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3 years ago

Show all work to factor x4 − 10x2 + 9 completely.

Mathematics

2 answers:

AlekseyPX3 years ago

8 0

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² =(a+b)(a−b) where a=x and b=3.

(x+3)(x-3)(x+1)(x-1)

leva [86]3 years ago

6 0

Answer:

(x+1)(x-1)(x+3)(x-3)

Step-by-step explanation:

x4-10x^2+9

Group expression so that the coefficients of the x^2 terms add up to +9.

= x^4 -9x^2 - x^2+9

match coefficients in both groups

= x^4 -9x^2 - (x^2-9)

factor each group

= x^2 (x^2-9) - 1(x^2-9)

now factor out the common factor (x^2-9)

= (x^2-1)(x^2-9)

Finally, factor each quadratic factor

= (x+1)(x-1)(x+3)(x-3)

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to rent a popcorn machine, it costs 35 dollars plus 6.95 dollars for each hour. Write and evaluate an expression to find the tot

nekit [7.7K]

Answer:

equation=35+6.95h=c

5 hours= $69.75

6 hours= 76.7

7 hours= 83.65

8 hours= 90.6

Step-by-step explanation:

the equation is found by adding 35 (the cost of the machine) and 6.95 times how many hours. To find the hours after 5 just add 6.95 every time.

5 0

3 years ago

A fashion designer makes and sells hats. The material for each hat cost $5.50. The Hats sell for $12.50 each. The designer spend

labwork [276]

The designer must sell 200 hats for breaking even.

Step-by-step explanation:

Given,

Cost for material for each hat = $5.50

Selling price of each hat = $12.50

Cost spend on advertising = $1400

Let,

x represents the number of hats.

Revenue = 12.50x

Costs = 5.50x+1400

For breaking even,

Revenue = Cost

$12.50x=5.50x+1400\\12.50x-5.50x=1400\\7x=1400$

Dividing both sides by 7

$\frac{7x}{7}=\frac{1400}{7}\\x=200$

The designer must sell 200 hats for breaking even.

Keywords: addition, division

Learn more about division at:

#LearnwithBrainly

7 0

3 years ago

Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule says that any number raised to zero is 1. For example, $3^{0} = 1$ .


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
1) x = 0
Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$

2) x = 2
Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$

3) x = 4
Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
1) x = 0
Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$

2) x = 2
Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$

3) x = 4
Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$

-------

Answers:
a = 1
b = $\frac{1}{16}$ 
c = $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

5 0

3 years ago

Camp counselors kept track of the number of granola bars they served each day.

marin [14]

Answer:

the median is 43

Step-by-step explanation:

5 0

2 years ago

A rectangular room is 3 3 times as long as it is wide, and its perimeter is 64 64 meters. find the dimension of the room.

lora16 [44]

Perimeter = 2L + 2W (where L = length and W = width)

And we are given that L = 3W

So substituting for L, we have the equation:-

2(3W) + 2W = 64

6W + 2W = 64

8W = 64

W = 8 meters

So the length = 3*8 = 24 meters

Answer:- Length = 24 m and Width = 8 m.

4 0

3 years ago