The cost of three tickets to a movie is at least $20. Write and solve an inequality that represents the situation.

The amount Denise charges to repair computers $50 an hour plus a $25 service fee write an expression to show how much she will c

Natalija [7]

The answer you are looking for is 50h+25
Hope that this helps!

4 0

2 years ago

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Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

Ratling [72]

Answer: point estimate = 3.88

Margin of error = 0.63

Step-by-step explanation:

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that

x - m = 3.25

x + m = 4.51

Adding both equations, it becomes

2x = 7.76

x = 7.76/2

x = 3.88

Substituting x = 3.88 into x + m = 4.51, it becomes

3.88 + m = 4.51

m = 4.51 - 3.88

m = 0.63

8 0

2 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

nalin [4]

Answer:

$519

Step-by-step explanation:

Given the amount of profit made expressed as y=-2x^2+105x-859

At maximum profit, dy/dx = 0

dy/dx = -4x + 105

0 = -4x + 105

4x = 105

x = 105/4

x = 26.25

Substitute into the original function

y=-2x^2+105x-859

y=-2(26.25)^2+105(26.25)-859

y = - 1,378.125+2,756.25-859

y = 519.125

Hence the maximum amount of profit the company can make is $519

8 0

2 years ago

The __________ are tissues where gases from the air and the blood are exchanged.

Artyom0805 [142]

air sacs or alveoli the lungs and blood 3 transport

of respiratory gases

7 0

2 years ago

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