The factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
The given expression is [tex]30a^{6} -24a^{2}[/tex].
We need to factorise the given expression.
What are the factors?Each of these numbers and expressions is referred to as a factor of algebraic expressions if it is possible to express algebraic expressions as the product of numbers, algebraic variables, or algebraic expressions.
Now, [tex]30a^{6} -24a^{2}=6a^{2} (5a^{4}-4 )[/tex]
Therefore, the factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
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If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.
Answer:
x
Step-by-step explanation:
[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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D − 37 = 40
D =
Check your solution.
− 37 = 40
10 problems for 50 points
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
What are m and b in the linear equation y=2x+8
Answer:
m=2 and b=8
Step-by-step explanation:
this is a linear equation, which takes on the formula of y=mx+b
therefore in the equation y=2x+8, 2 is the m, and 8 is the b
Rewrite the following expression
X 9/7
Answer:
X1 2/7
Step-by-step explanation:
Step-by-step explanation:
We can write it in radical form, and the denominator of the exponent became the power of the radical. That is
And
We can also write it as
And that's the simplified form of the given exponential form .
Can y’all help me with ! I need correct anwsers ! Please
Answer:
-0.875
Step-by-step explanation:
So you have the points -4.25 and 2.50. To find the midpoint you simply add the two and then divide by 2. This results in (-4.25 + 2.50) / 2 = -0.875
How many square decimeters are in 687.1 cm²?
Answer:
6.871 decimeters
Step-by-step explanation:
687.1 square centimeters = 6.871 square decimeters
1 dm² = 100 cm²
Answer:
6.871
Step-by-step explanation:
calculator
Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
Which statement about –2h2 – 15h – 7 is true?
One of the factors is (h + 2).
One of the factors is (3h – 2).
One of the factors is (2h + 1).
One of the factors is (h – 7).
Answer:One of the factors of the given expression is (2h + 1).
Step-by-step explanation:
ed
Answer:
C on edge 23
Step-by-step explanation:
because i said so
Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answer:
Step-by-step explanation:
Giving the brainliest to those who answer!
If k(x) = 5x-6, which expression is equivalent to (k+ k)(4)?
Example:
[tex](f+g)(x)=f(x)+g(x)[/tex]
To add this, we can substitute in the functions and combine like terms.
Solving the QuestionWe're given:
[tex]k(x)=5x-6[/tex][tex](k+k)(4)=?[/tex]Add k to k:
[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]
Input x as 4:
[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]
Answer[tex](k+k)(4)=28[/tex]
(k+k)(4) is equivalent to 28.
What is function ?If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.
Addition of two functions : If f(x) & g(x) be two functions, then
(f+g)(x) = f(x)+g(x)
What is the required result ?Given, k(x) = 5x-6
Now, Adding function k with k we get,
(k+k)(x) = k(x)+k(x)
= (5x-6)+(5x-6)
= 5x-6+5x-6
= 10x-12
We have to find, (k+k)(4)
∴ (k+k)(4) = (10×4)-12
= 40-12
= 28
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Need help with this geometry question
Answer: 59
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle intercepted by it.
GUYS HELP NOW PLS WHAT IS THE PROBABILITY NOTATION FOR THE PROBABILITY OF CHOOSING A GREEN MARBLE HELPPPP PLS
The probability notation for the probability of choosing a green marble is P(G)
What is probability?This is simply defined as the extent to which something is likely to occur.
The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.
How to determine the probability notationProbability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:
Event of green marble = nGTotal event = nTProbability of green marble = P(G)P(G) = nG / nT
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If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).
Answer:
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Step by step explanation:
Given that,
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = x - 1[/tex]
Solution:
Solving for (f•g)(x):
[tex] = f(x) \cdot g(x)[/tex]
Now substitute the given values.
[tex] = x {}^{2} \cdot(x - 1)[/tex]
[tex] = x {}^{2} (x - 1)[/tex]
Apply distributive property:
[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].
Given that G=ab find the percentage increase in G when both a and b
increase by 10%
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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I need help pronto!!
Answer:
There were 42 fewer students who chose Football than Hockey.
Step-by-step explanation:
Fraction of students who chose Hockey
= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] units = 21
1 unit = 42
No. of students who chose Football
= 2 units ([tex]\frac{2}{6}[/tex])
= 84 students
No. of students who chose Hockey
= 3 units ([tex]\frac{3}{6}[/tex])
= 126 students
Difference between no. of students who chose Football and Hockey
= 126 - 84
= 42 students
∴There were 42 fewer students who chose Football than Hockey.
Please help! Will give the brainliest :)
Answer:
First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.
Angle CBA and DBE are vertical angles, meaning they are congruent.
so set the equation as:
(2x+21)=(5x)
21=5x-2x
21=3x
x=7
It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees
So to find angle measure of ABE:
We know that ABE and DBE form linear pair, so
180-35=145 degrees
145 degrees is the answer.
Hope it helps!
Answer:
∠ABE = 145°
Step-by-step explanation:
because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees
and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees
we can set this up as a system of equations (I will be writing ABE as "y")
2x + 21 + y = 180
5x + y = 180
We can combine this to beL
2x + 21 + y = 5x + y
- 2x -2x
21 + y = 3x + y
- y - y
21 = 3x
x = 7
If we plug this back into our original equations (which is set to 180 degrees), we can find y
2(7) + 21 + y = 180
14 + 21 + y = 180
35 + y = 180
- 35 - 35
y = 145
(remember, "y" is angle ABE)
we can check this value (ABE = 145) by substituting our second equation
5(x) + ABE = 180
35 + 145 = 180
180 = 180
(TRUE)
so, the measure of ∠ ABE is 145°
hope this helps!!
The rectangular prism has a vertex at (5, 6, 2). Which
ordered triples represent other vertices of the prism?
Check all that apply.
(0, 0, 2)
(0, 5,6)
(2,0, 5)
(5, 0, 2)
(5, 6, 0)
(6,2,0)
Answer:
A, D, E
Explanation:
It's right on edge lol
What is the domain of the function y=√√x+6-7?
x>|-7
x>|-6
x>|6
x>|7
The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]
Domain of a function refers to the values or range of input values of a function for which the function exists in real.
In this problem the given function is
[tex]y=\sqrt{(x+6)}-7[/tex]
Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.
So, for existence of function it is must to
[tex]x+6\geq0[/tex]
[tex]x\geq-6[/tex]
Hence the domain of the given function is given by [tex]x\geq-6[/tex]
Hence the correct option is (B).
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Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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RQ=5x+1 and QT =3x+15. Find QT.
The length QT is 36 units
How to determine the length QT?The attached image represents the missing information in the question
From the image, we have:
RQ =QT
Substitute known values
5x + 1 = 3x + 15
Evaluate the like terms
2x = 14
Divide by 2
x = 7
Substitute x = 7 in QT = 3x + 15
QT = 3 * 7 + 15
Evaluate
QT = 36
Hence, the length QT is 36 units
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1) Which relation is a function?
es
A) x = y² - 3
B) x = y - 4x²
C) y² = 4x - 6
D) x² = y²-10
Answer:
B
Step-by-step explanation:
x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function
Solve the following systems using the elimination method. -3x+4y=-8 and 3x+ y=-17
Answer:
(-4, -5)
Step-by-step explanation:
-3x + 4y = -8
+
3x + y = -17
= 5y = -25 = y = -5
-3x + 4(-5) = -8
-3x - 20 = -8
-3x = 12
x = -4
Which of the following values are in the domain of the function graphed
below? Check all that apply.
Answer:
A. -2B. -1D. 0E. 4Step-by-step explanation:
The domain includes all x values, and here, it is [-2, 4].
A boat travels upstream for 42 miles in 3 hours and returns in 2 hours traveling downstream in a river. What is the rate of the boat in still water and the rate of the current?
The rate of the boat in still water is : miles per hour
The rate of the current is: miles per hour:
Answer:
17.5 mph
Step-by-step explanation:
Let the speed of the boat in still water be B mph
Let the rate of the current be R mph
When going upstream the effective speed is B-R mph. In terms of values given effective upstream speed = 42/3 = 14 mph
So,
B-R = 14 ... (1)
Similarly downstream speed is B + R (faster downstream)
B + R = 42/2 = 21 .... (2)
(1) + (2) ==> 2B = 35
B = 35/2 = 17.5 mph
Find the inverse of the function.
y=x+8
Answer:
y^-1= x +8
Step-by-step explanation:
this may be helpful for you
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms which ones should he check
Step-by-step explanation:
please attach a picture for us to see the choices
