Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
3 hours = minutes
2 hours 25 minutes. =. minutes
Answer:
180, 145
Step-by-step explanation:
There are 60 minutes in an hour, so we do 3*60=180 for the first one.
For the second one, we first find the minutes in 2 hours, which is 2*60=120. We add 120+25 and get 45.
How i can asnwer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answer:
B
Step-by-step explanation:
Each number you're adding 12.
24 + 12 = 36, 36 + 12 = 48,. etc..
B
A shows factors of 12 instead of multiples, and C just doesn’t show numbers of relation to 12
Maria's test scores for this semester were: 84, 80, 93, 74, 67, 99, 87, 72, 95, & 98. What is the mean of her test scores (rounded to the nearest whole
percent)?
Answer:
85%
Step-by-step explanation:
Add all the numbers together which gives 849. Divide 849 by 10 because there are ten numbers. This gives 84.9. Round it up to 85%
undefined slope through (74, 25)
slope-intercept form:
y=25
piont-slope form:
y-25 =0×(x-74)
The formula is:
y-y1=m9(x-x1)
Use the algebra tiles to help you solve 3x+6=12
Answer:
2
Step-by-step explanation:
We subtract both sides by 6 (3x=6)
And then we divide by 3 (x=2)
Hey there!
You have 3 x-tiles
+
6 = positive-tiles (+)
=
12 positive-tiles (+)
3x + 6 = 12
SUBTRACT 6 to BOTH SIDES
3x + 6 - 6 = 12 - 6
CANCEL out: 6 - 6 because it gives you 0
KEEP: 12 - 6 because it helps solve for the x-value
NEW EQUATION: 3x = 12 - 6
SIMPLIFY IT!
3x = 6
DIVIDE 3 to BOTH SIDES
3x/3 = 6/3
CANCEL out: 3/3 because it gives you 1
KEEP: 6/3 because it helps solve for the x-value
x = 6/3
SIMPLIFY IT!
x = 2
Therefore, your answer is: x = 2
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
In a week, Tracy earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45. How much does Kayla earn?
Answer:
$57.45
Step-by-step explanation:
102.45=2x-12.45
2x= 102.45+12.45
2x=114.90
x= 114.90/2
x=$57.45
On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negative 1, negative 1) If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle? 0. 625 units 0. 8 units 1. 25 units 1. 6 units.
The corresponding height of the triangle is 1.6 units
The formula for calculating the area of a triangle is expressed as:
[tex]A=\frac{1}{2} bh[/tex]
b is the base of the triangleh is the height of the triangleGiven the coordinates of the base BC of the triangle given as B(3, 2), and C(-1,-1). Using the distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\BC= \sqrt{(-1-2)^2+(-1-3)^2}\\BC=\sqrt{3^2+4^2}\\BC=\sqrt{25}\\BC=5units[/tex]
The area of the triangle passing through the coordinate points A(-1, 1), B(3,2), and C(-1, -1) is expressed as:
[tex]A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\\[/tex]
Substituting the coordinate points:
[tex]A=\frac{1}{2}[(-1)(2-(-1))+3(-1-1)+-1(1-2)]\\A=\frac{1}{2}[(-1)(3)+3(-2)+-1(-1)]\\A=\frac{1}{2}[-3-6+1]\\A=\frac{1}{2} (-8)\\|A| =4 units^2[/tex]
Recall that:
[tex]A = 0.5bh\\h=\frac{A}{0.5b}\\h=\frac{4}{0.5(5)}\\h=\frac{4}{2.5}\\h= 1.6 units[/tex]
Hence the corresponding height of the triangle is 1.6 units
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) Are 9:6 and 18: 12 equivalent?
Answer:
Yes
Step-by-step explanation:
9 18
_ = _
6 12
9*2=18
6*2=12
2=2 TRUE
Solve for y.
y + 3 = 8y + 3
y =
[tex]y + 3 = 8y + 3[/tex]
Subtract both sides 3
[tex]y + 3 - 3 = 8y + 3 - 3[/tex]
[tex]y + 0= 8y + 0[/tex]
[tex]y = 8y[/tex]
Subtract both sides y
[tex]y - y = 8y - y[/tex]
[tex]0 = 7y[/tex]
Divide both sides by 7
[tex] \frac{0}{7} = \frac{7y}{7} \\ [/tex]
[tex]y = 0[/tex]
There you go....
Ah
Have a great day ♡
Use the following system of equations to determine if each ordered pair is a solution: 1. Is (-4,-2) a solution to the system of equations below? Show your work. -3x+2y=8 x + 2y = -8
Peyton knows that 1/8 means “1 divided by 8.” She uses this to find the decimal equivalent for 1/8
Answer:
Peyton can multiply 1 by 100, to make 100 over 8, and divide 100 by 8 which is 12.5 then dividing by 100 to get .125 which is equal to 1/8
Step-by-step explanation:
Answer: I am assuming the question is asking if Peyton got the decimal equivalent of 1/8 correct. Well, since the question is incomplete, I do not know what Peyton got, however, I can tell you that the decimal equivalent for 1/8 is 0.125
This graph shows the amount of (s) money in Jack's account after (w) weeks.
Which equation represents the amount of (s) money in Jack's account after (w) weeks?
Answer:
s=6w
Step-by-step explanation:
the graph goes up by 6 on the y axis for everyone one that the x moves
Answer:
d
Step-by-step explanation:
A class is made up 15 girls and 12 boys. If a group is made up 3 girls and 3 boys, then how many groups can be created?
this is a COUNTING PRINCIPLE problem :")
solve the given problem
Step-by-step explanation:
the first step in my opinion would be find the norm(s) in this scenario.
100 pounds is a good norming weight.
the speed of these 100 pounds with a 10 HP motor is
50ft/30sec = 5/3 ft/s
so, then let's ask next what size of motor is needed to lift the same 100 pounds 40 ft in 40 seconds
40ft/40sec = 1 ft/s
to get the same speed as in the first case the motor need to be weaker (to move slower). and that goes by the same factor as the ratio between the 2 speeds :
5/3×f = 1
f = 3/5
10 HP × f = 10 × 3/5 = 30/5 = 6 HP
so, it takes a 6 HP motor to lift these same 100 pounds 40 ft in 40 seconds.
and now, how strong must the motor be to lift 800 pounds (= 8 times the original 100 pounds) with the same speed ?
well, 8 times
8×6 = 48 HP
so, it would take a 48 horsepower motor to lift 800 pounds 40 ft in 40 seconds.
the equation would then be
HP = p/100 × 6 = 6p/100 = 3p/50
HP = horsepower
p = pounds
the rest I cannot really answer, as I don't know your class and it's contents.
I hope I covered the topics of your class with that solution.
can you help with these problems please.
Answer:
ion kno
Step-by-step explanation
ssa
Help!! Ill give 100 points!
It is the 3rd one from the top
Answer:
I believe the answer would be C.
Step-by-step explanation:
First of all, the solution to the answer really is 1/20. If you figure out the decimal form of 4/5, it is 0.80, which is closer to 1 than to 1/2 and 0. The decimal form of 3/4 is 0.75, which is equally close to 1 and 1/2, being 0.25 from both. But it is closer to 1 than 0. I hope I’m right, and I hope this helps. :)
What is the solution to the inequality
Answer:
Search Results
Featured snippet from the web
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
Step-by-step explanation:
Determine the measurement of the missing angle
Answer:
31
Step-by-step explanation:
Find missing angle of lower triangle first
35+23=58
180-58=122
Because of some geometry rule, the other angle in the upper triangle that is not the ? is also 122
27+122=149
180-149=31
Work out
m
and
c
for the line:
3
x
+
2
y
−
1
=
0
Answer:
M = -3/2
C = 1/2
Explanation:
3 x + 2 y − 1 = 0
-> 2y = 1-3x
y=-3/2x+1/2
so M = -3/2 and C = 1/2
Charnise uses 3 gal. red paint to 5 gal. white paint to make pink paint. She
needs 24 gal. of pink paint. How many gallons of red paint will she need?
The method into creating pink paint is mixing 3 gallons of red paint and 5 gallons of white paint together. This mixture only creates 8 gallons of paint and she needs 16 more. List the factors of 16:
1, 2, 4, 8, and 16
We notice that 8 can be factored out of 16 and becomes:
16 / 8 = 2
If we multiply the sample by 3 (the one already counted plus the two extra), we can discover how much paint is needed. Multiply everything by 3:
3 x 3 = 9
5 x 3 = 15
So in this case, 15 gallons of white paint and 9 gallons of red paint are need and combine for 24 gallons in total.
To train for an upcoming marathon, Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following weeks.
There are many ways to approach this problem.
Week Miles
1 2
2 2.5
3 3
4 3.5
5 4
6 4.5
Write an equation to represent the nth term of the sequence.
Answer:
f(x)= .5x + 2
Step-by-step explanation:
Now this is not to complicated
first the constant is 2
after each day she gains .5 miles
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation to represent the nth term of the sequence is y=0.5x+2.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Let the distance travelled by Susie in any week,x be represented by y.
Given that Susie will run 2 miles in the initial or in the first week. Therefore, the distance for the initial work week will be,
Initial distance = y-intercept = c = 2
Further, if the daily distance is increased by half a mile each of the following weeks. Therefore, the slope of the equation is the change in the distance, therefore, we can write,
Slope, m = Change in the distance = 0.5
Now, if the equation represents the nth term of the sequence, then we can write,
y = mx + c
y = 0.5x + 2
Hence, the equation to represent the nth term of the sequence is y=0.5x+2.
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Shelly sleeps for 7 hours 30 minutes in a day. For how many hours did she sleep in the month of January?
Answer:
Shelly slept 232 hours and 30 minutes in the month of January
Step-by-step explanation:
31 days in January, so the equation will be
31 x 7.5 ( I wrote 0.5 because 30 minutes is half a day)
= 232.5 hours
Shelly slept 232 hours and 30 minutes in the month of January
Answer:
232.5 hours
Step-by-step explanation:
Well, the month of January has 31 days.
If shelly sleeps for 7.5 hours a day, and she sleeps 31 days, we need to do multiplication!
7.5*31=232.5 hours!
30 points.
the midpoint of AB is (4,8) and the coordinates of point A are (-6,4) what are the coordinates of point B?
Answer:
B = (14, 12)
Step-by-step explanation:
As you know, the midpoint is the average of the end point coordinates:
M = (A +B)/2
Solving for B gives ...
2M = A + B
B = 2M -A
B = 2(4, 8) -(-6, 4) = (8+6, 16 -4)
B = (14, 12)
Factors of 2x^2-13x+21
Answer:
(2x-7)(x-3)
Step-by-step explanation:
PLEASE HELP THIS IS A FINAL AND IM SO CONFUSED!!!!
Answer:
C
Step-by-step explanation:
yeah-ya............... right?
Find measure of <1
Answer ASAP!!
Answer:
105 degrees
Step-by-step explanation:
since both sides of a line will add up to 180 we must subtract 75 from 180 since we already have 75 on the triangle side we subtract and get 105
Answer:
here
Step-by-step explanation:
60⁰+45⁰+X=180
105⁰+X=180⁰
X=180⁰-105⁰
hence X=75⁰
Now
<1=60⁰+75⁰
=135⁰
Plz mark as brainlist
Thank you ™
Between 11 P.M. and 8:10 A.M., the water level in a swimming pool decreased by 5/24 in. Assuming that the water decreased at a constant rate, how much did the water drop each hour?
Answer:
1/44 inches per hour
Step-by-step explanation:
there are 9 hours and 10 minutes during which water decreased by 5/24"
9 hrs, 10 min can be converted to 9 1/6 hours (10 min is 1/6 of 60 min)
5/24 ÷ 9 1/6 = 5/24 x 55/6
5/24 x 6/55 = 1/44
PLEASE HELP!!! this is actually english but---
what is a counterargument and rebuttal in a persuasive speech?
A counterargument simply means the acknowledgement of the standpoints that go against one's argument and then re-affirming the argument.
A persuasive speech means a form if speech where the goal of the speaker is to convince the audience to accept hai or her point of view.
A counterargument shows that a individual is capable of understanding the multiple sides that are in an argument. A rebuttal simply means a form of evidence that's presented in order to nullify the other evidences that are provided by another party.
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John is a mechanic with a technical license. He has worked 40 hours at minimum wage
this week. How much is his gross wage for the week?
Answer:
$290
Step-by-step explanation:
if minimum wage is $7.25
7.25×40= 290
Easy math stuff- Geometry- **Requires big bran**
Answer:
8.2 CM
Step-by-step explanation:
ACCORDING TO THE MODEL
radius = 9*2 - 8*2
Diameter = 2 times radius
ok I cant too hard to explain because Im typing so its 8.2cm so
