flip the sign when you divide or multiply both sides by a negative number! You don't need to flip the sign with adding or subtracting as in the case of step one subtracting 35 from both sides.

The solution of the inequality −4x+35>2 will be x < (33 / 4).

The relationship between two phrases using a symbol like "not equal to," "greater than," or "less than" indicates that they are not equal.

The given inequality will be solved as below:-

−4x+35>2

−4x>- 35 + 2

−4x > - 33

−4x > - 33

x < ( 33 / 4 )

Therefore, the solution of the inequality −4x+35>2 will be x < (33 / 4).

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