Answer:
3x 3-x and 3+x
GUY HELP DID CLICK OF THE RIGHT ONE ?
Answer:
c
Step-by-step explanation:
it just is that's the right book
What is the 18th term to the sequence 14,18,22
Find area of the region under the curve y=9−3x^2 and above the x-axis.
Answer:
A = 12√3
Step-by-step explanation:
first find the limits by finding the zeros
0 = 9 − 3x²
3x² = 9
x² = 3
x = ±[tex]\sqrt{3}[/tex]
[tex]A = \int\limits^a_b ({9 - 3x^2\\}) - 0\, dx[/tex]
where b = [tex]-\sqrt{3}[/tex] and a = [tex]\sqrt{3\\}[/tex]
A = 9x - x³ [tex]\left \{ {{\sqrt{3} } \atop {-\sqrt{3} }} \right.[/tex]
[tex]A = 9\sqrt{3} - \sqrt{3} ^3 - (9(-\sqrt{3)} - (-\sqrt{3} )^3)[/tex]
[tex]A = 9\sqrt{3} -3\sqrt{3} +9\sqrt{3} - 3\sqrt{3}[/tex]
[tex]A = 12\sqrt{3}[/tex]
2. The sum of two cubes can be factored by using the formula q3 + b3 = (a + b)(a? - ab + b).
(a) Verify the formula by multiplying the right side of the equation.
(b) Factor the expression 8x3 + 27.
(c) One of the factors of 23 - bºis a - b. Find a quadratic factor of a3 - bº Show your work.
(d) Factor the expression x3 - 1.
Factorization involves breaking down an expression.
The factorized expression of [tex]8x^3 + 27[/tex] is [tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]The other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]The factorized expression of x^3 - 1 is [tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]The sum of cubes is given as:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
(a) Verify the formula
Expand the expression on the right-hand side
[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]
Collect like terms
[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]
[tex](a^3 + b^3) = a^3 + b^3[/tex]
The formula has been verified
(b) Factorized 8x^3+ 27
We have:
[tex]8x^3 + 27[/tex]
Express 27 as 3^3
[tex]8x^3 + 27 =8x^3 + 3^2[/tex]
Express 8 as 2^3
[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]
Rewrite as:
[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]
Given that:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
The expression becomes
[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]
[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]
(c)The other factor of 2^3 - b^3
By difference of cubes, we have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
So, the equation becomes
[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]
This gives
[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]
Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]
(c) Factor x^3 - 1
We have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
Express 1 as 1^3 in x^3 - 1
[tex]x^3 - 1 =x^3 - 1^3[/tex]
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes
[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]
[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]
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Can anyone help with this?
+
-
1. The amount M (in trillions of dollars) of mortgage debt outstanding in the United States from 1990
through 2009 can be approximated by the function M = f(0) = 0.0037(t + 14.979), where t = 0
represents the year 1990.
(a) Describe the transformation of the common function f(x) = x2. Then sketch the graph over the
intervalo s t < 19.
(b) Rewrite the function so that t = 0 represents the year 2000. Explain how you got your answer.
(c) Use the model from part (b) to predict the mortgage debt in the year 2014.
The give quadratic function is dilated by the given coefficient, and shifted
horizontally to the left.
(a) The transformation of the common function f(x) are;
f(t) is made more wider than f(x) f(t) is shifted more to the left than the common function f(x).Please find attached the required graph created with MS Excel
(b) Where t = 0, represent the year 2,000 we have;
f(t) = 0.0037·(t + 24.979)²(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion
Reasons:
The given function is f(t) = 0.0037·(t + 14.979)²
Year 1990 is t = 0
(a) The given common function is; f(x) = x²
The transformation of the quadratic function are;
The coefficient 0.0037 widens the common function such that f(t) is wider
than f(x).
The constant, 14.979 added to the variable, t, shifts the graph of the
common function horizontally to the left.
Therefore;
f(t) is wider and shifted to the left more than the common function f(x)Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.
(b) The amount of mortgage debt in 2,000 is given as follows;
With t' = 0 represent the year 2,000, we have;
At year 1990, t' = -10
Which gives, t' = t + 10
From which we have;
f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)² = 0.0037·(t' + 24.979)²
Therefore;
The function with t = 0 representing the year 2,000 is presented as follows;
f(t) = 0.0037·(t + 24.979)²
(c) In the year 2014, we have;
t = 2014 - 2000 = 14
Which gives;
f(14) = 0.0037·(14 + 24.979)² ≈ 5.622
The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars
Learn more about transformation of quadratic functions here:
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If any number in decimal numeration system is denoted by 723 then what is the value of the number in binary numeration system?
Answer:
723 -> 01011010011
Step-by-step explanation:
Malik needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 2.5 hours and charged him $73 for parts. The
total was $235.50. Write and solve an equation which can be used to determine x, the
cost of the labor per hour.
Answer:
2.5x+73=235.5
2.5x=162.5
x=65
ANSWER NUMBER 500 L GOOOOOOOO!!!!!!!!!!!!!!!!!
Hope This Helps!!!
The equation will be 2.5x+73=235.5 and the value of x will be 65.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Malik needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 2.5 hours and charged him $73 for parts. The total was $235.50.
The equation can be written as below:-
2.5x+73=235.5
2.5x=162.5
x=65
Therefore, the equation will be 2.5x+73=235.5 and the value of x will be 65.
To know more about an expression follow
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The initial balance of a savings account was $275 Adter which transactions will the balance of the savings account be the same as the initial balance?
A. a withdrawal or $232 followed by a deposit of $132
B. a deposit of $278 followed by a withdrawal of $278
C. a withdrawal of $115 followed by a deposit of $312
D. a deposit of $205 followed by a withdrawal of $317
The transactions that would leave the initial balance the same are a deposit of $278 followed by a withdrawal of $278.
The transactions that would leave the initial balance the same are transactions that net to zero. Withdrawals reduce the balance in the account. Deposits increase the value of the balance in the account.
Option A: Net balance
$275 - $232 + 132 = $175
Option B: Net balance
$275 + $278 - $278 = $275
Option C: Net balance
$275 - $115 + $312 = $472
Option D: Net balance
$275 + $205 - $317 = $163
To learn more about subtraction, please check: https://brainly.com/question/854115
Help, im incredibly confused
[tex]f[/tex](x) = 0.20x + 35 : 29.5
No clue if someone can explain
Answer:
your trying to find out how much each cookie cost
from looking at this we can see that 2 cookies is 1 dollar so each cookie is 50 cents
Hope This Helps!!!
Jackson bought 6 basketballs for 72 dollars what was the price per basket ball
Answer:
the answer would be 12 I say this because 72 divied by 6 would equal 12
Answer:
12 dollars
Set up a proportion.
6/72=1/x
Solve by cross-multiplying (my preferred method) and then you will end up with the final answer of x=12.
12 is the answer :)
PLEASE MARK BRAINLIEST!
THANK YOU & HAVE A WONDERFUL DAY :))
The equation x + y = z relates the whole numbers x, y, and z. How does z compare to x?
If it helps, consider an example where you substitute 3 for x, 5 for y, and 8 for z.
y is z less than x.
y is z more than x.
x is y less than z.
x is y more than z.
Answer:
C. x is y less than z
Step-by-step explanation:
x+y=z
by using transposition
x = z-y
whatever x is, it is equal to the value of y taken from z
one fifth of sum of two angles is 24 and their diffetence is 14 find the two angles
Answer:
Angles are [tex]67^0,53^0[/tex]
Step-by-step explanation:
Let the angles be [tex]x,y[/tex]
One fifth of sum of two angles is 24
[tex]\frac{x+y}{5} =24\\\\x+y=120[/tex]
The difference is [tex]14[/tex]
[tex]x-y=14[/tex]
[tex]2x=134\\\\x=67^0[/tex]
[tex]y=120-67\\\\=53^0[/tex]
A mailing carton in the shape of a cube has a volume of 684 cubic inches. What is the length of one side of the carton to the nearest tenth of an inch?
Check the picture below.
Pls Help! Actually give a legit answer (NO LINKS!)
Answer:
unfortunately i cannot tell you the exact answers; however, i can suggest something instead. my suggestion is that if there's any math notes that are available, maybe you could look over them-then apply that to the problems.
Step-by-step explanation:
I hope this helps you!
Please explain how you got to the answer. I am trying to understand the concept that went into it.
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
A. x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
B. x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
C. x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
D.x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Answer:
D. x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Step-by-step explanation:
Evaluate 0 and 1 (xe+ex)Dx
Use the counting techniques from the last chapter. A bag contains three red marbles, three green ones, one fluorescent pink one, two yellow ones, and four orange ones. Suzan grabs four at random. Find the probability of the indicated event.
She gets at least two red ones, given that she gets at least one green one.
Using the combination formula and the probability concept, it is found that there is a 0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.
A probability is the number of desired outcomes divided by the number of total outcomes.In this problem, the order in which the marbles are taken is not important, hence, the combination formula is used to solve this question.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
2 red from a set of 3.1 green from set of 3.1 from a set of 1 + 2 + 1 + 2 + 4 = 10.Hence:
[tex]D = C_{3,2}C_{3,1}{C_{10,1}} = \frac{3!}{2!1!} \times \frac{3!}{1!2!} \times \frac{10!}{1!9!} = 90[/tex]
Total outcomes:
Four marbles are taken from a set of 13, hence:
[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]
Then, the probability is:
[tex]p = \frac{D}{T} = \frac{90}{715} = 0.1259[/tex]
0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.
To learn more about the use of the combination formula and the probability concept, you can check combination formula and the probability concept,
What is the answer to this question?
Answer:
linear = 3x+y = 12, y = x/2 -3, y=x
nonlinear y = 6/x -2, y=3x³+5
1. Use precise mathematical language to justify and explain each mathematical process.
Use the rectangle with side lengths 5.22 – 8x + 9 and x + 5 for the following two questions.
1. What is the perimeter of the rectangle? Write a summary of the process used to determine the expression.
2. What is the area of the rectangle? Write a summary of the process used to determine the expression.
Mathematical processes are the steps used to determine the result of operations
The perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]The area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]The dimension of the rectangle is given as:
[tex]Length = 5x^2 - 8x + 9[/tex]
[tex]Width = x + 5[/tex]
(1) The perimeter of the triangle
This is the sum of the side lengths of the rectangle.
So, we have:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
This gives
[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]
Collect like terms
[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]
Open brackets
[tex]Perimeter = 10x^2 - 14x + 28[/tex]
Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]
(2) The area of the triangle
This is the product of the dimensions of the rectangle.
So, we have:
[tex]Area = Length \times Width[/tex]
This gives
[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]
Open brackets
[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]
Collect like terms
[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]
[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]
Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]
Read more about areas and perimeters at:
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how do i get more points? and why do i need it?
Answer:
You get more points by answering people's questions. You use points to get help from other people.
Answer: Answer people's questions to get points and use those points to get an answer to your question.
Rewrite each equation in exponential form:
log4(q) = m
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_4(q)=m\implies 4^m = q[/tex]
Zachery sold 85 shares of stock for $65 a share. He paid $43 for it three years ago. How much was his capital gain?
Answer:
85*65=5525
85*43=3655
5525-3655=1870
Hope This Helps!!!
some help, I need some answers
Answer:
Well your Hypotenuse is 10 and your other angle is 8 so it is most likely 6 because you see a change in 2 each time and it is about 2 units smaller because all right triangles follow a pattern
Step-by-step explanation:
if it was too go even higher it would go to 12,14,16 etcetera
I have 100 points
i need some help!!
Answer:
6c+2(5-7c)=6c+10-14c
=10-8c=-8c+10A. -8c+10 is correct option.
Thanks :)Please help me on this!!! I’d really appreciate it!!!
Answer:
B
Step-by-step explanation:
During a chess match there are 15 pieces left on the board. the ratio of the white pieces to black pieces is 3 : 2 how many white pieces are on the white board?
==========================================================
Explanation:
The ratio 3:2 scales up to 3x:2x for some positive whole number x.
We have 3x white pieces, 2x black pieces, and 3x+2x = 5x pieces total. Set this equal to the 15 mentioned and solve for x.
5x = 15
5x/5 = 15/5
x = 3
Therefore, there are 3x = 3*3 = 9 white pieces and 2x = 2*3 = 6 black pieces, which gives 9+6 = 15 total. The ratio 9:6 reduces to 3:2 after dividing both parts by the GCF 3.
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See explanation
Step-by-step explanation:
Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)
G (-1, 3) G' (-1.5, 4.5)
F (-2, -2) F' (-3, -3)
G'x / Gx = -1.5/-1 = 1.5
G'y / Gy = 4.5 / 3 = 1.5
F'x / Fx = -3 / -2 = 1.5
F'y / Fy = -3 / -2 = 1.5
How does the number 7 in 777.77 in the tenths place compare to 7 in the hundredths place
Answer:
0.7 is 7/10 Example out of ten cookies 7 are chocolate chip
0.07 is 7/100 Example out of 100 cookies 7 are chocolate chip
Hope This Helps!!!
-2 1/5 - 1 3/10 help!!