Factor when divides the function the remainder is zero. The factorized form of the function f(x)=125x⁶-8 is (5x²-2)(25x⁴ + 10x²+4).
What is a factor?A factor of a function is a factor which when multiplied by another the result is the function itself.
We know that in order to factorize a function, we need to take the common terms out from the expression,
[tex]f(x)=125x^6-8[/tex]
The given function can be written as,
[tex]f(x)=125x^6-8\\\\f(x)=5^3x^6-2^3\\\\f(x)=(5x^2)^3-2^3[/tex]
Now, we will use the algebraic property to solve the function.
[tex]f(x)=(5x^2)^3-2^3\\\\f(x)=(5x^2-2)(25x^4+10x^2+2^2)\\\\f(x)=(5x^2-2)(25x^4+10x^2+4)[/tex]
Hence, the factorized form of the function f(x)=125x⁶-8 is (5x²-2)(25x⁴ + 10x²+4).
Learn more about Factors:
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Answer:
C
Step-by-step explanation:
I need help in this question
Answer:
1a) a= -10
b) b= -5
c) c= -1068
d) d= -1000
2a) a and c
b) b and b
c) c and a
d) d and a
Step-by-step explanation:
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no solutions
Answer: no solutions
Step-by-step explanation:
6x+4x-1=2(5x+4)
10x-1=10x+8
+1 +1
10x=10x+9
The equation is not true. It has no solutions.
which of the following points would fall on the line produced by the point-slope form equation y-6=7(x+4)
A (-1,28)
B (0,-34)
C (-3,13)
D (2,20)
Answer:
[tex]a.( - 128)[/tex]
Step-by-step explanation:
#ThanksMeLater
#CarryOnLearning
Please help! There are only 3 choices.
Find the height of the tree in feet if the angle of depression is 31 degrees.
A) 7.2 feet
B) 10.3 feet
C) 6.2 feet
The value is approximate.
========================================================
Explanation:
Check out the diagram below.
The angle of depression being 31 degrees refers to the idea of looking straight horizontal, then looking down 31 degrees. I recommend adding a dashed horizontal line.
That horizontal line is parallel to the ground. This forms a pair of congruent alternate interior angles. Therefore, we have two angles that are 31 degrees as the diagram shows.
The 31 degrees at the bottom is the angle of elevation.
Use this angle of elevation to say...
tan(angle) = opposite/adjacent
tan(31) = x/12
x = 12*tan(31)
x = 7.210327 approximately
This rounds to 7.2 feet
can you answer this?
Which amount has the greatest value in Canadian dollars?
US$15
€11
£10
Answer:
US$15
Step-by-step explanation:
US$15 = 19.15 (Canadian)
€11 = 15.91 (Canadian)
£10 = 17.35 (Canadian)
______________________
$1 in the US (US) is $1.28 in Canada
$1 in Euros (€) is $1.45 in Canada
$1 in the UK (£) is $1.73 in Canada
A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal? StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 5 x 11 y = 62 EndLayout StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 5 x 11 y = 62 EndLayout StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 11 x 5 y = 2 EndLayout StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 11 x 5 y = 2 EndLayout.
The system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is
[tex]y = 2x^2 - 16x + 34\\11y = -5x + 62[/tex]
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
For the given situation, the quadratic equation has vertex (h,k) = (4,2) and it passes through (5,4).
If we consider the equation to be of the form [tex]y=a(x-h)^2 + k[/tex],
then, as h = 4, k = 2, it becomes [tex]y = a(x-4)^2 + 2[/tex]
Now since it passes through (5,4), thus at x = 5, and y = 4, the equation must be true, or:
[tex]y = a(x-4)^2 + 2|_{(x,y) = (5,4)}\\\\4 = a(5-4)^2 + 2\\4 = a + 2\\a = 2[/tex]
Thus, the quadratic equation in consideration is: [tex]y = 2(x-4)^2 + 2 = 2x^2 + 32 -16x + 2\\y = 2x^2 - 16x + 34[/tex]
The straight line in consideration connects points (–3, 7) and (8, 2).
Equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
Since we've got [tex](x_1, y_1) = (-3,7) \: \rm and \: \: (x_2, y_2) = (8,2)[/tex]
We get the equation of the straight line in consideration as:
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y-7) = \dfrac{2-7}{8 - (-3) } (x-(-3))\\\\y - 7 = -\dfrac{5}{11}(x+3)\\\\11y = -5x + 62[/tex]
Therefore, the system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is
[tex]y = 2x^2 - 16x + 34\\11y = -5x + 62[/tex]
These equations' graphs' intersection is the solution to this system
Learn more about system of equations here:
https://brainly.com/question/2825832
Answer:
y-2(x-4)^2=2
5x+11y=62
Step-by-step explanation:
a on edge 22
The cost of car repair includes labor and parts. Labor is 70% of the total cost. The cost of labor for a certain repair is $406. What is the total cost of the car repair?
Answer:
Your answer is 580
Step-by-step explanation:
HURRYY!!!!
An oil company fills 1 over 10 of a tank in 1 over 5 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely?
1 over 5 ⋅ 10 hours
1 over 10 ⋅ 5 hours
1 over 5 ⋅ 1 over 10 hours
5 ⋅ 10 hours
Answer:
I believe the answer is the 3rd one
Step-by-step explanation:
Please help with solution needed!!
Answer:
42,640
Step-by-step explanation:
[tex]205 \times 208 = (200 + 5)(200 + 8) \\ formula \: to \: be \: used \: \\ \red{ \boxed{ \bold{(x + a)(x + b) = {x}^{2} + (a + b)x + ab}}} \\ \\ \implies \: 205 \times 208 \\ \\ = (200 + 5)(200 + 8) \\ \\ = {(200)}^{2} + (5 + 8)(200) + (5)(8) \\ \\ = 40000 + (13)(200) + 40 \\ \\ = 40000 + 2600 + 40 \\ \\ = 42,640[/tex]
You start driving west for 3 miles, turn right, and drive north fer another 13 miles. At
the end of driving, what is your straight line distance from your starting point?
Round to the nearest tenth of a mile.
Answer:
13.3 miles
Step-by-step explanation:
So you're driving <----- for 3 miles
Then you start driving up for 13 miles
This makes a right triangle with sides of 3 and 13
using pathagoreas, a^2+b^2=c^2
3^2+13^2=c^2
9+169=c^2
178=c^2
Square root both sides
c= 13.3416640641
Rounding, it's 13.3 miles
Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0. 85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1. 08p. Using this information, which of the following represents the final price of a tablet, with the discount and taxes applied, based on its original price? c[p(t)] = 0. 918t t[c(p)] = 0. 918t c[p(t)] = 1. 93p t[c(p)] = 1. 93p.
Taxation is done on the discounted price. The equation representing the final price of a tablet for this condition is : Option A: c[p(t)] = 0. 918t
What are composite functions?Functions which are formed by composing two or more functions in a way that one's input is another's output unless its the last and first function is called composite functions.
For given case, it is given that
Discounted price for original 't' price of a tablet is
[tex]p(t) = 0.85t[/tex]
This discounted price is then passed as input to the tax calculating function as taxation is specified to be done on the discounted price and not on the original price.
The total cost calculating function is [tex]c(p) = 1. 08p[/tex]
Thus, for original price t, the total cost is given as:
[tex]c(p(t)) = 1.08(p(t)) = 1.08 \times 0.85t = 0.918t[/tex]
We composed the two available function to get the direct final cost from value of t.
Thus,
The equation representing the final price of a tablet for this condition is Option A: c[p(t)] = 0. 918t
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Identify the equation that describes the line in slope-intercept form. slope = 3/4 , point (2, 2) is on the line
Answer:
Step-by-step explanation:
You have more than 1/2 the solution just by knowing the slope.
General equation
y = mx + b where m is the slope and b is the y intercept.
m = 3/4
Solution
y = 3/4 x + b Now you need the point to solve for b
x = 2
y = 2 Substitute these values into the line
2 = 3/4 * 2 + b Simplify the right
2 = 1 1/2 + b
2 = 3/2 + b Subtract 3/2 from both sides
2 - 3/2 = b Combine
1/2 = b
So the y intercept is 1/2
Answer
y = 3/4 x + 1/2
or
y = 0.75 x + 0.5
Which statement shows how the product of (x 5)2 demonstrates the closure property of multiplication? x2 25 is a polynomial x2 25 may or may not be a polynomial x2 10x 25 is a polynomial x2 10x 25 may or may not be a polynomial.
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Example:
[tex]x^3 + 4x + 3[/tex]
is a polynomial.
Using both above facts, as the given expression is [tex](x+5)^2[/tex]
Its product result is obtained as
[tex](x+5)^2 = (x+5)(x+5) = x(x+5) + 5(x+5) = x^{1+1} + 5x + 5x + 25\\\\(x+5)^2 = x^2 + (5+5)x + 25 \text{\:(Addition of coefficients of like terms)}\\\\(x+5)^2 = x^2 + 10x + 25[/tex]
It is a fact that result of a polynomial product is polynomial. Thus, the obtained product is a polynomial since x + 5 was a polynomial.
Thus,
The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]
Learn more about polynomial product here;
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Two trains are 500 miles apart and traveling toward each other one train travels 20 mph than the other and after two hours the trains are 300 miles apart find the speed of the faster train
pls help!
Answer:
60 mph
Step-by-step explanation:
We calculate the combined distance travelled by the two trains in two hours.
As they were 500 miles apart at first, and 300 miles apart after, they have travelled 200 miles together.
I think the question means "one train travels 20 mph faster than the other".
Say the faster train has speed x mph. Then the slower has speed x - 20 mph.
Now, the combined distance travelled in 2 hrs is 2 * (x + x - 20) = 200
2x - 20 = 100
2x = 120
x = 60 mph
explain how to get the variable alone in the equation. 4x = 32
Step-by-step explanation:
since 4 is being multiplied with x we can take 4 to left hand side where it will be divided
4x = 32
x = 32/4
x = 8
I need help!
f(x)=-3x+6/4x-8
Answer:
same
Step-by-step explanation:
Jemma surveyed the students at her school to find out if they like the beach and/or the mountains for vacation. The table below shows the results of the survey: Like Beach Do Not Like Beach Total Like Mountains 36 28 64 Do Not Like Mountains 56 38 94 Total 92 66 158 If a student does not like the mountains, what is the probability that student also does not like the beach? 39. 1% 40. 4% 59. 5% 60. 8%.
Probability of an event is its chance of . The probability that a student not liking mountains doesn't like beach is: Option b: 40.4%
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]
Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For the given case, from the table (image attached below), we can see that, there are total 94 students who do not like mountains. Now, out of those 94, there are 38 students not liking beach.
Thus, if A = a student not liking beach
B = not liking mountains,
Then ,
P(A|B) = P(A ∩ B)/P(B) = [tex]\dfrac{38/158}{94/158} = \dfrac{38}{94} \approx 0.404 = 40.4\%[/tex]
Thus, probability of a student not liking beach given that that student doesn't like mountains is 40.4% approx.
Learn more about probability here:
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Answer:
40.4%
Step-by-step explanation:
Describe the vector that translates DEF to D’E’F’.
A. (-4, -3)
B. (3, 4)
C. (4, 3)
D. (-3, -4)
Answer:
(-3 , -4)
Step-by-step explanation:
Vector translation: graph slide without rotation on the coordinate plane
Marvin wrote a decimal on the whiteboard. The value of the 6 in Marvin’s decimal is equal to 1/10 of 0.06. Which of the following numbers could be Marvin’s decimal?
A) 63.576
B) 63.657
C) 63.679
D) 63.960
READ: Please leave a reasoning/explanation. You don't need to give a full paragraph of your explanation
Answer:
A) 63.576
Step-by-step explanation:
1/10 can also be 10/100 which is 10%
10% of 0.06 = 0.006
26, 54, 38, 65, 58, 35, 52, 43, 55, 41, 61
Question
What is the range of the set of data?
Answer:
range = 39
Step-by-step explanation:
The range is the difference between the largest value in the data set and the smallest value.
range = 65 - 26 = 39
Answer:
35
Step-by-step explanation:
26, 35, 38, 41, 43, 52, 54, 55, 58,61
The biggest number minus the smallest number
61- 26
35
help me please thank yo
Answer:
10*g
Step-by-step explanation:
How many golf balls were in each package?
10 packages
g =golf balls
The balls came in the 10 packages, we don't know how many there are so we use g as a substitute. Therefore being 10*g.
Ex:
lets assume there is 5 golf balls in each package and there is a total of 10 packages. 10*5=50 and if you count each ball it would be the same 5,10,15,20,25,30,35,40,45,50 balls in each. 10*5= 10*g. Same thing except I added a number making it a equation.
What are the solutions of the quadratic equation?
x² – 2x = 8
O x = 1
a) x = 1 or x = -8
b) x = 8 or x = -1
c) x = 2 or x = -4
Od) x = 4 or x = -2
Answer:
d)X=4 or x=-2
Step-by-step explanation:
X²-2x=8
X²-2x-8=0
(x-4)(x+2)=0
X-4=0 or x+2=0
X=4 or x=-2
Answer: D. x = 4 or x = -2
The correct answer is x = 4 or x = -2
Step-by-step explanation:
Hope this helps =)
Angles A and B are supplementary. Angle A measures (2x + 20).Angle B measures 130 degrees. Solve for X
Answer:
x = 15
Step-by-step explanation:
Supplementary = 180 °
Add the numbers
[tex](2x + 20) + 130 = 180[/tex]
[tex]2x + 150 = 180[/tex]
Subtract 150 from both sides of the equation
[tex]2x+150- 150 =180 - 150[/tex]
Simplify
[tex]2x = 30[/tex]
Divide both sides of the equation by the same term
[tex]\frac{2x}{2} =\frac{30}{2}[/tex]
Simplify/Solution =
[tex]x=15[/tex]
Hence, x = 15.
[RevyBreeze]
Find the inverse of f(x)=2x+7
Please help!! With solution needed!!
Answer:
There are [tex]3p^2[/tex] animals on the farm
Step-by-step explanation:
2p^2-p+4 . p^2+p+1
[tex](2p^2-p+4)+(p^2+p+1)\\2p^2+p^2+p-p+4+1\\3p^2+5[/tex]
Answer:
3p² + 5
Step-by-step explanation:
since no equations are given I will simply add on the number of cows and buffaloes.
total number of animal= number of cows + number of buffaloes
= 2p²- p + 4 + p² + p + 1
= 3p² +5
A rectangle has an area of 63 square yards and a width of 3. 5 yards. What is the length, l, of this rectangle? l = 9 yd l = 18 yd l = 28 yd l = 45 yd.
Answer:
18 yards
Step-by-step explanation:
Rectangle area = Length (L) x Width (W)
63 yd^2 = L*W
63 yd^2 = L*(3.5 yd)
L = 18 yards
Answer:
/ = 18 yd
Step-by-step explanation:
I took the quiz and this was the correct answer.
vector a= 2i+ 3j - 5k.what is the value of 3a?
Answer:
The answer is 6î + 9j – 15k
Step-by-step explanation:
Given;A = 2î + 3j – 5kTo Find;Value of 3ASo,
A = 2î + 3j – 5k
Multiply The value of A with 3 we get,
3A = 3(2î + 3j – 5k)
3A = 6î + 9j – 15k
Thus, The value of 3A is 6î + 9j – 15k
-TheUnknownScientist 72
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: Cos(33/65) or 0.99996
Step-by-step explanation:
Cos of an angle is described as
Cosine = adjacent / hypotenuse
where adjacent is the closest side to the angle so in this case adjacent is IH
Hypotenuse is the longest side of a right triangle ALWAYS
sooooo Cosine of angle h is cos(33/65) or decimal form 0.99996
Please help me with this please actually help me please and thank you
Answer:
y=3x-1
y=3x+4
this has no solutions from looking at this we can see that the slope is the same so thats means that these are parell and will never cross and will never intersecet
another way to look at this is if we look at these equation
so we now that y=y so
3x-1=3x+4
+1
3x=3x+5
-3x
0=5
wait at minute this makes no sense 0 doesn't equal 5 so
no solution
Hope This Helps!!!