According to the synthetic division below, which of the following statements are true? Check all that apply
Answers
The true statements are A , B , E
What is division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, In the synthetic calculation we use the coefficient of the dividend
with the factors of the function
∴ 2 , -2 , -12 are the coefficient of the dividend 2x² - 2x - 12
∵ The divisor is 3
∴ x = 3 is a root of F(x) = 2x² - 2x - 12
∵ x = 3 is the root of F(x) = 2x² - 2x - 12
- Subtract the two sides by 3
∴ x - 3 = 0
∴ (x - 3) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division
∴ The coefficients of quotient are 2 , 4
- The quotient is 1 degree less than the dividend
∵ The degree of the dividend is 2
∴ The degree of the quotient is 1
∴ The quotient is 2x + 4
* Lets check the answers to chose the write statements
A. The number 3 is a root of F(x) = 2x² - 2x - 12 ⇒ true
B. (x - 3) is a factor of 2x² - 2x - 12 ⇒ true
E. (2x² - 2x - 12) ÷ (x - 3) = 2x + 4 ⇒ true
Thus, the true statements are A , B , E.
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Related Questions
There are 2 green pens, 3 blue pens, 4 red pens, and 1 black pen in the teachers desk. The teacher selects 2 pens at random, and the pens are not replaced. What is the probability that the teachers will pick 2 red pens in a row?
Answers
Answer:
2/15
Step-by-step explanation:
2 green pens, 3 blue pens, 4 red pens, and 1 black pen =10 pens
P(red) = red/total = 4/10 = 2/5
Keep the pen
2 green pens, 3 blue pens, 3 red pens, and 1 black pen =9 pens
P(red) = red/total = 3/9 = 1/3
P(red,red) = 2/5 * 1/3 = 2/15
3. Which property of similarity can be used to prove triangles STR and VWU are similar?
Answers
Answer:
Not enough information
Step-by-step explanation:
Similar triangles must have congruent corresponding angles and proportional corresponding sides.
Answer:
not enough information
Step-by-step explanation:
okay can someone pls help me i literally am so confused
Answers
please help me is for my homework
Answers
Answer:
13/50
Step-by-step explanation:
Answer:
26/100
Method:
Fractions are much like percents, as they are both out of 100. The 26% is 26%/100% (26/100)
ASAP!! can i get some help on this question, and a step by step explanation please, it would help
a lot thanks.
Answers
Answer:
[tex]{ \tt{ {3x}^{2}(5 {x}^{3} ) = 15 {x}^{5} }}[/tex]
Step-by-step explanation:
[tex]{ \sf{3 {x}^{2}(5 {x}^{3} )}} \\ = { \sf{ {x}^{5} (3 \times 5)}} \\ = { \sf{15 {x}^{5} }}[/tex]
Find the missing value in each figure below. What does “y” equal?
Answers
Answer:
Step-by-step explanation:
The perpendicular is equal to 6. That's because the left triangle's missing angle is 180 - 45 -90 = 45
The angle in the right triangle is given as 52.
The cos(52) = adjacent side (which we just found to be 6) / y
Multiply both sides by y
y cos(52) = 6
cos(52) = 0.6157
Divide by sides by cos(52)
y = 6 / cos(52)
y = 6 / 0.6157
y = 9.76
The number of students in an school building that have the flu after t days is given by the function
()=800/1+49^−0.2
a) What was the initial number of students infected (think about what time is initially).
b) When will the number of students infected be equal to 200?
Round all of your answers to the NEAREST whole number and be sure to label your answers.
Answers
Step-by-step explanation:
[tex]p(0) = \frac{800}{1 + 49 {e}^{ - 0.2 \times 0} } = \frac{800}{1 + 49} = \frac{800}{50} = 16[/tex]
[tex]200 = \frac{800}{1 + 49 {e}^{ - 0.2t} } \\ 200(1 + 49 {e}^{ - 0.2t} ) = 800 \\ 200 + 9800 {e}^{ - 0.2t} = 800 \\ 9800 {e}^{ - 0.2t} = 600 \\ {e}^{ - 0.2t} = \frac{3}{49} \\ ln( {e}^{ - 0.2t} ) = ln( \frac{3}{49} ) \\ - 0.2t = - 2.793 \\ t = 13.96 = 14[/tex]
I don't understand this one
Answers
Answer:
9/8 = n
Step-by-step explanation:
9 = 8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
What is an equation of the line that passes through the points (-6, -8) and (-3,-3)?
Answers
Answer:
y = 5/3x+2
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( -3 - -8)/( -3 - -6)
= ( -3+8) / (-3+6)
= 5/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
Substituting the point (-3,-3)
-3 = 5/3(-3) + b
-3 = -5+b
-3+5 = b
2 = b
y = 5/3x+2
Given points
(-6,-8)(-3,-3)First find the slope
[tex]\boxed{\sf m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-3+8}{-3+6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{5}{3}[/tex]
Now
[tex]\boxed{\sf y=mx+b}[/tex]
[tex]\\ \sf\longmapsto -3=\dfrac{5}{3}(-3)+b[/tex]
[tex]\\ \sf\longmapsto b=2[/tex]
Hence the equation will be
[tex]\\ \sf\longmapsto y=\dfrac{5}{3}x+2[/tex]
Samia created the following tables of values for a linear system. She concluded that there is no
solution to the system
Answers
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
How many solutions do a system of linear lines have?A system of equations, involving two linear lines has solutions as follows:
Unique Solution: When the lines intersect, the point of intersection is the solution.No Solution: When the lines are parallel, no solution exists.Infinite Solution: When the lines coincide, then all points on the line become solutions, giving an infinite number of solutions.How to solve the question?In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.
We are asked to comment on her conclusion.
To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.
Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.
Thus, the slope for:-
Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.
Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.
Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
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Simplify this please
Answers
Answer:
4Step-by-step explanation:
[tex] \sqrt[3]{64} [/tex]
[tex] = \sqrt[3]{4 \times 4 \times 4} [/tex]
= 4 (Ans)
Answer:
Step-by-step explanation:
find the measure of the indicated angle to the nearest degree
Answers
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
plot -½ on the number line
Answers
Answer:
this would be towards the front and the very end
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
A. {(6, 5)}
B. {(5, 6)}
C. {(13/5, 6/5)}
D. {(6/5, 13/5)}
Answers
Step-by-step explanation:
+ Both equations
You will get : 5x=13 ; x=13/5
and put x to the first equation
2*13/5-y=4
y=6/5
(13/5;6/5)
Answer is C
Find the area of triangle ABC.
[PLEASE HELP ME!!]
A.12.16units
B.18.52units
C.31.27units
D.15.14units
Answers
Answer:
D
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] × product of 2 sides × sine ( angle between them ) , that is
A = 0.5 × 5.04 × 6.82 × sin61.73° ≈ 15.14 ( to 2 dec. places )
What is the value of this expression when g = -3.5?
8 − |2g − 5|
A. 20
B. 10
C. 6
D. -4
Answers
g = -3,5
8 - |2g - 5| = 8 - |2 · (-3,5) - 5| =
= 8 - |-7 - 5| = 8 - |-12| = 8 - 12 = -4
what is the formula to get combined mean value
Answers
Answer:
The combined mean can be calculated by plugging in our numbers into the formula given: [(57*82)+(23*63)/(57+23)]=76.5
Select the correct answer.
Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?
A.
x > -4
B.
x < -4
C.
x > -3
D.
x < -3
Answers
Answer:
C
Step-by-step explanation:
Given
10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides
30x + 20 > 14x - 28 ( subtract 14x from both sides )
16x + 20 > - 28 ( subtract 20 from both sides )
16x > - 48 ( divide both sides by 16 )
x > - 3 → C
find the area of parallelogram and round to the nearest tenth.
Answers
Answer:
A=b×h
A=13.8×6
A=82.8 in²
A≈83in²
Step-by-step explanation:
a boy rode his bike at an average speed of 11 kilometers per hour . how much far did he ride in four hours
Answers
Step-by-step explanation:
The answer is mentioned above.
Hope it helps.
PLz, Help fast! 100 points
A line is drawn on a scatter plot, as shown below:
A graph shows values till 10 on both x- and y axis with increments of 1.Dots are shown at 0.5, 7.5 and 1.8, 6.5 and 3, 6 and 4.4, 5 and 4.8, 4 and 5.9, 3.2 and 6.6, 2 and 7.5, 2.5 and 8, 1 and 8.8, 0. A straight line joins the ordered pairs 0, 7.9 and 10, 0.
Which statement best describes the line?
Answers
Answer:
It can be the line of best fit because it closely fits the data points.
Step-by-step explanation:
The line is near the data points and goes down from left to right just like the data points. It is just above or just below the data points.
Answer:
guy above is right
Step-by-step explanation:
A team of 5people to be selected from 7women & 6men. Find the number of different teams that could be selected if there must be more women than men in the team
Answers
Answer:i would say 2 differentt teams where there is more then women than men in the team
Step-by-step explanation:
well how i came to this answer is that the team is limited to only 5 people giving the only team where there is more women over men is this first team would be 4 women and 1 men , second team would be 3 women and 2 men anything lower then 3 make its where the team has more men than women so the only options would be 2 team where either they go with 4 women or 3 women and you can't go with more then 4 because then there would be no men in the team which is what the question asks for please go with 2 teams
if this helps please make me brainlist ?!
Please help !!!!!!!!!!!
Answers
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
Given the equation, 1 + 6k = 25, for some value of k, what is the value of k +7 for the same value
of k?
Answers
Answer:
k + 7 = 11
k = 4
Step-by-step explanation:
1 + 6k = 25
25 - 1 = 6k
24 / 6 = k
k = 4
4 + 7 = 11
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
k = 4
The value of k + 7 = 11
Step-by-step explanation:
1 + 6k = 25
To find the value of k we have to use inverse operations
1 + 6k = 25
1 - 1= 0
25 - 1 = 24
This cancels out the 1 in this equation. 25 becomes 24 now because what we do to one side we do to the other.
6k = 24
To find k we have to divide 6 from 6 and 24
6/6= 0
24/6= 4
Now we are left with the variable k and 4
Therefore, k = 4.
To solve the second part of the equation we plug in k to the equation
k = 4
so the equation becomes 4 + 7
4 + 7 = 11
abio and Carlos play on a basketball team together. In the last game, Fabio had 777 points less than 222 times as many points as Carlos. Fabio scored 313131 points in the game.Write an equation to determine the number of points (c)(c)(, c, )Carlos scored in the last game.
Answers
Answer:
The equation 31=2c-7 to determine the number of points Carlos scored in the last game.
Step-by-step explanation:
We are given with,(I think every number is repeating for 3 times. So, I took each number as once)
Fabio had 7 less than 2 times as many points as Carlos. And Fabio score 31 points.
Let Carlos scored in the last game as "C".
So, we can set up equation for Fabio had 7 less than 2 times Carlos as
Fabio= 2C-7
Like so for Fabio score 31 as
Fabio =31
So, substitute Fabio as 31 into the first equation, we get
31= 2c-7
So, the equation 31=2c-7 to determine the number of points Carlos scored in the last game.
(I will give brainliest!)
Solve for x using the distributive property
7(x-2)-3(x+3)=5(x-3)+x
Answers
Answer:
Step-by-step explanation:
7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis
7x -14 -3x -9 = 5x -15 +x , isolate like terms
7x -3x -5x -x = 14 +9 -15, combine like terms
-2x = 8, divide both sides by -2
x= -4
Hope this helps
if the radius of a sphere is7 cm find its volume
Answers
Answer:
1437.33 cm square
Step-by-step explanation:
Now we will use the frmula to et the volume of a sphere
volume of sphere is
4÷3pi r cube
where r is the radius of the sphere
Nina is making pink candles to use as decorations on Valentine's Day. She melts red and white wax together and pours them into a heart-shaped mould. Then, she melts double the amount of red wax and double the amount of white wax together and pours them into a flower-shaped mould. Which candle is a lighter shade of pink?
Answers
Answer:
answer is neither, they are both the same shade.
Step-by-step explanation:
if she doubled the colors exactly then it wouldn't be any different. Also IXL told me I'm right :)
Answer:
Neither.
Step-by-step explanation:
Originally, she used the same amount. For the second one, she used double the same amount, but it was still the amount of red wax as of white wax. So, they both had the same amount, which means it is neither.
help me with math pls;(
Answers
Answer:
as it is cbe the volume of cube is l*l*l
Step-by-step explanation:
the answercis 5*5*5= 125
please mark brainliest
cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với
Answers
[tex]\\ \sf\longmapsto 1+tan^2A[/tex]
[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]
[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]
Hence verified
