Answer:
[tex]a = -6, b = - 8[/tex]
Remaining factor = [tex]x+4[/tex]
Step-by-step explanation:
Given that:
Two polynomials:
[tex]x^{2} -x-2[/tex] and [tex]x^3 +3 x^2 +ax +b[/tex]
[tex]x^{2} -x-2[/tex] is a factor of [tex]x^3 +3 x^2 +ax +b[/tex].
To find:
The values of [tex]a[/tex] and [tex]b[/tex] from the cubic equation and the remaining factor.
Solution:
Let us first of all, factorize [tex]x^{2} -x-2[/tex].
[tex]x^{2} -2x+x-2=0\\\Rightarrow x(x-2)+1(x-2)=0\\\Rightarrow (x+1)(x-2)=0\\\Rightarrow x = -1, 2[/tex]
There are two factors of the given quadratic equation.
These two factors must also be factors of the cubic equation as well.
Putting [tex]x = 2[/tex]:
[tex]2^3 +3 \times 2^2 +a\times 2 +b =0\\\Rightarrow 2a+b=-20 ..... (1)[/tex]
Putting [tex]x = -1[/tex]:
[tex](-1)^3 +3 \times (-1)^2 +a\times (-1) +b =0\\\Rightarrow -a+b=-2 ..... (2)[/tex]
Subtracting (2) from (1):
[tex]3a = -18\\\Rightarrow a = -6[/tex]
From equation (1):
[tex]2\times (-6) + b=-20\\\Rightarrow b = -8[/tex]
Putting the values of [tex]a[/tex] and [tex]b[/tex] in the cubic equation, we get:
[tex]x^3 +3 x^2 -6x -8[/tex]
Dividing the cubic equation with quadratic, we get:
[tex]\dfrac{x^3 +3 x^2 -6x -8}{x^{2} -x-2} = x+4[/tex]
I NEED HELP ASAP PLSSSSSSS
Answer:
53 degrees
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
180-127=53
Which expression is equivalent to
7 + (3 + 11)
———————
-5+ 8
(Picture included)
HELP ASAP!!
Answer:
7
Step-by-step explanation:
start by adding 3+ 11 in the parenthesis, that should give you 14. now you should have 7 + 14 over -5 + 8.
-5 + 8 = 3 (another way to look at this problem is, 8 -5)
7+14 = 21
you should now have 21 over 3
to simplify this divide 21 by 3, this should give you 7
Answer: 21 divided by 3
Step-by-step explanation:
If you solve the top and the bottom you get 21 for the top and 3 for the top and you can divide 21 by 3 and get 7. You can double check the math if you want, hope this helps!
Plz help me if your a Genius at math!!!and I will gave Brainliest
Answer:
320
190
318
42.241951146971
Step-by-step explanation:
9514 1404 393
Answer:
320 units²190 units²318 units²43.8 units²Step-by-step explanation:
The area formula for a rectangular prism is ...
A = 2(LW +H(L+W))
For (L, W, H) = (8, 8, 6) ...
A = 2(8·8 +6(8+8)) = 2(64 +96) = 320 . . . square units
For (L, W, H), = (2, 9, 7) ...
A = 2(2·9 +7(2 +9)) = 2(18 +77) = 190 . . . square units
For (L, W, H) = (6, 7, 9) ...
A = 2(6·7 +9(6 +7)) = 2(42 +117) = 318 . . . square units
__
The area of the triangular prism is the sum of its triangular base areas and the lateral area. The lateral area is the product of the base perimeter and the length of the prism.
A = 2(1/2)bh +PL
= 3(2.6) +(3+3+3)·4
= 7.8 +9·4 = 43.8 . . . square units
which model represents 1/3
Answer:2nd one because 2/6=1/3
Step-by-step explanation:
A line includes the points (6, 9) and (3, 3). What is its equation in slope-intercept form?
Answer:
y=2x-3
Step-by-step explanation:
A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x , the time in minutes.
Which answer choice best describes the domain and range of the function for this situation?
Small problem....
There is no graph!
ill be happy to solve this if i saw a graph
AJKL-AXYZ. Find the scale factor from AJKL to AXYZ.
20
x
10]
8
16
2 10 y
L
20_k
2/1
172
524
4
/
5ܐ
Answer:
1/2
Step-by-step explanation:
Since you are going from the biggest to smallest, it would be 1/2. If you are going from the smallest to biggest it would be 2. So the answer is 1/2. :)
IN A GAME,THE PROBABILITY OF THE SPINNER LANDING ON A 2 IS 1/3. HOW MANY TIMES WOULD YOU SPIN EXPECT TO LAND ON A 2 IF YOU SPIN THE SPINNER12 TIMES. PLEASE HELP!!! PLEASE HELP ASAP!! WILL MARK BRAINLIIEST!!
Answer:
I’m pretty sure u would spin it 4 times
Step-by-step explanation:
I hope that helps check with someone else tho ❤️❤️
Kathryn's water bottle holds 20.25 ounces. Her doctor told her to drink half her body weight in ounces of water. Kathryn weighs 121.5 pounds. How many water bottles will she have to drink? (There is no convesion required from ounces to pounds)
Answer: She have to drink 3 bottles of water.
Step-by-step explanation:
Given: Weight of Kathryn = 121.5 pounds
half of her weight = [tex]\dfrac{121.5}{2}=60.75\text{ pounds}[/tex]
So, she need to drink 60.75 pounds of water.
Kathryn's water bottle holds 20.25 ounces.
Number of water bottles she need to drink = (half of her weight) ÷ (Capacity of bottle)
[tex]=\dfrac{60.75}{20.25}\\\\=\dfrac{6075}{2025}\\\\=3[/tex]
Hence, she have to drink 3 bottles of water.
Please answer correctly !!!!!!!!!!!! What is the triangle ?!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Isosceles Right
Isosceles, since the two side lengths are equal, and it is a right triangle since it has a 90 degree angle and two other 45 degree angles.
Answer:
Isosceles Right
Step-by-step explanation:
Which equation could have been used to create this table?
y = 4x
y = x + 3
y = x + 2
y = 3x
Table:
X Y
1 3
2 6
4 12
5 15
6 18
I need help with this
Answer:
1. y=14
2. x=22
3. z=3
4. n=14
5. a=10
6. m=-5
7. b=26
8. c=15
9. x=80
10. g=20
11. x=-5
12. w=-4
13. r=45
14. k=12
15. f=50
16. j=2
17. r=21
18. t=47
what is eqivalent to 1/11
Answer:
it may be different answers i.e 0.09 and 11^-1
Please help me with this homework
Answer:
your x's will be -2, -1 , 0 , 1, 2
and your y's will be -5, -2, 1, 4, 7
PLZ ANSWER.. I NEED HELP!?!?
factorise x^2+5x+6
Answer:
there is no like terms
Step-by-step explanation:
Answer:
(x+2)(x+3)
Explanation:
(x+2)(x+3)
If you simplify this, you get:
x*x = x^2
x*3 = 3x
2*x = 2x
2*3 = 6
If we add these all together we will have:
x^2 + 3x + 3x + 6
Combine like terms
x^2 + 5x + 6
Which of these tables represents a non-linear function?
х
17
18
19
y
20
19
18
17
20
х
17
18
19
20
y
-16
-17
-18
-19
Х
17
18
19
20
у
16
17
19
20
у
Answer:
Its C.Step-by-step explanation:
Non-linear functions address the problems of a linear activation function: They allow backpropagation because they have a derivative function which is related to the inputs. They allow “stacking” of multiple layers of neurons to create a deep neural network.
6th grade math i mark as brainliest
Answer:
9. 30/6
10. 7.6 and u
Step-by-step explanation:
Noah is solving an equation, and one of his moves is unacceptable. Here are the moves he made.
Which answer best explains why the “divide each side by step” is unacceptable?
a. When you divide both sides of 2x = 6x by X you get 2x² = 6x²
b. When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
c. When you divide both sides of 2x = 6x by x you get 2 = 6x.
d. When you divide both sides of 2x = 6x by x it could lead us to think that there is no solution while, in fact, the solution is x = 3
Answer:
b. When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
Step-by-step explanation:
The solution is correct up to the step 2x = 6x
2x = 6x
Subtract 2x from both sides.
0 = 4x
Divide both sides by 4.
x = 0
You cannot divide both sides by x since x could be zero, and in fact, it is.
Answer: b. When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
The correct option is (b) When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear equation is:
2(x + 6) - 4 = 8 + 6x
After simplifying the above linear equation in one variable:
2x = 6x
The correct steps are:
6x - 2x = 0
4x = 0
x = 0
When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
Thus, the statement best explains that “divide each side by step” is unacceptable" is When you divide both sides by 2x = 6x it could lead us to think that there is no solution while, in fact, the solution is x = 0.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ5
José paid $47.00 for 4 movie tickets. Each ticket cost the same amount. What was the cost of each movie ticket in dollars and cents?
alec is seven years younger than his older brother Ethan if alec is 24 years old how old is Ethan
Answer:
Ethan is 31 years old if Alec is 24 years old.
Step-by-step explanation:
24 + 7 since Alec is seven years younger than his older brother so you add seven to his age
Answer:
31
Step-by-step explanation:
Alec is seven years younger than his older brother Ethan
So
If Alec is 24 years old then Ethan will be
24+7
31
Write the equation of the line in slope intercept form that passes through the point (6, -1) and has a slope of -2.
Answer:
Y=6X-32
Step-by-step explanation:
Answer:
y-y1=m(x-x1)
y-6=-2(x-(-1))
y-6=-2(x+1)
y-6=-2x-2
y=-2x+4
Step-by-step explanation:
what is -1 1/2, -12, -4.3 least to greatest
With negative numbers the larger the number the lower the value. For example -2 is less than -1
The order from least to greatest would be:
-12, -4.3, -1 1/2
HELP CORRECT AWNSER GET BRAINLIEST
Answer:
A 33 degrees
Step-by-step explanation:
[tex]x \degree = 180 \degree - (23 \degree + 124 \degree) \\ \\ x \degree = 180 \degree - 147 \degree\\ \\ x \degree = 33 \degree \\ \\ x = 33[/tex]
Answer:
A) 33
Step-by-step explanation:
the angles of a triangle always add up to 180.
124 + 23 + x = 180
combine like terms
147 + x = 180
147 + x - 147 = 180 - 147
x = 180 - 147
x = 33
The coordinates of point K are (−3, 4.5). Which statement tells how to locate point K on the coordinate plane?
Answer:
-3
Step-by-step explanation:
Solve for u.
200 = 125 - u
Answer:
-75
Step-by-step explanation:
200 = 125-u
75 = -u
u = 75
Sophia's dad paid $43.25 for 12.5 gallons of gas. What is the cost of one gallon of gas
Answer:
It is $3.46
Step-by-step explanation:
Hope this helped have an amazing day!
PLEASE HELP! 5TH GRADE MATH! Select the best estimate of the product of Select the best estimate of the product of 52 x 89 = ____
Answer:
400
Step-by-step explanation:
50x80=400, you just ignore the ones digits so its easy to solve. (5x8x100)
CLASS TIME: You spend 150 minutes in three classes. Write and solve a proportion to find how many minutes you spend in five classes. (Section 3.4)
Answer:
250
Step-by-step explanation:
150 divided by 3 is 50. Meaning you spend 50 minutes per class. 50 times 5 would be 250.
Withby tuns 3/4miles in 1/6 hours at that rate how far can she run in one hour?
Answer:
4.5 miles ibelieve
Step-by-step explanation:
3/4 × 6/6 is 4.5 miles
A pickup truck carrying 10*3 identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick? Explain how you solved the problem.
Answer:
The truck now weighs 2130 kilograms. Hope this helps.
Step-by-step explanation: