Respond to all of the questions within the topic (see that there are six questions below). 1. Explain how you can determine if the parabola opens up or down by simply examining the equation. 2. Give an example of a quadratic function with the given characteristics: its graph lies below the x-axis. 3. Explain how the number of solutions for a quadratic equation relates to the graph of the function. 4. Explain how you solve an equation by factoring. 5. In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the sqaure? 6. Explain how the discriminant can be used to determine the number of solutions a quadratic equation has.

Answer:

The equation is [tex]x^{2} +2\cdot x + 2 = 0[/tex]-

Step-by-step explanation:

According to the statement, we have a second order polynomial of the form [tex]A\cdot x^{2}+ B\cdot x + C = 0[/tex], whose solutions can be found by Quadratic Formula:

[tex]x_{1,2} = \frac{-B\pm \sqrt{B^{2}-4\cdot A\cdot C}}{2\cdot A}[/tex] (1)

Where [tex]A[/tex], [tex]B[/tex] and [tex]C[/tex] are the coefficients of the polynomial.

If roots are conjugated complex numbers, then:

[tex]B^{2}-4\cdot A\cdot C < 0[/tex] (2)

[tex]B^{2} < 4\cdot A \cdot C[/tex]

If we know that [tex]A = 1[/tex], [tex]C = 2[/tex] and [tex]x_{1,2} = -1\pm i[/tex], then we find that:

[tex]-1\pm i = -\frac{B}{2}\pm \frac{\sqrt{B^{2}-8}}{2}[/tex]

[tex]-2 \pm i\,2 = -B \pm \sqrt{B^{2}-8}[/tex]

By comparing each side, we have the following system of equations:

[tex]-B = -2[/tex] (3)

[tex]\sqrt{B^{2}-8} = 2[/tex] (4)

Whose solution is [tex]B = 2[/tex].

In a nutshell, the equation is [tex]x^{2} +2\cdot x + 2 = 0[/tex]-

Answer:

9;11 is answer

Step-by-step explanation:

number of women=100 - 45 = 55

men; women= 45;55

= 45/55

=9/11

=9;11

Answer:

A.

Hope this helps :D

Answer:

$3.30

Explanation:

15/100 = 0.15

22*0.15 = 3.3

Answer:

Hi! The answer to your question is D. [tex]3.30[/tex]

Step-by-step explanation:

[tex]Price = 22[/tex]

[tex]Discount = 0.15[/tex]

[tex]22 * 0.15 = 3.3[/tex]

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Hope this helps!!

- Brooklynn Deka

Answer:

14 sides

Step-by-step explanation:

The sum of all interior angles of a polygon = (n - 2)180°

2160° = (n - 2)180°

[tex]n - 2 = \frac{2160 \degree}{180 \degree} \\ \\ n - 2 = 12 \\ \\ n = 12 + 2 \\ \\ n = 14[/tex]

Hence, the polygon has 14 sides.

Answer: A

Step-by-step explanation:

The answer is letter A..

Answer:

Step-by-step explanation:

Answer:

- 3.2

Step-by-step explanation:

- 5x + 4 = 20

- 5x = 20 - 4

- 5x = 16

x = 16 / - 5

x = - 3.2

Answer:

Sue has traveled 124 miles.

Step-by-step explanation:

Here, the distance covered by Sue is a fraction of the total distance to be covered.

The total distance to her aunt's = 372 miles

but the gas station is at one-third of the distance to be covered.

Thus,

Miles traveled by Sue = [tex]\frac{1}{3}[/tex] x 372

                                    = 124

Miles traveled by Sue = 124 miles.

Therefore Sue has traveled 124 miles.

Answer: The answer is D

The amount of paper needed to cover the rectangular bulletin board is 1,073 square inches. The correct answer is: D. 1,073 in²

To calculate the amount of paper needed to cover a rectangular bulletin board, we need to find the area of the board.

Given:

Width of the bulletin board = 29 inches

Height of the bulletin board = 37 inches

To find the area, we multiply the width by the height:

Area = Width * Height

Area = 29 inches * 37 inches

Area = 1,073 square inches

Therefore, the amount of paper needed to cover the rectangular bulletin board is 1,073 square inches.

The correct answer is:

D. 1,073 in²

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Knowing how to recognize congruent lines, we have Angles A&H are congruent.

Two line segments are collinear if they lie on a line. Two line segments are congruent when they have equal measures.

Parallel lines are lines in a plane that are always the same distance from each other. Parallel lines never intersect, while perpendicular lines are those that intersect at a right angle (90 degrees).

In this way, we can identify that the only lines that represent a congruent line are lines A and H.

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Answer:

C) x = 3.7

Step-by-step explanation:

sin 41° = x/5.6

0.6561 = x/5.6

x = 3.7

Answer:

$117.25

Step-by-step explanation:

To solve, multiply the interest by the total amount in savings.

You can calculate simple interest in a savings account by multiplying the account balance by the interest rate by the time period the money is in the account. Here's the simple interest formula: Interest = P x R x N. P = Principal amount (the beginning balance).

Brenda get $117.25 as interest from her bank.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Brenda learned that her bank would pay her 5% on her money in her savings account if she had at least $1,000 in it.

Brenda had $2,345 in her savings account.

So, the interest Brenda get

= 2345 x 5/ 100

= 2345 x 0.05

= $117.25

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Answer:

There are 67,600 possible combinations for this vault.

Step-by-step explanation:

First dial: 100 possible values

Second dial: 26 possible values

Third dial: 26 possible values.

How many possible combinations are there for this vault?

Multiplication of these values. So

100*26*26 = 67600

There are 67,600 possible combinations for this vault.

Answer:

2 one

Step-by-step explanation:

"Alternate exterior angles are the pair of angles that lie on the outer side of the two parallel lines but on either side of the transversal line."

YXZ and TUS

Answer:

if the numbers are together

Step-by-step explanation:

63210 is the correct answer friend

hope it helps

I believe it is A and C.

There are 6 slots on the wheel, so both the numbers in A and E can be divided/multiplied to fit this criterion.  For example, 3 times 2 is 6 (the number of gender slots) and 1 times 2 is two, so two out of 6 art teachers will be female.

I hope this helps!!!

Answer:

A = a^2 + b^2 = C^2

P = 144 + 25 = C^2

P = 169

square root 169 = 13

Step-by-step explanation:

[tex]

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<(￣3￣)> the cancel thingy wasn't needed until it's mathematics.

Answer:

[tex]{\huge\pink{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]

[tex] \huge\purple{\boxed{\mathfrak{Thanks}}}[/tex]

Answer:

9

Step-by-step explanation:

5x - 27 / - 3 = - 6

5x - 27 = - 6 x ( - 3 )

5x - 27 = 18

5x = 18 + 27

5x = 45

x = 45 / 5

x = 9

Answer:

B) Yes; POSN~KDAG; scale factor 5:4

Step-by-step explanation:

B) Yes; POSN~KDAG; scale factor 5:4

Same angles (If 3 are the same, the 4th is the same).

Comparing the 4 respective sides:

15/12=5/4

10/8=5/4

7.5/6=5/4

15/12=5/4

Answer:

x + 2 y − 9

Step-by-step explanation:

Answer:

x+2y-9

Step-by-step explanation:

[tex]2x+2y-x-(8+1)\\ 2x-x+2y-9\\ x+2y-9[/tex]

Answer:

[tex] 105 \: {m}^{3} [/tex]

Step-by-step explanation:

Volume of swimming pool

[tex] = 1 \frac{1}{2} \times 10 \times 7 \\ \\ = 1.5 \times 70 \\ \\ = 105 \: {m}^{3} [/tex]

Answer: The volume is 105 m3.

Step-by-step explanation:

V= l*w*h

V= 10* 1 1/2* 7

V= 105

Answer:

56,161

Step-by-step Thought Process:

Use the equation: [tex]a(1+r)^x[/tex] to solve this problem. Let x= time in years, a= initial amount, and r= growth rate.

[tex]a(1+r)^x[/tex] =  [tex]51368(1+0.018)^5[/tex]

When you solve you get this number:

56,160.57516085

Round to the nearest whole number:

56,161

Answer:

the answer is =2187

Step-by-step explanation:

hoped I helped:)

Answer:

C. The Transportation Security Administration

Step-by-step explanation:

Its C

The Transportation Security Administration was founded on 19 November 2001 to improve and safeguard transportation at the United States airports.

The Transportation Security Administration is one if the departments in the United States government whose primary function is to oversee the security of the country at airports.

The department was founded on 19 November 2001 to improve and safeguard transportation at the United States airports.

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Answer:

Skewed Right

Step-by-step explanation: