9. A ball is thrown into the air. The height is modeled by the function h(t) = -4t2 + 12+ + 2. Determine f(1) and explain what it represents

Answer:

~Male Y/n here~ I believe your y-intercept would be D. -5.

(Hope this helps!)

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Let's find the least common multiple of 25 and 15.Which is 75

75 min * 1h/60min = 1.25 h

In other words, the buses will arrive at the same time at the stop, 1 hour and 15 minutes later.

1 pm + 1:15 = 2:15 pm

The table represents a linear function and after one year 544 ants will there be in the ant​ farm.

Given:

You have an ant farm with 34 ants. The population of ants in your farm will double every 3 months.

From the table:

Let Number of months be x   population be y

if number of months = 3 the population is 34 after that double = 68 and so on..

It is increasing in a linear manner so the table represents linear function.

One year ants = 272*2

= 544 ants.

Therefore the table represents a linear function and after one year 544 ants will there be in the ant​ farm.

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Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

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Answer:D

Step-by-step explanation:

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The  work is required to stretch the spring 80 cm beyond its natural length is 256J.

What is work?

Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the same direction as the motion.

Let, 100J of work is required to stretch a spring 50cm beyond its natural length.

So,

W = 100 J,

x = 50 cm = 0.5 m

By using the work formula,

\(W = kx^2\\100 = k (0.5)^2\\k = 400\)

To to find the value of W at k = 400 and x = 80 cm = 0.8m

\(W = 400(0.8)^2\\W = 256J\)

Hence, the work is required to stretch the spring 80 cm beyond its natural length is 256J.

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The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

8.25 < m

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

(20a - 1) ÷ b

a = 2

b = 13

(20(2) - 1) ÷ 13

(40-1)÷13

39÷ 13

= 3

answer: 32a^{13}b

your welcome

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.

Hence, Median best describes the line.

Option A is the correct option,

Answer:

7

Step-by-step explanation:

the reciprocal of seven = 1/7

which means that the reciprocal of a number is one divided by that number

Answer:

The answer is 7

Step-by-step explanation: god bless y'all!!

The distance between the points (-5,4) and (1,0) is  7.21 .

In the question ,

it is given that ,

the two points are (-5,4) and (1,0) ,

we  have to find the distance between them .

we know that the distance between the points (x₁ , y₁) and (x₂ , y₂) is calculated using the distance formula

distance = √(y₂ - y₁)² + (x₂ - x₁)²

Substituting the values of the points , we get

distance = √(0 - 4)² + (1 -(-5))²

= √(-4)² + (1 + 5)²

= √16 + (6)²

= √16 + 36

= √52

= 7.21111

≈ 7.21

Therefore , The distance between the points (-5,4) and (1,0) is  7.21  .

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Answer:

nice pfp also 2507.99

Step-by-step explanation:

you would find out 3/5ths of the amount of money she earned then multiply 20 by 2 then take that away from whatevers left from paying bills then subtract 12.99 from the 2520.98 you got after paying for the shirts leaving you with 2507.99

Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

Step-by-step explanation:

m∠QDC = 5*12 + 17 = 77

You could use the lines by comparing the steepness of the lines. The one that has more slope is the one that would have the greater speed.

To compare the speed of the two objects, we can look at the steepness of their respective lines. The steeper the line, the faster the object is moving. If the lines have the same slope, then the objects are moving at the same speed.

To determine whether the speed of either object changed during the time shown on the graph, we need to look for changes in the slope of the lines. If the slope of a line becomes steeper, then the object is accelerating and its speed is increasing. If the slope becomes less steep, then the object is decelerating, and its speed is decreasing. If the slope remains constant, then the object is moving at a constant speed.

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Answer:

c=a2+b2=102+172≈19.72308

Step-by-step explanation:

a calculator bro its easy

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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The measure of the arc or angle is:

m∠NLM = 60 deg

From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).

Thus, we can say:

arc NM + arc ML = 180°

(3x + 21) + (8x + 16) =  180°

11x + 37 = 180

11x = 180 - 37

11x = 143

x = 143/11

x = 13

arc NM = 8x + 16

put x = 13:

arc NM = 8(13) + 16 = 120°

Recall that:

The measure of inscribed angle is half the measure of its intercepted arc. That is:

m∠NLM = 1/2 * 120°

m∠NLM = 60°

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Answer:

(1) Alternate Hypothesis.

(2) Null Hypothesis.

(3) Alternate Hypothesis.

(4) Null Hypothesis.

(5) Alternate Hypothesis.

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

(1)

The hypothesis statement is:

"The number of hours that grade-school children spend doing homework predicts their future success on standardized tests."

According to the hypothesis statement, we known that the test to be performed is for the relationship between the number of hours that grade-school children spend doing homework and their future success on standardized tests.

So, the null hypothesis here will be that there is no relation between the two variables, or the number of hours that grade-school children spend doing homework does not predicts their future success on standardized tests.

Thus, the provided statement is a Alternate hypothesis.

(2)

The hypothesis statement is:

"King cheetahs on average run the same speed as standard spotted cheetahs."

According to the hypothesis statement, we known that the test to be performed is for the difference between the mean running speed of king cheetahs and spotted cheetahs.

The statement provided is a statement of no difference, i.e. there is no difference between the mean running speed of king cheetahs and spotted cheetahs.

Thus, the provided statement is a Null hypothesis.

(3)

The hypothesis statement is:

"The mean length of African elephant tusks has changed over the last 100 years."

According to the hypothesis statement, we known that the test to be performed is for the significance of single mean.

The null hypothesis here would be there is no change in the mean length of African elephant tusks over the last 100 years.

Thus, the provided statement is a Alternate hypothesis.

(4)

The hypothesis statement is:

"The risk of facial clefts is equal for babies born to mothers who take folic acid supplements compared with those born to mothers who do not."

According to the hypothesis statement, we known that the test to be performed is for the difference between the proportion of risk of facial clefts for babies born to mothers who take folic acid supplements and with those born to mothers who do not.

The null hypothesis here would be that there is no difference between the two risk proportions.

Thus, the provided statement is a Null hypothesis.

(5)

The hypothesis statement is:

"Caffeine intake during pregnancy affects mean birth weight."

According to the hypothesis statement, we known that the test to be performed is for the significance of single mean.

The null hypothesis of this test will be that the mean birth weight is not affected by the caffeine intake during pregnancy.

Thus, the provided statement is a Alternate hypothesis.

The given statement that, decimal, fraction, and percent can all represent the same values is True.

Verification of the True Statement:

The ratio of two numbers results in a fraction which are often rational numbers (often integers). As an illustration, 11/59 is a fraction. Typically, absolute values for fractions should be larger than 0 and less than 1. A mixed fraction equivalent to 1 3/4 is 7/4.

A fraction stated in tenths are known as a decimal (or tenths of tenths, etc.). The decimal equivalent of one fourth, or 1/4 as a fraction, is 0.25 (which equals 25/100). (Remember that 1/100 is just a tenth of a tenth.)

Percentage (percent) is a decimal fraction multiplied by 100. Therefore, 0.25 is equivalent to 25 percent, for instance. The ratio of two numbers results in fractions, which are often rational numbers (often integers).

Let us take a number 3/5, this is a fraction.

Now, if we further divide, 3 by 5, we will get 0.6

This 0.6 is a decimal number, but it still represents the number 3/5

Similarly, it is equivalent to 60 percent which again represent the fraction 3/5 or decimal 0.6.

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In the given inequality 14 + x > 5, the graph represents the value of x greater than -9.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When the inequality is plotted on the graph it represents that the value of x is greater than -9.

The graph of the inequality  14 + x > 5, is attached with the answer below.

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Answer:

543.47826087

Step-by-step explanation: