Mathematics College

Use the information provided to find the vertex form equation of each parabola:-2x^2 + 36x -171

Answers

Answer 1

The vertex form of a parabola is expressed as

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

where

a is the leading coefficient

h and k are the horizontal and vertical coordinates of the vertex.

Recall, the general expression for a quadratic equation is

y = ax^2 + bx + c

By comparing with the given equation,

a = - 2, b = 36, c = - 171

The formula for the x coordinate of the vertex is

x = - b/2a

x = - 36/(2 * - 2) = - 36/- 4 = 9

Substituting x = 9 into the equation, we have

y = - 2(9)^2 + 36(9) - 171

y =

Related Questions

Find the measure of <1 and <2

Answers

Answer:

150°

Step-by-step explanation:

Both the measure of <1 and <2 are 150°

Which probability distribution table corresponds with this frequency distribution table?

Answers

The probability distribution table corresponds with the given frequency distribution table is option (D)

Probability is defined as the ratio of number of favorable outcome to the total number of outcomes. The value of the probability varies from 0 to 1.

Probability = Number of favorable outcomes / Total number of outcomes

The total frequency = 3+7+2+3+5

= 20

The probability of each outcomes

Substitute the values in the equation

p(1) = 3/20 = 0.15

p(2) = 7/20 = 0.35

p(3) = 2/20 = 0.1

p(4) = 3/20 = 0.15

p(5) = 5/20 = 0.25

Hence, the probability distribution table corresponds with the given frequency distribution table is option (D)

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Solve The Equation
-1.9 = 0.5(p +1.7)

Whoever answer first gets brainliest!

Answers

Answer:

p=-5.5

Step-by-step explanation:

To solve this equation, use the distributive property. Isolate the difference between the numbers from one side of the equation.

Distributive property:

A(B+C)=AB+AC

-1.9 = 0.5(p +1.7)

First, switch sides.

0.5(p+1.7)=-1.9

Divide by 0.5 from both sides.

[tex]\sf{\dfrac{0.5\left(p+1.7\right)}{0.5}=\dfrac{-1.9}{0.5}}[/tex]

Solve.

-1.9/0.5=-3.8

p+1.7=-3.8

Then, you subtract by 1.7 from both sides.

p+1.7-1.7=-3.8-1.7

Solve.

Add or subtract the numbers from left to right.

-3.8-1.7=-5.5

[tex]\rightarrow \boxed{\sf{p=-5.5}}[/tex]

Therefore, the correct answer is p=-5.5.

I hope this helps, let me know if you have any questions.

The value of p on the equation - 1.9 = 0.5(p +1.7) is - 5.5.

What is an equation?

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for p in the equation - 1.9 = 0.5(p +1.7).

0.5(p + 1.7) = - 1.9

First, we'll distribute the terms.

0.5p + 0.85 = - 1.9.

0.5p = - 1.9 - 0.85.

0.5p = - 2.75.

p = - 2.75/0.5.

p = - 5.5

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8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R

Answers

The triangles PTS and POR are similar, so we can take the ratios of the side to order

[tex]\frac{PT}{ST}=\frac{PQ}{SQ}[/tex]

[tex]\frac{36}{30}\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}[/tex]

[tex]\begin{gathered} \text{cross multiplying} \\ \\ 30\text{ (6x - 2) = 30 (5x + 13)} \\ \\ \text{Expanding the parenthesis} \\ \\ 30\text{ x 6x - 30 x 2 = 30 x 5x + 30 x 13} \\ \\ 180x\text{ -60 = 150x + 390} \end{gathered}[/tex]

We can then solve for x by collecting like terms

180x - 150x = 390 + 60

30x = 450

Divide both sides by 30

x = 450/ 30

x = 15

Solve systems using inverses:
Solve the system:
4x - 5y + z = 9 6X + 8y - Z=27 3x – 2y + 5z = 40
(?, ?, ?)

Answers

Answer:

Step-by-step explanation:

4 x - 5 y + z = 9z = - 27 + 6 x + 8 y3 x

Find each value.Show calculations for each problem

Answers

In the given expression :

[tex]a_n=-8n[/tex]

we need to find the value of n at which, an = -24

[tex]\begin{gathered} \text{Substitute the value of a}_n=-24\text{ in teh express}ionofa_n \\ a_n=-8n \\ -24=-8n \\ or \\ -8n=-24 \\ \text{Dividing both side by (-8)} \\ \frac{-8n}{-8}=\frac{-24}{-8} \\ n=3 \end{gathered}[/tex]

Thus, at n=3, the an = -24

Suppose you buy a phone for $750 and sign up for a one-year service contract that costs $110 per month. What is the total cost you will pay over the length of the contract?

Answers

Answer:

$2070

Step-by-step explanation:

→ Find the total cost of 12 months

750 + ( 12 × 110 ) = 2070

ANSWER:
$1,320

EXPLANATION:
If the contract is only one year and it is $110 per month in that year, we know that there are 12 months in a year, so our work should look like, 110 x 12 = 1,320

Have an AWESOME day! :)

Question 4c. Want to clarify something I want to ask right why does it become 3y square +6y-y-2

Answers

Answer:

Explanation:

Given the expression:

[tex]3y^2+5y-2[/tex]

We want to write the given expression in the form:

[tex](ay-b)(y+c)[/tex]

That is, to factorize the expression.

When an expression is to be factorized, follow the steps below:

Step 1: Multiply the coefficient of x² and the constant.

[tex]-2\times3y^2=-6y^2[/tex]

Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6

[tex]\begin{gathered} 6y\times-1y=-6y^2 \\ 6y+-y=5y \end{gathered}[/tex]

Step 3: Rewrite the middle term, 5y with those numbers.

[tex]\begin{gathered} 3y^{2}+5y-2 \\ =3y^2+6y-y-2 \end{gathered}[/tex]

Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.

[tex]\begin{gathered} =3y(y+2)-1(y+2) \\ =(3y-1)(y+2) \end{gathered}[/tex]

The expression below is scientificnotation for what number?9.9x10^7

Answers

To change the number from scientific notation to normal number multiply 9.9 by 10^7

[tex]9.9\times10,000,000=99,000,000[/tex]

The number is 99,000,000

Reduce 36/60 to simplest terms

Answers

Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

Answer:

3/5

Step-by-step explanation:

Match each word with the phrase that best defines it.
insurance
liability
compensate
premium
deductible
to pay the value of something that has been
lost or stolen
the amount of money a consumer must pay
an insurance company
a responsibility to pay for or to fix a problem
a financial service that protects a consumer
in exchange for payments
the money a consumer must pay for a claim
before the policy takes over

Answers

Insurance - A financial service that protects a consumer

Liability - A responsibility to pay for or to fix a problem

Compensate - To pay the value of something that has been lost or stolen

Premium - The amount of money a consumer must pay an insurance company

Deductible - The money of a consumer must pay for a claim before the policy takes over

Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses.

Liability is a general phrase that refers to many types of coverages to assist in defending you or your company in the event that a claim or lawsuit is made against you or your organization.

The amount that the insurance provider has agreed to pay for insured losses that are mentioned in your policy is referred to as "compensation."

You pay a premium when you purchase an insurance policy. Your recurring payments for many popular insurance products, such as life, car, business, homeowners, and renters, are known as premiums.

The sum of money you must contribute to an insured loss is known as a deductible.

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Let 0 be an angle in quadrant

Answers

If angle theta is given as;

[tex]\cos \theta=-\frac{4}{5}[/tex]

And angle theta is in the third quadrant, then we can find the value of y by using the pythagoras' theorem as follows;

[tex]\begin{gathered} r^2=x^2+y^2 \\ When\text{ cos}\theta=-\frac{4}{5},\text{ and cos}\theta=\frac{x}{r} \\ \text{Then,} \\ x=-4,r=5 \\ \text{Therefore,} \\ 5^2=-4^2+y^2 \\ 25=16+y^2 \\ \text{Subtract 16 from both sides;} \\ 9=y^2 \\ \text{Take the square root of both sides;} \\ y=3 \end{gathered}[/tex]

Note also that;

[tex]\sin \theta=\frac{y}{r}[/tex]

However, the angle theta is in the third quadrant where y is also negative. Therefore, sin theta would be;

[tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=-\frac{3}{5} \end{gathered}[/tex]

Note also that cosec theta is given as;

[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \csc \theta=\frac{1}{-\frac{3}{5}} \\ \csc \theta=-\frac{5}{3} \end{gathered}[/tex]

Note also that, tan theta is given as;

[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]

Therefore, we would have;

[tex]\begin{gathered} \tan \theta=-\frac{3}{5}\text{ / -}\frac{4}{5} \\ \tan \theta=-\frac{3}{5}\times-\frac{5}{4} \\ \tan \theta=\frac{3}{4} \end{gathered}[/tex]

ANSWER:

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The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!!)

Answers

We can see that the value of k is -3, then the line is:

y = -3*x + 4

By finding two points of the line, we can graph the line like in the image you can see below.

How to sketch a graph of the line?

Here we have the following linear equation:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.

-2 = k*2 + 4

Solving this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

So the value of k, the slope of the line, is k = -3.

Then the line is:

y = -3*x + 4

If we evaluate in x = 1, we get:

y = -3*1 + 4 = 1

So, at this point we know that the line passes through points (1, 1) and (2, -2).

Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.

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Solve the inequality & graph the answer.
3)>2
14
A) v> 280:
10
B) v<--:
7
C) v> -34:
D) v<-34:
11110
276 278 280 282 284 286
7
O
0 2
++++++ +0
-40 -38 -36 -34 -32 -30
-40 -38 -36 -34 -32-30

Answers

Answer:

Solve the inequality & graph the answer. 3)>2 14 A) v> 280: 10 B) v<--: 7 C) v> -34: D) v<-34: 11110 276 278 280 282 284 286 7 O 0 2 ++++++ +0 -40 -38 -36 -34 -32 -30 -40 -38 -36 -34 -32-30

Step-by-step explanation:

5. If c = -1 and d = -2, what is the value of the expression 2c²d-3cd?a. -10b. -24c. 2d. 10e. -2

Answers

Recall that to evaluate an expression at some given values, we substitute each variable with the corresponding given value.

Evaluating 2c²d-3cd at c=-1 and d=-2 we get:

[tex]2(-1)^2(-2)-3(-1)(-2).[/tex]

Simplifying the above result we get:

[tex]\begin{gathered} 2(1)(-2)-3(-1)(-2), \\ -4-6, \\ -10. \end{gathered}[/tex]

Answer: Option a.

Answer:

-10

Step-by-step explanation:

Substitute variable values for variables.

[tex]2(-1)^2(-2) - 3(-1)(-2)[/tex]

Simplify

2(1)(-2) - 6

-4 - 6

-10

Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, and D as the possible answers.

Answers

By definition, a sample space is a collection or a set of possible outcomes of a random experiment. In our problem, we have four different outcomes. A, B, C and D. This is our sample space

[tex]S=\lbrace A,B,C,D\rbrace[/tex]

2sinxcosx/sin^2x+cos^2x-1=1

Answers

The simplified equation is sin(2x) = 2

How to determine the value of the trigonometry formula?

The trigonometry ratio is given as

2sinxcosx/sin^2x+cos^2x-1= 1

Rewrite the equation of the trigonometry formula properly