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Anuta_ua [19.1K]
2 years ago
13

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y

-intercept. Decide which table best illustrates these values for the equation:
y = 3 x squared + 2 x minus 8

Mathematics
1 answer:
mariarad [96]2 years ago
7 0

Answer:

Table A

Step-by-step explanation:

y  = 3x^2 +2x -8

The quadratic is in the form

y = a x^2 +bx+c

a = 3  b = 2 c = -8

Since a > 0 it opens up

The y intercept is c so the y intercept is -8

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The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3
Zepler [3.9K]

Answer:

We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.

Its volume is equal to the area of its base times its height.

Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.

Let's test each of these answers to see which gives us the correct volume.

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

a base area of 4y square units and height of 4y² + 4y + 12 units

We find the volume by multiplying the base area by the height...

4y(4y² + 4y + 12)

Distribute the 4y to each term inside the parentheses.

16y³ + 16y² + 48y

This is not the right volume, so these can not be dimensions of our prism.

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

a base area of 8y² square units and height of y² + 2y + 4 units

We find the volume by multiplying the base area by the height...

8y²(y² + 2y + 4)

Distribute the 8y² to each term inside the parentheses.

8y⁴ + 16y³ + 32y²

This is not the right volume, so these can not be dimensions of our prism.

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

a base area of 12y square units and height of 4y² + 4y + 36 units

We find the volume by multiplying the base area by the height...

12y(4y² + 4y + 36)

Distribute the 12y to each term inside the parentheses.

48y³ + 48y² + 432y

This is not the right volume, so these can not be dimensions of our prism.

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

a base area of 16y² square units and height of y² + y + 3 units

We find the volume by multiplying the base area by the height...

16y²(y² + y + 3)

Distribute the 16y² to each term inside the parentheses.

16y⁴ + 16y³ + 48y²

The volume fits, so these could be the base area and height of our prism.

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

D. a base area of 16y² square units and height of y² + y + 3 units

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

Step-by-step explanation:

7 0
3 years ago
Find the equation of a circle with a center at (–7, –1) where a point on the circle is (–4, 3).
gogolik [260]

Answer:

(x + 7)^2 + (y + 1)^2 = 25.

Step-by-step explanation:

The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.

In this case, a = -7 and b = -1, so we have...

(x - (-7))^2 + (y - (-1))^2 = r^2

(x + 7)^2 + (y + 1)^2 = r^2

To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.

sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.

Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.

5^2 = 25

So, your equation should be (x + 7)^2 + (y + 1)^2 = 25.

Hope this helps!

8 0
3 years ago
Write an explicit formula for an, the nth term of the sequence 4, -24, 144, ....
nadezda [96]

Answer:

Tn = 4(-6)^n-1

Step-by-step explanation:

Write an explicit formula for an, the nth term of the sequence 4, -24, 144, ....

The sequence is a geometric sequence

Tn = ar^n-1

a is the first term

a = 4

r = -24/4 =144/-24

r = -6

Substitute

Tn = 4(-6)^n-1

3 0
2 years ago
Lena purchased a prepaid phone card for $20. Long distance calls cost 21 cents a minute using this card, Lena used her card only
slega [8]

<u>Answer:</u>

37 minutes

<u>Step-by-step explanation:</u>

Lena has 20 dollars. 20 - 12.23 = 7.77

Lena has $7.77 dollars left.

We divide this by .21 to see how many minutes her call was.

7.77 ÷ .21 = 37

Rate as Brainliest and Thanks plz

5 0
3 years ago
I have 3 questions, 20 points each please explain your answer and show work, and PLEASE GIVE AN ACTUAL ANSWER. PLEASE ANSWER SOO
alexdok [17]

Answer:

Step-by-step explanation:

1.From the given triangle, ABC, using the proportionality theorem, we get

\frac{FA}{CA}=\frac{EF}{BC}

⇒\frac{8}{40}=\frac{5}{x}

⇒x=25ft

Thus, the height will be 25 feet.

2.  

Statement                                                   Reason

1.∠C≅∠E                                                     Given

2. ∠ABC≅∠DBE                                Vertically opposite angles

3. ΔABC is similar to ΔDBE               AA similarity rule.

5 0
3 years ago
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