Answers
Answer:
First option, and the expanded form is:
f(x) = x^4 - 7*x^3 + 7*x^2 + 21*x - 30
Step-by-step explanation:
Notice that in the answer we have the general form:
p(x) = x^4 - a*x^3 + b*x^2 + c*x - d
Where a, b, c, and d, are real positive numbers.
Knowing that we have a polynomial of degree 4, we can discard the third and fourth options, because these ones have a degree of 2 and 3.
Now we can look only at the first and second option, let's expand them and see which one is the correct option.
First option:
f(x) = (x - 2)*(x - 5)*(x - √3)*(x + √3)
Remember that:
(x^2 - a^2) = (x - a)*(x + a)
then the last two parts of the f(x) equation can be rewriten as:
(x + √3)*(x - √3) = (x^2 - √3^2) = (x^2 - 3)
Now we can rewrite the f(x) equation as:
f(x) = (x - 2)*(x - 5)*(x^2 - 3)
Now we can just expand this, we have:
f(x) = (x^2 -5*x - 2*x + 10)*(x^2 - 3)
f(x) = (x^2 - 7*x + 10)*(x^2 - 3)
f(x) = x^4 - 3*x^2 - 7*x^3 + 21*x + 10*x^2 - 30
f(x) = x^4 - 7*x^3 + 7*x^2 + 21*x - 30
We can see that this option already matches the structure we wanted:
f(x) = x^4 - a*x^3 + b*x^2 + c*x - d
(look at the signs)
So we can conclude that the correct option is the first one, and the expanded form is:
f(x) = x^4 - 7*x^3 + 7*x^2 + 21*x - 30
Related Questions
n 1
n2
Question 6
Indicate the answer choice that best completes the statement or answers the question
Use the figure below. In the figure, line m is parallel to line n. List all pairs for the type of angle.
in 3
n 4
en 5
on 6
on 7
on 8
m1 2
43
On9
6
5
8
9
10
on 10
on 11
con 12
a
vertical
Oa Z1 and 23, 22 and 24, 25 and 210. 26 and 29, 27 and 28
Ob. 21 and 23, 22 and 24, 25 and 210, 26 and 29
Oc. 21 and 25, 23 and 210
Od 27 and 210. 25 and 27, 25 and 28, 28 and 210, 28 and 21
Answers
Answer:
A and B are both correct, but answer A has one more opposite angle and is the best choice
Step-by-step explanation:
a pair of non-adjacent angles formed by the intersection of TWO lines.
It is clearly not D 7&10 are adjacent
It is not C 1&5 are formed by THREE lines
The only difference between answer A and B is the extra angle 7&8 in answer A. IF angles 5&10 and 6&9 are good angles then it looks like to me that angle 7&8 is a good angle
After a shipwreck, Sam is stranded on a desert island. He needs to build a shelter, so he
makes an axe using materials from the wreckage and starts cutting down trees.
There is a proportional relationship between the number of days Sam is stranded on the
island, x, and the total number of trees he cuts downy
Answers
The constant of proportionality is gotten from the graph to be 5
How to solve for constant of proportionalityThe complete part of the question is in the attached image which is a graph.
The graph has a positive slope, which implies a direct proportionality
hence we have that the number of trees is directly proportional to the number of days spent.
Let t represent the number of tress, d represent the number of days, and k constant of proportionality
The relationship is expressed mathematically as:
t ∝ d
t = kd
using any arbitrary point from the y axis ( t ) and tracing to the x axis ( d ). We have t = 5 and d = 1. substituting the values gives
5 = k* 1
Therefore
k = 5
The constant of proportionality is 5
Read more on proportional relations here: https://brainly.com/question/23318486
#SPJ1
Answer:
Step-by-step explanation:
i don't know but the answers is 5
3.
Find the area of a square if its side length is:
Open Up. Resources Student Template
download for free at openupresources.org
1
6-8 MATHEMATICS
NAME
DATE
PERIOD
3 inches
b.
7 units
C.
100 cm
a
40 inches
e.
* units
Answers
Answer:
a is 40
b is 7 cm
c is 100 cm
d is 3 in
Step-by-step explanation:
Joe and three friends went to Texas Roadhouse for dinner the total bill was $76.25 they left server a 20% tip how much was the tip what was the total bill how much should each person pay
Answers
Answer:
Step-by-step explanation:
Tip is $15.25
Total would be $91.5 =76.25+15.25
Help me with this!! Will mark Brainliest
Answers
Answer:
TU = 19 cm
coz both the triangles are same.
helpppp pweeaasseee?
Answers
Answer:
0
Step-by-step explanation:
Step One: Identify two points on the line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
Step Three: Use the slope equation to calculate slope ----> m= y2-y1/x2-x1
What is the range of the function f(x) =3x +4 when the domain is {-3, 0, 2}
Answers
Answer:
See a solution process below:
Step-by-step explanation:
Explanation:
To find the range, substitute each value of the domain into the formula and calculate the result:
For x = 0
f
(
0
)
=
[
(
3
×
0
)
−
4
]
f
(
0
)
=
[
0
−
4
]
f
(
0
)
=
−
4
For x = 1
f
(
1
)
=
[
(
3
×
1
)
−
4
]
f
(
1
)
=
[
1
−
4
]
f
(
1
)
=
−
3
For x = 2
f
(
2
)
=
[
(
3
×
2
)
−
4
]
f
(
2
)
=
[
6
−
4
For x = 0
f
(
0
)
=
[
(
3
×
0
)
−
4
]
f
(
0
)
=
[
0
−
4
]
f
(
0
)
=
−
4
For x = 1
f
(
1
)
=
[
(
3
×
1
)
−
4
f
(
1
)
=
[
1
−
4
]
f
(
1
)
=
−
3
For x = 2
f
(
2
)
=
[
(
3
×
2
)
−
4
]
f
(
2
)
=
[
6
−
4
]
f
(
2
)
=
2
For x = 3
f
(
3
)
=
[
(
3
×
3
)
−
4
]
f
(
3
)
=
[
9
−
4
]
f
(
3
)
=
5
Therefore, the Range is:
{
−
4
,
−
3
,
2
,
5
If the point (2k− 3,k + 2) is a solution of linear equation 2x + 3y + 15 = 0, find the value of k.
Answers
Answer:
value of k = -15/7
Step-by-step explanation:
...........
k + 3 ——> y-coordinate
2x + 3y + 15 = 0
Sub (2k-3 , k+2) into the equation,
2(2k - 3) + 3(k + 2) + 15 = 0
4k - 6 + 3k + 6 + 15 = 0
4k + 3k = 0 - 15 - 6 + 6
7k = -15
k = -15/7
Sam owns a small business. There was a loss of $16 on Thursday and a loss of $9 on Friday. On Saturday there was a loss of $5, and on Sunday there was a profit of $27. Find the total profit or loss for the 4 days.
A. $27 profit
B. $57 profit
C. $36 loss
D. $3 loss
Answers
someone please help me find the area of this shape using pi
Answers
Answer:
that is easy 90
Step-by-step explanation:
Answer:
78.5 units2
Step-by-step explanation:
terms of or use 3.14 for I and enter your answer I put the answer in a
decimal form if is easier you can simplify and get your normal answer.
I hope this helps I think this is the answer <3
factor the following quadratic equation 4x^2-8x+3
Answers
Answer:
[tex](2x - 1)(2x - 3)[/tex]
Step-by-step explanation:
1) Split the second term in 4x² - 8x + 3 into two terms.
[tex] {4x}^{2} - 2x - 6x + 3[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2x(2x - 1) - 3(2x - 1)[/tex]
3) Factor out the common term 2x-1.
[tex](2x - 1)(2x - 3)[/tex]
Therefor, the answer is (2x - 1) (2x - 3).
How many 1/4 teaspoons are equal to 4 3/4 teaspoons
Answers
Answer:
19 times
Step-by-step explanation:
Divide 4 3/4 ts by 1/4 ts:
4 3/4 ts 19/4 ts
---------------- = ------------- = 19
1/4 ts 1/4 ts
1/4 ts goes into 4 3/4 ts 19 times.
Steve and Marcia bought soda, chips, and gum. • They bought twice as many chips as pieces of gum. • They bought 3 fewer sodas than chips. • Let P represent the total items purchased, s represent soda, c represent chips, and g
Answers
Answer:
ok so S=soda C=chips and G=gum
Step-by-step explanation:
From the information,
s+3=c
(1/2)c=g
from this P=s+c+g
P=s+(s+3)+((s+3)/2)
P=5/2s+9/2
Please help me friends??
Answers
Answer:
the answer is D
Step-by-step explanation:
Select the figure that can be formed by a slice through the sphere
Answers
Answer:
circle
Step-by-step explanation:
Which is the graph of y = 5x5?
DONE
Answers
Answer:
The graph looks like this
Step-by-step explanation:
Hope it helped, heres the link for the graphing calculator I use
desmos com/calculator
Add a . between desmos and com
[tex]y = {5x}^{ 5} [/tex]
Hope it help{45x+6y=15-x+18y=11 is..........................
Answers
Answer:
Step-by-step explanation:
45x+6y=15
-x+18y = 11
let's use elimination, the other way is by substitution, either way works but, it looks to me like elimination would be easy with the 'y'
3(45x+6y=15)
135x + 18y = 45 ( subtract 2nd eq. from 1st )
-( -x+18y = 11 )
136x +0y =34
x = 34 /136
x = 1 /4
there is X
plug that back into either of the 1st or 2nd equations to solve for y
- 1/4 + 18 y = 11
18y = 11 1/4
18y = 45/4
y = 45/4 * 1/18
y = 45/ 72
the fractions seem "difficult" but that's just what the given problem finds
sent a message if you don't "get it" :)
what is the volume in cubic feet of the tent?
5 ft
4ft
6ft
8ft
Answers
Answer:
its 8ft Like see The Cube a cube will be a square
Mrs.Green wants to make some toys for a store. She starts working at 8AM and stops at 12PM everyday. The store needs 120 toys and requires Mrs. Green to make them in three days. What must be her average rate of toys made per hour?
Answers
Answer:
10 toys per hour
Step-by-step explanation:
Given that she starts working at 8AM and stops at 12PM everyday, that means she works
= 12 - 8
= 4 hours daily
If the store needs 120 toys and requires Mrs. Green to make them in three days, the total time available for her to make the number of toys required
= 4 * 3
= 12 hours
Hence her average rate of toys made per hour
= 120/12
= 10 toys per hour
Which choice is the equivalent to the fraction below when x is an appropriate value?
Answers
Five people will equally share two pizzas. How much pizza will each person recieve.
Answers
Answer:
2 Slices
Step-by-step explanation:
Divide both Pizza into 5 slices each and
10 Slices divide by 5 people equals 2
Find a pair of numbers that have a sum of 75 and will produce the largest product.
(Be prepared to justify your reasoning)
A.1 and 74
B.25and 50
C.37 and 38
D.39 and 36
Answers
help me please and thank you
Answers
Answer:
The answer is A, B, and C.
Step-by-step explanation:
All the others are on the wrong side of the graph.
Energy= _______________
Answers
Answer: I think Energy is the ability to do work · Potential or stored energy · Kinetic or working energy. hope this helps
Step-by-step explanation:
What is the opposite of -4? *
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
The best answer gets brainliest
2+2=
Answers
Answer:
4
Step-by-step explanation:
Answer:
2+2=4
Step-by-step explanation:
In order to figure out this simple proplem we must break it down to make it easy. let's say you had 2 apples, and someone gave you 2 more apples. You now have 4 apples
Which pair of functions have the same domain?
Answers
Answer:
i think its 3
Step-by-step explanation:
Answer:
It’s option three because both of their domains are all real numbers
Step-by-step explanation:
Jane goes to H&M for some Fall clothes. She finds a scarf for $24.99, a shirt for $35.50, and a pair of jeans for $67.85. If H&M was having a Fall Day sale where everything was 35% off, how much did Jane spend at H&M?
Answers
Answer: $75.92
Step-by-step explanation:
pls mark me branliest
Dilate Point B by a scale factor of 1/2
Answers
Answer:
( -1.5 , 1 )
Step-by-step explanation:
Hello There!
When dilating a point we divide or multiply the coordinates by whatever the scale factor is
Because the scale factor is 1/2 we just have to divide the coordinates of point B by 2
Preimage coordinates - ( -3 , 2 )
-3/2=-1.5 or -3/5
2/2=1
Dilated image coordinates ( -1.5 , 1 )
1) James deposited $4,000 into an account. He made
no additional deposits or withdrawals. James earned
5.75% annual simple interest on the money in the
account.
What was the balance in dollars and cents in James
account at the end of 5 years?
Answers
Answer:
$5150
Step-by-step explanation:
Given data
Principal=$4000
Rate=5.75%
Time= 5 years
The expression for the balance on simple interest is
A=P(1+rt)
substitute
A=4000(1+0.0575*5)
A=4000(1+0.2875)
A=4000X(1.2875)
A=$5150
Hence the balance is $5150