To factor a[tex]x^{2}[/tex]+bx+c, you have to group it as (a[tex]x^{2}[/tex]+ux)+(vx+c) so that uv=ac and u+v=b. Both addition and multiplication are commutative, so how do you determine which value is assigned to u and which to v? Or are they interchangeable?
For example, let's expand out (x+3)*(2x+1). Use of the FOIL rule should get to you 2x^2 + 7x + 3.
Now imaging that you handed 2x^2 + 7x + 3 to a friend to be factored. They do not know the factorization yet.
They would see that a = 2, b = 7, c = 3.
The friend needs to find two numbers u,v such that they multiply to a*c = 2*3 = 6 and add to b = 7
Through trial and error (I recommend making a table of values), your friend would get
u*v = 1*6 = 6u+v = 1+6 = 7But as you mentioned, your friend could easily swap the order of addition and multiplication to say
u*v = 6*1 = 6u+v = 6+1 = 7----------------------
If we go with the first option, then the factor by grouping looks like this
2x^2 + 7x + 3
2x^2 + 1x + 6x + 3 ... break up 7x into 1x+6x
(2x^2+1x) + (6x+3) .... group up the terms into pairs
x(2x+1) + 3(2x+1) .... factor each grouping
(x+3)(2x+1) ..... factor out the overall GCF
---------------------
Or we could have the factor by grouping looks like this
2x^2 + 7x + 3
2x^2 + 6x + 1x + 3 ... break up 7x as 6x+1x
(2x^2+6x) + (1x+3)
2x(x+3) + 1(x+3)
(2x+1)(x+3)
(x+3)(2x+1)
We end up with the same factorization.
please help i’ll mark brainliest
A group of friends hires a bus for a day for
$480, agreeing to share the cost equally. At
the last minute, two more people decide to go
on the trip, and as a result each person pays
$8 less.
How many people go on the trip and how much
does each person pay?
Step-by-step explanation:
i think 52 people was there cause 8×60=480 and you said that in the last minute two more people decide to go so i added two more and 52 people was the result
Find a country located in the temperate zone (USA, Canada, India, Europe Japan, New Zealand etc.) then using their climatic data from a two-year period, complete the following tasks:
a) Find the highest and the lowest temperatures recorded.
b) Use these two numbers to find the amplitude.
c) Find the period of the function.
d) Draw the graph using the Sine or cosine function.
e) What can you infer about the trend of the temperature now?
Answer:
i dont see what the top part says??
Step-by-step explanation:
Find the value of x
help asap
Answer:
56 + 56 = 112
180 - 112 = 68
68 + 68 = 136
180 - 136 = 44
x= 44
A person can bike 48 miles in 2 hours. At this rate how long will it take this person to travel 66 miles? Show work please!!!
Answer:
Convert to a decimal by dividing the numerator by the denominator.
2.75 hours
1. What is the slope of a line that is perpendicular to the x-axis
Answer:
The slope of a line that is perpendicular to the x-axis is undefined.
Step-by-step explanation:
We know that the x-axis is a horizontal line.
We also know a line that is perpendicular to the x-axis is basically a vertical line.As the slope of a perpendicular line is undefined because no matter what the value of y is, the x-value remains the same.Therefore, the slope of a line that is perpendicular to the x-axis is undefined.
For example, the slope between (1, 2) and (1, 4) is:
Using the slope formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [4 - 2] / [1 - 1]
= 2 / 0
= ∞
solve 4x^2 - 3 = 3x^2 + 13 by using square roots
Answer:
x = - 4, x = 4
Step-by-step explanation:
[tex]4x^2 - 3 = 3x^2 + 13 \\ \\ 4x^2 - 3 - 3x^2 - 13 = 0 \\ \\ 4 {x}^{2} - 3 {x}^{2} - 16 = 0 \\ \\ {x}^{2} - 16 = 0 \\ \\ {x}^{2} - {(4)}^{2} = 0 \\ \\ (x + 4)(x - 4) = 0 \\ \\ x + 4 = 0 \: \: or \: \: x - 4 = 0 \\ \\ x = - 4 \: \: or \: \: x = 4 \\ \\ x = - 4, \: \: 4[/tex]
A beam bridge has a total length of 168 yards. The bridge is supported at both ends and has three additional supports in the water. What is the span between any two consecutive supports?
The answer is 6
Step-by-step explanation:
6-65
The total length of a beam bridge is 168 yards. then the span between any two consecutive supports is 23 approx.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that the total length of a beam bridge is 168 yards.
The Total number of supports on the bridge = 1 at both end + 3 additional = (1 + 3 + 1) = 5 supports
Arch lies in between two successive supports ;
Hence, the number of archs = 5
Hence, width of arch = (5 * x) = 5x meters
Width of support = 2 meters
The Total width of support : (2 * x+ 1) = 2(x + 1) meters
Hence, the total distance of bridge :
Total arch width + total support width
5x + 2(x + 1) = 168 meters
5x + 2x + 2 = 168
7x = 166
x = 23 approx
Hence, the span between any two consecutive supports is 23 approx.
Learn more about equations here;
https://brainly.com/question/10413253
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I need help on this subject
Answer:
D (3,-4)
Step-by-step explanation:
i graphed it on desmos lol
What is the product?
3(-10.50)
Answer: -31. 5
Step-by-step explanation: Hope this helps! Next time search to make it easier for you ;)
The product of the given numbers is -31.5.
The given expression is 3(-10.50).
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The product of given whole number and decimal number is as follows:
3×(-10.50)
= -31.5
Therefore, the product of the given numbers is -31.5.
Learn more about the multiplication here:
https://brainly.com/question/1562995.
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If (1/4)^2-y, =1 find the value of y
Can someone help me please with all these pleaseeee
The function f(x) = ( )* is translated up 4 units. Which equation represents the translated function?
g() = (5)***
g(x) = ()
g() = ()' +4
g(x) = (13) -4
Answer:
c
Step-by-step explanation:
find the slope of the linear function
Answer:
that one over there
Step-by-step explanation:
Answer:
2/3 = slope
Step-by-step explanation:
Slope is rise over run. If you look at (3,1), to go to the next point, it goes up 2 (rise) and right 3 (run). so 2/3 would be the slope.
PLEASE HELP!!!! will give brainliest!!!!
Answer: A Good luck :)
please help me my brain is to small for dis I need da right answer
Answer:
it is in its simpliest form there are no equivalent expressions because all factors are odd numbers
Step-by-step explanation:
pls give me brainliest
Whos your favorite operator in rainbow six seige
Answer:
It has to be Maverick how about u
Step-by-step explanation:
Answer:
Niclas "Pengu" Mouritzen
Step-by-step explanation:
Simplify to create an equivalent expression
(4+2k)•6+3k=
Answer:
24+15k=
Step-by-step explanation:
First we multiply the 6 to the numbers in the parentheses, so 4x6=24, and 2x6=12, making the expression look like this: 24+12k+3k=
Then we combine like terms, which would be the number that are attached to 'k'. So that makes the expression look like this: 24+15k=
I'm not sure what else you're suppose to do to create a new expression since there's nothing on the other side of the equal sign, but that's as much as the expression will simplify.
I can do your homework for you
Answer:
thanks for the free points
Step-by-step explanation:
Answer:
can u answer these ones
Step-by-step explanation:
Write the
following in
slope-intercept
form:
7x - 2y = -6
2y = 7x + 6 or the simplified version would be y = 7/2x + 3
Step-by-step explanation:
u just gotta know that slope intercept form is the equation y=mx+b
Tyesha has x feet of wood for a project. She has lengths of wood that are 7 1/2 feet, 5.25 feet, and 6 3/4 feet long. What is the total length of wood she has for this project?
A: 70x+30=20x+50
B: 70x-30=20x-50
C: 70+30x=20+50x
D: (70+30)x=(20+50)x
it d probably think it's d
Donovan was playing a basketball shooting game in the arcade. He made 15 shots and missed 25 shots. What is the percentage of shots Donovan made in the basketball game?
Do not round your answer.
Thank you for the help :)
Answer:
r
Step-by-step explanation:
an online company lets you download songs for 1$ each after you have payed a 5$ membership fee the maximum amount of songs you can download in a month is 100 how much do you pay
Answer:
$105
Step-by-step explanation:
5 + 1 (100)
5 + 100
105
Each month, Mrs. Donovan sets aside $1,550 for her retirement. Her monthly income, including profits from her bakery, totals $3,875. What percentage of her income goes to retiremen
Answer:
40%
Step-by-step explanation:
1550 / 3875 = 0.4 = 40%
What is the length of segment TR with T(-4,5) and R(2, -1)
Answer:
The length of segment TR with T(-4,5) and R(2, -1) is 8.49
Step-by-step explanation:
We need to find the length of segment TR with T(-4,5) and R(2, -1)
The length of segment can be found using distance formula.
The distance formula is: [tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Putting values and finding length
We have: [tex]x_1=-4, y_1=5, x_2=2, y_2=-1[/tex]
[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance = \sqrt{(2-(-4))^2+(-1-5)^2}\\Distance = \sqrt{(2+4)^2+(-1-5)^2}\\Distance = \sqrt{(6)^2+(-6)^2}\\Distance = \sqrt{36+36}\\Distance = \sqrt{72}\\Distance=8.49[/tex]
We found Distance = 8.49
So, The length of segment TR with T(-4,5) and R(2, -1) is 8.49.
What is the gradient of the line that passes through the points (0,0) and (5,-10)
Answer:
[tex]\displaystyle m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (0, 0)
Point (5, -10)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m. Slope and gradient is the same.
Substitute in points [SF]: [tex]\displaystyle m=\frac{-10-0}{5-0}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{-10}{5}[/tex][Fraction] Divide: [tex]\displaystyle m=-2[/tex]Answer:
Let "m" be the slope of the line passing through the point.
[tex]m = \frac{y_ 2 - y_1}{x_ 2 - x_1 } = \frac{( - 10 - 0)}{(5 - 0)} = \frac{ - 10}{5} = \boxed{- 2 }[/tex]
-2 is the gradient of the line that passes through the points (0,0) and (5,-10).
Is the equation 72 ÷ 6 = 64 ÷ 4 true or false? (2 points)
True
False
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
72/6=12
64/4=16
what is the rate and equation
Answer:
The rate law or rate equation for a chemical reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders).
Step-by-step explanation:
Directions: Find the value of x.
Round each answer to the nearest tenth.
Answer:
this answer is not available at the moment
Step-by-step explanation: