help
state the multiplicity for each root
[tex]3(x^{2} + 5)^ {2} ( {x}^{2} - 25)^{3} (x - 8)^{4} = 0[/tex]
state the multiplicity for each root​

Answers

Answer 1
x
=
i

5

x
=
i

5
,

i

5
,

5
,
5
,
8
Answer 2

Answers:

The two complex or imaginary roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex] have multiplicity 2.The two real roots x = 5 and x = -5 have multiplicity 3The root x = 8 has multiplicity 4

======================================================

Explanation:

We'll use the zero product property to solve.

[tex]3(x^2+5)^2(x^2-25)^3(x-8)^4 = 0\\\\(x^2+5)^2=0 \text{ or } (x^2-25)^3=0 \text{ or } (x-8)^4 = 0\\\\x^2+5=0 \text{ or } x^2-25=0 \text{ or } x-8 = 0\\\\x^2=-5 \text{ or } x^2=25 \text{ or } x = 8\\\\x=\pm\sqrt{-5} \text{ or } x=\pm\sqrt{25} \text{ or } x = 8\\\\x=\pm i\sqrt{5} \text{ or } x=\pm 5 \text{ or } x = 8\\\\[/tex]

where [tex]i = \sqrt{-1}[/tex]

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

The notation [tex]x=\pm i\sqrt{5}[/tex] breaks up into [tex]x=i\sqrt{5} \text{ or } x=-i\sqrt{5}[/tex]. The multiplicity of these two roots is 2 as it's the exponent of the factor [tex](x^2+5)^2[/tex]. Focus on the outermost exponent.

The notation [tex]x = \pm 5[/tex] becomes [tex]x = 5 \text{ or } x = -5[/tex]. The multiplicity of these two roots is 3 since it's the outermost exponent of the factor [tex](x^2-25)^3[/tex]

And finally, the multiplicity of the root x = 8 is 4 because it is the outermost exponent of the factor [tex](x-8)^4[/tex]


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Joseph is reading a 32 page book he read 6 pages in 15 minutes if he continues to read at the same rate how long will it take him to read the entire book

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Answer:

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Step-by-step explanation:

first we can set this up as a proportion.

so it would be 15 over 6 and your other side would be x over 32

so when u cross multiple your equation would be 6x = 480

then you divide both sides by 6 and when you divide 480 by 6 u will get 80

                         

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Step-by-step explanation:

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A person who weighs 105 pounds on Earth weighs 175 pound on the moon How much does a pound person weigh on the moon?

Answers

Answer:

1.67 pounds

Step-by-step explanation:

The problem above can be solved by using "direct proportion." This proportion shows that as one quantity increases, the other quantity increases and vice-versa.

Step 1: Represent the weight of the person on the moon by n.

Step 2: Set up a proportion.

            [tex]\frac{105}{175}[/tex] = [tex]\frac{1}{n}[/tex]

Step 3: Cross multiply.

            105 x n = 175 x 1

            105n = 175

Step 4: Find n by dividing both sides by 105.

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Please help
How many solutions can be found for the system of linear equations represented on the graph?
A)
no solution
B)
one solution
C)
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Answers

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Answer: One solution

Step-by-step explanation:

When the lines intersect in one spot, there's one solution. The lines have different slopes, so there's only one solution.

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Answer:

b

Step-by-step explanation:

What is the fraction 24/4 simplified?

Answers

Answer:

6

Step-by-step explanation:

The fraction 24/4 simplified is 6.

To simplify the fraction 24/4, we find the greatest common divisor (GCD) of the numerator (24) and the denominator (4), and then divide both the numerator and denominator by the GCD to obtain the simplified form.

Step 1: Find the GCD of 24 and 4.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 4 are 1 and 4.

The GCD of 24 and 4 is 4, as it is the largest number that divides both 24 and 4.

Step 2: Divide both the numerator and denominator by the GCD.

24 ÷ 4 = 6

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So, the simplified form of 24/4 is 6/1. However, any fraction divided by 1 remains the same, so the simplified fraction is 6.

Therefore, 24/4 simplified is 6.

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Answers

Step-by-step explanation:

angle MNP = angle QPL (corresponding angles, //lines) (A)

angle QLP is common angle (A)

By AA, the 2 triangles are similar.

Topic: congruence and similarity

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Answers

Answer:

x = 12 m

Step-by-step explanation:

Length = x m

Width = 3⅔ = 11/3

Area = 44 m²

Area of rectangle = length × width

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[tex] 44 = x \times \frac{11}{3} [/tex]

[tex] 44 = \frac{11x}{3} [/tex]

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[tex] 44 \times 3 = \frac{11x}{3} \times 3 [/tex]

[tex] 132 = 11x [/tex]

Divide both sides by 11

[tex] 12 = x [/tex]

x = 12

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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(p + 3)(1 - p)​

Answers

Answer:

p²-2p+3

Step-by-step explanation:

(p + 3)(1 - p)​

p-p²+3-3p

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One afternoon, Supreme sub shop sells 15 subs in 45 minutes. If the shop continues to sell subs at the same rate, about how many subs will the shop sell in 3 hours?

Answers

60 subs
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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

8-2=6 minutes and 5-3=2 inches so it lost 2 inches in 6 minutes. This means it loses an inch every three minutes. Since we have to go back by 2 minutes we will have to figure out how much length we have to add to the candle to figure out how long it was originally by multiplying by 2/3 as 2 inches is 2/3 the required to remove an inch, so 1 inch * 2/3 = 2/3 of an inch. Add that to the length at two minutes and we have 5 2/3 inches as its original size.

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Answers

Answer:

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Step-by-step explanation:

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80 points!

A store had 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.

Which recursive function best represents the number of bottles of water in the store, given that f(0) = 250?


A. f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0

B. f(n) = 250 − f(n − 1) ⋅ 0.4 + 48, n > 0

C. f(n) = f(n − 1) ⋅ 0.4 + 48, n > 0

D. f(n) = 250 − f(n − 1) ⋅ 0.6 + 48, n > 0

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Answers

Answer:

A

Step-by-step explanation:

Given:  

Initial number of bottles = 250

Every week = 40% is sold and 48 bottles arrive.

Week 1 = 250 - (250 x 0.40) + 48 = 250 - 100 + 48 = 198

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Answers

Answer:

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Step-by-step explanation:

or you can just put a line over the 27

Answer:

682.27

Step-by-step explanation:

7505÷11= 682.272727

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Answers

Answer:

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378/4 = 94.5

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Answers

Answer:

was

went

began

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I don't know if it's right though?

Answer:

was

went

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Answers

-2x+4y=36
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Answers

Answer:

The walkway is approximately 34.64 feet long

Step-by-step explanation:

The length of the sides of the equilateral triangle shaped the city garden = 40 feet

The path of the walkway = From the midpoint of a side to the opposite vertex

Therefore, we have;

Let x, represent the length of the walkway

We have that the x, a side of the equilateral triangle, and half the side of the location of the gate, forms a right triangle, with a side of the equilateral triangle representing the hypotenuse side

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

on google

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

We can use the rise over run method to do this question.

Let's start at the coordinates (1,1)

If we go down 2 from that point and to the right 3 times then we see another point on the line (3, -1).

We would express this as 2 over 3 or [tex]\frac{2}{3}[/tex].

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The line is sloping downwards and this means that the slope is negative.

So, the final answer is [tex]-\frac{2}{3}[/tex]

I hope this helps!!

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Answers

Answer:

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Step-by-step explanation:

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Answer:

Purplemath

Recall that negative exponents indicates that we need to move the base to the other side of the fraction line.

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In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process.

Step-by-step explanation:

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