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3 years ago

The vertex form of the equation of a parabola is y=3(x-40)^2-22. What is the standard form of the equation?

1 answer:

3 0

y=3(x-40)^2-22
y = 3(x^2 - 80x + 1600) - 22
y = 3x^2 - 240x + 4800 - 22
y = 3x^2 - 240x + 4778

answer
 standard form of the equation
y = 3x^2 - 240x + 4778

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Distributive property 3(x-1)=3x-

user100 [1]

The answer is 3x-3. You have to distribute the 3 to both of the variables in the equations. The 1 in the parentheses is a negative and multiplying the 3 will result in a negative 3.

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2 years ago

Which is the completely factored form of 3x^2-12x-15

Luba_88 [7]

Find the GCF (Greatest Common Factor)

GCF = 3

Factor out the GCF ( Write the GCF first. Then, in parentheses, divide each term by the GCF)

3(3x^2/3 + -12x/3 - 15/3)

Simplify each term in parentheses

3(x^2 - 4x - 5)

Factor x^2 - 4x - 5

3(x - 5)(x + 1)

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3 years ago

Type the correct answer in each box. Use numerals instead of words.

Alex_Xolod [135]

Answer:

Step-by-step explanation:

Given that prices for a pair of shoes lie in the interval

[80,180] dollars.

Delivery fee 20% of price.

i.e. delivery fee will be in the interval [4, 9]

(1/20th of price)

Total cost= price of shoedelivery cost

Hence f(c) = c+c/20 = 21c/20

The domain of this function would be c lying between 80 to 180

So domain =[80,180]

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

Amount to be repaid = 42 dollars

Once he received this amount, the price would be

105+42 =147

But since price range is only [21*80/20, 21*180/20]

=[84, 189]

Since now Albert has 147 dollars, he can afford is

[80,147]

6 0

3 years ago

Read 2 more answers

g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur

sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

$\displaystyle V = \pi r^2h$

Substitute:

$\displaystyle (300) = \pi r^2 h$

Solve for h:

$\displaystyle \frac{300}{\pi r^2} = h$

Recall that the surface area of a cylinder is given by:

$\displaystyle A = 2\pi r^2 + 2\pi rh$

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for h.

$\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r} \end{aligned}$

Find its derivative:

$\displaystyle A' = 4\pi r - \frac{600}{r^2}$

Solve for its zero(s):

$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

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3 years ago

Add and simplify 9 sixteenths plus one half equals

brilliants [131]

9/16 + 1/2 = 9/16 + 8/16 = 17/16 = 1 1/16

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3 years ago