How can you factor binomials and trinomials in one variable?
Answers
To factor binomials and trinomials in one variable, you look for the common factors in the terms
How to factor a binomial and trinomial?Binomials are polynomials with two terms while trinomial have three terms.
For instance, we have:
Binomial: x^2 - 4Trinomial = x^2 + 4x + 4To factor x^2 - 4, we use the following steps:
x^2 - 4
Express 4 as 2^2
x^2 - 4 = x^2 - 2^2
Apply the difference of two squares
x^2 - 4 = (x - 2)(x + 2)
To factor x^2 + 4x + 4 we use the following steps:
x^2 + 4x + 4
Express 4x as 2x + 2x
x^2 + 4x + 4 = x^2 + 2x + 2x + 4
Factorize
x^2 + 4x + 4 = x(x + 2) + 2(x + 2)
Factor out x + 2
x^2 + 4x + 4 = (x + 2)x + 2)
Rewrite as:
x^2 + 4x + 4 = (x + 2)^2
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To factor binomials and trinomials in one variable, you look for the common factors in the terms below.
What is Polynomial?A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).
Binomial: x² - 4
Trinomial = x² + 4x + 4
To factor x² - 4, we use the following steps:
x² - 4 = x² - 2²
x² - 4 = (x - 2)(x + 2)
To factor x² + 4x + 4 we use the following steps:
x² + 4x + 4
x² + 4x + 4 = x² + 2x + 2x + 4
x² + 4x + 4 = x(x + 2) + 2(x + 2)
Factor out x + 2
x² + 4x + 4 = (x + 2)²
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Related Questions
Help help help math math
Answers
Answer:
3
Step-by-step explanation:
pemdas
()x^2x/+-
step one solve the exponents. 2^2 = 4
rewrite equation 4x3/4
then 4x3 = 12
12/4=3
hope this helps.
please help me? this answer
Answers
Move it to the left 4 times, move it up once
Answer:
1. c; 2. a; 3. b
Step-by-step explanation:
A(3,-1) translated to (3-4, -1+1)=(-1,0); then reflecting to x=1 (in this case, y doesn't change, and only x value change. x=-1 is 2 unit left side of x=1 line, so new reflected x value would be 2 unit right side of x=1 line, which is 3) gives (3,0).
B(7,1) --> (3,2) --> (-1,2)
C(5,-4) --> (1,-3)--> (1,-3)
Write a verbal expression for 4• f³.
Answers
Answer: 4 times f over 3
Step-by-step explanation:
Solve the following proportion: 14/22=x/9
Answers
Step-by-step explanation:
14/22 = x/9
or, 14×9÷22 = x
hence, x = 5.72
Hi, let me help you out!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
In order to solve proportions, apply cross-multiplication:
\(\longrightarrow\tt{\displaystyle\frac{14}{22}=\frac{x}{9}}\)
\(\longrightarrow\tt{14\cdot9=x\cdot22}\)
Simplify:
\(\longrightarrow\tt{126=22x}\)
Divide both sides by 22:
\(\longrightarrow\tt{\displaystyle\frac{126}{22}=\frac{22x}{22}}\)
Reduce the fraction:
\(\longrightarrow\tt{\displaystyle\frac{63}{11}=x}\)
I hope this helps you! Have an awesome day!
If you need any explanation or clarification, don't hesitate to ask! :D
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the population of a city was 10000 in 2010 the population increases at an annual rate of 4% per year is the growth model function that represents the population of the city linear
Answers
No, the growth model function that represents the population of the city is not linear in this case.
A linear function has a constant rate of change, meaning that the population would increase by the same amount each year. However, in this scenario, the population is increasing at an annual rate of 4% per year. This means that the population growth is exponential, not linear.
To model the population growth over time, you would need to use an exponential function, such as:
P(t) = P₀ * (1 + r)^t
Where:
P(t) represents the population at time t,
P₀ represents the initial population (in this case, 10000),
r represents the annual growth rate (4% or 0.04),
and t represents the number of years.
Using this exponential function, you can calculate the population at any given year based on the initial population and the growth rate.
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There are 1250 students at Cypress Middle School. 42% of the students are enrolled in PE. How many students are enrolled in PE?
Answers
Answer:
The answer is 525 students.
Step-by-step explanation:
1250 total students
42% = PE
42% of 1250 = \(525\)
Thus, the answer is 525.
Answer: 525 students are enrolled in PE.
Step-by-step explanation:
Which fraction is equivalent to 2/-6
Answers
Answer:
-1/3
Step-by-step explanation:
Which set of parametric equations over the interval 0 ≤ t ≤ 1 defines a line segment with initial point (–5, 3) and terminal point (1, –6)?
Answers
Answer:
x(t) = –5 + 6t; y(t) = 3 – 9t
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I got the Edg Test right
If the half life of a substance is 4 weeks, how long will it take for 400 mg of this substance to decay to 25 mg?
Answers
Answer:
I believe the answer is 16 weeks.
Step-by-step explanation:
Sorry for the wait
How many factors are in a B + CD + EF + GH
Answers
The given expression is
=ab+cd+ef+gh
The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.
→The expression consists of four terms which are, ab, cd, ef, and gh.
→Each term contains
Two factors.
plz mark as brainliest
F(x)= x^3 +3G(x)= x^2 +2Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use this graph as a starting point.
Answers
At the point of intersection, f(x)=g(x)
\(\begin{gathered} x^3+3=x^2\text{ + 2} \\ \text{collect like terms} \\ x^3-x^2\text{ +3 - 2 = 0} \\ x^{3\text{ }}-x^2+\text{ 1= 0} \end{gathered}\)\(x^3-x^2+1=\text{ 0}\)The above graph is that of the equation
\(x^3-x^2\text{ + 1 = 0}\)The solution is = -0.755 which is approximately -0.8
From the options provided
For option A, x= -13/16 = -0.8125
For option B, x = -5/4 = -1.25
For option C, x = -15/16 = -0.9375
For option D, x = -7/8 = -0.875
From the options provided, The closest to the solution is Option A
Because - 0.8125 is approximately -0.8
Write an exponential equation, given initial population of 2500 and doubling time of 2 years
Answers
A population of 32,000 with a 5% annual growth rate would be modeled by the equation:
y=32000(1.05)t
with t in years.
lol I am stumped and I don’t know where to start
Answers
Answer: 130
Step-by-step explanation:
Scale factor = BY / TY = 72 / 45 = 1.6
So the perimeter of TZY is 208/1.6 = 130
On a shelf at a gaming store, there are five Sony Playstations and three Nintendo Wii consoles left. If one gaming system is selected at random, find the probability that the system is a Wii console.
Answers
Step-by-step explanation:
a probability is always desired cases over total possible cases.
so, we have actually 8 systems (5 + 3) we can pick from.
therefore, the total possible cases are 8.
the desired case is in this question to pick one of the 3 Wii consoles.
the probability to pick a Wii is therefore
3/8 = 0.375
Answer:
3/8, or 37.5%
Step-by-step explanation:
There are 8 different playing devices there.
There are only 3 Nintendo Wii consoles.
So, the probability is 3/8
Resolver para x
141-x=291
Answers
Answer:
x= 291-141= 150
x=150
Hope that helped! :D
Answer:
\(\boxed{\boxed{\sf x=-150}}\)
Step-by-step explanation:
\(\sf 141-x=291\)
Subtract 141 from both sides:
\(\sf 141-x-141=291-141\)
\(\sf -x=150\)
Divide both sides by -1:
\(\sf \cfrac{-x}{-1}=\cfrac{150}{-1}\)
\(\sf x=-150\)
______________________________
5 is what percent of 8 I need ASAP
Answers
Answer:
62.5%
Step-by-step explanation:
Answer:
Fraction Percent
4/8 50%
5/8 62.5%
6/8 75%
7/8 87.5%
Step-by-step explanation:
I think this is right
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.13 and 2.99
Answers
Answer:
Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this question, we have that:
Mean = 2.56
Standard deviation = 0.43
What percentage of the students have grade point averages that are between 2.13 and 2.99?
2.56 - 0.43 = 2.13
2.56 + 0.43 = 2.99
Within one standard deviation of the mean, so, by the Empirical Rule:
Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.
The vertices of a triangle are p(-1,4) Q (8,-3) and R(2,-6) Name the vertices of R y-x (PQR)
Answers
The reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).
First, let us understand the reflection of a point:
The reflection of a point or set of points across the line y = x results in a point or set of points whose coordinates are the interchange of the x-value and the y-value of the original point or set of points.
We are given:
The vertices of a triangle are P(-1, 4), Q(8, -3) and R(2, -6).
We need to find the reflection of the points across the line y = x.
So,
P(-1, 4) = P'(1, -4)
Q(8, -3) = Q'(-8, 3)
R(2, -6) = R'(-2, 6)
Thus, the reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).
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Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y-intercepts of the graphs are the same but the slopes are different, what is the greatest possible number of intersections for these graphs?
none
one
two
infinitely many
Answers
Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y-intercepts of the graphs are the same but the slopes are different, then graphs has 1 intersection.
What is Slope intercept form?y=mx+c is the slope intercept form of a line.
If the y-intercepts are the same, then the two linear have the same y-intercept as a solution. That is one common solution for both expressions. The two expressions intersect at that point. Since the slopes are different, there are no more common solutions since if two different lines intersect, they intersect at exactly one point and no more.
Therefore one is the greatest possible number of intersection for those graphs.
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Answer:its b one
Step-by-step explanation:
im right on edge and simple answer
Which of the following has the least value?
5/7; 7/8; 11/15; 7/10
Answers
Answer:
7/10
Step-by-step explanation:
solve 5 divide by 7 =0.714
solve 7 divided by 8 = 0.875
11 divided by 15 = 0.73333
7 divided by 10= .70
is every was contacted by the leader of a hiking trail to find out whether 30 members also enjoy two other activities rafting and circling the two-way table shown display some of the results of servery
Answers
Given:
Number of members = 30
We have the table below:
Enjoy Cycling Do not Enjoy Cycling Total
Enjoy Rafting 14 21 - 14 = 7 21
Do not enjoy Rafting 20 - 14 = 6 9 - 6 = 3 30 - 21 = 9
Total 20 7 + 3 = 10 30
ANSWER:
Therefore, the complete table is:
Enjoy Cycling Do not Enjoy Cycling Total
Enjoy Rafting 14 7 21
Do not enjoy Rafting 6 3 9
Total 20 10 30
Use the Pythagorean theorem to find the value for ( show work )
Answers
Answer:
x = 12
Step-by-step explanation:
x^2 + (x - 7)^2 = (x + 1)^2
x^2 + x^2 - 14x + 49 = x^2 + 2x + 1
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
One side has length x - 7.
For x = 4, x - 7 = 4 - 7 = -3.
Since a side of a triangle cannot have a negative length, x = 4 must be discarded.
Answer: x = 12
What type of angles are labeled and what is the value of m? Show your work.
Answers
Answer: I believe
M = 80
Step-by-step explanation:
100 - 20 = 80
what is the perimeter of a regular pentagon whose sides are 6 incges long
Answers
Answer: 30inches
Step-by-step explanation:
P=5a
a=side length
P=5(6)
5*6=30
You have 5 cups of fruit punch concentrate. The recipe calls for 3/4 cup of concentrate for one bowl of punch. how many bowls can you make?
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Matthew rode his bike 5/8 mile in 1/4 hour. What is the unit rate in miles per hour?
Answers
Answer:
The unit rate in miles per hour is 2.5 mph.
Step-by-step explanation:
Since Matthew rode his bicycle for 5/8 of a mile in a quarter of an hour, to determine the speed at which he was traveling we must perform the following calculation:
1/4 x 4 = 1 hour
5/8 x 4 = miles that would have been covered in one hour
20/8 of a mile would have been covered in one hour
20/8 = 2.5
2.5 miles would have been covered in an hour, with which his speed was 2.5 mph.
How many rows are left?
Answers
7/15 rows are left after crows ate some rows.
Total no. of rows he planted = 1 2/3
= 1 + 2/3
= (3 + 2)/3
= 5/3
No. of rows crows ate = 1 1/5
= 1 + 1/5
= (5 + 1)/5
= 6/5
No. of rows left = 5/3 - 6/5
= (25 - 18)/15
= 7/15
Hence, no. of rows left is 7/15.
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Plzz help me I am bad at math!!
Answers
Answer:
you are correct
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
Divide 104 by 2 to find out how many words per minute she can type. To check, divide 156 by 3 and you find the same answer.
help me plz god bless
Answers
Explanation
Answer:
D.
Step-by-step explanation:
When graphing, start by the y intercept.
y = 3x + 3 meaning 3 units up since the y intercept is 3
y = 3x + 3 then 3 extra units up since the slope and then one unit to the right
God bless you as well!
please help
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
f(x) = (x − 5)2 − 2
f(x) = (x − 4)2 − 1
f(x) = (x + 4)2 − 1
f(x) = (x + 5)2 − 2
Answers
Answer:
Step-by-step explanation:
From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.
Our model is
\(y=a(x-h)^2+k\) where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:
\(-1=a(-4+5)^2-2\) and
\(-1=a(1)^2-2\) and
-1 = a - 2 so
a = 1.
Now we can fill in the equation with the coordinates of the vertex and the value found for a to get
\(y=(x+5)^2-2\) You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.