Use these functions to answer the questions.
f(x)=(x+3)2−1
g(x)=−2x2+8x+3
h(t)=−16t2+28t
Part A What are the x- and y-intercepts of the graph of the function f(x)? Identify the coordinates of any maxima or minima of the function. Explain your answers. Part B Write the function g(x) in the form y=a(x−h)2+k . Write the equation for the line of symmetry for the graph of g(x). Show all your work and explain your answer. Part C The function h(t) gives the approximate height, in feet, of a dolphin's jump out of water, where t represents the time,

Answer:

The answer is D) $897.12

Step-by-step explanation:

3 years = 36 months

173.33 * 36 = 6239.88

5 years = 60 months

118.95 * 60 = 7137.00

7137.00 - 6239.88 = 897.12

The value of x is -3 and the solution to this system of equations is (-3 , 7).

When a number of variables are involved, the system of equation is generated. The system of equation has been the set of simultaneous equations as well.

Given :

[tex]y = -3x-2[/tex]   ----  (1)

[tex]y=7[/tex]  -----  (2)

Solution :

From, equation (1) and (2) we get the value of x to be:

[tex]7=-3x-2[/tex]

[tex]9=-3x[/tex]

[tex]x=-3[/tex]

Therefore, the value of x is -3.

For more information, refer the link given below

https://brainly.com/question/13911928

Answer:

A is rational, but B is irrational.

Step-by-step explanation:

Answer: A.) Point.

Step-by-step explanation:

Answer:

Mucus

Step-by-step explanation:

Answer:

1)  Area of ΔABD = Area of ΔACD and

2)  Area of ΔABO = Area of ΔCDO

Step-by-step explanation:

1) In the given trapezoid ABCD,

AD || BC

Triangles ΔABD and ΔACD lie on the same base AD and lie between the parallel lines AD and BC.

Hence, they are equal in area.

Therefore, Area of ΔABD = Area of ΔACD.

2) From 1), we have

Ar (ΔABD) = Ar(ΔACD)

Subtract Ar (ΔAOD) from both sides,

Ar (ΔABD) - Ar (ΔAOD) = Ar(ΔACD) - Ar (ΔAOD)

Ar (ΔABO) = Ar (ΔCDO)

The other monomial must have the factors of 3x^2y, with the possibility of having higher powers of y, but not lower, as this would change the GCF. An example of a compatible monomial with 3x^4y is 3x^2y^2.

The question is asking for the other monomial given that the greatest common factor (GCF) of two monomials is 3x^2y and one of the monomials is 3x^4y. Since the GCF is the product of the lowest powers of common factors in the monomials, the other monomial must have at least the factors 3, x^2, and y to a certain power. It can have these factors to higher powers as well, but not to lower powers, since it would then alter the GCF.

An example of another monomial that could be paired with 3x^4y is 3x^2y^2, because it has the factors of the given GCF with potentially higher powers, without affecting the GCF. Therefore, any monomial of the form 3x^2y^n (where n is greater than or equal to 1) could be the other monomial.

The height formed by this 25 foot ladder that leans against a wall is 24 feet.

Given the following data:

Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.

Mathematically, Pythagorean's Theorem is given by this formula:

[tex]h^2 = a^2 + b^2[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]h^2 = a^2 + b^2\\\\25^2 = 7^2 +b^2\\\\625=49+b^2\\\\b^2=625-49\\\\b=\sqrt{576}[/tex]

b = 24 feet.

Read more on Pythagorean Theorem here: https://brainly.com/question/16176867

Answer: x = 17.5

Step-by-step explanation:

You're using interior angles

Use the law of cosine: c^2 = a^2 +b^2 - 2ab times cos (C)

h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80) so h = 11.67

11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)

sin -1 ((8 times sin (80)) over 11.67)  is equal to S

sin -1 ((10 times sin (80)0 over 11.67)) is equal to T

t over sin (T) = s over sin (S)

t = 10 + x

s = 8 + 18 = 22

10 + x over sin (57.54) = 22 over sin (42.45) 

x = 22 times sin (57.54) over sin (42.45) and next to this is -10

the answer of x = 17.50

Hope this helps, have a BLESSED and wonderful day! :-)

-Cutiepatutie <3

Given a circle with a circumference of 21.4 inches, first calculate the radius using the circumference formula, then use the radius to calculate the circle's area, which results in approximately 36.29 square inches.

This question involves determining the area of a circle given its circumference. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a constant (approximated to 3.14). Given that the circumference is 21.4 inches, we can rearrange this formula to find the radius (r = C/2π), giving us a radius of approximately 3.4 inches.

Now, knowing the radius, we can use it to find the area using the formula for the area of a circle, which is A = πr². Plugging in the values, we find that the area is approximately 36.29 square inches.

https://brainly.com/question/28642423

#SPJ12

Here, we need to calculate the expected number of students who are liberal arts major.

It is given that, 60 out of 65 students are liberal arts major.

So, we will calculate the percentage of liberal arts major from the total.

Percentage of liberal arts major = [tex] \frac{Number of liberal arts major}{Total students} [/tex] X 100

Percentage of liberal arts major = [tex] \frac{60}{65} [/tex] X 100

Percentage of liberal arts major = 92.31 %

Now, we will calculate for 8,943 liberal arts majors -

In total students of 8,943, liberal arts majors = 92.31 % X 8,943

In total students of 8,943, liberal arts majors =8,256 students (approximately)

A) This equation has only one solution. B) The solution would be x = 2.

For that ,we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

Given equation is 5(2x − 3) = 5

By solving further,

10x -15 = 5

10x = 20

x = 2

A) This equation has only one solution.

B) The solution would be x = 2

Learn more about the case of solutions here:

https://brainly.com/question/26254258

#SPJ2

Final answer:

The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.

Explanation:

To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.

Final answer:

The average of three numbers that sum to 144 is 48, found by dividing 144 by 3.

Explanation:

The average of three numbers is the sum of those numbers divided by three. In this case, if the sum of three numbers is 144, then the average can be found by dividing 144 by 3. Calculating this, we get the average, which is 48 (144 ÷ 3 = 48). Hence, the average of the three numbers is 48.

The probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

To find the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5.

Since, From 1 to 5, there are three numbers 1, 3, 5 are odd numbers.

Hence, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is,

P = 3/5

Change into percent as;

P = 3/5 x 100%

P = 60%

Thus, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ3

Answer:

6 checks

Step-by-step explanation:

The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

For this case, we're specified that:

The spinner has 10 parts.

Thus, the probability of getting the spinner fall on treehugger is 3/10 (three favorable parts of spinner to ten total parts, all parts assumingly equally probable and spinner assumingly not falling in the mid of two parts).

20 checks, all will be accompanied with 20 spins, all independent of each other.

Let X = total number of times the spinner falls on Treehuggers

And let Success for a spin = It landing on Treehugger

Failure for a spin = It not landing on Treehugger

n = 20, so we get:

[tex]X \sim B(n=20,p=0.3)[/tex]

The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign = expected number of successes in those 20 spins =  the expected number of values of X.

Since X follows a binomial distribution, we get:

[tex]E(X) = np = 20 \times 0.3 = 6[/tex]

Thus, the expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

Learn more about binomial distribution here:

https://brainly.com/question/13609688

Answer: (x+b) (a+2y)

Step-by-step explanation:

ax+ab+2by+2xy

split the equatuion in half

1.  ax+ab                    2.     2by+2xy

        gcf=a                          gcf=2y

        ax/a=x                        2by/2y= b  

        ab/a=b                        2xy/2y= x

a(x+b)                                 2y(x+b)

          Answer :(x+b)(a+2y)