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3 years ago

Identify the vertex and the y-intercept of the graph of the function y--(x+3 +4

Mathematics

1 answer:

Daniel [21]3 years ago

7 0

The vertex is at (-3, 4)

This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = 4. This means the vertex is at (-3, 4).

The y-intercept is at 13. To find this we must first square the parenthesis and get the equation into standard form.

y = (x + 3)^2 + 4

y = x^2 + 6x + 9 + 4

y = x^2 + 6x + 13

Now we know that the y-intercept is equal to the constant, which is the last number in the equation.

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HELP Luna observed that in the last 12 issues of Rise Over Run Weekly, 384 of the 960 pages contained an advertisement.

Veseljchak [2.6K]

Well, 12 issues end up as 960 pages total

so... if in 960 pages, 384 are ads, what about 80 pages?

well $\bf \begin{array}{ccllll}
pages&ads\\
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960&384\\
80&x
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solve for "x"

7 0

3 years ago

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Valuate the line integral, where c is the given curve. ∫c zdx + xdy + ydz

Semenov [28]

$\displaystyle\int_{\mathcal C}z\,\mathrm dx+x\,\mathrm dy+y\,\mathrm dz=\int_{\mathcal C}\langle z,x,y\rangle\cdot\mathrm d\langle x,y,z\rangle$
$\displaystyle=\int_{t=0}^{t=1}\langle t^2,t^2,t^3\rangle\cdot\mathrm d\langle t^2,t^3,t^2\rangle$
$=\displaystyle\int_0^1\langle t^2,t^2,t^3\rangle\cdot\langle2t,3t^2,2t\rangle\,\mathrm dt$
$=\displaystyle\int_0^15t^4+2t^3\,\mathrm dt=\frac32$

3 0

3 years ago

Giving brainiest

mestny [16]

Answer:

7x2 is 14

I will adopt you

Step-by-step explanation:

5 0

2 years ago

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A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.

jarptica [38.1K]

Formula for perimeter of rectangle:
P=2(L+w)
P=2L+2w
Here Perimeter, p= 72 ft
And scale factor of length and width=3.5 which means rectangle is enlarged.
So perimeter of rectangle= 3.5 x 72
P=252ft

Answer: 252 ft

8 0

3 years ago

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A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago