Step-by-step explanation:
Find the Greatest Common Factor (GCF) of a polynomial.
Factor out the GCF of a polynomial.
Factor a polynomial with four terms by grouping.
Factor a trinomial of the form .
Factor a trinomial of the form .
Indicate if a polynomial is a prime polynomial.
Factor a perfect square trinomial.
Factor a difference of squares.
Factor a sum or difference of cubes.
Apply the factoring strategy to factor a polynomial completely
Answer:
See explanation
Step-by-step explanation:
We can factor polynomials by breaking down the expression.
For instance, let's say we have the polynomial [tex]x^2 - 9x + 14[/tex].
We can start solving this because this polynomial is in standard form, meaning that the highest exponents go first. ([tex]ax^2 + bx + c[/tex].)
To factor a polynomial, we are looking for two numbers that:
A. When multiplied, get us [tex]c[/tex] (in this case, 14)
B. When added, get us [tex]b[/tex] (in this case, -9).
If we play around with numbers, looking at the factors of 14, we see that the numbers 7 and 2 might be useful here. They add up to 9 and multiply to be 14.
However, these numbers ADD to be -9, meaning that they both need to be negative.
[tex]-7 + -2 = -9\\-7\cdot-2=14[/tex]
Now that we know our numbers, -7 and -2, we can make these our factors (which are represented by [tex](x + y)[/tex], y being our factor.
So our factors turn out to be [tex](x-7)[/tex] and [tex](x-2)[/tex].
Let me know if you need anything explained more, and I hope this helped!
Find the x-intercept(s) of the equation: y =3x^2-3x-6
a. x-intercepts: (-1,0) and (2,0)
b. x-intercepts:(0,-3) and (0,2)
c. x-intercept: (-6,0)
d. x-intercept: (0,-6)
Answer:
(2,0) ( -1,0)
Step-by-step explanation:
y =3x^2-3x-6
Let y = 0 and solve for x to find the x intercepts
0 =3x^2-3x-6
Factor out a 3
0 =3(x^2-x-2)
Factor inside the parentheses
0 = 3( x-2) (x+1)
Using the zero product property
x-2 =0 x+1 = 0
x=2 x = -1
(2,0) ( -1,0)
Answer:
[tex]\large \boxed{\mathrm{a. \ x-intercepts: (-1,0) \ and \ (2,0)}}[/tex]
Step-by-step explanation:
The x-intercept(s) is when y = 0.
3x² - 3x - 6 = 0
Factor left side of the equation.
3(x + 1)(x - 2) = 0
Set factors equal to 0.
x + 1 = 0
x = -1
x - 2 = 0
x = 2
The x-intercepts are (-1, 0) and (2, 0).
I NEED YOUR HELP PLS
Answer:
For question 1 you can try dividing each of the value
For instance, you can divide 9 by 25 and see if you get a nice number
e.g. 1/8=0.125, numbers like these
For the second question, you can find the fraction by dividing 1000 starting with the decimal points
e.g 0.650, you would be plotting 650/1000 and you would simplify the fraction to the lowest value any value above the decimal point you can multiply by the denominator and add the nominator value to get your final answer.
Step-by-step explanation:
Answer:
Write the denominator in its prime factors. If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
example: 9/25
25 = 5*5, so it will be terminating
example: 7/12
12 = 3*2*2, which contains a 3, so it will be repeating.
Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?
Answer:
The number of minutes Nikki needs to listen to the radio to hear 20 commercials is 63.275 minutes
Step-by-step explanation:
The given dependent and independent variables are;
The number of minutes spent by Nikki listening = x
The number of commercials aired = y
The relationship between the independent variable, x ans the dependent variable, y, was given by the Nikki's graphing tool line of best fit as follows;
y = 0.338·x - 1.387
Therefore, the number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y is given as follows;
20 = 0.338·x - 1.387
20 + 1.387 = 0.338·x
0.338·x =20 + 1.387 = 21.387
x = 21.387/0.338 = 63.275 minutes
The number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y = 63.275 minutes.
Answer:
C. 63 minutes
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answer:
2/5
Step-by-step explanation:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now for the difference
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5 , which is the answer :)
The answer is 2/5.
To find the fraction bar in the box.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now substract the sum,
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5
So, the answer is 2/5.
Learn more about fraction here:
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If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
7800 brownies will be produced in an 8 hour shift
Step-by-step explanation:
Given : The production rate is 975 brownies per hour at a bakery
To Find : how many brownies will be produced in an 8 hour shift?
Solution:
No. of brownies produced in 1 hour = 975
We are supposed to find No. of brownies produced in 8 hour
No. of brownies produced in 8 hour = 975 x 8=7800
Hence 7800 brownies will be produced in an 8 hour shift
Hope this helps ФωФ
PLEASSSSSEEE HELPPP ASPPP PLEASEEE
Answer:
x=1
i hope this helps!
Step-by-step explanation:
x+2/-1 =3
x+2 (1) =3
x+2 = 3
x=1
10) Find the least number that must be subtracted from the following numbers to make them perfect squares. a) 1098 b) 4498
Answer:
a. 9
b. 9.
Step-by-step explanation:
a) √1098 = 33.136
33^3 = 1089
So the answer is 1098 - 1089
= 9.
b) √4498 = 67.067
67^2 = 4489
Answer = 9.
Answer:
a). 9
b). 9
Step-by-step explanation:
a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.
√1089 = 33
33² = 33 × 33 = 1089
So the answer is 9.
b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.
√4489 = 67
67² = 67 × 67 = 4489
So the answer is 9.
Hope you understand ◉‿◉ (◠‿◕)
Square Roots and Cube Roots - Tutorial - Level H
Pepper Jackie has 225 square inches for the area for her square mosaic.
How can she figure out how long each side should be?
Area of a Square
A= 225 in.
S
S
Find the positive square
root of 225.
Divide 225 by 4.
Divide 225 by 2.
She doesn't have enough
information to do this.
Answer:
s = 15 in (positive square root of 225)
Step-by-step explanation:
A = 225 in²
side of square mosaic is sq. root of 225 = 15 in
therefore the side (s) = 15 in
If you vertically compress the linear perent function, F(x) = x, by multiplying by 1\2
what is the equation of the new function?
Answer: [tex]y=\dfrac12 x[/tex] .
Step-by-step explanation:
We know that [tex]a f (x)[/tex] compresses f(x) vertically such that
if 0 < a < 1 (a fraction), the graph is compressed vertically by a factor of a units.if a > 1, the graph is stretched vertically by a factor of a units.If we vertically compress the linear parent function, F(x) = x, by multiplying by [tex]\dfrac12[/tex].
Then, the equation of the new function is [tex]y=\dfrac12 F(x)=\dfrac12 x[/tex] .
i.e. [tex]y=\dfrac12 x[/tex] .
what is this supposed to be bro pls help
Answer: 1
Step-by-step explanation:
so i put the amount of flour to servings into ratios (fractions)
28:14
9:12
10:13
then I put them into the same denominators
2184:1092
819/1092
840/1092
the first one is the greatest
i need help with this question please :(
Answer:
C
Step-by-step explanation:
[tex](2^7 \cdot 3^{-5}\cdot 9)^4[/tex]
Use the Power of a Product Property, where:
[tex](ab)^n=a^nb^n[/tex]
Therefore:
[tex](2^7 \cdot 3^{-5}\cdot 9)^4\\=(2^7)^4\cdot(3^{-5})^4\cdot(9)^4\\=2^{28}\cdot3^{-20}\cdot9^4[/tex]
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
When and , the value of the expression is
Answer:
-2, 6
Step-by-step explanation:
(x - 6)(x + 2) = 0
x - 6 = 0 x+ 2 = 0
x = 6 x = -2
The values of x that would result in the given expression being equal to 0, in order from least to greatest, are -2 and 6.
Morgan rewrote the expression 90 + (10 + 4.8) as (90 + 10) + 4.8. How will this change the work that is needed to evaluate the expression? PLZ I NEED THIS PLZ HELP ME
Answer: Because of PEMDAS, the way Morgan rewrote the expression would change the the order of the steps to simplify it.
Step-by-step explanation: PEMDAS is the order of operations and it stands for Parenthesis, Exponents, Multiply, Divide, Addition, and Subtraction. If we simplify Morgan's version of the expression, we would add 90+10 first, which makes 100, then add 4.8 which makes 104.8. We come to the same conclusion when simplifying the original expression, 104.8. The difference is that we add 10+4.8 first and then add it to 90. While in this situation, the outcome was not different, the order of operations was changed.
Complete the equation. Answer as a fraction in its simplest form.
9xy * (2/3x)*3 = ( [ ] a0 / [ ] a1 ) x*4y
Answer:
a0 = 8a1 = 3Step-by-step explanation:
[tex]9xy\cdot(\frac{2}{3}x)^3=3^2xy\cdot\dfrac{2^3x^3}{3^3}\\\\=\dfrac{8}{3^{3-2}}x^4y=\boxed{\dfrac{8}{3}}x^4y[/tex]
__
The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)/(a^c) = 1/(a^(c-b))
How do I solve 3(x+1)=5(x−2)+7?
Answer:
x = 3Step-by-step explanation:
[tex]3\left(x+1\right)=5\left(x-2\right)+7\\Expand\\3x+3 =5x -10+7\\Collect \:like\: terms\\3x-5x = -10+7-3\\-2x = -6\\Divide \:both\:sides\:of\:the\:equation\:by\:-2\\\frac{-2x}{-2} = \frac{-6}{-2}\\ \\x = 3[/tex]
Answer:
x = 3
Step-by-step explanation:
3(x+1)=5(x−2)+7
Use the distributive property to multiply 3 by x+1.
3x+3=5(x−2)+7
Use the distributive property to multiply 5 by x−2.
3x+3=5x−10+7
Add −10 and 7 to get −3.
3x+3=5x−3
Subtract 5x from both sides.
3x+3−5x=−3
Combine 3x and −5x to get −2x
−2x+3=−3
Subtract 3 from both sides.
−2x=−3−3
Subtract 3 from −3 to get −6.
−2x=−6
Divide both sides by −2.
x = -6/2
Divide −6 by −2
x = 3
A spray irrigation system waters a section of a farmer’s field. If the water shoots a distance of 85 feet, what is the area that is watered as the sprinkler rotates through an angle of 60 degrees? Use 3.14 for pi . Round your answer to the nearest square foot, and enter the number only.
Answer:
3,781
Step-by-step explanation:
To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.
First, recognize the formula for the area of a circle:
A = 3.14[tex]r^{2}[/tex]
In this scenario, the radius (r) is 85 feet:
A = 3.14(85[tex])^{2}[/tex]
A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:
A = [tex]\frac{3.14(85)^{2} }{6}[/tex]
Finally, we will simplify and round:
A = 3,781
Las dos compañías cobran el mismo precio por viaje, cada viaje vale $100.00 pesos, los pobladores dicen que uno de los camiones tiene una capacidad de 3 toneladas y el otro de 4 toneladas, en total se hicieron 23 viajes y se transportaron 80 toneladas de tierra.
The row-echelon form of the augmented matrix of a system of equations is given.Find the solution of the system
Answer:
x = 9/4
y = 3/5
z = 2/3
w = -9/5
Step-by-step explanation:
Technically, the matrix is in reduced row echelon form. If there are zeros above and below the ones, it is RREF. If there are zeros only below the ones, then it's REF.
Since it is in RREF, the augmented numbers to the right of the bar are already your solutions. Simply label the variables.
What is the value of x, when -25(x - 4) = -55(x - 10)? A) x = 5 B) x = -5 C) x = 8 1/ 8 D) x = 15
[tex]-25(x - 4) = -55(x - 10)\\-25x+100=-55x+550\\30x=450\\x=\dfrac{450}{30}=15[/tex]
Answer:
x=15
Step-by-step explanation:
Select the equivalent expression,
(9^6*7^-9)^-4 =?
Choose 1 answer:
А
9^24*7^-36
B
9^24/7^36
C
7^36/9^24
Answer:
c
Step-by-step explanation:
The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ (9⁶ x 7⁻⁹)⁻⁴
Simplify the expression, we have
⇒ (9⁻⁶ x 7⁹)⁴
⇒ 9⁻²⁴ x 7³⁶
⇒ 7³⁶ / 9²⁴
Then the correct option is D.
More about the equivalent link is given below.
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6,926,300,000 in scientific notation.
Answer:
6.9263 × 109
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
State the value of the digit 3 in 41,039
d Write: £12 and 35 pence as a decimal
Answer:
3 tens or 30
£12.35
Step-by-step explanation:
41,039
ten thousand thousands, hundreds tens ones
The three is in the tens place
3 tens or 30
£12 and 35
1p = £0.01
£12.35
Manuel made at least one error as he found the value of this expression. Identify the step in which Manuel made his first error. After identifying the step with the first error, explain the corrected steps and find the final answer.
Answer:
Manuel made his first mistake in step 2 leading to the continuous mistakes
Final answer=185
Step-by-step explanation:
Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.
2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)
Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)
Step 2: -40 - 75 + 100 +
200
Step 3: -115 + 300
Step 4: 185
Manuel made his first error in step 2 by combining two different terms into one as he has done
(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)
Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)
Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405
He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.
what is the area of the kite ? PLEASE HELP BEING TIMED
Answer:
7 * 4 / 2 = 28/2 = 14
Step-by-step explanation:
You are timed. I will just give you the formula where its multiplying the Diagonals and dividing by 2.
x= -4 w= 1 z= -3 y= 5
This is the answer!
A transformation T : (x, y) (x + 3, y + 1). The preimage of the point (4, 3) is (-1, -2) (7, 4) (1, 2)
Answer:
(1, 2)
Step-by-step explanation:
'Undo' the rule on the image to get the pre-image.
[tex](4,3)\rightarrow(4-3,3-1)\rightarrow\boxed{(1,2)}[/tex]
(1,2) would be the pre-image to (4,3).
To see if it's correct:
[tex](1,2)\rightarrow(1+3,2+1)\rightarrow(4,3)[/tex]
(1,2) should be correct.
Answer:
the correct answer is (1,2)
Step-by-step explanation:
Which of the variable expressions below is a trinomial with a constant term? A. 3x5 – 2x3 B. x5 – 3x2 + 5x C. 7x6 + 2x4 – x3 + 7 D. 4x2 – 3 + x3
Answer:
Option (D)
Step-by-step explanation:
Option (A).
3x⁵ - 2x³
There are two terms with the variable 'x' in the given expression. therefore, it's a binomial with no constant term.
Option (B).
x⁵ - 3x² + 5x
This expression has three terms with variable 'x'.
Therefore, it's a trinomial without no constant term.
Option (C).
7x⁶ + 2x⁴ - x³ + 7
It's a quadrinomial having 4 terms. '7' is the constant term in the given expression.
Option (D).
4x² + x³ - 3 ≈ x³ + 4x² - 3
It's a trinomial with a constant term 3.
Therefore, Option (D) is the answer.
help me with this promblem THXXXX
Function 1 = negative y intercept
Function 2 = positive y intercept
====================================================
Explanation:
A. This is false because function 2 has a positive y intercept. Each time x goes up, y goes down. Reverse this and decreasing x leads to increasing y.
B. False. Function 1 has a negative y intercept. The y intercept occurs where the diagonal line crosses the y axis.
C. True. The graph shows a negative y intercept. The y intercept of function 2 is (0,2).
D. False. This contradicts choice C.
Factorise the following
Answer:
4ny²+4n²-4n-8+y⁴-2y²
5x+4(-x-2) = -5x + 2(x-1)+12 solve for x
Hello!
Answer:
[tex]\huge\boxed{x = 4.5}[/tex]
Starting with:
5x + 4(-x - 2) = -5x + 2(x - 1) + 12
Distribute terms outside of the parenthesis:
5x + 4(-x) + 4(-2) = -5x + 2(x) + 2(-1) + 12
5x - 4x - 8 = -5x + 2x - 2 + 12
Combine like terms:
x - 8 = -3x + 10
Isolate for the "x" variable by adding 3x for both sides:
4x - 8 = 10
Add 8 to both sides:
4x = 18
Divide both sides by 4:
x = 18/4
x = 4.5
Hope this helped! :)
Answer:
[tex] \boxed{x = 4.5}[/tex]
Step-by-step explanation:
[tex] \mathrm{5x + 4( - x - 2) = - 5x + 2(x - 1) + 12}[/tex]
Distribute 4 through the parentheses
Similarly, Distribute 2 through the parentheses
[tex] \mathsf{ 5x - 4x - 8 = - 5x + 2x - 2 + 12}[/tex]
Collect like terms
[tex] \mathsf{ x - 8 = - 3x - 2 + 12}[/tex]
Calculate the sum
[tex] \mathsf{x - 8 = - 3x + 10}[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] \mathsf{ x + 3x = 10 + 8}[/tex]
Collect like terms
[tex] \mathsf{4x = 10 + 8}[/tex]
Calculate the sum
[tex] \mathsf{4x = 18}[/tex]
Divide both sides of the equation by 4
[tex] \mathsf{ \frac{4x}{4} = \frac{18}{4}} [/tex]
Calculate
[tex] \mathsf{x = 4.5}[/tex]
Hope I helped!
Best regards!
Is Figure B a scale copy of Figure A? Choose 1 answer: A. Yes B. No
Answer:
A Yes
Step-by-step explanation:
the ratio is 2:1
Answer:
A. yes
Step-by-step explanation:
