Translate then simplify <br><br> A number n decreased by the difference nine and the number

HELP 20 POINTS..... roline bought 20 shares of stock at 101/2, and after 10 months the value of the stocks was 111/4. If Carolin

zhuklara [117]

I believe the answer is:

D. $15

6 0

3 years ago

If you go out to eat, a good tip is $18 when the bill costs $100. What is this percent?

dlinn [17]

Answer:

This is a good tip and $18 is 18% of what the meal cost.

Step-by-step explanation:

On average the proper tip is 15% of the cost of your meal cost. In this case you have paid 18% of your meal cost.

4 0

3 years ago

Read 2 more answers

Subtract and simplify: (10x4 – 2x + 7) – (6x4 + 2x3 – 4x2 – 1) A. 4x4 – 2x3 + 4x2 – 2x + 6 B. 4x4 + 2x3 – 4x2 – 2x + 8 C. 4x4 –

Masja [62]

(10x^4 - 2x + 7) - (6x^4 + 2x^3 - 4x^2 - 1)=

$= 10x^4-2x+7-6x^4-2x^3+4x^2+1=\\\\ = 4x^4-2x^3+4x^2-2x+8$

8 0

3 years ago

Solve: 2(x - 5) < -6(1 - x)

Marizza181 [45]

Answer:

B. x > -1

Step-by-step explanation:

Subtract the left side:

... 0 < -6(1 -x) -2(x-5)

... 0 < -6 +6x -2x +10 . . . . eliminate parentheses

... 0 < 4 +4x . . . . . . . . . . . collect terms

... 0 < 1 +x . . . . . . . . . . . . . divide by 4

... -1 < x . . . . . . . . . . . . . . . add -1. Matches selection B.

4 0

3 years ago

A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

antiseptic1488 [7]

Answer:

a) 0 m

b) 16.8 m

Step-by-step explanation:

A piece of wire, 30 m long, is cut in two sections: a and b. Then, the relation between a and b is:

$a+b=30\\\\b=30-a$

The section "a" is used to make a square and the section "b" is used to make a circle.

The section "a" will be the perimeter of the square, so the square side will be:

$l=a/4$

Then, the area of the square is:

$A_s=l^2=(a/4)^2=a^2/16$

The section "b" will be the perimeter of the circle. Then, the radius of the circle will be:

$2\pi r=b=30-a\\\\r=\dfrac{30-a}{2\pi}$

The area of the circle will be:

$A_c=\pi r^2=\pi\left(\dfrac{30-a}{2\pi}\right)^2=\pi\left(\dfrac{900-60a+a^2}{4\pi^2}\right)=\dfrac{900-60a+a^2}{4\pi}$

The total area enclosed in this two figures is:

$A=A_s+A_c=\dfrac{a^2}{16}+\dfrac{900-60a+a^2}{4\pi}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}$

To calculate the extreme values of the total area, we derive and equal to 0:

$\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}\\\\\\\dfrac{dA}{da}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2a)-\dfrac{60}{4\pi}+0=0\\\\\\\left(\dfrac{1}{8}+\dfrac{1}{2\pi}\right)a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8\pi}\cdot a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8}\cdot a=15\\\\\\a=15\cdot \dfrac{8}{\pi+4}\approx 16.8$

We obtain one value for the extreme value, that is a=16.8.

We can derive again and calculate the value of the second derivative at a=16.8 in order to know if the extreme value is a minimum (the second derivative has a positive value) or is a maximum (the second derivative has a negative value):

$\dfrac{d^2A}{da^2}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2)-0=\dfrac{1}{8}+\dfrac{1}{2\pi}>0$

As the second derivative is positive at a=16.8, this value is a minimum.

In order to find the maximum area, we analyze the function. It is a parabola, which decreases until a=16.8, and then increases.

Then, the maximum value has to be at a=0 or a=30, that are the extremes of the range of valid solutions.

When a=0 (and therefore, b=30), all the wire is used for the circle, so the total area is a circle, which surface is:

$A=\pi r^2=\pi\left( \dfrac{30}{2\pi}\right)^2=\dfrac{900}{4\pi}\approx71.62$

When a=30, all the wire is used for the square, so the total area is:

$A=a^2/16=30^2/16=900/16=56.25$

The maximum value happens for a=0.

3 0

3 years ago

Translate then simplify A number n decreased by the difference nine and the number