[tex] \red{\large\underline{\sf{Solution-i}}}[/tex]
Given that,
[tex] \rm \longmapsto\: p(x) = {x}^{4} - {x}^{3} - {x}^{2} - x - 2[/tex]
and
[tex]\rm \longmapsto\:g(x) = x - 2[/tex]
We know,
Factor theorem states that if g(x) = x - a is a factor of polynomial f(x), then remainder f(a) = 0.
So, using Factor theorem, Consider
[tex]\rm \longmapsto\:p(2)[/tex]
[tex]\rm \: = \: {2}^{4} - {2}^{3} - {2}^{2} - 2 - 2[/tex]
[tex]\rm \: = \: 16 - 8 - 4 - 4[/tex]
[tex]\rm \: = \: 16 - (8 + 4 + 4)[/tex]
[tex]\rm \: = \: 16 - 16[/tex]
[tex]\rm \: = \: 0[/tex]
[tex]\rm\implies \:p(2) \: = \: 0[/tex]
So,
[tex]\bf\implies \:g(x) \: is \: factor \: of \: p(x)[/tex]
[tex] \red{\large\underline{\sf{Solution-ii}}}[/tex]
[tex]\rm \longmapsto\: p(x) = 2{x}^{3} + {x}^{2} - 2x + 1[/tex]
and
[tex]\rm :\longmapsto\: g(x) = x + 1[/tex]
Now, By using Factor Theorem, Consider
[tex]\rm \longmapsto\:p( - 1)[/tex]
[tex]\rm \: = \: 2 {( - 1)}^{3} + {( - 1)}^{2} - 2( - 1) + 1[/tex]
[tex]\rm \: = \: - 2 + 1 + 2 + 1[/tex]
[tex]\rm \: = \: 2[/tex]
[tex]\rm\implies \:p( - 1) \: \ne \: 0[/tex]
So,
[tex]\bf\implies \:g(x) \: is \: not \: a\: factor \: of \: p(x)[/tex]
Find the value of GM If DM = 35
1. Allison is a recent college graduate. She got a job as a marketing executive making $82,000 a year, and she will have to move across the country for the new job. Her moving expenses are $7500. She has also started paying back her student loans, and this year will pay back $1386 in student loan interest. What is Allison's adjusted gross income (AGI)?
Answer:
82,000+7500+1,386=168,136
Step-by-step explanation:
You have to do Addition
Johan and Rahul shared a chocolate bar. Johan took 3\7
and Rahul took 4\9
of
the chocolate bar. Who took the biggest part of the chocolate bar? And by
how much?
Answer:
Rahul by 1
Step-by-step explanation:
Johan - 3/7
Rahul - 4/9
1. Convert fractions
3/7 -> 27/63
4/9 -> 28/63
28/63 > 27/63
Rahul took more by 1/63
The number of 90° angles formed by the intersections of and the two parallel lines and is
Answer:
is there supposed to be a picture that goes with this
Step-by-step explanation:
: 0
A Spanish teacher informed her class that she would be giving 4 quizzes each month. Write an equation that shows the relationship between the number of months elapsed, x, and the total number of quizzes, y.
Answer:
y = 4x
Step-by-step explanation:
Since there are going to be four quizzes a month (x), we know that we will multiply the number of months (x) by the number of quizzes (4). However, because we don't know how many months there are, we can define the months as (x), and instead put the total (y) is equal to the number of quizzes per month (4), multiplied by the number of months (x). Out final result is
(y = 4x)
2. A line passes through the points (4,7) and
(8, 6). The line also passes through the point
(a, 3.5) for what value of a?
Answer:
a = 18
Step-by-step explanation:
Slope = (7-6)/(4-8) = -1/4
y-intercept = 7 - (-1/4)(4) = 8
Equation of the line: y = - 1/4x + 8
(Substitute y for 3.5. When y is 3.5, what is x)
3.5 = - 1/4x + 8
3.5 - 8 = - 1/4x
(-4.5) / (- 1/4) = x
x = 18
Write an
exponential function in the form y = ab^x
that goes through points (0,13) and (3,832).
Answer:
y = 13 × [tex]4^{x}[/tex]
Step-by-step explanation:
Substitute the given values into the exponential
Using (0, 13 ) , then
13 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , so
a = 13
y = 13 [tex]b^{x}[/tex]
Using (3, 832 )
832 = 13 b³ ( divide both sides by 13 )
64 = b³ ( take cube root of both sides )
b = [tex]\sqrt[3]{64}[/tex] = 4
The exponential function is
y = 13 [tex](4)^{x}[/tex]
Hello 100 point Question with Explaining please
Select all statements that are true about the triangles.
Answer:
D and E
Step-by-step explanation:
D) Δ ABC , ΔDCB
AB = DC
BC = CB
AC = DB
Side Side Side congruent.
E)Δ ABC , ΔDCB
AB = DC
∠D = ∠A
AC = DB
Side Angle Side congruent.
Answer:
E
Step-by-step explanation:
When we write that 2 triangles are congruent we have to write the letters in order of their corresponding sides so ΔABC has the sides in order
AB, then BC, and then CA
the corresponding sides of the other triangle are
DC, then CB, then BD so the other triangle should be Δ DCB
because (AB≅DC, BC≅CB, CA≅BD)
In this case we eliminate the A,B,C answers.
D is also not correct because we do not know if <ABC is congruent with <DCB
E is correct because we are given the sides AB≅DC, and CA≅BD and we know that BC≅CB because of the reflexive property (a line segment is congruent with itself).
We have 3 ≅sides so we can use the Side-Side-Side Congruence Theorem
F is not correct because we have enough information.
R.
Y.
12 cm
20 cm
13 cm
-
Find volume
Answer:
3120
Step-by-step explanation:
v=lxbxh
...........
Step-by-step explanation:
The volume = 12 × 13 × 20 = 3120
please give me a brainliest answer
The quantities x and y are proportional. Find the constant of proportionality (r) in the equation y=rx
Answer:
y=rx 1/4/5/5/5
Step-by-step explanation:
Answer:
r = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The proportional equation is
y = rx ( divide both sides by x )
[tex]\frac{y}{x}[/tex] = r
Substitute any ordered pair from the table
Using (14, 7 ) , then
r = [tex]\frac{7}{14}[/tex] = [tex]\frac{1}{2}[/tex]
A 56-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answer:
14-inch
Step-by-step explanation:
let the length of shorter piece be x
x+3x=56
4x=56
x=56/4
x=14
maths .....................
Answer:
in simplify this is- 9a2i+42ab+49b2
Step-by-step explanation:
Helpppppppppppppppppppppppppppppppppppp
Answer:
m = - 1
Step-by-step explanation:
9m + 13 = 4
subtract 13 from both sides
9m = 4 - 13
9m = - 9
divide both sides by 9
m = - 1 (negative 1)
no need to explain just answer
Answer:
5
Step-by-step explanation:
The whole angle is 180 degrees.
90 degrees is already taken by the angle dividing the two vertical angles.
So you have 90 degrees left. then you have to subtract 49 from 90 to get the angle of '5t+6'.
So 5t+6 = 41, 41-6 is 35. 35/5 is 5, so t is 5.
I didn't go too far into explaining since you asked to not explain it.
M is the midpoint of segment AB.
AM=13x
BM=8x+10
AB=
help with this question
Answer:
option D is correct
x=O and x=-8
help please! no links!
-
-
-
-
Answer:
A
2,3 3,4.5 5,7.5
B
every 1:1.5
C
3,4.5 4,6 5,7.5
Step-by-step explanation:
because this is eqauling to all of the numbers
a model of a ship is made to a scale of 1:200
the surface area of the model is 7500 cm²
calculate the surface area of the ship, giving your answer in square meters
The surface area of the ship is 1500000 cm²
Scaling is used to either increase or decrease the size of a figure so as to create an image.
Given a scale of 1:200, this means that it is a scaling down (decrease in size) of the ship to create a model.
The surface area of the model is 7500 cm², hence that of the ship is:
Surface area of ship * (1 : 200) = surface area of model
Surface area of ship = surface area of model * 200 = 7500 * 200 = 1500000 cm²
The surface area of the ship is 1500000 cm²
Find out more on surface area at: https://brainly.com/question/16519513
60% of all bald eagles survived their first flight. If 25 randomly selected bald eagles are observed, what is the probability that at least 15 of them will survive their first flight.
a) Use the binomial distribution to approximate the probability.
Answer:
[tex]100%[/tex][tex]\%[/tex]
Please help me in this!
Answer:
5000
ghsjdjdjdjdjdjdjdkdkdkdkdkdkdkdk
Please put into slope intercept form and please SHOW THE WORK
4-2y=-2x
-y+6=x
6x-y-3=0
3y+15x=-15
Answer:
[tex]4 - 2y = -2x [/tex]
subtract the 4 from one side
[tex] - 2y = - 2x - 4[/tex]
divide the -2 from the y and the-2x and 4
[tex]y = - x + 2[/tex]
-y + 6 = x
subtract the 6 and add -6 after the x
[tex] - y = x - 6[/tex]
6x - y - 3 = 0
add the y so it cancels out
y = 6x - 3
3y + 15x = -15
subtract the 15x
3y = -15x - 15
divide the 3
y = -5x -5
I was not taught this lesson in class today.
Answer:
C
Step-by-step explanation:
No slope is given so your slope is 0. Since both have no slope, they are both flat and therefore parallel
[tex]\textbf{Hey!}[/tex]
My little sister, needs help on this.
Rushawn lined up the interior angles of the triangle along line p below.
When the measure of angle C decreases, what happens to the measures of angles A and B on line p?
A. Both sections increase.
B. Both sections decrease.
C. One section increases, and the other section decreases.
D. What will happen to the individual sections cannot be determined, but the size of the two sections together increases.
answers/w explanation ✅ Nonsense answers, that's not the question I didn't ask for will be reported.
D is the correct option as the decrease in angle C will make angle A increase thus making the section with both angle A and B to increase.
Answer:
D :))
Step-by-step explanation:
A count went from 605 to 203. What was the approximate percent decrease? Round the numbers to find an estimate of the percent decrease.
A. The percent decrease was approximately 25%.
B. The percent decrease was approximately 33%.
C. The percent decrease was approximately 50%.
D. The percent decrease was approximately 66%.
IT'S D
HOPE THIS HELP MARK ME BRAINLIST
Simplify by prime factorization.
15
27
5/9 is a simplified fraction for 15/27
Answer:
15/27 simplified to lowest terms is 5/9.
Your Welcome!
U= 1 A solution to the inequality below??
10>u
Answer:
Yes
Step-by-step explanation:
10>1
Hmm I’ve spent time on it… help pls anyone?
Please help me solve this
From the graph, write the linear equation in slope-intercept form
Answer:
1.y=1/2+2
2.y=-2+1
3.y=3/2+3
4.y=-2/3-2
Step-by-step explanation: