Answer:
p(x) = -4*x^4 - 2*x^3 + 3*x^2 + 1*x - 2
Step-by-step explanation:
We want to find a polynomial p(x), such that if we add that polynomial to:
f(x) = 4*x^4 + 2*x^3 - 2*x^2 + x - 1
we get:
g(x) = x^2 + 2*x - 3
This is:
f(x) + p(x) = g(x)
Notice that f(x) is a polynomial of degree 4 and g(x) is a polinomial of degree 2, so p(x) must be also a polynomial of degree 4.
p(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e
Then we get:
(4*x^4 + 2*x^3 - 2*x^2 + x - 1) + (a*x^4 + b*x^3 + c*x^2 + d*x + e) = x^2 + 2*x - 3
We can simplify the left side to:
(4 + a)*x^4 + (2 + b)*x^3 + (-2 + c)*x^2 + (1 + d)*x + (-1 + e) = x^2 + 2*x - 3
Because in the right side we do not have terms with exponent 4 and 3, we must have that:
4 + a = 0
2 + b = 0
and for the other exponents of x we just match the exponent in the left side with the correspondent one in the right side:
(-2 + c) = 1
(1 + d) = 2
(-1 + e) = -3
Solving the 5 equations we get:
a = -4
b = -2
c = 1 + 2 = 3
d = 2 - 1 = 1
e = -3 + 1 = -2
Then the equation for p(x) is:
p(x) = -4*x^4 - 2*x^3 + 3*x^2 + 1*x - 2
IF THE INTEGERS IS 12,-6,8,-5,7,-4,3 ARE MARKED ON THE NUMBER LINE, THE ONE THAT COMES ON THE EXTREME LEFT
Answer:
- 6
Step-by-step explanation:
Given the integers : 12,-6,8,-5,7,-4,3
To obtain which one falls on the extreme left, the integers are arranged in ascending order, and the least value is chosen as this is the number which falls to the extreme left of arranged on a number line.
Ordered value in ascendibg order :
-6, -5, -4, 3, 7, 8, 12
The value which will. Fall. On the extreme left is : - 6
Help plz..And No links!! I repeat No links!!
Answer:
38sq yards
Step-by-step explanation:
Separate it into parts
3x2 for the top section
8x4 for the bottom
6+32=38
Please help worth 20 points
e is the the answer.....
please i need help, right now!!! i give the person the brainliest answer!! im giving 15 points… please help
Answer:
Ummmm its just a black screen
Step-by-step explanation:
Find the value of z.
A. 118
B. 100
C. 93.5
D. 42.5
Answer:
[tex](180-73)=z+114/2[/tex]
[tex]107*2=z+114[/tex]
[tex]z=214-114[/tex]
[tex]z=100[/tex]
❄ B. 100
------------------------
hope it helps...
have a great day!!
In the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.
What is circle?Circle is a shape consisting fall points in a plane thata are at a given distance from a given distance from a given point which is the centre of the circle.
How to find angle?In the circle we can see the following:
(180-73)=(z+114)/2
107*2=z+114
214=z+114
z=214-114
=100
Hence in the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.
Learn more about angles at https://brainly.com/question/25716982
#SPJ2
David measures a side of a piece of wood. The length is 8 feet and the width is one-half if the length. What is the area, in square feet, of the piece of wood?
A=lw
A: 4
B: 16
C:32
D:108
Answer: The area, in square feet, of the piece of wood is [tex]32 ft^{2}[/tex].
Step-by-step explanation:
Give: Length = 8 feet
Width = [tex]\frac{1}{2} \times 8[/tex] = 4 feet
As piece of wood is similar to that of a rectangle. Hence, formula to calculate area is as follows.
[tex]Area = length \times width[/tex]
Substitute the values into above formula as follows.
[tex]Area = length \times width\\= 8 feet \times 4 feet\\= 32 ft^{2}[/tex]
Thus, we can conclude that the area, in square feet, of the piece of wood is [tex]32 ft^{2}[/tex].
Blue
A bowl contains:
• 3 red erasers
• 4 blue erasers
.6 green erasers
• 7 pink erasers
An eraser will be drawn from
the bowl and replaced 50 times.
What is a reasonable prediction
for the number of times a green
eraser will be drawn?
Answer:
i think it will be chose 3 times
Step-by-step explanation:
im not sure thats my pridiction
Answer:
0.4
Step-by-step explanation:
Margo borrows $200, agreeing to pay it back with 2% annual interest after 16 months. How much interest will she pay?
Answer:
$4
Step-by-step explanation:
2/100 x 200 = 4
Segments BD and CE are axes of the ellipse below.
Which of the following reflective symmetries apply to the ellipse below?
Answer:
Yes and Yes
Step-by-step explanation:
If you fold them over on both sides then they overlap perfectly, therefore they are reflective.
can you guys help me please!
Answer:
Step-by-step explanation:
Mike just hopped on the edge of a merry-go-round. What are his linear and angular speeds if the diameter of the merry-go-round is 14 feet and it takes 6 seconds for it
to make a complete revolution? Round the solutions to two decimal places.
Step-by-step explanation:
Given that,
The diameter of the merry-go-round, d = 14 feet
Time taken, t = 6 seconds
Radius, r = 7 feet
The linear speed of the merry-go-round is given by :
[tex]v=\dfrac{2\pi r}{t}\\\\v=\dfrac{2\pi \times 7}{6}\\\\=7.33\ m/s[/tex]
Also,
[tex]v=r\omega[/tex]
Where
[tex]\omega[/tex] is the angular speed
So,
[tex]\omega=\dfrac{v}{r}\\\\\omega=\dfrac{7.33}{7}\\\\=1.04\ rad/s[/tex]
Hence, his linear and angular speeds are 7.33 m/s and 1.04 rad/s.
in how many ways can a principal choose 3 of their 30 teachers to attend a conference
need ko po ng explanation please.....
Answer:
[tex]4,060[/tex]
Step-by-step explanation:
[tex]\binom{30}{3}=\boxed{4060}[/tex]
There are 30 teachers for the principal to choose from initially. After the principal chooses one, there will be 29, 28, 27, and so on.
Since the principal is only choosing 3, there are [tex]30\cdot 29\cdot 28=24,360[/tex] permutations. However, the order of which the principal chooses the teachers does not matter. In other words, without loss of generality, let the name of three of the teachers be Adam, Bernie, and Carla. Regardless of whether the principal chooses Adam then Bernie then Carla or Carla then Adam then Bernie, etcetera, the same three teachers are still being chosen.
Thus, we must divide by the number of ways you can rearrange three distinct teachers, which is [tex]3![/tex].
Therefore, the desired answer is [tex]\frac{24360}{3!}=\frac{24360}{6}=\boxed{4,060}[/tex]
what are the factors of x^3-2x^2+x+2
Dmitri began working on his homework at 3:15 p.m. He worked for 1 5/6 hours and then stopped to have dinner. He started working on his homework again at 6:32 p.m. and worked for 1 1/3 hours longer. How many minutes did Dmitri work on his homework in all?
1 5/6 + 1 1/3 = 3 1/6
3 1/6 * 60 = 190
Help ASAP math homework no spam links or i will report
Answer:
[tex]x = \frac{19-2y}{3}[/tex]
[tex]y=-\frac{3x+19}{2}[/tex]
Step-by-step explanation:
4x + y = 22
y = x - 3
4x + y + y = 22 + x - 3
4x + 2y = 19 + x
4x - x + 2y = 19 + x - x
3x + 2y ÷ 3 = 19 ÷ 3
[tex]x = \frac{19-2y}{3}[/tex]
[tex]y=-\frac{3x+19}{2}[/tex]
Answer:
a)Let's solve for x.
4x+y=22
Step 1: Add -y to both sides.
4x+y+−y=22+−y
4x=−y+22
Step 2: Divide both sides by 4.
4x
4
=
−y+22
4
x=
−1
4
y+
11
2
a)y=x−3
b)y=
−1
2
x+6
b)x=y-12
1.en cada unos de los siguientes monomios identificó el coeficiente y la parte literal , halló el grado y el valor numérico para los valores . ×=3,Z =5. (a) 3ײ (b) 4ײ y (c) - 5ײy²z².
porfa me ayudan
whats 3 plus 4 times 3?
Answer:
3+(4*3)=15.....................
Answer:
21
Step-by-step explanation:
3+4=7
7×3=21
you are going to add 3 and 4.
After adding, you multiply 7by 3
giving yout 21
Hi, I'm really struggling with this question, any help?
A function inputs values for x and outputs values for y. The ordered pairs below represent three points on the graph of the function. (2,4) (3,0) (5,−1)
Is the function linear? Justify your response.
Answer:
Nope it isn't linear.
Step-by-step explanation:
Use a coordinate plane. The slope is y = -4x+12. if you plug that in, you will get all of the lines correctly
for instance you put 2,4
4 = -4(2)+12
4 = -8+12
that is true
but if you put in (5,-1)
-1 = -4(5)+12, which is not true
if all of them is true, then it would be true.
if even ONE of them is not true, then the who line is not linear
CAN SOMEONE PLEASE HELP ME??!!
Answer:
RO = 17.9
Step-by-step explanation:
If they're similar, the fraction between their sides need to be equal, so do this:
NK/NM = RO/RQ
71.6/64 = RO/16
71.6•16/64 = RO
RO = 17.9
What is 4/5 of 2kg in grams
Answer: 1600g
Step-by-step explanation: (4 * 2kg) / 5 = 8/5kg
8/5kg = 1.6kg
1.6kg * (1000g / 1kg) = 1600g
Answer:
1 3/5kg.
Step-by-step explanation:
So, to figure this out, lets go over what we know.
There is 2kg.
We need to find 4/5 of this.
A way you can think of this is 2kg*4/5. Or:
2*4/5
Remember, all whole numbers have a denominator of 1. So this is:
2/1*4/5
Or
[tex]\frac{2}{1} *\frac{4}{5}[/tex]
When doing multipaction, the numerator multipies hte numeraot, and the denominator multiplies the denominator.
So in the numerator, it will be 2 times 4:
2*4=8
And in the denominator, it will be 1 times 5:
1*5=5
So the answer is:
8/5
Hope this helps!
The average height of middle school students at Seton Grove School is found to be 5.25 feet. Which sample makes this generalization valid?
Answer:
every other student who enters the school
Step-by-step explanation:
It is given that the middle school students have an average height of 5.25 feet. The students belongs to Seton Grove School.
It means that every student who comes to this school or enters the school has a height that is around 5 feet or more.
Thus we can say that every other student who enters the school has a average height of 5.25 feet.
This sample makes the generalization about the heights of the school students valid.
Answer:
c
Step-by-step explanation:
correct on edmentum / plato
Mr.Caldwell has 10 full size pizzas and half of another one.He wants to share the pizza with 8 of students. Mr.Caldwell doesn't want any pizza.How much pizza did will each student get?
Answer: [tex]1\ \text{Pizza}\ \text{and}\ \dfrac{5}{16}\ \text{pizza}[/tex]
Step-by-step explanation:
Given
Mr. Caldwell has 10 full pizzas and half of another one
he wants to distribute it in among 8 of his students
Total pizzas are [tex]10+\frac{1}{2}=\frac{21}{2}[/tex]
So, each student gets
[tex]\Rightarrow \dfrac{\dfrac{21}{2}}{8}\\\\\Rightarrow \dfrac{21}{16}\ \text{or}\ 1\dfrac{5}{16}[/tex]
that is 1 pizza and five-sixteenth part of a pizza.
evaluate the function for x = -8.
f(x) = -2x - 12
Answer:
4
Step-by-step explanation:
f(-8)=-2(-8)-12
f(-8)=16-12
=4
Ricky has nine quarters, thirteen dimes, six nickels, and seven pennies. How much money does he have? WHOEVER ANSWERS THIS FIRST GETS BRAINLIEST
Step-by-step explanation:
3.92 - uwuehehrvgrsiehhehehhe
Answer:
He has $3.92.
Hope this helps!
Write the exact value of the side length of a square with an area of
100 square units,
95 square units.
36 square units.
30 square units.
Find measure of angles B, E, D and C and the length of BC.
Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.
Answer:
BC = 16 B=85 E=85 D=30 C=65
Step-by-step explanation:
Step-by-step explanation:
< B = 180-30-65=85°
< E = 85°
< D = 30°
< C = 65°
BC = 20/35 × 28 = 16
Determine a function a(w) that models the area of the top surface of the swimming pool in terms of the width , w
Answer:
[tex]A(w) = (40 - w) * w[/tex]
Step-by-step explanation:
Given
[tex]P = 80[/tex] ---- perimeter
Required
Write the area as a function of width
The perimeter of a rectangle is:
[tex]P =2(l + w)[/tex]
Where
[tex]l \to length\\ w \to width[/tex]
So, we have:
[tex]80 = 2*(l+w)[/tex]
Divide by 2
[tex]40 = l + w[/tex]
Make l the subject
[tex]l =40 - w[/tex]
The area of a rectangle is:
[tex]A = l * w[/tex]
Substitute: [tex]l =40 - w[/tex]
[tex]A = (40 - w) * w[/tex]
Hence, the function is:
[tex]A(w) = (40 - w) * w[/tex]
factorize 6×square + 5× - 4 =o
Answer:
6×square + 5× - 4 =o
6×square+(8-3)×-4=0
6×square+8×-3×-4=0
2×(3×+4)-1(3×+4)=0
(3×+4)(2×-1)=0
either,
3x+4=0
3×=-4
×= -4/3
or,
2x-1=0
×=1/2,,
The graph of f(x) is the solid black graph below. Which function represents the
dotted graph?
Answer: The answer is y= f(x+1)+5
Step-by-step explanation: The reason is that when you are translating the graph, the information in the parenthesis (In this case: (x+1)) is always on the x axis moving either left or right. You just go one in the opposite direction of what the sign is, so since the sign in the parenthesis is "+" you would go left in the opposite direction. Then, for the upward translation, you would have to move 5 units upward and this is done by just adding five to the end of it.
HELP WITH THIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B., E.
Step-by-step explanation:
what was the difficulty ? this is just to understand the movement of a thrown rock.
what happens, when you throw a rock through the air ? it will first move up a little bit, reaches a maximum height, and then drops down again.
that is what the graphic shows.
so, can A. be correct ? no. as we move from 0 seconds to the right (time passes) the height of the rock increases first (before decreasing again later on).
can C. be correct ? no, it would mean that the function would look the same on both sides of the x-axis. this is clearly impossible.
can D. be correct ? no, nowhere in the graph is the height (= the functional value, the y to the x) negative.
can F. be correct ? no, we clearly see the maximum height at 1.5 seconds. at 3 seconds the height is actually at its minimum.
