Answer:
The linear factors are:
[tex]x - 2[/tex]
[tex]x + 3[/tex]
[tex]x + 1[/tex]
Step-by-step explanation:
Given
[tex]x^3 + 2x^2 - 5x - 6[/tex]
Required
Select all linear factors of the polynomial
Solving for x - 2;
Equate x - 2 to 0 and solve for x
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
Substitute 2 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex]2^3 + 2(2^2) - 5(2) - 6[/tex]
[tex]= 8 + 8 - 10 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x - 2 is a factor
Solving for x + 3;
Equate x + 3 to 0 and solve for x
[tex]x + 3 = 0[/tex]
[tex]x = -3[/tex]
Substitute -3 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](-3)^3 + 2(-3^2) - 5(-3) - 6[/tex]
[tex]= -27 + 2(9) + 15 - 6[/tex]
[tex]= -27 + 18 + 15 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x + 3 is a factor
Solving for x - 1;
Equate x - 1 to 0 and solve for x
[tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
Substitute 1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](1)^3 + 2(1^2) - 5(1) - 6[/tex]
[tex]= 1 + 2(1) - 5 - 6[/tex]
[tex]= 1 + 2 - 5 - 6[/tex]
[tex]= -8[/tex]
Because, we did not arrived at 0, then x - 1 is not a factor
Solving for x + 1;
Equate x + 1 to 0 and solve for x
[tex]x + 1 = 0[/tex]
[tex]x = -1[/tex]
Substitute -1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](-1)^3 + 2(-1^2) - 5(-1) - 6[/tex]
[tex]= -1 + 2(1) + 5 - 6[/tex]
[tex]= -1 + 2 + 5 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x + 1 is a factor
is x=-3 a function plz respond in one minute
Answer:
x = -3 is not a function because, for one thing, its graph does not pass the vertical line test.
Step-by-step explanation:
1. f(x) = x² - 4 ; if x is even = 3x – 2; if x is odd solve for f(4) and f(5)
=======================================================
Explanation:
This is a piecewise function as it is composed of two pieces.
The equation for f(x) depends on what x is. Specifically whether it is even or odd.
If x is even, then f(x) = x^2-4. If x is odd, then f(x) = 3x-2
------------
f(4) means f(x) when x = 4. We have an even number input for x, so we'll go with f(x) = x^2-4
f(x) = x^2 - 4
f(4) = 4^2 - 4
f(4) = 16 - 4
f(4) = 12
------------
When x = 5, x is now odd, so use f(x) = 3x-2
f(x) = 3x-2
f(5) = 3(5) - 2
f(5) = 15 - 2
f(5) = 13
Please answer this!!! Thank you!!!
I hope this helped! Good luck with the rest of your class :)
Please help me I am bad at this stuff
UGH ONLY EXPERT GIVE ME ANSWER PPL DO WRONG ANSWERS Find the number of rectangles in 6×6 chessboard. ITS NOT 36
Answer:
I think it is 441
Step by step explanation:
To make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. So there would be 91 squares and 441 rectangles.
Calculate the coefficient of x14,4 in the expansion of (x + y)18,
Answer: 3060
Step-by-step explanation:
Formula : (r+1)th term of [tex](a+b)^n[/tex] : [tex]T_{r+1}=\ ^nC_r(a)^{n-r}(b)^r[/tex]
To find: Coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex].
Let the term in the expansion of [tex](x + y)^{18}[/tex] be [tex]^{18}C_r x^{18-r}y^r=x^{14}y^4[/tex]
[tex]\Rightarrow\ r=4[/tex]
Now, Coefficient = [tex]^{18}C_r=^{18}C_4=\dfrac{18!}{4!14!}[/tex] [[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
[tex]=\dfrac{18\times17\times16\times15\times14!}{14!(24)}\\\\=3060[/tex]
Hence, the coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex] is 3060 .
PLEASE ANSWER ASAP!!!!!! WILL MARK BRAINLY
Answer:
i think u r correct
Step-by-step explanation:
good job
Answer:
B, C, and E ([tex]x\leq -7,[/tex] The graph has a closed circle, and -7 is part of the solution.)
Step-by-step explanation:
Let's first solve the inequality of [tex]15\geq 22+x[/tex].
[tex]15\geq x+22[/tex]
[tex](15)-22\geq( x+22)-22[/tex]
[tex]-7\geq x[/tex]
[tex]x\leq -7[/tex]
So the final equation comes out to be [tex]x\leq -7[/tex].
This graph has a closed circle as it is a greater than OR equal to.
And -7 is a part of this solution as it is the number x is being compared to.
Let me know if I got anything wrong.
Pls Help!! Jazzmin has 2/5 of a pie. How many 1/10's of a whole pie are there in 2/5 of a whole pie?
Answer options: a.) 1/25 b.) 1/4 c.) 25 d.) 4
PLS write the correct answer
Answer:
d
Step-by-step explanation:
2/5÷ 1/10 = [tex]\frac{2}{5}*\frac{10}{1}[/tex]
= 2 * 2
= 4
Answer:
b
Step-by-step explanation:
LCD of (5, 10): 10
2/5=4/10(multiply top and bottom by 2)
(4/10)/(1/10)= 4
Therefore, 1/10 is 1/4th of 2/5
Ice cream bars come in a container that cost $3.12 for 6. What is the unit rate for the ice cream bars
Answer:
$1.92
Step-by-step explanation:
The equation would be 6/3.12
that equals 1.92.
Help please I will name the Brainily answer
Answer:
B
Step-by-step explanation:
So, for five cups of water, you need one cup of sugar. 1s=5w.
Now, you divide both sides by five.
1/5s=1/w
Find the smallest four digit number which Is divisible by 18 24 and 32
Answer:
The smallest four digit number divisible by 18, 24, and 32 is 1152.
Step-by-step explanation:
The LCM of the 3 numbers are 288
Then, the smallest four-digit number would equal 1152 (288*4)
Take L.C.M. of 18,24,32= 288
Resulting in 1152 :)
P(n) models the probability, when rolling a pair of dice, of obtaining two numbers whose sum is n 2 6 7 P(n) 1/36 5/36 6/36 when does the probability increase faster? a)Between a sum of 2 and a sum of 6 b) Between a sum of 6 and a sum of 7 c)the probability increases at the same rate over both intervals
Answer:
Option c.
Step-by-step explanation:
From the given table, it is clear that
[tex]P(2)=\dfrac{1}{36}[/tex]
[tex]P(6)=\dfrac{5}{36}[/tex]
[tex]P(7)=\dfrac{6}{36}[/tex]
The increasing rate of probability between a sum of 2 and a sum of 6 is
[tex]r_1=\dfrac{P(6)-P(2)}{6-2}[/tex]
[tex]r_1=\dfrac{\dfrac{5}{36}-\dfrac{1}{36}}{4}=\dfrac{1}{36}[/tex]
The increasing rate of probability between a sum of 6 and a sum of 7 is
[tex]r_2=\dfrac{P(7)-P(6)}{7-1}[/tex]
[tex]r_2=\dfrac{\dfrac{6}{36}-\dfrac{5}{36}}{1}=\dfrac{1}{36}[/tex]
Since [tex]r_1=r_2[/tex], therefore the probability increases at the same rate over both intervals.
Hence, the correct option is c.
Answer:
c)the probability increases at the same rate over both intervals
Step-by-step explanation:
it was right on khan academy
Maurice has a String that is 15 inches long. He has beads that are 3 inches long. How many beads will fit on the string?
Answer:
5
Step-by-step explanation:
Take the length of the string and divide by the length of a bead
15/3 = 5
We can fit 5 beads
Answer:
5 beads
Step-by-step explanation:
In order to find out how many 3-inch beads could fit onto a 15-inch string, we have to divide the numbers to find out how many beads could fit onto the string.
[tex]\frac{15}{3} =5[/tex]
Maurice can fit 5 beads onto the 15-inch string.
Write an algebraic equation to match each graph. (These graphs are not drawn to scale!) help pls fast
Answer y=x
Step-by-step explanation:
y=x when x equal one y equals one
The algebraic equation to match each graph will be y = | x |.
What is an equation?
The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
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.
The given graph shows that for every value of y the value of x will always be positive. Then the algebraic equation will be written as below:-
y = | x |.
Therefore, the algebraic equation to match each graph will be y = | x |.
The graph of the equation is attached with the answer below.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ5
PLEASE HELP ME OUT! Check out the first two questions on my profile please! It will really help me out
NIJFNC JFVNJNFDVCMK DSN CHSFBNCODJ MKNVF
Step-by-step explanation:
When simplified, 4x/7y + 3x/5y is written as?
Answer:
41x/35y
Step-by-step explanation:
combine like terms
If a function f has an inverse function, then fis one-to-one.
A) True
B) False
Answer:
true
Step-by-step explanation:
An airplane takes 5 hours to travel a distance of 3900 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is _____ (mph,hour,miles) and the speed of the wind is ____(mph,hour,miles)
Answer:
not quite sure what this is asking for but the average speed is 7800/11
ASAP!! can someone help answer these and include work, whoever answers most gets brainliest!! i underlined the questions
your work for the first one is perfect!!
the second one gives you the side lengths of x+2 and x-5. the formula for the area of a rectangle is l×w so you have to multiply (x+2)(x-5) and im sure you can figure that out but the answer to that is x^2-3x-10
you set up number 3 right, you just need to continue with the distribute property which would give you 4x^2-20x+25
number 4 is the same as the other ones and the answer is 36x^2-1
number 5 is just distributing the -z^3 into everything in the parenthesis giving you -5z^3-z^4+4z^5
I cant see all your work for number 6, but I can see that your term for c is 5, when it is actually -5. it looks like you didnt subtract it to make the quadratic equal to zero and to do that you would have to subtract 5.
tbh I cant read number 7
hope that helped :)
How to find constant M ? did I do anything wrong here ?
Answer:
M=-1, N=7
Step-by-step explanation:
Something went wrong on the 4th line.
From the third line, it should read
2x^2-x+6Mx-3M+4
=x(2x-1+6M) - 3M+4
Equating with the RHS,
2x-1+6M = 2x-7
6M = -7+1 = -6
M = -1
Therefore
N = -3M+4 = -3(-1)+4 = 7
or
M=-1, N=7
Find the measure of y.
Multiply and simplify (x2)(x4)(x-5)
Answer:
(x45)
Step-by-step explanation:
(x2) (x4) (x-5)
(x8) (x-5)
(x45)
In a particular year, a total of 44,064 students studied in two of the most popular host countries when traveling abroad. If 8382 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were _______ students who studied abroad in the most popular host country.
Answer:
The answer would be 35066 :)
Step-by-step explanation:
(y+5554) + y = 64578
Combine like terms
2y = 64578-5554
2y = 59024
y = 29512
x = 29512 + 5554 = 35066
why is it important to break down the radical into its prime factor?
Answer:
The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorization of a number by using a factor tree and dividing the number into smaller parts.
Step-by-step explanation:
Mike bought four new baseball trading cards to add to his collection. The next
day his dog ate half of his collection. There are now only twenty-nine cards left.
How many cards did Mike start with ?
Answer:
58 Cards
Step-by-step explanation:
fill in the blank with <,>,or,= to make the statement true -1 1/2 _ -1/4
Answer:
<
Step-by-step explanation:
Since it is a negative value, whatever fraction is closer to 0 will be greater.
Determine whether quadrilateral DEFG is similar to quadrilateral QRST. If so, give the similarity statement. options: A) QRST ∼ GFED B) Impossible to determine. C) QRST ∼ DEFG D) The quadrilaterals are not similar.
Answer:
A) QRST ∼ GFED
Step-by-step explanation:
We have to compare the ratios of all the sides one by one. Once I divided each side length by the equivalent side length on all four sides of both quadrilateral, make sure they are all equal.
Answer:
A) QRST is similar to GFED
Step-by-step explanation:
quadrilateral GFED is 1.25 times larger than quadrilateral QRST not to be confused with QRST is similar to DEFG because then the sides would not correspond to each other
Let f(x) = 5x + 4 and g(x) = −2x + 1. Find the indicated value f(6)+g(-8) plz help quickly
Answer:
The answer is 51
Step-by-step explanation:
f(x) = 5x + 4
g(x) = −2x + 1
To find f(6)+g(-8) first find f(6) and g(-8) and add them
For f(6) we have
f(6) = 5(6) + 4
= 30 + 4
= 34
For g(-8)
g(-8) = - 2(-8) + 1
= 16 + 1
= 17
So we have
f(6)+g(-8) is
34 + 17
= 51
Hope this helps you
Rectangle has DEFG vertices D(-6, -5), E(-6,-2), F(-2,-2) and G(-2, -5). The figure is first translated 3 units up and then rotated 90 degree clockwise about the origin. What is the shape of the figure after this sequence of transformations?
Answer:
a rectangle
Step-by-step explanation:
Translation and rotation are rigid transformations. They do not change the shape or size. The figure is still a rectangle after these transformations.
HELPPPP PLEASEEE I DONT WANNA GOT TO GRANNYS HOUSE
Answer:
15
Step-by-step explanation:
f(5) = (5)^2 - 2(5) = 25 - 10 = 15