You want to purchase a new bike that costs $142.68. To save for the bike, you mow your neighbor's yard for $40 each week. How much money will you have left over if you buy the bike after saving for 4 weeks?

The simplified result is :

[tex]4x/x^{2}[/tex] - 1

= 4/x -1

4-x / x.

Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.

An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.

In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.

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The values of the variables are:

a = -3

b = 2

c = -4

d = 6

e = -7

Given, the expressions are:

4a + 2 = -10

4a = -10-2

4a = -12

a = -3

substitute a value in the next expression.

a(2+b) = -12

-3(2+b) = -12

-6-3b = -12

-3b = -12+6

-3b = -6

b=6/3

b = 2

now substitute b value in the next expression.

-5c+b= 22

-5c+2 = 22

-5c = 22-2

-5c = 20

c = -20/5

c = -4

substitute c value in the next expression.

7(c+d) = 14

7(-4+d) = 14

-28+7d = 14

7d = 14+28

7d = 42

d=42/7

d=6

In the last expression substitute c and d values to find e.

d-c-e= 17

6-(-4)-e = 17

6+4-e = 17

10-e = 17

-e = 17-10

-e = 7

e = -7

hence we get the values of all the variables.

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Answer:

Hayley will have 200 milliliters of paint left.

Step-by-step explanation:

1 liter=1000 milliliter

1000-800=200

Answer:

305

Step-by-step explanation:

There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.

Answer:    Find the square roots and the multiply that by 4

Step-by-step explanation:

hope this helped

The price the machinery have initially cost rounded to the nearest dollar is $244,693

The formula for calculating depreciation is expressed according to the formula:

P(t) = P0e^-rt

Given the following parameters

P(t) = $100,000

rate = 12% = 0.12

time =7 years

Substitute

100,000 = P0e^-(0.12)(7)

100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693

Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693

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The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.

An item or particle that is thrown toward the planet's surface and moves somewhere along a curved route only under the influence of gravity is said to be experiencing projectile motion.

Let u be the initial speed and θ be the angle at which the ball hits. Then the range of the call is given as,

R = (u² sin 2θ) / g

Where 'g' is the acceleration due to gravity.

A tennis player strikes the ball at a height of 1.8 feet with an initial speed of 55 feet per second and an angle of 17°.

R = [55² x sin (2 x 17°) ] / 9.81

R = [3025 x sin 34° ] / 9.81

R = 172.43 meters

The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.

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Answer:

61.988 feet

Step-by-step explanation:

I took the test and got it right :)

Number of servings of Gerber mixed cereal for baby = 1

Number of servings of Gerber mango tropical fruit dessert for baby = 3

Given information about Gerber products are,

Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.

Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.

We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.

Since 1 x 60 + 3 x 80 = 60 +240 = 300

and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,

we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert  will do.

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Answer:

See Explanation

Step-by-step explanation:

Answer:

1.3^24 / 1.5)^18

Step-by-step explanation:

[1.5^3 / 1.3^4]^-6

= 1.5^(3*-6) / 1.3^(4*-6)

= 1.5^(-18) / 1.3^(-24)

= 1.3^24 / 1.5)^18

If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.

An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of function f over the interval [-3, 0]:

a = -3; f(a) = -4.5

b = 0; f(b) = 0

Substituting the given parameters into the formula, we have;

Average rate of change = (0 - (-4.5))/(0 - (-3))

Average rate of change = 4.5/3

Average rate of change = 1.5.

Also, we would determine the average rate of change of function g over the interval [-3, 0]:

a = -3; f(a) = 5

b = 0; f(b) = 14

Substituting the given parameters into the formula, we have;

Average rate of change = (14 - 5)/(0 - (-3))

Average rate of change = 9/3

Average rate of change = 3.

In conclusion, the average rate of change of function f is less than the average rate of change of function g.

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Answer:

The average rate of change of f is less than the average rate of change of g.

Step-by-step explanation:

Plato/Edmentum

During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

Given the expression, a³ - b³ / 5, where:

a = 2

b = -3

Substitute the values into the expression

Step 1: (2)³ - (-3)³ / 5

Evaluate

Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)

Step 3: 8 + 27/5

Step 4: 35/5 [addition]

Simplify

Step 5: 35/5 = 5 [division]

Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

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Answer:

8 1/4 or 33/4

Step-by-step explanation:

How to muliply fractions: just multiply all the denominators together and the numerators together

However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator

**Make sure to put the same numerator as you had before when you change to an improper fraction!!!

-4 1/2 = -9/2

-2 1/5 = -11/5

5      -9    -11        5 x -9 x -11        -45 x -11 (use a calculator)       495

--   x  -- x  ---   =   ---------------  =   -------------                              =  ------------

6       2     5         6 x 2 x 5           12 x 5                                         60

                      1         33

=  8.25 or  8  ---- =  --------

                       4         4

The dimensions of the bulletin board is 2 ft and 9 ft.

Let the width of board = x

Then, the length of board = 7+x

Area of board = 18 ft²

Area of rectangle = L×W

so, (7+x) × x = 18 ft²

7x + x² = 18 ft²

7x + x² + 18 = 0

x² + 9x -2x -18 = 0

x(x+9) -2(x+9) = 0

(x+9) (x-2) = 0

x+9 =0, x -2 = 0

Dimension can not be in negative number, so

x = 2, Width = 2 ft

Length = 2+7 = 9 ft

Hence, the dimensions of board will be:

The width of board = 2 ft

And, the length of bard = 9 ft.

According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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The expression that represent the total area in square feet covered by the wood panels is: 6x² feet²

The formula and procedure to solve this geometry exercise is:

A = s²

Where:

Problem information:

Using the formula of the square area we get the area of 1 panel:

A(1 panel) = s²

A(1 panel) = (x feet)²

A(1 panel) = x² feet²

Calculating the total area of the 6 wood panels we get:

A(total): No. panels * A(1 panel)

A(total): 6x² feet²

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2

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Maria should leave home for the airport terminal at 14:30.

We all know that one hour equals sixty minutes.

As a result, 6 hours = (6 × 60) minutes = 360 minutes.

For, the given question;

The time at which Maria need to be at airport terminal is 16:15.

Time taken for the driving is 1 1/3 = 4/3 hours.

convert this in minutes;

= 4×60/3

= 80 minutes.

Now, extra 25 minutes is requires to park.

Total time = 80 minutes + 25 minutes

Or we can write 60 minutes + 45 minutes.

Total time = 1 hour + 45 minutes.

The time at which Maria has to reach = 16:15 - 1:45 = 14:30

Therefore, the time at which Maria must reach the airport is 14:30 in 24-hour clock.

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There are 1680 ways to construct the octahedrons.

Here,

Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron.

An octahedron has 8 equilateral triangles.

We have to find number of ways to construct the octahedron.

What is Regular octahedron?

An octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.

Now,

An octahedron has 8 equilateral triangles.

We have to fix 2 faces before applying the colors.

So, the first face that can be fixed for any of the 8 faces but each faces are similar.

Hence, there are 8/8 ways.

And, When we fix one face, three adjoining faces are similar.

So, we have 7 colors for the second face.

Hence, 7/3 ways

Now, we can place any color anywhere, it will be different arrangement.

So, 6! ways.

Hence, Total number of ways = (8/8) * (7/3) * 6! = 7 * 6 * 5 * 4 *2 = 1680

So, There are 1680 ways to construct the octahedrons.

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The Janitor used 8/15 of the bottle

How to calculate the amount of the solution of the bottle used ?

The Janitor has 3/5 of a spray bottle solution

He uses 1/9 of the solution in a day

The amount of solution used can be calculated as follows

3/5 × 1/9

= 3/45

= 1/15

The initial amount  in the bottle is

3/5 - 1/15

= 8/15

Hence the amount of solution he has used is 8/15

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Answer:

Step-by-step explanation:

Let the speed of the cars be x and y.

When moving in opposite directions, the speeds add up and when moving in the same direction the speeds subtracted.

Convert time from minutes to hour:

Add up the two equations and find the value of x:

Find y:

The answer for the given function g(x) is  |x - 4|² - 2.

Given parent function is f(x) = |x|

Given vertex (h, k) = (-2, 4)

The simplest function in a family of functions, a parent function maintains the definition of the entire family.

The parent function that has vertex must be used to create the function of g, as shown below.

vertex form can be written as

a ( x - k )² + h

Here a = 1 , k = 4, h = -2

Now the function g(x) = | x -4 |² + ( -2)

                            g(x) = |x - 4|² - 2

Therefore, the function g(x) is found to be  |x - 4|² - 2.

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Answer:

82 , 162, 322

Step-by-step explanation:  

So basically add the number by two and then subtract that number by 2.  4.5(2)=9   9-2=7  and 7(2)=14  14-2=12 and so on

Answer: 4x10²

Step-by-step explanation:

The -2/3 is an  integer and rational number.

It is required to choose the number.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

Given:

-2/3 is an integer and rational number.

The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.

Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)

Whole numbers are positive numbers start with  zero  (0, 1, 2, 3,...)

Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)

Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)

Irrational numbers are numbers that can not be written as a simple fraction.  Its decimal goes on forever without repeating (π = 3.14159....)

5 is a natural number, whole number, integer, and rational number.

Therefore, the -2/3 is an  integer and rational number.

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Number of drinks = 3

From the question we are told that:

Ordered drink 4 1/2 ounces of 80-proof liquor

Generally,

80-proof liquor contains 40\% alcohol

Giving the drink a standard 1.5 ounce of distilled spirit

Therefore,

Number of drinks = 4.5 / 1.5

So, Number of drinks = 3

A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified. The avoirdupois ounce, or precisely 28.349523125 g, is 116 of an avoirdupois pound and is used in both the United States and the United Kingdom. Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items. Although the avoirdupois ounce is the standard unit of mass for most applications.

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Answer:

0.24 ounces for 3 teabags.

Step-by-step explanation:

Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.

Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.