Given:
The expression is
[tex]81x^4-1[/tex]
To find:
The factorized form of given expression.
Solution:
We have,
[tex]81x^4-1[/tex]
It can be rewritten as
[tex]=3^4x^4-1^2[/tex]
[tex]=(3x)^4-1^2[/tex] [tex][\because a^xb^x=(ab)^x][/tex]
[tex]=((3x)^2-1)((3x)^2+1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]=(3x+1)(3x-1)(3x+1)(3x-1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
This is the complete factorized form. It can also written as
[tex]=(3x+1)^2(3x-1)^2[/tex]
Therefore, the complete factorized form is [tex](3x+1)(3x-1)(3x+1)(3x-1)[/tex].
3/ If f(x) = 2x -5 Find f(x-1)=
Explanation: Here we have function f(x) = 2x - 5
and we're asked to find f(x - 1).
Don't be thrown off if you're asked to plus a variable into a function.
If f(x) = 2x - 5, then f(x - 1) = 2(x - 1) - 5.
Remember to use parenthses when substituting into a function.
So simplifying on the right side, we would distribute the 2
through the parenthses and we have 2x -2 - 5.
Now combining like terms, we have 2x - 7
A survey is conducted to find out the average number of hours
Americans work an average of 34.4 hours per week. The average hours per week worked varies based on gender, marital status, and race.
Calvin is comparing the growth of two plants. Plant A started at a height of four inches and grows two inches each month. Plant B grew according to this equation, h = 4m + 2, where h, is the height after m, months. At what month will the two plants be the same height?
Answer:
After 1 month, they will have same heights.
Step-by-step explanation:
Calvin is comparing the growth of two plants.
Plant A started at a height of four inches and grows two inches each month.
h'=4+2m
where
h' is height of plant after m months.
Plant B grew according to this equation, h = 4m + 2, where h, is the height after m, months.
We need to find at what month the plants have the same height. ATQ.
h = h'
4+2m = 4m + 2
Taking like terms together,
4-2 = 4m-2m
2=2m
m = 1
Hence, after 1 month, the plants will have same height.
PLZ HELP Will give you brainly if it works
Answer:
The prime number is only 11
11 is the only one i seee
-16x^2 +64x + 60
What is the max height
Answer:
x=5/2,3/2
so 5/2 is the maximum height. (2.5)
Step-by-step explanation:
can I get some B plz
Answer:
What do you mean?
Step-by-step explanation:
If z = 1 - square root 3i, what is z^3
Answers
-8
8
-8i
8i
Answer:
[tex]z = 1 - \sqrt{3} i \\ {z}^{3} = (1 - \sqrt{3} i) ^{3} \\ =(1 - \sqrt{3} i)(1 - \sqrt{3} i)(1 - \sqrt{3} i) \\ open \: brackets \\ = (1 - 2 \sqrt{3} i + ( { \sqrt{3} i})^{2} )(1 - \sqrt{3} i) \\ but \: {( \sqrt{3}i) }^{2} = - 3 \: since \: {i}^{2} \: is \: - 1 \: in \: complex \: numbers \\ = (1 - 2 \sqrt{3} i - 3)(1 - \sqrt{3} i) \\ = ( - 2 - 2 \sqrt{3} i)(1 - \sqrt{3} i) \\ = ( - 2 + 2 \sqrt{3} i - 2 \sqrt{3} i + 2( { \sqrt{3} i)}^{2} ) \\ = - 2 - 6 \\ = - 8[/tex]
Answer:
A
Step-by-step explanation:
Edge 2023
K/-3 + 3 =-2
Find the estimate of k
Answer:
K= 15
Step-by-step explanation:
K/-3 +3 = -2
Simplify by subtracting 3 on each side:
K/-3 = -2-3
K/-3 = -5
Simplify further by multiplying each side by -3:
K= -5*-3
K = 15
Javon has 1/2 a cup of flour, Sam has 1 1/6 cups of flour, and Antoine has 1 3/4 cups of flour. How many cups of flour do they have all together A. 41/12 B. 17/12 C 2.17 D 2.1712
Charlie bikes 9 miles every day.
Days (d)
1
2
3
4
5
Miles (m)
9
18
27
36
45
Which equation models the situation?
9 = dm
d = 9m
9d = m
d = 9 + m
Answer:
C. 9d=m
Step-by-step explanation:
Answer:
Step-by-step explanation:
HELPPPPP PLZZZZ
Which of the following are solutions for 2x ≥ 10? Choose ALL that apply.
Group of answer choices
4
5
6
Answer:
5 and 6
Step-by-step explanation:
5×2=10 equal to
6×2=12 greater than
Suppose both factors in a multiplication problem are the multiples of 10. Explain why the number of zeros in the product may be different than the total number of zeros in the factors. Include an example.
Answer:
Step-by-step explanation:
Take 20 and 50.
20 * 50 = 1000.
We have the 2 zeros in 20 and 50 , also 2 * 5 = 10, making 3 zeroes.
Write a number with 2 decimal places that is bigger than 4 1/5 but smaller than 4.25
will give brainiest
Answer :
11.45
step-by-step explantion :
4.25=17/4
when we add 41/5 and 17/4, we get
41×4+17×5/4×5
164+65/20
229/20
11.45
find the slope of the lines
Answer:
Zero
Step-by-step explanation:
The graph depicts a horizontal line.
All horizontal lines have no slope. If you pick two points from the line and use the slope formula, the numerator would be zero.
Zero divided by any number is zero.
Hope this helps.
Explain to me how you would convert 120 dollars to quarters. How many
quarters would that be?
Answer:
180 quarters
Step-by-step explanation:
Garrett arrived at the train station at 12:35 P.M. His train finally came at 1:30 P.M. How long
did Garrett have to wait for the train?
Answer:
55 minutes
Step-by-step explanation
He started waiting at 12:35 P.M. If we're assuming this is the same day, you're able to add the minutes until you get to 1:00 P.M., which is around 25 minutes. Afterwards, you need to add another 30 minutes to get to the train's time of arrival, which means you should get 55 minutes!
which statement is not true of the given diagram?
whats the equation of the straight line on this graph
a) y=3x+4
b) y=2x+4
c) y=4x+4
What is the sum of the exterior angles in a regular 15 gon
9514 1404 393
Answer:
360°
Step-by-step explanation:
The sum of exterior angles of any convex polygon is 360°.
Look/read the picture please!
1) Sarah bought 12 meters of fabric to make a patchwork quilt. If the fabric was on sale for $6.29 per meter, how much did Sarah spend? HELP PLS
Answer:
She spent $75.48
Step-by-step explanation:
multiply the price per meter by the amount of meters she purchased.
Explain how to solve 5d = 35
Answer:
D=7
Step-by-step explanation:
SO isolate the variable y dividing 5 on both sides
d=7
Answer: d = 7
Step-by-step explanation:
5d = 35
You have to divide both sides by 5 since we need to isolate the variable 'd' to figure out what d is.
5d ÷ 5 = d
35 ÷ 5 = 7
So d = 7
A larger number is 2 more than 4 times a smaller number. The larger number is also 8 more than 2 times the smaller number. y = 4x+2, y = 2r+8 What is the value of the smaller number in the mathematical problem?
Answer:
3
Step-by-step explanation:
I got it wrong so then it told me what the correct answer was:)
i'll mark brainliest just tell me how to.
Answer:
a = 12
b = 2
c = 11
Step-by-step explanation:
[tex] \frac{( {x}^{5}y {z}^{4} )^{3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{5 \times 3}y^{3} {z}^{4 \times 3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{15}y^{3} {z}^{12} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{15 - 3} {y}^{3 - 1} {z}^{12 - 1} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{12} {y}^{2} {z}^{11} = {x}^{a} {y}^{b} {z}^{c} \\ \\ equating \: like \: terms \: from \: both \: sides \\ \\ {x}^{12} = {x}^{a} \: \implies \: a = \boxed{ 12}\\ \\ {y}^{2} = {y}^{b} \: \implies \: b = \boxed{ 2} \\ \\ {z}^{11} = {z}^{c} \: \implies \: c = \boxed{ 11}[/tex]
ABCD is a parallelogram, find the value of y
Answer:
33
Step-by-step explanation:
angles A and B should add up to 180, so A must be 40, and because it is a parallelogram the anlge across from it should also equal 40. 33+7=40.
If two legs of a right triangle are 2 inches and 3 inches, can the hypotenuse be 4 inches? Justify your answer.
Answer:
No
Step-by-step explanation:
2^2+3^2 = 13, and 4^2 = 16.
9514 1404 393
Answer:
No
Step-by-step explanation:
The only Pythagorean triple that is three integers in sequence is 3, 4, 5.
2, 3, 4 is not a Pythagorean triple (will NOT form a right triangle).
__
A 2-3-4 triangle is an obtuse triangle.
This is an absolute value problem with LETTERS?! Absolute madness (no pun intended)
Answer:
a
Step-by-step explanation:
sjejeneissbebdejjesj
Write a linear function f with the given values. f(6)=-2, f(0)=-5
Answer:
y = 0.5m - 5
Step-by-step explanation:
the equation of a line can be written as
y = mx + b, with x being the input and y the output
let's plug in our two values.
-2 = m(6) + b
-2 = 6m + b
-5 = 0m + b
-2 = 6m+b
-5 = b
plug -5=b into the first equation
-2 = 6m - 5
add 5 to both sides
3 = 6m
divide both sides by 6
0.5 = m
our function is now
y = 0.5m - 5
A restaurant borrowed
$15,000 to remodel.
The loan is for 7 years and
the yearly interest rate is
4.25%. How much interest
will the restaurant pay?
Answer:
$4462.50
Step-by-step explanation:
simple interest =principal × rate × time\100
Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid $1360, how many first class and tourist class passengers were there?
There were 40 tourist class passengers and 12 first class passengers.
Explanation:
Let the number of passengers who booked for tourist class be
=
x
Then, number of passengers who booked for first class
=
52
−
x
According to question,
Total money paid = $25(tourist class)+$30(first class)
$
1360
=
$
25
(
x
)
+
$
30
(
52
−
x
)
1360
=
25
x
+
1560
−
30
x
1360
−
1560
=
25
x
−
30
x
−
200
=
−
5
x
x
=
−
200
−
5
x
=
40
So, there were 40 tourist class passengers.
Now first class passengers
=
52
−
x
=
52
−
40
=
12
∴
There were 40 tourist class passengers and 12 first class passengers.
As a check
Total money paid = $25(tourist class)+$30(first class)
R
H
S
=
$
25
(
40
)
+
$
30
(
12
)
$
1000
+
$
360
=
$
1360
L
H
S
=
$
1360
Hence verified.