Divide the polynomial in the numerator by the binomial in the denominator and simplify.
x³ + 11x² + 6x +4/x+7

Answer:

2 liters of oil are left at the end of two days

Step-by-step explanation:

Quantity of oil that leaks = 25% of 4 liters

                                         = 0.25 * 4

                                         = 1.00 = 1 liter per day

2 liters of oil leaks for 2 days

Quantity of oil left at the end of two days = 4 - 2 = 2 liters

Answer:

The first five values are 12, 14, 16, 18 and 20

The recursive formula is as follow

Step-by-step explanation:

Since we need to find the first 5 values  we start with n = 1 to n = 5. Note that we don't start from n = 0 as the question states that  n ≥ 1.

For the first 5 values we just replace the value of n with 1, 2, 3, 4 and 5 and calculate the answer

The first five values are 12, 14, 16, 18 and 20

A recursive formula is one that

a) Mentions the initial term

b) provides a formula connecting the previous term to the existing term.

Since we know the first term is 12, i.e  and we know that the difference between consecutive terms is 2 we can conclude that the recursive formula is made up of the following two formulas

The over all formula is as follow

Step-by-step explanation:

Hope this helps:)

Answer:

−10x4+17x2y−6y2-10x4+17x2y-6y2

or the second option

Answer:

−3/2x−7

Step-by-step explanation:

1/2x+7−(2x+14)

1/2x+7+−1(2x+14)

1/2x+7+−1(2x)+(−1)(14)

1/2x+7+−2x+−14

Combine Like Terms:

1/2x+7+−2x+−14

(1/2x+−2x)+(7+−14)

Answer:

7 = 2x - 4x + 14.

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

150 / 30 = 5

8 x 5 = 40

40 of 150 students is equivalent to 8 of 30 students.

The angle m∠BAC is 54 degrees.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore, let's find the angle BAC.

Hence,

10x + 4 = 1 / 2 (12x + 15 + 9x - 12)

10x + 4 = 1 / 2 (21x + 3)

10x + 4 = 10.5x + 1.5

10x - 10.5x = 1.5 - 4

-0.5x = -2.5

divide both sides by -0.5

x = -2.5 / -0.5

x = 5

Therefore,

m∠BAC = 10(5) + 4

m∠BAC = 50 + 4

m∠BAC = 54 degrees

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Answer:

∅ = 40.3°

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Define

Looking for m∠A

Step 2: Identify

adjacent leg of ∠A = AC = 7.4

hypotenuse = AB = 9.7

Step 3: Find theta

The body surface area is given by the equation A = 1.6865 m²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the body surface area be represented as A

Now , the equation will be

A = ( HW / 3600 )^1/2

A = √( HW / 3600 )   be equation (1)

where H is the height in centimeters and W is the weight in kilograms

Now , the value of H = 160 cm

The value of W = 64 kg

Substituting the values in the equation , we get

A = √ [ ( 160 x 64 ) / 3600 ]

On simplifying the equation , we get

A = √ ( 10240/3600 )

A = √ ( 2.8444 )

A = 1.6865 m²

Therefore , the body surface area is 1.6865 m²

Hence , the equation is A = 1.6865 m²

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Answer:

x = 5

Step-by-step explanation:

The sides are in proportion.

The proportion is 20/36

The other sides must be in the same proportion: 5x / 45

5x/45 = 20/36        You can reduce the left side by dividing top and bottom by 5

1x / 9 = 20/36          You can reduce the right side by dividing by 4

x / 9 = 5/9                at this point you should be able to see that x = 5, because the denominators are the same.

That is the answer.

However you can extend this by cross multiplying

9x = 45                      Divide by 9

x = 45/9

x = 5

Answer:

-11-(-5)= -6

25-(-3)= 28

-7-(-2)= -5

4-15= -11

6-(-9)= 15

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer:

-10 sqrt(10)

Step-by-step explanation:

-2 sqrt(250)

We know that sqrt(ab) = sqrt(a) sqrt(b)

-2 sqrt(25*10)

-2 sqrt(25)*sqrt(10)

-2 *5*sqrt(10)

-10 sqrt(10)

Answer:

\(7x+8y+33\)

Step-by-step explanation:

\(2y+8(y+1)+5(x+5)\\\\2y+(8)(y)+(8)(1)+(5)(x)+(5)(5)\\\\2y+8y+8+5x+25\\\\7x+8y+33\)

Answer:

a)2

B)2

Step-by-step explanation:

The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.

here, we have,

given expression is,

16p+5+9p+25

=25p+30

=5(5p+6)

Hence, The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).

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Answer:

\(\frac{1}{5}\) = \(\frac{2}{10}\) = \(\frac{20}{100}\)

Step-by-step explanation:

It's all about equivalent fractions.

\(\frac{1}{5}\)

\(\frac{2}{10}\)

\(\frac{20}{100}\)

\(\frac{1}{5}\) 1 × 2 = 2. 5 × 2 = 10. That is what makes \(\frac{2}{10}\).

\(\frac{2}{10}\) 2 × 10 = 20. 10 × 10 = 100. That is what makes \(\frac{20}{100}\).

The percent markup of the supplied statement is equal to 50% after the problem is solved.

There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Cost price of game=$25

Selling price of game=$37.50

Profit =  selling price - cost price

Profit =  37.50 - 25

Profit / markup percentage = (profit /cost price ) * 100

= (12.50/25) * 100

= 50%

The percent markup of the supplied statement is equal to 50% after the problem is solved.

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Answer:

\( \sqrt{50x^2} \)

\( \sqrt{72x^2} \)

Step-by-step explanation:

Simplify each given options as much as possible to see which of them has a result that is like a radical.

Option 1: \( \sqrt{50x^2} \)

\( \sqrt{25*2*x^2} = 5x\sqrt{2} \)

This is like a radical

Option 2: \( \sqrt{32x} \)

\( \sqrt{16*2*x} = 4\sqrt{2x} \)

This is NOT like a radical

Option 3: \( \sqrt{18n} \)

\( \sqrt{9*2*n} = 3\sqrt{2n} \)

This is NOT like a radical

Option 4: \( \sqrt{72x^2} \)

\( \sqrt{36*2*x^2} = 6x\sqrt{2} \)

This is like a radical

33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

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

12 inch = 1 ft

Total perimeter of patio not counting the side against the house = 12 + 12 + 14 = 38 feet

38 feet = 38 feet * 12 inch per feet = 456 in

Number of stone pavers needed = 456 in / 14 in = 32.57 ≅ 33

33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long

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Answer:

4x-y=3

Step-by-step explanation:

IT'S standard form

The maximum height reached by the ball is 908.5 feet.

Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:

\(h(t) = -16t^2 + 152t + 6\)

This quadratic function models the height of the ball at any time t after it is thrown.

To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:

t = -b / 2a

where a = -16 and b = 152 are the coefficients of the quadratic function.

t = -152 / 2(-16) = 4.75

So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:

\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet

Therefore, the maximum height reached by the ball is 908.5 feet.

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Question

A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0

Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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Answer:

what we have to find or to prove.

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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Answer:

the average number of trucks per 5 hours is 3.750 trucks per 5 hours

Step-by-step explanation:

The computation of the average number of trucks per 5 hours is given below:

= Number of trucks passed ÷ time taken × given time

= 18 trucks ÷ 24 trucks × 5

= 3.750 trucks per 5 hours

Hence, the average number of trucks per 5 hours is 3.750 trucks per 5 hours

The same is to be considered by applying the above formula

One would pay $5,232.96 in interest over the 5-year loan term.

To get interest paid on the loan, we will the formula for compound interest \(Interest = Principal * (1 + Annual Interest Rate)^{Number of Years} - Principal\)

The principal is the loan amount which is $9,000.

The annual interest rate is 9.6%

The number of years is 5.

Interest = $9,000 * (1 + 0.096)^(5) - $9,000

Interest = $9,000 * 1.58144018701 - $9,000

Interest = $5,232.96168

Interest = $5,232.96.

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