MATHEMATICS HIGH SCHOOL

Choose one of the factors of x6 + 1000.x2
x2 − 10
x4 − 10x2 + 100
x4 + 10x2 + 100

Answers

Answer 1
Answer: x^6 + 1000
x^6 - 10x^4 + 10x^4 + 100x^2 - 100x^2 + 1000
x^6 - 10x^4 + 100x^2 + 10x^4 - 100x^2 + 1000
x^2(x^4) - x^2(10x^2) + x^2(100) + 10(x^4) - 10(10x^2) + 10(100)
x^2(x^4 - 10x^2 + 100) + 10(x^4 - 10x^2 + 100)
(x^2 + 10)(x^4 - 10x^2 + 100)

The factors of x^6 + 1000 is x^2 + 10 and x^4 - 10x^2 + 100.
Answer 2
Answer:

One of the factors of the given polynomial is: Option C: x⁴ - 10x² + 100.

How to find the factors of the polynomial?

The factors of the polynomial given as x⁶ + 1000 is as follows:

Since we have 1000 isolated, we can guess that one of the factors will have 10 and as we can break down as follows:

x⁶ - 10x⁴ + 10x⁴ + 100x² - 100x² + 1000

We can now rearrange as:

x⁶ - 10x⁴ + 100x² + 10x⁴ - 100x² + 1000

This can be factored further as:

x²(x⁴) - x²(10x²) + x²(100) + 10(x⁴) - 10(10x²) + 10(100)

x²(x⁴ - 10x² + 100) + 10(x⁴ - 10x² + 100)

(x² + 10)(x⁴ - 10x² + 100)

The factors of x⁶ + 1000 is x² + 10 and x⁴ - 10x² + 100.

Read more about factors of polynomial at: brainly.com/question/30937687

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What is the height of a triangle if the base is 10 cm and the sides are 13 cm

Answers

if the sides (plural, meaning more than 1) and the base is 10

that means
2 sides=13 cm
base=10
since 2 sides equal legnths, isocolees
draw a line from the top angle, opposite the base side, perpendicular to the base
you will form 2 right triangles each with a base of 10/2=5 and a hypotonuse of 13 solve for other leg

a^2+b^2=c^2
c=hypotonuse=13
a=10=1 leg
b=mystery leg (height)

10^2+x^2=13^2
100+x^2=169
subtract 100 from both sides
x^2=69
take square root of both sides
x=√69

it would be safe to put √69 as the answe since it cannot be simplified into a whole number (about 8.3066238629181)
because the sides are the same it is an isosceles triangle, therefore the altitude forms two right triangles and also bisects the base

Apply the Pythagorean Theorem
5^2 + h^2= 13^2
 
25+h^2= 169
     h^2= 144
       h=12

FYI  there are familiar combinations for right triangles, might be worthwhile to check them out, it will save a lot of time.

Some examples are 3,4,5  /  5,12. 13  / 9,40,41 etc

Hope this helps
                                    

PLZ HELP WORTH A LOT OF POINTS AND I HAVE 10 MINUTES!!!!A certain forest covers an area of 1700 km^2. Suppose that each year this area decreases by 3.5%. What will the area be after 9 years? Use the calculator provided and round your answer to the nearest square kilometer.

Answers

Answer:

The area after 9 years will be 1,234 km^2

Step-by-step explanation:

In this question, we are tasked with calculating what the area of a certain forest that decreases at a certain percentage would be after some years.

To answer this question, we shall be using an exponential approximation.

Now, to use this exponential approximation, we shall be needing a supporting exponential mathematical equation.

This can be written as;

A = I(1-r)^t

where A is the new area we are looking for

I is the initial area which is 1700 according to the question

r is the rate of decrease which is 3.5% = 3.5/100 = 0.035

t is time which is 9 years according to the question

We plug these values and have the following;

A = 1700(1-0.035)^9

A = 1700(0.965)^9

A = 1,233.66

This is 1,234 km^2 to the nearest square kilometer

A new car is purchased for 15500 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 6 years?

Answers

The answer is $9,709.17

Solve 2 log2 2 + 2 log2 6 − log2 3x = 3.

Answers

Answer:

 x = 6

Step-by-step explanation:

  Given : 2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3

We have to solve the given expression 2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3

Subtract 2\log _2\left(2\right)+2\log _2\left(6\right) both sides , we have,

2\:log_2\:2\:+\:2\:log_26-\:log_2\:3x-(2\log _2\left(2\right)+2\log _2\left(6\right)):=\:3-(2\log _2\left(2\right)+2\log _2\left(6\right))

Simplify, we have,

\log _2\left(3x\right)=3-2\log _2\left(2\right)-2\log _2\left(6\right)

Divide both side by -1, we have,

(-\log _2\left(3x\right))/(-1)=(3)/(-1)-(2\log _2\left(2\right))/(-1)-(2\log _2\left(6\right))/(-1)

Simplify, we have,

\log _2\left(3x\right)=-3+2\log _2\left(2\right)+2\log _2\left(6\right)

Apply log rule, a=\log _b\left(b^a\right)

2\log _2\left(6\right)-1=\log _2\left(2^(2\log _2\left(6\right)-1)\right)=\log _2\left(18\right)

When log have same base,

\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)

\mathrm{For\:}\log _2\left(3x\right)=\log _2\left(18\right)\mathrm{,\:\quad solve\:}3x=18

3x = 18

x = 6
log(base2)[2² * 6² / 3x] = 3 
144 / 3x = 2^3 = 8 
144/8 = 3x 
18 = 3x 
x = 6

To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?

Answers

4.16666667 is what i got 

Jan's scores on five quizzes were 2, 8, 8, 9, and 10. Is the mean or median the best measure of center to summarize Jan's scores?

A.median

B.mean

C.Both mean and median summarize the data equally well.

Answers

the median is truly the middle of the data set. But the mean describes the average i want you to decide so i wont get this wrong. Thus, is the mean more important than the median according to this information?
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