a cannonball was launched with an initial upward velocity of 55 feet per second from a tower 28 feet off the ground. The height of the ball above the ground, in feet, can be modeled by an expression having the form -16t^2 + bt + c, where t is the number of seconds since the cannonball was launched.

What is the value of b, the coefficient of t? ___

What is the value of c, the constant term? ___

Therefore, the expression for the height of the ball at time t is ___

Answer:

314.25

Step-by-step explanation:

To find the total of all three checks, we add them together, lining up the decimals

 36.98

  17.27

260.00

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

314.25

The total is 314.25

The base is 11 cm and the height is 8 cm.

Answer:

(-8+i )

Step-by-step explanation:

We'll multiply these 2 binomials like any other pair of binomials: using the FOIL method.

(-3+2i)•(2+i) after being FOILed is:

(-3•2)+(-3•i)+(2i•2)+(2i•i)

this equation simplified equals

-6-3i+4i+2i²

Whenever we see i², we should know that is equals -1, so our equation rewritten again is

-6-3i+4i+(2•-1)

Simplifying that, we get

-6-3i+4i+-2

From here, we just continue to simplify by subtracting  2 from −

6.

−8−3i+4i

Finally, add −3i and 4i to get our answer of

−8+i

Answer:

Step-by-step explanation:

1)

f(x) = x + 4

f(3) = 3 + 4 = 7

g(x) = 12x - 6

g(-1) = 12(-1) - 6 = -12 - 6 = -18

f(3) + g(-1) = 7 + (-18) = -11

2)

f(x) = 2x + 3, g(x) = 4x

f(x) · g(x) = (2x + 3)(4x)             use the distributive property

f(x) · g(x) = (2x)(4x) + (3)(4x)

f(x) · g(x) = 8x² + 12x

3)

f(x) = 2x - 3

f(2) = 2(2) - 3 = 4 - 3 = 1

g(x) = 4x

g(3) = 4(3) = 12

f(2) - g(3) = 1 - 12 = -11

1) Given f(x)=x+4 and g(x)=12x-6, what is f(3)+g(-1)?

C) -11

2) what is f(x).g(x) if f(x)= 2x+3 and g(x)=4x?

C) 8x^2+12

3) f(x)=2x-3 and g(x)=4x what is f(2)-g(3)

B) -11

Answer:

Finance charge =  $2.32

new balance = $201.51

Step-by-step explanation:

Finance charge = Previous balance×Periodic percentage rate

The previous balance is 199.19

The annual percentage rate is 0.14. Therefore, the periodic percentage rate is; (0.14/12)

Finance charge = 199.19 * (0.14/12)

                           = 2.3239 = $2.32

new balance = previous balance + finance charge

                      = 199.19 + 2.32

                      = $201.51

You start by distributing the 5x, so that it’s 5x(2x) and 5x(3y). That becomes 10x^2 and 15xy. Put it back, and it’s 10x^2 - 15xy.

Expand

5x × 2x + 5x × -3y

Rake out the constants

(5 × 2)x + 5x × -3y

Simplify 5 × 2 to 10

10x + 5x × -3y

Use the product rule: x^ax^b = x^a + b

10x^2 + 5x × -3y

Simplify 5x × -3y to -15xy

= 10x^2 - 15xy

Answer:

9

Step-by-step explanation:

To complete the square, divide the coefficient of the b term 6x in two. This becomes -6/2=-3. Now square the number -3 and it becomes 9. To complete the square add 9 to both sides.

Answer:

9

Step-by-step explanation:

[tex]x^2-6x = 5\\[/tex]

We know the binomial formula: [tex](a-b)^2 = a^2 -2ab + b^2[/tex]

Let's consider 6x = 2ab, we know a is our first term - x;

6x = 2axb

6 = 2b

b = 3

So to make a perfect square, we need to add [tex]b^2[/tex] to both sides

[tex]x^2 - 6x + 3^2 = 5 + 3^2\\x^2 - 6x + 9 = 5 + 9\\(x-3)^2 = 14[/tex]

Answer:

- 1/5

Step-by-step explanation:

Slope of a line passing through two points can be calculated as:

[tex]\text{slope}=\frac{\text{rise}}{\text{run}} \\\\ \text{slope}=\frac{\text{Difference of y coordinates}}{\text{Difference of x coordinates}}[/tex]

The given points are (-2, -1) and (8, -3). Using the values in above formula, we get:

[tex]\text{slope}=\frac{-3-(-1)}{8-(-2)}\\\\ \text{slope}=\frac{-3+1}{8+2}\\\\ \text{slope}=\frac{-2}{10}\\\\ \text{slope}=\frac{-1}{5}[/tex]

Thus the slope of the line through the given points is -1/5. So 2nd option gives the correct answer

Answer:

The correct answer is second option

-1/5

Step-by-step explanation:

Points to remember

The slope of line passing through (x₁, y₁) and (x₂, y₂) is given by,

Slope = (y₂ - y₁)/(x₂ - x₁)

To find the slope of given line

Here, (x₁, y₁) = (-2, -1) and (x₂, y₂) = (8, -3)

Slope = (y₂ - y₁)/(x₂ - x₁) = ( -3 - - 1)/(8 - -2)

 = (-3 + 1)/(8 + 2) = -2/10

 = -1/5

Therefore the correct answer is second option -1/5

Answer:

Option C. AB/BC=CD/DE

Step-by-step explanation:

we know that

In the triangle ABC the slope is equal to

m=AB/BC -----> equation A

In the triangle CDE the slope is equal to

m=CD/DE -----> equation B

Remember that the slope of a line is a constant

so

equate equation A and equation B

AB/BC=CD/DE

Answer:

C is the answer

Step-by-step explanation:

ANSWER

Average Rate of Change

[tex] = \frac{f(b) - f(a)}{b - a} [/tex]

EXPLANATION

To find the average rate of change of y=f(x) from x=a to x=b means finding the slope of the secant line joining the points

(a,f(a)) and (b,f(b))

The slope of the secant line joining these points is

[tex] = \frac{f(b) - f(a)}{b - a} [/tex]

This gives the average rate of change of the function.

To find the average rate of change of a function, you need to subtract the function values at two different points and divide by the difference in the input values.

To find the average rate of change of a function, you need to calculate the change in the function's output divided by the change in its input. This can be done by subtracting the function values at two different points and dividing by the difference in the input values. For example, if you have a function f(x) and want to find the average rate of change between x = a and x = b, you would use the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

This will give you the average rate at which the function is changing over the interval from a to b.

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Answer:

18 is the GCF

Step-by-step explanation:

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Answer is provided in the image attached.

Hey

Since a coin has 1/2 chances on both sides and a six-sided cube has 1/3 chance of getting a less than three, multiply those chances and you will get the probability of 1 / 6

So the answer is option A, [tex]\frac{1}{6}[/tex]

The probability that the coin lands on tails in the outcome on the number cube is a number less than 3 is 1/6.

Given:

Find:

Solution:

A coin is tossed and a six-sided cube is rolled.

We have to find the probability of getting a tail on the coin and a number less than 3 in the cube.

The probability of getting a tail in the coin is 1/2.

The probability of getting a number less than 3 is 2/6 = 1/3.

Probability of getting a tail on the coin and a number less than 3 on a cube is 1/2*1/3 = 1/6.

Hence, The probability that the coin lands on tails in the outcome on the number cube is a number less than 3 is 1/6.

Therefore, Option A is the correct answer.

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it might be wrong but i am pretty sure it’s right but 537.15

Answer:

The estimated volume would be 594 feet.

Step-by-step explanation:

Well, since this is an estimate you should round all your numbers and multiply them together.

5.6 is rounded to 6

8.8 is rounded to 9

and 10.9 is rounded to 11

Multiply 6 and 9 and you get 54. Then multiply 54 by 11 and that gives you 594.

- Your freshman friend :)

Answer:

1 → D

2 → A

3 → B

4 → C

Step-by-step explanation:

You need to remember that:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}\\\\sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

Then:

-For angle B, you can identify in the figure that:

[tex]opposite=b\\adjacent=c\\hypotenuse=a[/tex]

Then, you can substitute values and get:

[tex]cosB=\frac{c}{a}[/tex]

[tex]sinB=\frac{b}{a}[/tex]

[tex]tanB=\frac{b}{c}[/tex]

- For angle C, you can identify in the figure that:

[tex]opposite=c\\adjacent=b[/tex]

Therefore, substituting values, you get that:

[tex]tanC=\frac{c}{b}[/tex]

Answer:

1. cosB = c/a

2. tanC = c/b

3. sinB = b/a

4. tanB = b/c

Step-by-step explanation:

Plato Answer!!

Ellipse is your answer, because if you plug the equation into a graphing calculator and identify the conic, the term ellipse is given-

Answer:

D

Step-by-step explanation:

If x° and y° are complementary angles, then x°+y°=90° and

[tex]\sin x^{\circ}=\cos y^{\circ} \ [\text{Cofunctions rule}][/tex]

Check all options:

A. 18°+72°=90°, so

[tex]\sin 18^{\circ}=\cos 72^{\circ}\ [\text{true}][/tex]

B. 55°+55°=110°, these angles are not complementary and

[tex]\sin 55^{\circ}\neq\cos 55^{\circ}\ [\text{false}][/tex]

C. 72°+18°=90°, so

[tex]\sin 72^{\circ}=\cos 18^{\circ}\ [\text{true}][/tex]

D. Both A and C are true.

The payment that is the same amount each time that it is paid is given as follows:

B) PMI.

The monthly payment formula is defined as follows:

[tex]PMI = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed and defined as follows:

The monthly payment is calculated before a purchase is made, meaning that it assumes the same amount each time it is paid, and thus option B is the correct option in this problem.

The principal is a one time payment, while taxes and interest vary over time.

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In a thirty-year fixed-rate mortgage, the principal portion of the payment is the same amount each time it is paid, while the interest decreases over time, thus maintaining a consistent total payment amount.

The student is asking which of the following payments is the same amount each time it is paid: Property Taxes, PMI (Private Mortgage Insurance), Interest, or Principal. The answer is Principal in the context of a thirty-year fixed-rate mortgage.

This type of mortgage has a consistent monthly payment that includes both the principal and the interest. Early in the loan, the payment consists of more interest than principal, but as the loan matures, the portion of the payment that goes towards the principal increases while the interest portion decreases.

This ensures that the total payment amount remains the same throughout the life of the loan.

Example of Principal Payment Over Time

If you have a thirty-year fixed-rate mortgage, your monthly payment is calculated at the outset to ensure that each payment is the same, even though the principal paid increases over time as the outstanding balance of the loan decreases.

Answer:

Third Option

[tex]P(x\geq 9) =0.212[/tex]

Step-by-step explanation:

Note that the variable x is a discrete random variable that can be modeled using a binomial distribution. For a discrete random variable the probability that x is greater than a number b is:

[tex]P(x\geq b) =\sum_{x=1}^{b}{P(x)} = P(1) + P(2) + P(3) + ... + P(b)[/tex]

In this case we look for the probability of selecting 9 or more girls

This is:

[tex]P(x\geq 9) =\sum_{x=9}^{14}{P(x)} = P(9) + P(10) + P(11) +P(12)+ P(13) + P(14)[/tex]

Looking in the attached table we have to

[tex]P(x\geq 9) =0.122 + 0.061 + 0.022 + 0.006+ 0.001 + 0[/tex]

[tex]P(x\geq 9) =0.212[/tex]

Answer: It would be both because there is no number to it

Step-by-step explanation:

For example if there were 15 red crayons and 10 yellow ones it would be the red crayons because there is a bigger amount of them in the bag but because there is no number you have the same possibility of picking both.  

To estimate the probability of selecting a red crayon OR a yellow crayon from the bag, calculate the individual probabilities of each color and use the OR probability formula to find the estimate.

Estimate for the probability of selecting a red crayon OR a yellow crayon from the bag:

I believe you just multiply 150x3 and get 450

A basketball court that is 150 feet long is equivalent to 50 yards, calculated by dividing the total length in feet by the conversion factor of 3 feet per yard.

To determine how many yards make up a basketball court that is 150 feet in length, we use the conversion factor that 1 yard equals 3 feet. Therefore, we divide 150 feet by 3 to convert feet to yards:

150 feet / 3 = 50 yards.

Thus, a basketball court that is 150 feet long is 50 yards long. This is a calculation often used in converting units, an essential skill in mathematics and various practical contexts, such as sports, construction, and everyday measurements. Knowing how to convert between feet and yards can be useful in understanding the dimensions of a playing field, like a basketball court or football field.

The answer is B (6x-5)(x+2)

Answer:

B) (6x-5)(x+2)

Step-by-step explanation:

Distribute each until you find the answer:

A) 6x^2+17x+10

B) 6x^2+7x-10

Answer:

B:  The salaries

Step-by-step explanation:

B:  The salaries.  While not strictly continuous, the range of salaries is closest of these four choices to being continuous.  In contract, "number of employees," "number of printers," and "number of phone calls" are all discrete random variables.

The statement at D "The number of phone calls made daily from an office" is a continuous random variable.

A random variable is defined for all the values in an interval or between two values.

A. The number of employees in an office.

It is a constant value. It's not a continuous random variable.

B. The salaries of employees in an office

It is a constant value. It has only one value means represented in a closed interval. So, not a continuous random variable

C. The number of printers in an office

This is also a constant value. So, not a continuous random variable

D. The number of phone calls made daily from an office

The number of phone calls made daily, may not be the same and are continuous. If the interval of a month, there may be a different number of phone calls. So, it is a continuous random variable.

So, option D is correct.

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Answer:

78°

Step-by-step explanation:

The angular distance of an arc is twice the angle that forms it if that angle lies of the edge of the circle.

By this, Arc AK has angular distance 158°.

Arc JL = 202°.

Arc KL = 122°.

By subtracting these we get 80° for Arc JK.

Arc KA = 158°.

Arc AJ = KA - JK

AJ = 158-80

AJ = 78°

Answer:

[tex]\large\boxed{D.\ y=\dfrac{5}{7}x+10}[/tex]

Step-by-step explanation:

[tex]Ax+By=C\qquad\text{it's a standard form of an equation of a line}\\\\\\y=mx+b\qquad\text{it's a slope-intercept form of an equation of a line}\\\\\text{We have the equation in the standard form:}\\\\5x-7y=-70\\\\\text{Convert it to the slope - intercept form:}\\\\5x-7y=-70\qquad\text{subtract 5x from both sides}\\\\-7y=-5x-70\qquad\text{divide both sides by (-7)}\\\\y=\dfrac{5}{7}x+10[/tex]

132+396=528 is 100%

132 is ?%

?=132x100/528=25%

Answer is 25% ate CFA

Answer:

25%

Step-by-step explanation:

Although the problem statement doesn't say so, you have to find the total number of people who bought hamburgers.  It's 132 + 396, or 528.

132 people out of a total of 528 people ate at Chick-a-Fil.  This comes to

132

------- = 0.25, or 25%

528

You must write out your conclusion:  "25% of these people ate at Chick-a-Fil.

7.44÷24=c because to find the unit price you need divide 7.44 by 24

Answer:

c=0.31b

Step-by-step explanation:

$7.44 divided by 24 = 0.31

Answer: C. [tex]\dfrac{6}{336}[/tex]

Step-by-step explanation:

Given: The number of different prizes = 3

The number of people entered the drawing = 8

The total number of ways to award the prizes. = 336

Now, The number of ways to select for 3 prizes, such that  you win first prize and your mom wins second prize is given by :-

[tex]1\times1\times(8-2)=6[/tex]

Hence, the probability that you win first prize and your mom wins second prize=[tex]\dfrac{6}{336}[/tex]

Answer:

the answer is D.  576 square cm

Step-by-step explanation:

Find the area of one of the rectangular faces using the formula, Area = lw.

A = (12 cm) (6 cm)

A = 72 square cm

Since there are 4 rectangular faces, multiply the area of one rectangular face by 4 to get a total of 288 square cm.

The area of one of the congruent squares is 12 cm × 12 cm, or 144 cm2. Multiply 144 cm2 by 2 to get a total of 288 cm2.

To find the surface area of the rectangular prism, add the area of the four rectangular faces to the area of the two square faces.

288 square cm + 288 square cm = 576 square cm

Answer:

sin(62)=18/x

Step-by-step explanation: sine = opp/hyp

Answer: Third option.

Step-by-step explanation:

Given the right triangle in the figure attached, you know that, for the known angle of 62 degrees, the lenght of the opposite side is 18 and the hypotenuse is "x"

Therefore, you need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Then, having that:

[tex]\alpha=62\°\\opposite=18\\hypotenuse=x[/tex]

 You need to substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex], then  you get that the correct trigonometry formula to use to solve for "x" is:

 [tex]sin(62\°)=\frac{18}{x}[/tex]

Answer:

The surface area is [tex]404.8\ in^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the figure is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the trapezoidal face

P is the perimeter of the trapezoidal face

L is the length of the figure

Find the area of B

[tex]B=\frac{1}{2}(15+5)8\\ \\B=80\ in^{2}[/tex]

Find the perimeter P

[tex]P=(8+5+12.8+15)=40.8\ in[/tex]

we have

[tex]L=6\ in[/tex]

substitute the values

[tex]SA=2(80)+(40.8)(6)=404.8\ in^{2}[/tex]