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3 years ago

Determine the equation for the quadratic relationship graphed below.

Mathematics

1 answer:

kap26 [50]3 years ago

6 0

Answer:

$\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }$

Step-by-step explanation:

Hello, please consider the following.

We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.

$y=a(x-1)^2-4$

And the point (0,-1) is on the graph so we can write.

$a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3$

So the equation is.

$y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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Question 7

serg [7]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - a cone with volume 769?3 ft³ , having a height of 15 ft

To calculate - radius of the cone

We know that ,

$\bold{Volume \: of \: cone = \frac{1}{3}\pi \: r {}^{2} h }\\$

substituting the values in the formula stated above ,

$\bold{769.3 = \frac{1}{3} \times 3.14 \times r {}^{2} \times 15} \\ \\\bold{\implies r {}^{2} = \frac{769.3 \times 3}{3.14 \times 15} } \\ \\\bold{\implies r {}^{2} = \cancel\frac{2307.9}{47.1}} \\ \\\bold{ \implies \: r {}^{2} = 49} \\ \\ \bold{\implies \: r = 7 \: ft}$

therefore ,

radius = 7 cm

hope helpful ~

4 0

2 years ago

Margaret wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 18 in. 12 in. 10 in.

user100 [1]

Answer:

No, she cannot completely cover the footrest.

Step-by-step explanation:

First of all, we need to find the total surface area of the prism to be covered using the cotton cloth

the total surface area of the prism is

A = 2wl + 2lh + 2hw,

l is the length of the prism = 18 in,

w= width of the prism = 12 in,

h is the height of the prism = 10 in

hence $A = 2(12 \times 18 ) + 2(18 \times 10) + 2(10 \times 12)=1032in^{2}$

We need to convert the area of the fabric to be in the same unit as that of the prism

Area of cotton fabric = $1 yd^{2}= 1296 in ^{2}$

since the surface area of the foot rest is more than the area of fabric she has, she cannot completely cover the footrest

6 0

3 years ago

Read 2 more answers

What’s -3 + 6k + 11k - 10

leva [86]

Step-by-step explanation:

-3+6k+11k-10-9y+5x-y-13x

-13+17k-10y-8x

-5x+6x-9x+5xy

-8x+5xy

8 0

2 years ago

What is the equation of the line that passes through the point (-6,-8) and has a slope of 1/3

Arturiano [62]

y + 8 = 1/3 (x+6)

With the given information, we can use the point-slope formula, , to write the equation of the line. Substitute values for the , , and in the formula to do so.

The represents the slope, so substitute in its place. The and represent the x and y values of one point the line intersects, so substitute -6 for and -8 for . This gives the following answer and equation (just make sure to convert the double negatives into positives:

8 0

2 years ago

PLEASE HELP ASAP PLEASE

Juliette [100K]

Answer: #20, x = 3

#21, x = 1/2

Step-by-step explanation:

#20) x + 4 + x + 2+ x + 5 = x + 3 +x+3+x+1+x+1

3x + 11 = 4x + 8

-3x -3x

11= x + 8

- 8 - 8

3 = x

#21) 12x(5) = 6x + 9 + x + 10 + x + 7

60x =8x + 26

-8x -8x

52x = 26

divide both sides by 52

x = 1/2

3 0

2 years ago