Answer:
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
Step-by-step explanation:
Given
[tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
[tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Required
Simplify and categorize the result based on their degree and number of terms
Simplifying [tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex]x(6x + 2) - \frac{1}{2}(6x + 2)[/tex]
Open bracket
[tex]6x^2 + 2x - 3x - 1[/tex]
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
Simplifying [tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
Open bracket
[tex]7x^2 + 3x -\frac{1}{3} * 21x^2 -\frac{1}{3}*- 12[/tex]
[tex]7x^2 + 3x -7x^2 + 4[/tex]
Collect like terms
[tex]7x^2-7x^2 + 3x + 4[/tex]
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
Simplifying [tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Open brackets
[tex]4*5x^2-4*9x+4*7+2*-10x^2+2*18x-2*13[/tex]
[tex]20x^2-36x+28-20x^2+36x-26[/tex]
Collect like terms
[tex]20x^2-20x^2-36x+36x+28-26[/tex]
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
plz help me i have a fever and i don't want to do math
Answer:
Four books because there are the most dots over that spot on the bottom number line thingy
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
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.
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
The factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot: 1 is labeled + x, 1 is labeled negative. 5 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 10 tiles are in the Product spot: 1 is labeled + x squared, 1 is labeled negative x, the 4 tiles below + x squared are labeled + x, and the 4 tiles below the negative x tiles are labeled negative. What are the factors of x2 + 3x – 4? (x + 4) and (x – 4) (x + 3) and (x – 4) (x + 4) and (x – 1) (x + 3) and (x – 1)
Answer:
[tex]\Large \boxed{(x+4)(x-1)}[/tex]
Step-by-step explanation:
Hello,
[tex]x^2+3x-4\\\\\text{*** The product of the zeroes is -4=-1*4 and their sum is -3=-4+1. ***}\\\\\text{*** So we can factorise. ***}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=\large \boxed{(x+4)(x-1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The factors of given function are (x + 4) and (x - 1)
To undestand more, check below explanation.
Factors of function:The modeled for algebra tiles is given as,
[tex]f(x)=x^{2} +3x-4[/tex]
We have to find the factors of given function.
Factoring means finding expressions that can be multiplied together to give the given equation.
If a quadratic equation can be factored, it is written as a product of linear terms.
[tex]f(x)=x^{2} +3x-4\\\\f(x)=x^{2} +4x-x-4\\\\f(x)=x(x+4)-1(x+4)\\\\f(x)=(x+4)(x-1)[/tex]
Hence, the factors of given function are (x + 4) and (x - 1)
Learn more about the factors here:
https://brainly.com/question/25829061
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:
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.
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:
Please answer this!!! Thank you!!!
I hope this helped! Good luck with the rest of your class :)
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
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 .
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
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.
Please help me I am bad at this stuff
When simplified, 4x/7y + 3x/5y is written as?
Answer:
41x/35y
Step-by-step explanation:
combine like terms
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:
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
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
If a function f has an inverse function, then fis one-to-one.
A) True
B) False
Answer:
true
Step-by-step explanation:
Multiply and simplify (x2)(x4)(x-5)
Answer:
(x45)
Step-by-step explanation:
(x2) (x4) (x-5)
(x8) (x-5)
(x45)
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.
Rectangle GHJK is rotated 180º using the origin as the center of rotation. What are the coordinates of the image’s point K after the rotation? On a coordinate plane, rectangle G H J K has points (2, negative 3), (8, negative 3), (8, negative 7), (2, negative 7). (–2, 7) (–7, –2) (–7, 2) (2, 7)
Answer:
(-2,-7)
Step-by-step explanation:
Answer:
-2,-7
Step-by-step explanation:
Find the measure of y.
HELPPPP PLEASEEE I DONT WANNA GOT TO GRANNYS HOUSE
Answer:
15
Step-by-step explanation:
f(5) = (5)^2 - 2(5) = 25 - 10 = 15
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
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
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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
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
A person stands 12 meters east of an intersection and watches a car driving away from the intersection to the north at 4 meters per second. At a certain instant, the car is 9 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
Answer: the rate of change of the distance between the car and the person at that instant is 4 meters per second
Step-by-step explanation:
According to the Pythagorean theorem, we have:
d^2 = (12^2 + 9^2)
Differentiating both sides with respect to time:
2d * (dd/dt) = 0 + 2(9) * (9''), Simplifying the equation, we get:
2d * (dd/dt) = 2(9) * (9'')
Substituting the given values:
2d * (dd/dt) = 2(9) * (4) [the car is moving at a constant velocity of 4 m/s]
Simplifying further:
2d * (dd/dt) = 72
we divide both sides by 2d:
dd/dt = 72 / (2d)
substitute this value into the equation to find the rate of change of the distance:
dd/dt = 72 / (2 * 9) = 4 m/s
The rate of change of the distance between the car and the person at that instant is -12/5 meters per second.
Given information:
The person is standing 12 meters east of the intersection.
The car is driving away from the intersection to the north at a constant speed of 4 meters per second.
At a certain instant, the car is 9 meters from the intersection.
Using the Pythagorean theorem, determine D(t) in terms of the car's distance from the intersection, which we'll call x(t).
Since the person is 12 meters east of the intersection, the distance D(t) can be expressed as:
[tex]D(t) = \sqrt{(x(t)^2 + 12^2)[/tex]
Differentiating both sides of the equation with respect to time, we get:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * dx(t)/dt[/tex]
So, dx(t)/dt = -4
Substituting this value into the equation for dD/dt, we have:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * (-4)[/tex]
[tex]dD/dt = -4x(t) / \sqrt{(x(t)^2 + 144)[/tex]
At the instant when the car is 9 meters from the intersection, substitute x(t) = 9 into the equation:
[tex]dD/dt = -4(9) / \sqrt{(9^2 + 144)[/tex]
= -36 / √(81 + 144)
= -36 / √225
= -36 / 15
= -12/5
Therefore, the rate of change is -12/5 meters per second.
Learn more about Rate of change here:
https://brainly.com/question/29181688
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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 :)