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]
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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]
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?
Given ABC, m A= 60 degrees, m c=45 degrees, AB=8 Find the perimeter of ABC
Answer:113
Step-by-step explanation:
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
pls give reason
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
Week 2 = 198 - (198 x 0.40) + 48 = 198 - 79 + 48 = 167
Answer is: A. f(n ) = f(n - 1) • 0.6 + 48, n > 0.
a city has a garden in the shape of an equilateral triangle with 40 feet sides. there is a walkway that runs from a gate located at the midpoint of one side of the equilateral triangle to a fountain at the opposite vertex. approximately how long is the walkway?
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
Therefore, we have;
40² = x² + (40/2)²
40² = x² + 20²
x² = 40² - 20² = 1200
x = √1200 = 20·√3
The length of the walkway = x = 20·√3 ≈ 34.64 feet.
deandreh can work three math problems in five minutes . How long will it take him to work fifteen problem ? Plz show ur working out and thank u so much
Answer:
25 minutes
Step-by-step explanation:
Because 3 × 5 is 15 problems so multiple he 5 minutes by 5 and you get 25 minutes.
What is the fraction 24/4 simplified?
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
4 ÷ 4 = 1
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.
To know more about fraction:
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Please help!
Find the slope
-2x + 4y = 36
Thank you!
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)
Two solutions
D)
Infinitely many solutions
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.
help plss me ndfkfhfiklfjkfbufjriowxrkoek
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Answer:
[tex]-\frac{2}{3}[/tex]
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].
We aren't done yet however.
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!!
- Kay
solve the equation:
(p + 3)(1 - p)
Answer:
p²-2p+3
Step-by-step explanation:
(p + 3)(1 - p)
p-p²+3-3p
=p²-2p+3
Hope this helps :)
The Answer and yea idk
a candle is burning at a linear rate. The candle measures five inches two minutes after it was lit. It measures three inches eight minutes after it was lit. What was the original length of the candle?
Answer:
5 2/3 inches.
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.
Explain how to simplify an expression with negative exponents using the rules for multiplying monomials.
PLZZZZZ I NEED HELP ILL MAKE YOU BRAINLIEST
Answer:
Purplemath
Recall that negative exponents indicates that we need to move the base to the other side of the fraction line.
(The "1's" in the simplifications above are for clarity's sake, in case it's been a while since you last worked with negative powers. One doesn't usually include them in one's work.)
In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process.
Step-by-step explanation:
A person who weighs 105 pounds on Earth weighs 175 pound on the moon How much does a pound person weigh on the moon?
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.
n = [tex]\frac{175}{105}[/tex]
n = 1.666 or 1.67 pounds (lowest term)
A pound of person on Earth will weigh 1.67 pounds on the moon.
Express it in slope-intercept form.
What is 7505 divided by 11?
Answer:
7505÷11 = 682.27272727
Step-by-step explanation:
or you can just put a line over the 27
Answer:
682.27Step-by-step explanation:
7505÷11= 682.272727
In the diagram below, AB≅AD, m∠A=48° and m∠BCD=40°. Which statement is true?
Answer:
3
Step-by-step explanation:
Find the simple past tense of these verbs in the passage.
is
go
begin
do
make
grow
sell
get
ring
Answer:
was
went
began
did
made
grow
sell
get
rang
I don't know if it's right though?
Answer:
was
went
began
did
made
grew
sold
got
rang
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
Answer:
80 minutesssssss
Answer:
(edit) your answer is 80 min
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
Someone help meee I hate my teacher she asssign nvm I’m not even gonna say
Answer:
eating lunch
Step-by-step explanation:
the total time is 60 minutes. 10 minutes is 1/6 of that. 1/6 of 18 (from eating lunch) is 3 minutes. eating lunch is correct. also i hate my teacher sm too
I’m failing all my classes please help
Answer:
b
Step-by-step explanation:
A coach brought 12,000 milliliters of water to a tournament. How many liters of water did the coach bring?
Answer:
0.012
Step-by-step explanation:
Answer:
12 liters
Step-by-step explanation:
on google
are my answers correct
Answer:
yesn't
Step-by-step explanation:
Answer:
yes last Friday i did this and i do it the same i got it correct.
Step-by-step explanation:
the sum of twice a number and three is 21
Answer:
9
Step-by-step explanation:
9+9+18
18+3=21
Heyyyyy plz help I don’t bite
Answer:
50.24
Step-by-step explanation:
A = Πr^2
A = 3.14(4)^2
A = 50.24
Find x no need for explanation I just need answer thanks
Answer:
x = 12 m
Step-by-step explanation:
Length = x m
Width = 3⅔ = 11/3
Area = 44 m²
Area of rectangle = length × width
Plug in the values into the equation
[tex] 44 = x \times \frac{11}{3} [/tex]
[tex] 44 = \frac{11x}{3} [/tex]
Multiply both sides by 3
[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
determine whether the triangles are similar by angle-angle similarity. if yes, write a similarity statement.
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
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
in the example,-38+(-24)will be negative before finding the sum?
Answer:
-62
Step-by-step explanation:
Jyoti collects stamps. The table shows the number of stamps she collected over a 12-week period.
Find the rate of change for each time period to the nearest hundredth. Identify the time period
during which the number of stamps increased at the fastest rate.
2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4. How many votes did she get?
Answer:
473 or 472, depends on how you round
Step-by-step explanation:
378/4 = 94.5
94.5 x 5 = 472.5
The number of votes she gets will be 473.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4.
Then the number of votes she gets that will be
→ 378 x 5 / 4
→ 378 x 1.25
→ 472.5 ≅ 473
More about the multiplication link is given below.
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