4/5(720-240)-180 step by step

wo mechanics worked on a car the first mechanic worked for 10 hours and the second mechanic worked for 15 hours together they charged a total of $2,450 what was the rate charge per hour by each mechanic if the sum of the two rates was $185 per hour

Let

x -----> the rate of the first mechanic

y -----> the rate of the second mechanic

we have that

x+y=185 -------> equation A

10x+15y=2,450 ------> equation B

Solve the system of equations by graphing

see the attached figure

therefore

When he buys the cheapest soap, the amount he save per bar is $0.25.

Money is anything that's used as a medium of exchange.

In this case, three bars of soap cost $3.75. Each bar will bre:

= $3.75 / 3

= $1.25

Also, a package of eight bars of soap for $12. Each bar will be:

= $12 / 8

= $1.5

The amount that will be saved will be the difference between the values above. This'll be:

= $1.5 - $1.25

= $0.25

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[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18 This is a degree 3 polynomial with real coefficients having zeros 3 and 4 − 3 i and a lead coefficient of 1

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

complex zeros always occur in pairs.

zeros are 2,3i,-3i

f(x)=(x-2)(x-3i)(x+3i)=(x-2)([tex]x^{2}[/tex]-[tex]3i^{2}[/tex])

=(x-2)([tex]x^{2}[/tex]-[tex]9i^{2}[/tex])

=(x-2)([tex]x^{2}[/tex]+9)

=[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18

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We need to solve the equation

In order to do so, we can first divide both sides of the equation by 400:

Now, to isolate the variable t on the left side and find its value, we can divide both sides by 1.065:

Therefore, rounding to two decimal places, the answer is 2.00.

To calculate the balance on the account after 5 years you have to calculate the simple interest using the formula:

A= total accured amount

P= principal amount

r= interest rate expressed in decimals

t=time

For

P=$5250

r=0.035

t=5years

The balance on the account will be:

At the end of the 5 years there will be $6168.75

The number of letters in the word MATH IS

To rearrange a letter with n letters to form a four-letter code will be

Hence,

The number of ways of rearranging the words will be

This problem is a bit different. Instead of choosing one item from each of several different

categories, we are repeatedly choosing items from the same category (the category is: the

letters of the word MATH) and each time we choose an item we do not replace it, so there is

one fewer choice at the next stage: we have 4 choices for the first letter (say we choose A),

then 3 choices for the second (M, T, and H; say we choose H), then 2 choices for the next

letter (M and T; say we choose M) and only one choice at the last stage (T). Thus, there are

4 · 3 · 2 · 1 = 24 ways to spell a code word with the letters MATH.

Hence,

The final answer = 24 ways

The given multiplication expression is 3/4÷3/8 or 3/4×8/3

Mathematical expressions that include multiplication are called multiplication expressions. We combine the integers and then the like variables to simplify the equation. We will therefore obtain x to the second power if we multiply two xs together.

An answer to a multiplication sentence is obtained by multiplying the various components. The multiplier (first number), multiplicand (second number), and product are the components of a multiplication phrase (third number).

The simplest form of an expression is one in which terms cannot be concatenated. In order to write 3 + (2 5) simply: Start by carrying out the procedure between parenthesis. The addition should then be done.

Given, 3/4÷3/8

3/4×8/3

=2

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Answer:

Tim will stop for a drink 12 times

Step-by-step explanation:

Tim drinks water 3 times every twenty minutes. 80 divided by 20 equals 4. Take the 4 times and multiply it by 3 to get the amount of times he stopped to drink water.

I hope this helps

The graph A is the one that accurately represents the side length of the bigger frame S(x).

Modeling the function S(x) by

S(x) has experienced the following changes:

a 1 shift to the right, as shown by the square root's value of -1;

S(x) travels to the right by 1 = 0 + 1 = 1 whereas f(x) stays at 0.

The graph is stretched by a factor of 3 (a number that multiplied the square root).

Consequently, the graph A shows the two changes on S. (x). As a result, it is the best choice.

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Answer:

WHAT IS THATT??

Step-by-step explanation:

OSKSKQKANSNSNSNSZKNSNSNSN

Triangle area is equal to

Height = (x + 2) feet

= 24 square feet

24 = 0.5(x)(x+2) \s0.5(x)(x + 2) = 24

The formulas that can be used to determine the triangle's leg lengths must be equivalent to 0.5(x)(x + 2).

To elaborate on this: 0.5(x)(x + 2) = 24

2(x2 + 2x + 48)= 0 is equivalent to 0.5(x2 + 2x) = 24.

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The formula for the simple interest I after an amount P is invested for period t at a simple interest rate r is:

In this problem, the simple interest annual rate is 8% = 0.08. But the period t of the investment is

t = 90 days = 3 months = (12/4) months = (1/4) year

And the rate is:

Then, using P = 175, the interest, in dollars, is:

And the amount A, in dollars, in the account after that period is:

Answers:

Simple interest: $3.50

Ammount: $178.50

Answer:

B

Step-by-step explanation:

Using a minor key within a song is usually to make it more sad or negative in emotion, though with this question the fast tempo should already rule out A because it is quite the opposite to laziness.

-12/5

This is a improper fraction, so lect's corvert it into a mixed fraction

2

5 12

2

Written as a mixed fraction -2 2/5

It's negative

The possible answers are -2 2/5

12/-5

-12/5

The question is really asking for the unit rate but on a supposedly linear graph that is not to scale, so it is difficult to evaluate real rates.

Answer:

the answer is f'(x)=3x^2-6x-4

Step-by-step explanation:

Answer:

150 is the number

Step-by-step explanation:

The equation we should set up is from the sentence "14% of what number is 21"
To rearrange it into a proper equation, replace "of what number" with " * x "
and "is" with "="
The sentence becomes:

14% * x = 21

since 14% = 0.14, replace 14% with 0.14 in the equation

0.14 * x = 21

divide both sides by 0.14

x = 21 / 0.14

x =  150

Use the formula for the simple interest

I= interest

p= initial deposit

r=rate

t= time

clear the equation for r

replace data in the formula

pass the decimal to percentage

7%

the interest rate is 7%

Solution

The answer is given in the graph below

Utilizing differentiation, the biggest value of y=0 in the system's solution set.

One of the two fundamental concepts of calculus is differentiation. Differentiation is a method for finding a function's derivative. Differentiation is a mathematical technique used to calculate the instantaneous rate of change of a function based on one of its variables. Velocity, or how quickly a distance varies in respect to time, is the most common example. Differentiation's opposite is finding an antiderivative.

Differentiating the 1st equation, we get

x=5.5

Putting back in the equation.

y = -5.75

and differentiating the 2nd equation, we get

x=3

Putting back in the equation

y= 0

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A line is uniquely defined by two points. So, we only need to find two points that lie on the line.

[tex]x=1 \implies y=4(1)-1=3\\\\x=2 \implies y=4(2)-1=7[/tex]

So, you can draw the line through (1, 3) and (2, 7).

Solution:

The slope-intercept form of a line with slope m and y-intercept b is given by the following formula:

On the other hand, the slope m is given by the following equation:

where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:

(X1,Y1) = (1,2)

(X2,Y2) = (-1,-1)

replacing this data into the slope equation, we get:

thus, the slope of the line would be:

now, replacing this into the slope-intercept form of the line we get:

EQUATION 1

We only need to find the y-intercept b. For that, take any point on the line, for example (x,y) = (1,2), and replace it into the previous equation:

this is equivalent to:

solving for b, we get:

that is:

finally, replacing this into the EQUATION 1, we get:

then, the slope-intercept form of a line with the points (1,2) and (-1,-1) would be:

Answer:

(3y + 11)° = 50°

10y° = 130°

(4x - 22)° = 50°

(7x + 4)° = 130°

Explanation:

First, find the value of the variable. Let's find y.

(3y + 11) + 10y = 180 (sum of adjacent angles on a straight line)

Simplify and solve the equation.

13y + 11 = 180

13y = 169

y = 13

Substitute y into the angle measures to find values.

3(13) + 11 = 50

10(13) = 130

Hence, (3y + 11)° = 50° and 10y° = 130°.

Next, find x.

(7x + 4) + (4x - 22) = 180 (sum of adjacent angles on a straight line)

Simplify and solve the equation.

11x - 18 = 180

11x = 198

x = 18

Substitute x into the angle measures to find values.

4(18) - 22 = 50

7(18) + 4 = 130

Hence, (4x - 22)° = 50° and (7x + 4)° = 130°.

Alternatively, you do not have to find x to find (4x - 22)° and (7x + 4)°.

4x - 22 = 3y + 11 = 50° (vertically opposite angles)

7x + 4 = 10y = 130° (vertically opposite angles)

If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then he had spend a total of $ 2.76, and if 10 ice cream cones were brought for $0.35 each, then the total amount paid is $3.5

As per the question statement, Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98,

And the coach bought 10 ice cream cones for $0.35 each.

We are required to calculate the following:

(a) The total amount Mark had to pay

(b) The total amount the coach had to pay

Starting with part (a),

If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then the total amount he will have to pay will simply be the summation of the individual costs, that is, $[0.49 + 1.29 + 0.98] = $ 2.76.

Now solving part (b),

If the coach bought 10 ice cream cones for $0.35 each, then the total amount he/she will have to pay, will be a simple multiplication of the price of one ice cream, with the number of ice creams bought, that is,

$[0.35 * 10] =$3.5

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Graphing the function:

The formula rewritten for b1 is b1 = 2a/h - b2

The unknown base of the trapezoid is 5 inches

A subject of formula is simply described as the variable that is made to stand alone on one side of the equality sign.

It is the variable expressed in terms of other variables in an expression.

Given the formula for the area of a trapezoid as;

a = 1/2h(b1+b2)

Where;

Let's make b1 the subject of formula

cross multiply

(b1+b2)h = 2a

Now, divide both sides by h, we have!

b1 + b2 = 2a/h

Take b2 over the equality sign

b1 = 2a/h - b2

Now, substitute the values into the formula

b1 = 2(78)/12 - 8

Expand the bracket

b1 = 156/12 - 8

Find the quotient

b1 = 13 - 8

find the difference

b1 = 5 inches

Hence, the value is 5 inches

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a rental car company charges $42.50 per day to rent a car intense sense for every mile driven Lydia wants to run a car knowing that she plans to drive 225 miles in she has at most $150 to spend

Let

x -------> the number of miles

y -----> the total charge

we have that

the linear equation that represent this problem is

y=0.10x+42.50

For x=225 miles

substitute teh value of x

y=0.10(225)+42.50

y=$65

Given:

You can find the antiderivative by integrating it:

1. Set up:

2. You can rewrite it in this form:

3. Apply this Integration Rule:

Then, you get:

4. Simplify:

Remember this Property for Radicals:

You can rewrite the expression in this form:

Applying this Property for Radicals:

You get:

5. Knowing that:

You obtain:

Hence, the answer is: