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
Expand and simplify (x - 2)(x - 1)
Answer:
x^2 -3x+2
Step-by-step explanation:
(x - 2)(x - 1)
FOIL
first: x*x = x^2
outer: -1*x = -x
inner: -2*x =-2x
Last: -2*-1 =2
Add together
x^2 -x-2x+2
Combine like terms
x^2 -3x+2
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(x - 2)(x - 1)}[/tex]
[tex]\large\textsf{DISTRIBUTE}[/tex]
[tex]\large\textsf{x(x) + x(-1) - 2(x) -2(-1)}[/tex]
[tex]\large\textsf{x(x) = }\mathsf{\bf x^2}[/tex]
[tex]\large\textsf{x(-1) = -1(x) = \bf -1x}[/tex]
[tex]\large\textsf{-2(x) = \bf -2x}[/tex]
[tex]\large\textsf{-2(-1) = \bf 2}[/tex]
[tex]\mathsf{= \bf x^2 - 1x - 2x + 2}[/tex]
[tex]\large\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(-1x - 2x)}[/tex]
[tex]\mathsf{= \bf -3x}[/tex]
[tex]\large\textsf{SOLVE for the ANSWER:}[/tex]
[tex]\mathsf{x^2 - 3x + 2}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: }\mathsf{\bf x^2 - 3x + 2}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve.
5. The graph of f(x)= x is reflected across the x-axis. The graph is then
translated 11 units up and 7 units to the left. Write the equation of the
transformed function.
Given:
The function is:
[tex]f(x)=x[/tex]
The graph of this function reflected across the x-axis. The graph is then translated 11 units up and 7 units to the left.
To find:
The equation of the transformed function.
Solution:
The translation is defined as
[tex]g(x)=kf(x+a)+b[/tex] .... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If k<0, then the graph is reflected across the x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The graph of this function reflected across the x-axis. The graph is then translated 11 units up and 7 units to the left. So, [tex]k=-1, b=11, a=7[/tex]. Putting these value in (i), we get
[tex]g(x)=(-1)f(x+7)+11[/tex]
[tex]g(x)=-(x+7)+11[/tex] [tex][\because f(x)=x][/tex]
[tex]g(x)=-x-7+11[/tex]
[tex]g(x)=-x+4[/tex]
Therefore, the required function is [tex]g(x)=-x+4[/tex].
Choose the expression equivalent to: (10 x 18) + (10 x s)
A) 20x18s AND 180 + 10s
B) 180 + 10s AND 10(18 + s)
C) 10(18 + s) AND 20 x 18s
Giving brainlest
B. 180 + 10s. AND 10(18 + s)
Hope this helps! :)
Now Kathy is 3 times as old as Kaity. In 6 years Cathy will be twice as old as Kaity. How old is each girl right now
Kathy is 18 and Kaity is 6. In six years, Kathy will be 24 and Kaity will be 12.
Good luck :)
Answer:
Katie is 6; Cathy is 18!
Happy learning!
--Applepi101
Help please, my 2nd time asking this question.
(1 / 4) + (1 / 2)
= (1 / 4) + {(1 × 2) / (2 × 2)}
= (1 / 4) + (2 / 4)
= 1 + (2 / 4)
= 3 / 4
(1 / 2) + (3 / 8)
= {(1 × 4) / (2 × 4)} + 3 / 2
= (4 / 8) + (3 / 8)
= (4 + 3) / 8
= 7/8
Answer:
#3 is [tex]\frac{3}{4}[/tex] #4 is [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
you must find a common denominator in both problems.
For #3 the common denominator is 4 so you would multiply [tex]\frac{1}{2}[/tex] by [tex]\frac{2}{2}[/tex] to get [tex]\frac{2}{4}[/tex] then add the numerators together to get 3 and the denominator stays 4.
[tex]\frac{1}{4} + \frac{2}{4} = \frac{3}{4}[/tex]
For #4 the common denominator is 8 so you would multiply [tex]\frac{1}{2}[/tex] by [tex]\frac{4}{4}[/tex] to get [tex]\frac{4}{8}[/tex]
then add the numerators together to get 7 and denominator stays 8.
[tex]\frac{4}{8} + \frac{3}{8} = \frac{7}{8}[/tex]
I really need help❤️
Answer:
about (-3,1.5)
Step-by-step explanation:
Hope this helps!
What would be your first step in solving for x in this problem. Please EXPLAIN in words?
Answer:
Step-by-step explanation: distribute the 1.5 and the 2
Answer:
hey you need to multiple the number behind the parentheses by the number into the parentheses, like 1.5×2x
the you put Xs on the left side of the = and the numbers on the right side
then you do the sentence and at the end you got the amount for x :)
please help ty !!! :)
Answer: $9,240
Step-by-step explanation:
If the car was sold at 40% off,
That is 40/100=0.4
selling price=$6600
So, 40% of $6600= 0.4*$6600=$2640
this means that the seller deducted this amount from his cost price to sell it to you.
Therefore,original price he bought will be a sum of both,that is
the amount he sold to you + the amount he deducted =$6600+$2640=$9,240.
Therefore the original price is $9,240
hope it’s correct !
Answer:
Answer :-(40/100) × X = 6600
X = (6600×100)/40
X = 16500$
Hope it helped :)A.)90
B.)80
C.)56
D.)24
Answer:
your answer is C
In which number does the digit 9 have a value that is ten times greater than the value of the digit 9 in the number 593,104? 95,378 529,092 691,525 922,198
Answer: (d)
Step-by-step explanation:
Given
The digit 9 in the number 593,104 is at the ten-thousandths place and the value which is 10 times its value must be at lakh place.
Matching with highest place values in the option
(a) Ten-thousand place
(b) Thousand place
(c) Ten-thousand place
(d) lakh Place
Therefore, (d) is the correct option.
Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
Answer:
See explanation for matching pairs
Step-by-step explanation:
Equations
(1)
[tex]x - y = 25[/tex]
[tex]2x + 3y = 180[/tex]
(2)
[tex]2x - 3y = -5[/tex]
[tex]11x + y = 550[/tex]
(3)
[tex]x - y = 19[/tex]
[tex]-12x + y = 168[/tex]
Solutions
[tex](-17,-36)[/tex]
[tex](47, 33)[/tex]
[tex](51, 26)[/tex]
Required
Match equations with solutions
(1) [tex]x - y = 25[/tex] and [tex]2x + 3y = 180[/tex]
Make x the subject in: [tex]x - y = 25[/tex]
[tex]x = 25 + y[/tex]
Substitute [tex]x = 25 + y[/tex] in [tex]2x + 3y = 180[/tex]
[tex]2(25 + y) + 3y = 180[/tex]
[tex]50 + 2y + 3y = 180[/tex]
[tex]50 + 5y = 180[/tex]
Collect like terms
[tex]5y = 180-50[/tex]
[tex]5y = 130[/tex]
Solve for y
[tex]y =26[/tex]
Recall that: [tex]x = 25 + y[/tex]
[tex]x = 25 + 26[/tex]
[tex]x = 51[/tex]
So:
[tex](x,y) = (51,26)[/tex]
(2) [tex]2x - 3y = -5[/tex] and [tex]11x + y = 550[/tex]
Make y the subject in [tex]11x + y = 550[/tex]
[tex]y = 550 - 11x[/tex]
Substitute [tex]y = 550 - 11x[/tex] in [tex]2x - 3y = -5[/tex]
[tex]2x - 3(550 - 11x) = -5[/tex]
[tex]2x - 1650 + 33x = -5[/tex]
Collect like terms
[tex]2x + 33x = -5+1650[/tex]
[tex]35x = 1645[/tex]
Solve for x
[tex]x = 47[/tex]
Solve for y in [tex]y = 550 - 11x[/tex]
[tex]y = 550 - 11 * 47[/tex]
[tex]y = 550 - 517[/tex]
[tex]y = 33[/tex]
So:
[tex](x,y) = (47,33)[/tex]
(3)
[tex]x - y = 19[/tex] and [tex]-12x + y = 168[/tex]
Make y the subject in [tex]-12x + y = 168[/tex]
[tex]y = 168 + 12x[/tex]
Substitute [tex]y = 168 + 12x[/tex] in [tex]x - y = 19[/tex]
[tex]x - 168 - 12x = 19[/tex]
Collect like terms
[tex]x -12x = 168 + 19[/tex]
[tex]-11x = 187[/tex]
Solve for x
[tex]x = -17[/tex]
Solve for y in [tex]y = 168 + 12x[/tex]
[tex]y =168-12 *17[/tex]
[tex]y =-36[/tex]
So:
[tex](x,y) = (-17,-36)[/tex]
A pack of six cans of coffee cost $12. How much would 15 cans of
coffee cost?
Answer $30
Bc 6can = $12
If 1can =2$
So 15 cans =30$
Answer:
$30
Step-by-step explanation:
$12/6=$2/can
$2/can x 15 cans=$30
the number 32747 written to 4 significant figure is
Answer: 3275
Step-by-step explanation:
Use elimination to solve the system of equations:
3x + y = 10
- 4x - 2y = 2
Work:
HELP ME PLEASE!
What is the probability that the card drawn is a face card or a club?
Answer:
52
52
is the correct answer the probability that card drawn is a faace card
Answer:
the probability of a drawing club is 13/52.
The probability of drawing a face card is 12/52.
Step-by-step explanation:
hope it's helpful
what is the correct answer
Answer:
the answer is D
Step-by-step explanation:
from :
Tan(60) = x/4 then X = Tan(60) × 4
X = 4×√3
f(x)=2x^2−3x+5 Identify the quadratic term in the function.
Answer:
2×2-3×-5=0
Step-by-step explanation:
(2×2-3×)- 5=0
Help With the answer Please
??????
Answer:
not sure
Step-by-step explanation:
Answer:
b) FIGURE A AND FIGURE B
Step-by-step explanation:
figure c has
all the sides equal so its not a rectangle
Help me please!!!!!!!!!!!!!
Answer:
The answer is 70 ways.
Step-by-step explanation:
8C4 = 70.
40320/576 is equal to 70.
what is the angle of x
Answer and Step-by-step explanation:
To find x, subtract all of the given angles from 180.
We subtract from 180 because the angles in a triangle (when added together) add up to 180.
180 - 90 - 35 = 55
x = 55 is the answer.
#teamtrees #PAW (Plant And Water)
Answer:
55°
Step-by-step explanation:
Given :-
Angles = x , 35° and 90°.We know :-
Angle sum property of∆ = 180° .→ 35 + x + 90 = 180
→ x + 125 = 180
→ x = 55°
What is the y-intercept of 4(0.6)^x
Answer:
4
Step-by-step explanation:
The y-intercept is where x = 0
y = 4(0.6)^0
y = 4(1)
y = 4
Below is a list of numbers. Use them to answer question 3.
2, 19, 31, 43, 59, 67
Question 3*
What type of numbers are shown?
A
B.
C.
composite numbers
even numbers
odd numbers
prime numbers
D.
Answer:
prime numbers
Step-by-step explanation:
not composite since,example, 2 is prime
not even since,example, 19 is odd
not odd since,example, 2 is even
Answer:
the answer is
prime numbers.
Express 0.0003754 in scientific notation
Answer:
Scientific Notation: 3754 × [tex]10^{-4}[/tex]
Step-by-step explanation:
Have a great summer :)
Answer:
3.754 • 10^-4
Step-by-step explanation:
Put decimal point back until in front of a whole number( not zero ;D). So it would be 3.754 and since it was going left or backwards the exponent would be negative. Therefore, giving our answer!
Hope this helped, good luck! :)
solve m-13=8 please help me
Answer: 5
Step-by-step explanation:
13-8=5
5-13=8
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.
Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answer:
Sample Response: To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Answers are cost of Arcade game per play and cost of each ferry ride and we can solve.
What is Solution to Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Maya used some of her allowance to ride the ferris wheel and play a few rounds of an arcade game.
We could develop a two-variable equation if we knew the total allotment, the cost of each arcade game played, and the cost of each ferry ride.
We can solve the equations to determine how many times Maya visited the Ferris wheel and how many times she played arcade games.
Learn more about Equation here:
https://brainly.com/question/505879
#SPJ2
If any one could please help
Answer:
I believe it’s the 3rd option but I’m not completely confident
Step-by-step explanation:
who am I kidding I’m never confident lol
A boy is twice as old as his sister who is x years old now. In 2 years, the boy will be
Answer and Step-by-step explanation:
2x + 2 is the answer.
If the boy is twice as old, and the sister's age is represented by x, then we multiply 2 to x to represent the boy's age.
Then we add 2 when 2 years pass by.
#teamtrees #PAW (Plant And Water)
Need answer fasttt
Find the volume of a pyramid with a square base, where the side length of the base is
11.5 in and the height of the pyramid is 6.7 in. Round your answer to the nearest
tenth of a cubic inch.
Answer:
295.4 [tex]in^3[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3}(b)^2(h)\\\\ =\frac{1}{3} (11.5)^2(6.7)\\\\=\frac{1}{3}(135.25)(6.7)\\\\[/tex]
= 295.358
≈ 295.4
How many moles are in 30.0g of N2
Answer:1.0709
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
To be very accurate 1.1
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cent.
int
A09) P(124
A. $512.63
B. $669.11
C. $674.43
D. $886.41
Answer:
$669
Step-by-step explanation:
Given data
Principal= $500
Rate= 6%
Time= 5 years
The compound interest formula is given as
A= P(1+r)^t
A=500(1+0.06)^5
A=500(1.06)^5
A=500*1.338
A=$669