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3 years ago

If A = –2p + 7 and B = p2 + 3p – 5, find an expression that equals A – 3B in standard form.

Mathematics

1 answer:

Sophie [7]3 years ago

4 0

Answer:

-3p^2 - 11p + 22

Step-by-step explanation:

A - 3B becomes (-2p + 7) - 3*(p^2 + 3p - 5).

Perform the indicated multiplication, obtaining:

(-2p + 7) - 3p^2 - 9p + 15, and then:

-2p + 7 - 3p^2 - 9p + 15, or (combining like terms):

-3p^2 - 11p + 22

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David made a class banner out of a large rectangular piece of paper. He

spin [16.1K]

Given:

A triangular piece is cut out of a rectangular piece of paper to make the class banner.

To find:

The area of the class banner.

Solution:

The rectangular piece of paper is 14 inches long and $5+3=8$ inches wide.

From the given diagram, the triangle has a base length of the same 8 inches and has a height of $14-11=3$ inches long.

To determine the area of the banner, we subtract the area of the triangle from the area of the rectangle.

The area of a triangle $= \frac{1}{2} (b)(h).$

The area of the triangle $= \frac{1}{2} (8)(3) = 12$ square inches.

The area of a rectangle $= (l)(w).$

The area of the rectangle $= (14)(8)= 112$ square inches.

The area of the class banner $= 112-12=100$ square inches.

So the banner has an area of 100 square inches which is the first option.

7 0

3 years ago

Sketch a cylinder with radius 8 feet and height 3 feet, then find the volume.

4vir4ik [10]

Answer: 339.29ft^3

Step-by-step explanation:

The formula for a cylinder is πr^2h

In your scenario, r=8 and h=3 so put those into the equation -

π8^2(3) and just solve!

7 0

3 years ago

The average ticket price for a concert at the opera house was $50. The average attendance was 4000. When the ticket price was ra

kotegsom [21]

Answer

given,

opera house ticket = $50

attendance = 4000 persons

now,

opera house ticket = $52

attendance = 3800 person

assuming these are the points on the demand curve

(x, p) = (4000,50) and (x,p) = (3800,52)

using point slope formula

$p-50 = \dfrac{50-52}{4000-3800}(x - 4000)$

$p-50 = \dfrac{-2}{200}(x - 4000)$

$p-50 = \dfrac{-x}{100}+ 40$

$p = \dfrac{-x}{100}+ 90$

R(x) = x . p

$R(x) = x (\dfrac{-x}{100}+ 90)$

$R(x) = \dfrac{-x^2}{100}+ 90x)$

$\dfrac{d}{dx}(R(x)) = \dfrac{d}{dx}(\dfrac{-x^2}{100}+ 90x))$

$\dfrac{d}{dx}(R(x)) = (\dfrac{-2x}{100})+90)$

at $\dfrac{d}{dx}(R(x)) = 0$

$\dfrac{-2x}{100}= -90$

x = 4500

$\dfrac{d^2}{d^2x}(R(x)) = -ve$

hence at x =4500 the revenue is maximum

for maximum revenue ticket price will be

$p = \dfrac{-4500}{100}+ 90$

p = $45

6 0

3 years ago

What is 20℅ of 350℅ please help

Ad libitum [116K]

What is 20 percent (%) off $350?

Using the formula 1 and replacing the given values:

Amount Saved = Original Price x Discount % / 100. So,
Amount Saved = 350 x 20 / 100
Amount Saved = 7000 / 100

Amount Saved = $70 (answer)

3 0

3 years ago

How to write nine hundred fifteen thousands four hundred and nine

hoa [83]

This is how you write it. 915,409

3 0

3 years ago

Read 2 more answers