For questions 3 & 4, name the applicable polynomial identity and use the identity to multiply each expression.
3. (2 + 8)(2 − 8)
4. ( + 33)2
Answer:
The quadratic x2 − 5x + 6 factors as (x − 2)(x − 3). Hence the equation x2 − 5x + 6 = 0
has solutions x = 2 and x = 3.
Similarly we can factor the cubic x3 − 6x2 + 11x − 6 as (x − 1)(x − 2)(x − 3), which enables us to show that the solutions of x3 − 6x2 + 11x − 6 = 0 are x = 1, x = 2 or x = 3. In this module we will see how to arrive at this factorisation.
Polynomials in many respects behave like whole numbers or the integers. We can add, subtract and multiply two or more polynomials together to obtain another polynomial. Just as we can divide one whole number by another, producing a quotient and remainder, we can divide one polynomial by another and obtain a quotient and remainder, which are also polynomials.
A quadratic equation of the form ax2 + bx + c has either 0, 1 or 2 solutions, depending on whether the discriminant is negative, zero or positive. The number of solutions of the this equation assisted us in drawing the graph of the quadratic function y = ax2 + bx + c. Similarly, information about the roots of a polynomial equation enables us to give a rough sketch of the corresponding polynomial function.
As well as being intrinsically interesting objects, polynomials have important applications in the real world. One such application to error-correcting codes is discussed in the Appendix to this module.
Step-by-step explanation:
What is the slope from the following ordered pairs? (-2,0) (0,4) (2, 8) (4, 12)
Answer:
the slope is 2
Step-by-step explanation:
y2-y1
divided by
x2-x1
equals
4-0
divided by
0- (-2)
equals
4/2 which is 2
Which of the following completes the proof?
Triangles ABC and EDC are formed from segments BD and AC, in which point C is between points B and D and point E is between points A and C.
Given: Segment AC is perpendicular to segment BD
Prove: ΔACB ~ ΔECD
Reflect ΔECD over segment AC. This establishes that ∠ACB ≅ ∠E'C'D'. Then, ________. This establishes that ________. Therefore, ΔACB ~ ΔECD by the AA similarity postulate.
translate point E' to point A; ∠E'D'C' ≅ ∠ABC
translate point D' to point A; ∠E'D'C' ≅ ∠BAC
translate point D' to point A; ∠D'E'C' ≅ ∠BAC
translate point E' to point A; ∠D'E'C' ≅ ∠BAC
From the given question, the required answer is option D. It can be deduced that: Reflect ΔECD over segment AC. This establishes that ∠ACB ≅ ∠E'C'D'. Then, (translate point E' to point A). This establishes that (∠D'E'C' ≅ ∠BAC). Therefore, ΔACB ~ ΔECD by the AA similarity postulate.
Rigid transformation is a process of resizing a given shape or figure. This can be done by either increasing or decreasing its dimensions (size) or changing its orientation. Some of the methods required in rigid transformation are: reflection, translation, rotation etc.
From the given question,
if ΔECD is first reflected over (turned about) segment AC, it would be deduced that m∠ACB ≅ m∠E'C'D' = [tex]90^{o}[/tex](right angle principle).
Then, the next process is to translate (extend) point E' to point A, so that m∠D'E'C' ≅ m∠BAC.
This would also ensure that m∠E'D'C' ≅ m∠ABC due to the translation.
This implies that ΔACB ~ ΔECD by the AA similarity postulate.
Therefore, performing reflection and translation operations on ΔECD step-wisely can be used to prove that ΔACB ~ ΔECD by the AA similarity postulate.
A sketch for more clarifications is herewith attached to this answer.
For more clarifications, visit: https://brainly.com/question/20486329
Answer:
its d, i took the test
(at the bottom of the photo it says earned 1 point meaning it right)
Expectations: Post at least 3 different ways to represent the number
Answer:
Step-by-step explanation:
8 1/4%
8.25%
0.0825
What is 1 1/3 as a percent pls?
Answer:
133.3333333333333333%
Step-by-step explanation:
never ending 3
Answer:133.3%
Step-by-step explanation:
-x+ 5y = 1
- 2x + 10y = 2
Answer:
24
Step-by-step explanation:
Calculate the value of 4x2 + xy when x = 3 and y=-2.
Answer:
Step-by-step explanation:
4x squared + xy
4x(4x) + xy
12(12) + 3 x 2
144 + 6
= 150
Camaro's are the best.
Answer:
I would love me a camaro
Step-by-step explanation:
Answer:
First car i wanted my whole life!!!!!
Step-by-step explanation:
Let a, b, and c be constants, and let x be a variable. Which of the following is
equivalent to a(x + b) < c when a < 0? (Rearranging Formulas) IMAGE BELOW :D
Answer:
C
Step-by-step explanation:
We are given that:
[tex]a(x+b)<c[/tex]
Where a < 0.
To solve for x, we can divide both sides by a.
Since a < 0, a is negative. Hence, we must flip the inequality sign. This yields:
[tex]\displaystyle x + b > \frac{c}{a}[/tex]
Subtract b from both sides. Hence:
[tex]\displaystyle x>\frac{c}{a}-b[/tex]
In conclusion, our answer is C.
Simplify: √x16y36
Possible answers
x8y18
x8y6
x4y18
x4y6
Answer:
result(s) found
x8y18
See steps
Step by Step Solution:

Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y3" was replaced by "y^3". 1 more similar replacement(s).
Simplify :sqrt(x16y36)
Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x16y36) = x8y18
Simplified Root :
x8y18
Step-by-step explanation:
please mark me as the brainliest thank you
Match the percent on the left with the sum of friendly percents on the right
Answer: See explanation
Step-by-step explanation:
25% + 25% + 25%
= 75%
10% + 25%
= 35%
50% + 10%
= 60%
10% + 10%
= 20%
1. The monthly rent (1) for an office place is directly proportional to the size of the office
(a) if a 420 sq foot office rents for 12, 600 pesos per month, then what is the rent for a
900 sq foot office?
3. If F, G, and H are the midpoints of the sides
of AJKL, FG = 37, KL = 48, and GH = 30,
find each measure.
K
a) FH =
G
b) JL =
c) KJ =
d) FJ =
Answer:
Step-by-step explanation:
(a). FH = KL / 2 = 48 ÷ 2 = 24
(b). FG = JL / 2 = 37 ⇒ JL = 2 × FG = 74
(c). KJ = 2 × GH = 2(30) = 60
(d). FJ = KJ ÷ 2 = 30
HELPPPP
solve the equation log(2x-3)=2
Answer:
I put it in a calculator and got 51.5
Step-by-step explanation:
Answer:
If I'm understanding the question right it's -.05
Step-by-step explanation:
(2x - 3) = 2
There is no more simplifying to be done in the parentheses.
2x - 3 = 2
Subtract 3 on each side to get the x value by itself.
2x = -1
Divide each side by 2 so the x is by itself.
x = -.05
And that's it, hope I helped :)
Which is the best estimate for (6.3 times 10 Superscript negative 2 Baseline) (9.9 times 10 Superscript negative 3 Baseline) written in scientific notation? 6 times 10 Superscript negative 4 60 times 10 Superscript negative 5 6 times 10 Superscript 7 60 times 10 Superscript 6
Answer:
A
Step-by-step explanation:
can 0 go into 4 and 4 go into 8 an 8 go into 12
Answer:
No
Step-by-step explanation:
Answer:
0 cannot go into 4
4 can go into 8
8 cannot go into 12
The temperature of dry ice is -78.5° C. Which is colder, dry ice or liquid nitrogen?
Answer:
Liquid nitrogen is 1. Liquid and 2. 90°C and dry ice is, well, ice. So dry ice is obviously colder.
Step-by-step explanation:
Lakita wants to go to trade school and study electronics for a two-year program. Her tuition and books will cost about $5,500 per year. She will also spend about $100 a month commuting from her parents' house to school. How much will her education cost her in total?
Answer:
$13,400
Step-by-step explanation:
We will first have to take account of the commuting cost, years at school, and total cost of tuition and books
It would cost $5,500 per year, she is studying at the school for 2 years, we will multiply 5,500 by 2
$5,500 * 2
= $11,000
The cost of commuting per month will be multiplied by 12 to represent a year and another 2 for two years
$100 * 12 * 2
= $2400
We all these together for the total cost of her education
$11,000 + $2,400
= $13,400
Factor the polynomial expression 8x^2 + 2.
Answer: 4096
Step-by-step explanation:
(2x+i)(2x-1)
HELP!!
I have the answer all I need is to show the work pls help if u can
What is the measure angle of angle A in the triangle?
Answer: 62
Step-by-step explanation:
find angle c: 180-116= 64
solve for x:
(2x+4)+(3x-13)+64=180
5x+55=180
5x=125
5x/5 = 125/5
x=25
plug in x: 3(25)-13= 62
Graph the function.
5. g(x) = 3(x - 2)
10
8
03
N
2 4
6
8 10
10 8 6 4 2
-2
44
-6
-8
-101
Answer:
10 8 6 4 2 hope that helps
If you invest $1000 into an account that earns 8.5% interest each year, WHAT
EQUATION WOULD MODEL how much you would have after 35 years?
Answer:
i believe it would be 35(1000 x 8.5%)
Step-by-step explanation:
pleaseee helpppp!!!!
Answer:
Substitute the given value into the function and evaluate.
2 x 3 + 7 x 2 − 4 x − 15
Step-by-Step Process
A fair coin is flipped 5 times
What is the probability that no two consecutive flips have the same result?
Express ur answer as a common fraction
HELP ME!!
Answer:
2/5
Step-by-step explanation:
The answer is common sense.
The probability that no two consecutive flips have the same result is [tex]\frac{1}{16}[/tex].
If a coin is flipped then there are two possible outcomes Head(H) and Tail (T).
So each flip can have 2 possible outcomes. It means 5 flips have [tex]2^5=32[/tex] possible outcomes.
Among these 32 outcomes only 2 outcomes : HTHTH and THTHT have "no two consecutive flips have the same result".
So the probability that no two consecutive flips have the same result is = [tex]\frac{2}{32} =\frac{1}{16}[/tex].
Learn more: https://brainly.com/question/13604758
Which equation represents the line containing the points (8,1) and (-4,-2)
Answer:
Answer is the 2nd one
Hope it was helpful
The sum of the ages of John and Mary is 32. Four years ago, John was twice
as old as Mary. Find the present age of each. Please use algebraic equations.
john: 56
Mary: 24
(Tbh I'm probably really wrong, I'm so sorry )
Answer: john is 20 and mary is 12
Step-by-step explanation:
J + M = 32
J - 4 = 2(M-4)
solve
A square-base pyramid has the following measurements: The base edges are 3cm The height of the pyramid is 8cm What is the slant height of the pyramid?
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
good luck
Harolds computer hard drive has 131.25 GB of free space which is about 17.5 of the capacity of his hard drive what is the capacity of the hard drive in GB
Answer: 1,000 gigabytes
Step-by-step explanation:
pleasee help mee ;-; i can't stand algebra, determine how many terms the geometric series has, and then find the sum of the series
-12 -4 - 4/3 - . . . - 4/243
Answer:
The series has 7 terms
[tex]\displaystyle S_7=\frac{4372}{243}[/tex]
Step-by-step explanation:
Geometric Series
In the geometric series, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the series:
-12, -4, -4/3, ..., -4/243
We can find the common ratio by dividing one term by the previous term:
[tex]\displaystyle r=\frac{-4}{-12}[/tex]
Simplifying:
[tex]\displaystyle r=\frac{1}{3}[/tex]
Sum of terms: Given a geometric series with first term a1 and common ratio r, the sum of n terms is:
[tex]\displaystyle S_n=a_1\frac{1-r^n}{1-r}[/tex]
We need to find how many terms the series has. Using the explicit formula of a geometric series:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
The last term is an=-4/243 and the first term is a1=-12. Solving for n:
[tex]\displaystyle n= \frac{\log(a_n/a_1)}{\log r}+1[/tex]
[tex]\displaystyle \frac{\log(-4/243/-12)}{\log 1/3}+1[/tex]
[tex]\displaystyle \frac{\log(1/729)}{\log 1/3}+1[/tex]
n=7
The series has 7 terms
Thus, the sum of the 7 terms of the series is:
[tex]\displaystyle S_7=-12\frac{1-(1/3)^7}{1-(1/3)}[/tex]
[tex]\mathbf{\displaystyle S_7=\frac{4372}{243}}[/tex]
simplify
-5v+3v
simplify
k-2-6+5k
Answer:
-5v+3v = -2v
k-2-6+5k = 6k - 8
Step-by-step explanation:
For -5v+3v
-5 + 3 = -2
V is left so it's -2v
For k-2-6+5k
k + 5k - 2 - 6
6k - 2 - 6
6k - 8
1) -5v + 3v
= -2v
2) k - 2 - 6 + 5k
First take all like terms (everything with the same letters):
k + 5k = 6k
6k - 2 - 6
-2 - 6
= -8
6k - 8