Let $x$ be the positive number such that $2x^2 = 4x + 9.$

If $x$ can be written in simplified form as $\dfrac{a + \sqrt{b}}{c}$ such that $a,$ $b,$ and $c$ are positive integers, what is $a + b + c$?

Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

The required number we're looking for is x = 3.

The outcome or conclusion we arrive at when we add two or more integers is known as the SUM. Addends are the integers that are added. In the previous illustration, the total of the addends, 6, and 4, is 10. In other terms, we can say that 8 plus 5 equals 13 or that 8 plus 5 equals 13.

We can start by translating the problem into an equation. Let x be the number we're trying to find. Then the problem can be expressed as:

\($$7(x+1) = 28$$\)

Simplifying the equation, we first distribute the 7 on the left-hand side:

7x + 7 = 28

Then we isolate the variable x by subtracting 7 from both sides:

7x = 21

Finally, we solve for x by dividing both sides by 7:

x = 3

Therefore, the number we're looking for is x = 3.

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Complete question:

Seven times the sum of a number and 1 is 28.

What is the number?

The amplitude of the function is 1/2, and the period of the function is π.

We know that,

The general form of a sine function is,

⇒ f(x) = A sin(Bx + C) + D,

where:

A is the amplitude

B is the angular frequency or 2π divided by the period

C is the horizontal shift

D is the vertical shift

Now, We have;

The function is,

⇒ f (x) = 1/2 sin 2x

Hence, By Comparing this to the function f(x) = 1/2 sin 2x, we can see that:

A = 1/2, which means that the amplitude of the function is 1/2.

B = 2, which means that the angular frequency is 2,

Or equivalently, the period of the function is 2π/2 = π.

Therefore, the amplitude of the function is 1/2, and the period of the function is π.

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The correct statement regarding the angle measures is given as follows:

m < 1 + m < 4 > m < 3.

The given angle measure is as follows:

m < 3 = 119º.

Angles 3 and 4 form a linear pair, meaning that they are supplementary, that is, the sum of their measures is of 180º.

Hence the measure of angle 4 is given as follows:

m < 4 + m < 3 = 180º.

m < 4 = 180º - 119º

m < 4 = 61º.

Angles 1 and 4 are opposite by the same vertex, hence they are congruent, thus the measure of angle 1 is given as follows:

m < 1 = m < 4

m < 1 = 61º.

Hence:

m < 1 + m < 4 = 2 x 61

m < 1 + m < 4 = 122º

122º > 119º

m < 1 + m < 4 > m < 3.

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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

Ten miles

Step-by-step explanation:

Use this inequality

20 + 3m = 5m

The base area of the prism is 2x² + 5x - 18

From the question, the given parameters are

Volume = 2 x cubed + 9 x squared minus 8 x minus 36

Height =  x + 2

Rewrite properly as

Volume = 2x³ + 9x² - 8x - 36

Height =  x + 2

The base area is calculated as

Base area = Volume/Height

Using the synthetic division, we have

Set the divisor to 0

x + 2 = 0

This gives

x = -2

So, we have the representation to be

-2 | 2   9  - 8  - 36

Write out 2

So, we have

-2 | 2   9  - 8  - 36

     2

Multiply 2 and -2

This gives

-2 | 2   9  - 8  - 36

          -4

     2

So, we have

-2 | 2   9  - 8  - 36

          -4

     2    5

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10

     2    5   -18

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10   36

     2    5   -18    0

This means that

Base area = 2x² + 5x - 18

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

If the 3 friends work on 2 yards, then together they will earn:

If the 3 friends work on 3 yards, then together they will earn:

If the 3 friends work on 4 yards, then together they will earn:

If the 3 friends work on 5 yards, then together they will earn:

Answer:

Therefore, if the 3 friends work on 5 yards, then together they will earn $180.

Answer: w=4, y=4

Step-by-step explanation:

For this problem, we can use the 30-60-90 triangle to find out what the length of w and y are. 30-60-90 triangle is a special triangle. The hypotenuse is 2x in length. It is directly opposite the right angle. The leg opposite of 60° is x√3 in length. The leg opposite of 30° is x. For all 3 legs, wherever you see x, you plug in the same number.

We can look at the figure as 2 separate triangles.

For the triangle on the right, we can see the hypotenuse is 8. Since we know the length of the hypotenuse is 2x, we can plug in 8 for 2x to find x.

2x=8

x=4

Now that we know x=4, we can directly plug it into the lengths above.

W is across from 30°. Above, we have established that the leg across from 30° has the length of x. Since x=4, w=4.

Since w=4, we can use this information to find the length of y by looking on the left triangle. Now, y is across from 30°. In the first paragraph, we stated that the leg across from 30° is x. Since we know x, we can directly plug it into this. After we plug it in, y=4.

The answer to the expression is  \(166\frac{67}{100}\)

First, you must turn the mixed numbers into improper fractions.

\(\frac{3811}{10} -\frac{21443}{100}\)

Then, you must find like denominators.

\(\frac{38110}{100} -\frac{21443}{100}\)

Next, subtract the numerators of the fractions.

\(38110-21443=16667\)

\(\frac{16667}{100}\)

Finally, convert the improper fraction into a mixed number.

\(166\frac{67}{100}\)

Answer:

B and F should be right since the angle in the middle of them anchors in the the middle of the circle

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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Answer:

  AB = 8

Step-by-step explanation:

Since C is the midpoint, ...

  AC = CB

  5x -6 = 2x

  3x = 6 . . . . . . . add 6-2x

  x = 2

Then the length of AB is ...

  AB = 2(CB) = 2(2x) = 4(2)

  AB = 8

Answer:

D. all real numbers

Step-by-step explanation:

i think this is the answer sorry if you get it wrong.

where the question??????????????

Answer:This number line represents all number. Although 1

8

is not labeled, it still exists on the number line and can be plotted. 1

8

is located halfway between 0 and 1

4

hope this help!

Answer:

\(\huge\boxed{\sf x = -14}\)

Step-by-step explanation:

4(x + 2) = 3(x - 2)

4x + 8 = 3x - 6

4x - 3x + 8 = -6

x + 8 = -6

x = -6 - 8

\(\rule[225]{225}{2}\)

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Answer:

It is Option D

Step-by-step explanation:

-2 + 12 = 10

and

8 - 6 = 2

The measure of the angle m∠PBM is calculated as; 54°

An inscribed angle is defined as an angle with its vertex on the circle.

The measure of an inscribed angle is half the measure the intercepted arc.

The formula is:

Measure of inscribed angle = 1/2 × measure of intercepted arc

Now, we are given that;

MB = PB

Arc PB = 27°

Thus;

Arc MBP = 2 * 27°

Arc MBP = 54°

Thus, using the Measure of inscribed angle we have;

∠PBM = 27 * 2 = 54°

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Answer Step-by-step explanation:

2x-7

-14

3x

2+7

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

-----------------------

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

-----------------

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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The number of 3 / 16 yards pieces that can be cut from 3 / 4 yard of ribbon is 4.

The actual length of the ribbon is 3 / 4 yards.

He wants to cut 3 / 16 yards pieces from the actual length of the ribbon.

Therefore, the number of 3 / 16 yard that can be cut from 3 / 4 yard of ribbon can be calculated as follows;

number of pieces of ribbon = 3 / 4 ÷ 3 / 16

number of pieces of ribbon = 3 / 4 × 16 / 3

number of pieces of ribbon =  48 / 12

Therefore,

number of pieces of ribbon =  4 yards

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