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]
Ryan and his brother, Russell, made photo frames for their grandma's birthday. They used shells they collected from the beach near her house. Ryan glued 9 white shells and 15 orange shells to the border of his frame. Russell glued 8 white shells and 10 orange shells to the border of his frame. Did the two frames have the same ratio of white shells to orange shells?
Answer: No. The two frames does not have the same ratio of white shells to orange shells.
Step-by-step explanation:
Ryan glued 9 white shells and 15 orange shells to the border of his frame. This will give us a fraction of:
9/15 = 3/5
The ratio is 3:5
Russell glued 8 white shells and 10 orange shells to the border of his frame. This will give us a fraction of:
= 8/10 = 4/5
The ratio will be 4:5.
Therefore, the two frames does not have the same ratio of white shells to orange shells.
Hurry please. What is the slope of the line represented by the equation y = -2/3 - 5x? O-5 O-2/3 O2/3 O5
Answer:
Step-by-step explanation:
y = -5x - 2/3
the slope is -5
Which expression is equivalent to 4{12 + 5} + 3?
Answer:
71
Step-by-step explanation:
6. Solve the following equation for y.
3x - 4y = 6
Answer:
3x−4y+−3x=6+−3x
−4y=−3x+6
Step 2: Divide both sides by -4.
−4y
−4
=
−3x+6
−4
y=
3
4
x+
−3
2
Step-by-step explanation:
Answer:
y = 0.75x - 1.5
Step-by-step explanation:
3x - 4y = 6
-4y = -3x + 6
y = 3/4x - 6/4
y = 0.75x - 1.5
hope this helps, pls mark brainliest :D
38.3 cm
Р
0 12.6 cm R
Answer:
Step-by-step explanation: F 50.9 cm (H 25.7 cm. G 46.3 cm. -38.3 cm. G 46.3 cm. 921.3 cm. Ø 12.6em Å ... Р. 3 - с. 2, +6:48 348 р. 8. Find the distance between P(2, 8) and Q15, 3). F9 ... REVIEW VOCABULARY!!!!! R=0 tre of the two angles. Atab=180. 2 ДО - Чx 49.
what is the value of (-0.7)(6.0)
Answer: Look below
Step-by-step explanation: its not letting me put the answer in its said its i
helpp meee pleaseeee
Answer:
I think its b:/ srry if I'm wrong
What is the approximate Square Root of 81.183?
A.9.5
B.9
C.8.1
D.8
Answer:
B
Step-by-step explanation:
Find x such that f(x) = 10 given f(x) = 4x+2
Answer:
x=2
Step-by-step explanation:
So you make the equation equal. f(x)=10 so you would put it as 10=4x+2, than you subtract two from both sides making it 8=4x and than divide both sides by 4 making it 2=x.
Answer:
[tex]\boxed {\boxed {\sf x=2}}[/tex]
Step-by-step explanation:
We know that:
[tex]f(x)=4x+2 \\f(x)= 10[/tex]
Both 4x+2 and 10 are equal to f(x). We can use substitution and set 4x+2 and 10 equal to each other.
[tex]4x+2=10[/tex]
Now, solve for x. Perform the inverse operations to isolate x on one side of the equation.
2 is being added to 4x. The inverse of addition is subtraction. Subtract 2 from both sides of the equation.
[tex]4x+2-2=10-2[/tex]
[tex]4x=10-2 \\[/tex]
[tex]4x=8[/tex]
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides of the equation by 4.
[tex]\frac{4x}{4} =\frac{8}{4}[/tex]
[tex]x=\frac{8}{4}[/tex]
[tex]x=2[/tex]
For the function f(x)= 4x+2, when f(x)=20, x=2
1, 3, 2, 2, 1, 3, 3, 1 What is the mean absolute deviation
Answer:
6
Step-by-step explanation:
Given the data:
1, 3, 2, 2, 1, 3, 3, 1
The mean absolute deviation :
Sum of (1, 3, 2, 2, 1, 3, 3, 1) = 16
Mean = 16 / 8 = 2
Mean absolute deviation :
|1 - 2|+ |3 - 2| + |2 - 2| + |2 - 2| + |1 - 2| +|3 - 2| + |3 - 2| + |1 - 2|
= 1 + 1 + 0 + 0 + 1 + 1 + 1 + 1
= 6
what is the range of the data 79, 52, 85,94, 71, 82, 84, 66, 58, 98, 72, 100
Answer:
48 pllz can i have brainiest plzz
Step-by-step explanation:
Answer:
48 is a answer
Step-by-step explanation:
formula for range is highest - lowest
100 - 52
48
Anyone else chew on there hoodie strings?
Answer:
yes only when in nervous or bored
Jordana drew the function below. Which statement correctly explains whether or not her function is linear?
On a coordinate plane, a parabola opens up.
It is linear because it has a constant rate of change.
It is linear because it does not have a constant rate of change.
It is not linear because it has a constant rate of change.
It is not linear because it does not have a constant rate of change.
Answer:
It is not linear because it does not have a constant rate of change
Step-by-step explanation:
See attachment for Jordana's graph
From the attachment, it'll be observed that the graph has a curved line.
This means that the graph is not a linear and does not represent a linear function.
In functions, a linear representation has a constant slope (in other words, constant rate of change) while non linear representations do not.
So, since we've been able to establish that the graph is non linear, then we can conclude that the graph do not have a constant slope.
Base on the analysis above and from the list of given options, option (d) is correct.
Answer:
D
Step-by-step explanation:
credit to person above :)
have a nice day <3
The sum of the speeds of two trains is 717.4 miles per hour. If the speed of the first train is 4.6 miles per hour faster than that of the second train, find the speed of each
Answer:
The second train speed is 356.4 miles per hour
And, the first train speed is 361 miles per hour
Step-by-step explanation:
The computation of the speed of each train is as follows
Given that
The Sum of the speed of two trains is 717.4 miles per hour
Let us suppose the second train speed be x
So for the first train, the speed is x + 4.6
Now the equation is
x + x + 4.6 = 717.4
2x + 4.6 = 717.4
2x = 717.4 - 4.6
2x = 712.8
x= 356.4
Therefore the second train speed is 356.4 miles per hour
And, the first train speed is = 356.4 + 4.6 = 361 miles per hour
If the two triangles shown below are congruent, select the corresponding 1 point
postulate that proves they are congruent. If the triangles are not
congruent, select not congruent. *
Answer:
SSS
Step-by-step explanation:
The two triangles both share a side (the middle line), and it is shown that the other lines are congruent to each other. So all 3 sides are congruent, meaning SSS is the postulate that proves this.
PLS HELP 50 POINTS IF YOU DONT KNOW DONT ANSWER THE QUESTION
Answer:
It is C or t < 6
Step-by-step explanation:
The line starts at 6 and goes left. The way I remember which way it goes is the greater than or less than sign looks like the tip to the arrow
< ---- and ---- >
It is an open circle so it will not be a greater than or equal to sign
Simplify 4x + 8 = 0.1x + 3 +3.9x
Answer:
Step-by-step explanation:
4x+8=.1x+3+3.9x
4x+8=4x+3
No solution since the 4x's will cancel each other out
Friendship’s soccer team purchased uniforms and equipment for a total of $912. The equipment cost $612 and the uniforms cost $25 each. How many uniforms did the school purchase?
Answer:
12
Step-by-step explanation:
912 - 612 = 300
300 ÷ 25 = 12
The number of uniforms the school purchased based on the given data and equation formation will be $12.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's suppose the school purchase x number of uniforms.
Total cost = equipment cost + x uniforms cost
912 = 612 + 25x
912 - 612 = 25x
25x = 300
x = 12
Hence "The number of uniforms the school purchased based on the given data and equation formation will be $12".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
Find the percent of increase from 15 lbs. to 31 lbs. Round to the nearest tenth if necessary.
Solve the Proportion: 3/8 = x/12
x = 9/2
Get variable on one side of equation and solve"
x/12 = 3/8
x = (3/8)(12)
x = 9/2
9. The diameter of the Earth is 7899.83 miles from the North Pole to the South Pole and 7926.41 miles from opposite points at the equator.
a. Find the approximate surface area of Earth using each measure.
b. About 75% of Earth's surface is covered by water. Find the surface area of water on Earth, using the diameter of the Earth is 7926.41 miles from opposite points at the equator.
Answer:
We could think of the Earth as a sphere, where the diameter of this sphere will the mean diameter between the measure from the North pole to the Soth pole and the measure from opposite points of the equator.
Remember that the mean between two numbers A and B is:
Mean = (A + B)/2
In this case, the mean diameter will be:
D = (7,899.83mi + 7,926.41mi)/2 = 7,913.115 mi
And we know that the surface of a sphere of diameter D is:
S = 4*pi*(D/2)^2
Where pi = 3.14
Then the surface of the Earth will be something like:
S = 4*3.14*(7,913.115mi/2)^2 = 196,618,601.47 mi^2
b) We know that 75% of the Earth's surface is water, now we will use the diameter 7,926.41 mi to compute the surface.
First, the total surface of the Earth will be:
S = 4*3.14*(7,926.41mi/2)^2 = 197,279,843.03 mi^2
And 75% of this is water, then the total water surface is 0.75 times that area, this is:
water surface = 0.75*197,279,843.03 mi^2 = 147,959,882.27 mi^2
The sum of 6 consecutive even numbers is 126
.
What is the fourth number in this sequence?
||EXTRA POINTS + BRAINLET||
help me please 20 points!!!!!
Answer:
20
Step-by-step explanation:
4x + 12x = 320
16x = 320
x = 320/16
x = 20
Fill in the blank 8(? +3) =48+24
Answer:
6
Step-by-step explanation:
treat the ? as an x. you need to get it by itself. but first you should distribute the 8.
8x + 24 = 48 +24
8x+24 = 72
take the 24 and subtract it from 72
8x= 48
now divide both sides by 8
x= 6
Answer:
6
Step-by-step explanation:
8(6 + 3) =48+24
8(9) = 48+24
72 = 48 + 24
72 = 72
I need help I’m timed
what is the y- intercept of the linear function?
y= 1/2 x + 4
Answer: (0,4)
Step-by-step explanation:
Look at the subtraction expression below. ( Please. Help. Quick.)
- 1/2 - 1/4
Which number line models this expression?
Answer:
A.
Step-by-step explanation:
Because they are both subtracting, both lines have to go to the left
Answer:
The answer is A
Step-by-step explanation:
I got a 100 on my test ;)
what is the solution for X in the equation 4x - 3 + 5 = 2x + 7 - 8x
A. X = 2
B. X = -2
C. X = 1/2
D. X = -1/2
Answer:
C. X = 1/2
Step-by-step explanation:
4x - 3 + 5 = 2x + 7 - 8x
4x +2 = - 6x + 7
4x + 6x = 7 - 2
10x = 5
x = 1/2
Dwayne got a raise, and his hourly wage increased from $12 to $15. What is the percent of change?
A. 20% increase
B. 25% increase
C. 20% decrease
D. 25% decrease
Answer:
B
Step-by-step explanation:
The pay increases, so it clearly cannot be C or D, and 25% of 12 is 3 because 12/4 = 3, so it would have to be B.
p l e a s e h e l p a s a p:) will mark brainliest and answer any q if correct:))
Answer:
last one
Step-by-step explanation:
Whats the error in this problem 19 - 2k = 3k - 1
+ 3k + 3k
19 + 1k - 1
- 19
- 19
k = - 20
Step-by-step explanation:
Just collect like terms. Follow the +ve and _ve signs as they go over the equation sign where they then become an inverse of themselves and use the signs to work