According to the synthetic division below, which of the following statements
are true?
Check all that apply.
Answers
The question is not complete, so i have attached it.
Answer:
Options A, B & E are correct
Step-by-step explanation:
In the synthetic division attached, we see that:
: 2 , -2 & -12 are the coefficient of the dividend of the function 2x² - 2x - 12
: The divisor is 3
Thus;
x = 3 is a root of f(x) = 2x² - 2x - 12
Thus, (x - 3) is a factor of the dividend which is the function f(x) = 2x² - 2x - 12
- Now, from the attached image, the coefficients of the quotient are 2 , 4
- The quotient will be 1 degree less than the dividend since it was divided by the factor (x - 3)
The degree of the dividend will be 2 since it contains x²
Thus, the degree of the quotient will be 1
Therefore, the quotient in factor form is (2x + 4)
Looking at the given statements in the options;
- Option A is true, because we have established earlier that 3 is a root of f(x) = 2x² - 2x - 12
- Option B is true because we have established that (x - 3) is a factor of 2x² - 2x - 12
- Option C is not true because the factor is (x + 3) and not (x - 3)
-Option D is not true because the root is 3 and not -3
- Option E is true because we have established that quotient as a factor is: (2x + 4)
Thus, the correct options are A , B , E
Related Questions
What is the solution of 13 = t + 7 t
Answers
Answer:
t=1.625
Step-by-step explanation:
13=8t
divide both sides by 8
t=1.625
Please help me?? Solve for x
Answers
This is because 180-95= 85 which would make 8x+5= 85
Subtract 5 from both sides and get 8x=80
Then, divide 8 from both sides and get x=10
Step-by-step explanation:
95+8x+5=180
100+8x=180
8x=80
X=80/8
x=10
2/3(-2)+4
2/3(-1)+4
2/3(0)+4
2/3(1)+4
2/3(2)+4
SOLVE PLEASE!!
Answers
Answer:
how do u want meto read it?
Step-by-step explanation:
Suntract ( p-q)-(p+q)
Answers
The answer is -2q
hope this helps <3
PLS HELP WITH ALGEBRA QUESTION ON MATRICES. WILL GIVE BRAINLIEST
Answers
Answer:
Step-by-step explanation:
I think A but for sure on C and D. Good luck
What is 4 1/3 times 4 1/2
Answers
Answer:
19 1/2
Step-by-step explanation:
4 1/3 = 13/3
4 1/2 = 9/2
13/3 x 9/2
13/1 x 3/2 ( 3 goes into nine so i simplified)
13 x 3/1 x 2 = 39/2 = 19 1/2
PLEASE HELP ME!!!!!
This is due tomorrow and I am struggling. I don’t understand anything my math teacher teaches. I’m online cause I don’t like going to school and Im trying to make the best of it. I never thought this year I would have a math teacher like this. Last year my math teacher was such a good teacher. I passed every test in her class it was a piece of cake. But this year I’m not so lucky. So I’m asking if anyone can HELP ME PLEASE!!!! Oh and as a reminder there’s two math problems. U going to have to click it cause it’s an photo.
Answers
Step-by-step explanation:
2.
(2 + √3)(2 - √3)
x² - y² = (x + y)(x - y)x = 2, y= √3x² = 2² = 4y² = √3² = 3(2 + √3)(2 - √3) = 4 - 3 = 13.
(6 + √5)/(6 - √5)
Multiply both numerator and denominator by (6 + √5) to simplify(6 - √5) ((6 + √5) = 6² - √5² = 36 - 5 = 31(6 + √5)/(6 +√5) = 6² + 2*6*√5 + √5² = 36 + 12√5 + 5 = 41 + 12√5(6 + √5)/(6 - √5) = (41 + 12√5)/31What are some rules you need to know when solving absolute value inequalities and equations?
Answers
Answer:
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. This holds true for all absolute value inequalities. You can replace > above with ≥ and < with ≤.
Step-by-step explanation:
hope this helps!
Answer: -absolute value inequalities work two ways, not 1
-if it's greater than anything less than 0, then the solution is all real numbers
- if it's less than zero, there is no solution
-dividing by -1 flips the sign
Step-by-step explanation:
These are just some of the rules that I know
Find the value of y
Answers
Answer:
69 degrees
Step-by-step explanation:
The triangles are congruent because one of the angles is congruent to the other and the angle at the top is the same. The total number of degrees in a triange is 180. 180-(66+45 (the angle lenghts of the other 2 angles)) is equal to 180-111=69 degrees.
A pizza shop sells pizzas that are 12 inches in diameter or larger a 12 inch cheese pizza cost eight dollars each additional inch cost $2.50 and each additional toppings cost $1.25 write an equation that represents the cost of the pizza be sure to specify what variables represent they'll be three variables
Answers
Answer:
C(x, y) = 8 + 1.25x + 2.50(y - 12)
Step-by-step explanation:
Given that:
Cost of 12 inch cheese pizza = $8
Each additional inch cost $2.50
Each additional topping cost $1.25
The cost equation :
Let x = additional topping ; y = diameter of pizza, cost of pizza = C
C(x, y) = cost of 12-inch + (cost of additional topping * number of additional topping) + (cost per additional diameter * extra diameter)
C(x, y) = 8 + 1.25x + 2.50(y - 12)
Answer: C(x, y) = 8 + 1.25x + 2.50(y - 12)
Step-by-step explanation:
Describe the pattern in the table using words, an equation, and a graph. Extend the pattern for x=5, 6 and 7.
Answers
Answer:
Step-by-step explanation:
x y Difference [tex](y_2-y_1)[/tex]
1 15 -
2 25 25 - 15 = 10
3 35 35 - 25 = 10
4 45 45 - 35 = 10
There is a common difference of 10 in each successive term of y.
Therefore, table represents a linear function.
Let the equation of the linear function is,
y = mx + b
Here 'm' = slope of the line
b = y-intercept
Since, two points (1, 15) and (2, 25) lie on the graph of the function,
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{25-15}{2-1}[/tex]
m = 10
Equation of the line will be,
y = 10x + b
For the value of 'b' (y-intercept),
Since, (1, 15) lies on the graph of the linear function,
15 = 10(1) + b
b = 15 - 10
b = 5
Equation of the line on the graph will be,
y = 10x + 5
Now we can determine the output value of the function with the input values, x = 5, 6 and 7
[tex]y_1[/tex] = 10(5) + 5 = 55
[tex]y_2[/tex] = 10(6) + 5 = 65
[tex]y_3[/tex] = 10(7) + 5 = 75
What is the equation of the line that passes through the point (-4,8) and has a slope of -1/4
Answers
Shyryia read a book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 out of the total 480 pages left to read. Let y represent the number of pages left to read after x hours.
Complete the equation for the relationship between the number of pages left and number of hours.
Answers
Answer:
[tex]y=-52x+480[/tex]
Step-by-step explanation:
Linear Modeling
Some events can be modeled as linear functions. If there is a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The linear function can be expressed in the slope-intercept format:
[tex]y=mx+b[/tex]
The event into consideration is the number of pages of a book left to read by Shyryia.
We know that for x=1.5 hours, she had y=402 out of the total 480 pages left to read. This is the point ( 1.5, 402 ). The other point is not obvious but can be inferred by context. If she hasn't used any time to read (x=0), then she would have y=480 pages left to read. This is the point (0,480).
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substituting the given points:
[tex]\displaystyle y-402=\frac{402-480}{1.5-0}(x-1.5)[/tex]
[tex]\displaystyle y-402=\frac{-78}{1.5}(x-1.5)[/tex]
Operating:
[tex]y-402=-52(x-1.5)[/tex]
[tex]\mathbf{y=-52x+480}[/tex]
Answer:
-52x+480.
Step-by-step explanation:
I took the test, definitely correct
Sara walks at a constant speed. She walked 1 mile in 15 minutes. Which equation represents the amount of time in minutes, t, that it took for her to walk a distance of d miles? *
t = (1/15)d
t = 15d
t = d + 15
t = d - 15
Answers
Answer:
t=15d
Step-by-step explanation:
The problem is asking for total time, so we can set everything equal to t. If it takes 15 minutes for 1 mile and she's walking at a constant speed, we know that the solution is t=15d.
We can plug in one mile to verify this answer.
t=15(1)
t=15
Hope this helped!
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5, and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. ) 1:4
B. ) 1:5
C. ) 1:25
D. ) 3:10
Answers
Answer:
D) 3:10
Step-by-step explanation:
Well only blues and yellows are at least $5. there are 25 yellows and 5 blues and if you add them together there's 30 in total. Now compare that 30 to 100 and you have 30:100. In the simplest form you have to divide both sides by 10 and it becomes 3:10.
Which expression shows the sum of the polynomials with like terms grouped together?
10x’y+2xy2 - 4x2 - 4x^y
o [(-4x) + (-4x²y) + 10x?y] + 2xy?
o 10x+y+2xy?= [(-4x2)+(-4x²y)]
• (-4x2) + 2xy +[10x²y+ (-4x?y)]
o (10x+y+2xy?+ (-4x+y)]+(-4x)
Answers
Answer:
C (-4x2) + 2xy + (10x^2 y + ( -4x^2 y )
Step-by-step explanation:
I got it right on the test :3 UNUS ANNUS
Polynomial (3) [tex](-4x^2)+2xy^2+[10x^2y+(-4x^2y)][/tex] gives the sum of the given polynomial [tex]10x^2y+2xy^2-4x^2-4x^2y[/tex] with like terms grouped together.
What is Polynomial?Polynomial is a mathematical expression made of one or more algebraic terms (variable) with different powers and different combinations and coefficients.
We can add or subtract only like terms in a polynomial, and like terms are which have the same variable combination with similar power but the coefficient can be different.
Here given polynomial is [tex]=10x^2y+2xy^2-4x^2-4x^2y[/tex]
Here we have to group the like terms in the given polynomial which are [tex]10x^2y,(-4x^2y)[/tex].
So grouping the like terms we can write the sum of the given polynomial as [tex](-4x^2)+2xy^2+[10x^2y+(-4x^2y)][/tex].
Hence option (3) is correct.
Learn more about Polynomial here -
https://brainly.com/question/1600696
#SPJ2
Delilah does 184 jumping jacks in 4 minutes. She does her jumping jacks at a constant rate. How many jumping jacks can Delilah do per minute?
Answers
Answer:
414829.243 jumping jacks/minute
Step-by-step explanation:
Divide the total number of jumping jacks done by the total time.
[tex]\frac{184184184}{444} =414829.243[/tex]
Answer:
46
Step-by-step explanation:
Use the properties of logarithms to expand the expression as a sum or difference, and/or constant multiple of logarithms. (Assume all variables are positive)
Answers
Answer:
[tex]\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)[/tex]
Step-by-step explanation:
[tex]\log_5(\frac{9\sqrt{x}}{y^3})[/tex]
First rule I'm going to use is the quotient rule:
[tex]\log_b(\frac{m}{n})=\log_b(m)-\log_b(n)[/tex]
[tex]\log_5(9\sqrt{x})-\log_5(y^3)[/tex]
Secondly, I'm going to rewrite the radical.
[tex]\sqrt{x}=x^\frac{1}{2}[/tex]
[tex]\log_5(9x^\frac{1}{2})-\log_5(y^3)[/tex]
Third, I'm going to use the product rule on the first term:
[tex]\log_b(mn)=\log_b(m)+\log_b(n)[/tex]
[tex]\log_5(9)+\log_5(x^\frac{1}{2})-\log_5(y^3)[/tex]
Fourth, I'm going to use power rule for both of the last two terms:
[tex]\log_b(m^r)=r\log_b(m)[/tex]
[tex]\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)[/tex]
PLEASE HELP
If this is the graph of f(x)=a^(x+h)+k then.
Answers
Answer:
a
Step-by-step explanation:
Answer: 0<a<1
Step-by-step explanation:
Which statement best explains whether the table represents a linear or nonlinear function?
It is a linear function because there is a constant rate of change in both the input and output values.
It is a nonlinear function because there is a constant rate of change in both the input and output values.
It is a linear function because the input values are decreasing.
It is a nonlinear function because the input values are increasing.
Input
(x) Output
(y)
−2 7
−5 4
−8 1
−11 −2
Answers
Answer:
The correct answer is:
It is a linear function because there is a constant rate of change in both the input and output values.
Step-by-step explanation:
Given table is:
Input (x) Output (y)
−2 7
−5 4
−8 1
−11 −2
It can clearly be observed that the values for x and y are changing with the same rate.
In case of x, -3 is added to the previous input to get the next input.
Similarly, in case of y, the next output value is obtained by subtracting 3 from the previous value.
Hence,
The correct answer is:
It is a linear function because there is a constant rate of change in both the input and output values.
Jim earns 3% commission every month on his total sales. This month, his total sales were $620,000. How much commission did Jim earn?
Group of answer choices
A-$18,600
B-$20,600
C-$206,000
D-$186,000
Answers
pretty sure its A.
Brainliest?... thx
HELP PLZ!
Which fraction is equal to 0.7?
A) 7/99
B.) 7/11
C.) 7/10
D.) 7/9
Which fraction is equal to 0.54?
A.) 27/50
B.) 49/90
C.) 6/11
D.) 5/4
How can the decimal 0.57 be written as a fraction?
A.) 19/33
B.) 57/100
C.) 56/99
D.) 577/999
Answers
Answer:
the first one is A the second one D the third one B
Step-by-step explanation:
hope this will help you
Answer:
Which fraction is equal to 0.7?
C.) 7/10
Which fraction is equal to 0.54?
A.) 27/50
How can the decimal 0.57 be written as a fraction?
B.) 57/100
Step-by-step explanation:
Hope this helps and have a great day :)IF THE SUM CONSECUTIVE ODD NUMBERS IS 45, FIND THEM. (STEP BY STEP PLZ)
Answers
Answer:
[tex]\huge\boxed{\sf 13 , 15 , 17}[/tex]
Step-by-step explanation:
Let x , x+2 and x+4 be the consecutive numbers
Given Condition:
x + x + 2 + x + 4 = 45
3x + 6 = 45
Subtract 6 to both sides
3x = 45 - 6
3x = 39
Dividing both sides by 3
x = 13
So,
The numbers are:
x = 13
x + 2 = 13 + 2 = 15
x + 4 = 13 + 4 = 17
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Answer:
let the number be n
n+n+2+n+4 =45
3n+6=45
3n+6+6=45-6
3n/3=39/3
n=13
n=13
n+2=13+2
=15
n+4=13+4
=17
13,15,17
Step-by-step explanation:
pliz mark brainliest
A) Side measures of the triangle are given. Apply the Pythagorean Inequality to
classify each triangle as Acute, Obtuse or Right triangle.
1) 15 yd ; 8 yd ; 17 yd
2) 10 in ; 9 in; 5 in
3) 18 ft; 11 ft; 14 ft
4) 17 yd; 13 yd ; 20 yd
Pls solve all it due soon plsssssssssss
Answers
Answer:
1 obtuse
2 acute and
3 acute and
4 obtuse
Step-by-step explanation:
Two hot air balloons are traveling along the same path away from a town,
beginning from different locations at the same time. Henry's balloon begins
30 miles from the town and is 48 miles from the town after 2 hours. The
distance of Tasha's balloon from the town is represented by the function y =
8x+ 20.
Which balloon was farther from the town at the beginning, and which traveled
more quickly?
A. Henry's balloon was farther from the town at the beginning, and it
traveled more quickly.
O B. Henry's balloon was farther from the town at the beginning, but
Tasha's balloon traveled more quickly.
O C. Tasha's balloon was farther from the town at the beginning, and it
traveled more quickly
D. Tasha's balloon was farther from the town at the beginning, but
Henry's balloon traveled more quickly.
Answers
Answer:
it si this
Step-by-step explanation:
Simplifying
4y + -10 = 5 + -1y
Reorder the terms:
-10 + 4y = 5 + -1y
Solving
-10 + 4y = 5 + -1y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add 'y' to each side of the equation.
-10 + 4y + y = 5 + -1y + y
Combine like terms: 4y + y = 5y
-10 + 5y = 5 + -1y + y
Combine like terms: -1y + y = 0
-10 + 5y = 5 + 0
-10 + 5y = 5
Add '10' to each side of the equation.
-10 + 10 + 5y = 5 + 10
Combine like terms: -10 + 10 = 0
0 + 5y = 5 + 10
5y = 5 + 10
Combine like terms: 5 + 10 = 15
5y = 15
Divide each side by '5'.
y = 3
Simplifying
y = 3
Answer: A.
Step-by-step explanation: Henrys balloon was farther from the town at the beginning, and it traveled more quickly
I got this right so don't let anyone tell you different
Please help... Question is in the picture
Answers
Answer:
B) (0,1)
Step-by-step explanation:
The line crosses the y-axis at (0, 1), so that makes (0, 1) the y-intercept.
Hope this helps!
101 = -4 + 5(x + 2)
please help
Answers
Answer:x=19
Step-by-step explanation:
101 = -4 + 5(x + 2)
101= -4 +5x+10
91=-4+5x
95=5x
x=19
19
Step-by-step explanation:
Distribute 5
101=-4+5x+10
Combine like terms
101=5x+6
Get x alone on one side by subtracting 6
95=5x
Simplify
19=x
help asap do all these show work posting more after this one
Answers
Answer:
1) (2,10) is solution of y=4x+2
2) (7,5) is not solution of 2x+y=5
3) (-3,3) is not solution of y=6-x
4) (10,-1) is solution of x+8y=2
5) (2,21) is not solution of y=6x+7
6) (6,-8) is solution of 3x-y=26
Step-by-step explanation:
1) y=4x+2 (2,10)
Put x=2 and y=10 and check if both sides are equal or not
10=4(2)+2
10=8+2
10=10
So, (2,10) is solution of y=4x+2
2) 2x+y=5 (7,5)
Put x=7 and y=5 and check if both sides are equal or not
2x+y=5
2(7)+5=5
14+5=5
19≠5
So, (7,5) is not solution of 2x+y=5
3) y=6-x (-3,3)
Put x=-3 and y=3 and check if both sides are equal or not
y=6-x
3=6-(-3)
3=6+3
3≠9
So, (-3,3) is not solution of y=6-x
4) x+8y=2 (10,-1)
Put x=10 and y=-1 and check if both sides are equal or not
x+8y=2
10+8(-1)=2
10-8=2
2=2
So, (10,-1) is solution of x+8y=2
5) y=6x+7 (2,21)
Put x=2 and y=21 and check if both sides are equal or not
y=6x+7
21=6(2)+7
21=12+7
21≠19
So, (2,21) is not solution of y=6x+7
6) 3x-y=26 (6,-8)
Put x=6 and y=-8 and check if both sides are equal or not
3x-y=26
3(6)-(-8)=26
18+8=26
26=26
(6,-8) is solution of 3x-y=26
20. If g(x) = x^3+9/3x evaluate g(-3)
Answers
Answer:
2
Step-by-step explanation:
-3^3+9/3*-3= 2 ypu have tu substitute the x by -3 always.
SOMEONE HELP ILL KISS U
Answers
Answer:
0, 5x
Step-by-step explanation:
0 in the first box
5x in the second box