Answer:
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Factor the polynomial expression x^4 + x^2 − 20.
The factors of polynomial expression x^4 + x^2 − 20 is [tex](x - \sqrt{5})(x + \sqrt{5})(x - i \sqrt{5})(x + i \sqrt{5})$[/tex].
We are given that;
The polynomial expression =[tex]x^4 + x^2 − 20.[/tex]
Now,
To factor a polynomial expression, we need to find the common factors of each term and then use the distributive property to write the expression as a product of two or more factors.
For example,[tex]x^4 + x^2 − 20[/tex] can be written as:
[tex]$x^4 + x^2 - 20 = x^2(x^2 + 1) - 20$[/tex]
We can use the difference of squares formula to factor x^2 + 1 and 20:
[tex]$x^2 + 1 = (x + i)(x - i)20 = (2 \sqrt{5})(2 \sqrt{5})[/tex]
where i is the imaginary unit such that i^2 = -1. Now, we can write the expression as:
[tex]$x^4 + x^2 - 20 = x^2(x + i)(x - i) - (2 \sqrt{5})(2 \sqrt{5})$[/tex]
We can use the difference of squares formula again to factor the whole expression:
[tex]$x^4 + x^2 - 20 = (x^2 - 2 \sqrt{5})(x^2 + 2 \sqrt{5})$[/tex]
we can still factor each factor further into prime factors. We have:
[tex]x^2 - 2 \sqrt{5} = (x - \sqrt{5})(x + \sqrt{5})$\\$x^2 + 2 \sqrt{5} = (x - i \sqrt{5})(x + i \sqrt{5})[/tex]
Therefore, by factorization answer will be [tex](x - \sqrt{5})(x + \sqrt{5})(x - i \sqrt{5})(x + i \sqrt{5})$[/tex]
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Point A is located at (0,4) and point B is located at (-2, -3). Find the x value for the point that is 1/4 the distance firm point A to point B. -1.5 -2 -0.5 -1
Answer:
.25
Step-by-step explanation:
distance between 0,4 is 1. The distance between _2 and _3 is minus 5. X equals.
.25
pls pls pls help due soon!!
1 over 3b = 4 over 5. Which of the following equals b in this equation?
22 over 5
11 over 8
2 over 5
1 over 4
Answer:
b = 5/12
Step-by-step explanation:
1. Cross multiply -> 1 x 5 = 5 and 3b x 4 = 12 b
2. Simplify -> 5 = 12b and switch sides so it's easier: 12b = 5
3. Divide both sides by 12 -> 12b ÷ 12 = b and 5 ÷ 12 = 5/12
4. So, the answer is b = 5/12
Hope this helps! :)
Use symbolab, it's very helpful
Answer:
The answer is 2 2/5
Step-by-step explanation:
help please i need it like really
Answer:
The first question is 11.25
The second question is 35.5
Step-by-step explanation:
I need the answer to this fast
Answer:
Bro I need the problem so I can answer the question not the asnwers I need to see the question too.
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
Answer:
C
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 3, 1) ← 2 points on the line
m = [tex]\frac{1-0}{-3-0}[/tex] = - [tex]\frac{1}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x ← equation of line
8(4x-1)-12x=2(11x-3)
Answer:
Solving for X? would be 1
Step-by-step explanation:
32x-8-12x=22x-6
20x-8=22x-6 then subtract 20x from each side and add 6 to each side
2=2x then divide by 2 and getting 1 is x
Answer:
x=-1
Step-by-step explanation:
The value of an antique car is modeled by the function V(x)=107,000(1.009)^(2/3x) where x is the number of years since 2005. By what APPROXIMATE percent rate is the value of the car increasing per year? SHOW AN EXPLANATION WHY YOU CHOOSE THAT ANSWER!!
A. 0.04%
B. 0.14%
C. 0.60%
D. 1.40%
here you go i hope this helps
Mark bought a loaf of bread. The label says the bread weighs 24 ounces. What is the weight of the bread in pounds?{1 pound = 16 ounces}
A. 1 1/2
B. 2
C. 2 1/2
D. 3
uh yes ok i need help rn.
Answer:
y = 8.5x
Step-by-step explanation:
the amount of money (y)
amount per hour (8.5) times the hours (x)
Answer:
C). y = 8.5x
Step-by-step explanation:
it would be the third one because in order to find out how make she’s makes every hour when she’s paid $8.50 you would have to multiply the amount she’s paid by how many hours she works.
hope this helped!
WILL GIVE BRAINIEST IF COMPLETE
Answer:
1st blank = Shorter
2nd blank = shorter
3rd blank = will not
Step-by-step explanation:
Base of the box
a² + b² = c²
Lets input the numbers
32² + 8² = c²
1024 + 64 = c²
1088 = c²
Sq rt c = 32.9
32.9<34 so it will not fit.
Interior of the box
32² + 6² = c²
1024 + 36 = c²
1060 = c²
Sq root = 32.6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
will give brainliest to the correct answer (no links or account will be reported) :)
Answer:
122
Step-by-step explanation:
64 + 58 = (l)
(l) = 122
Choose all of the equations that represent a parabola with the focus (0,4) and the vertex (0, -6).
A. x2 = 20 (y + 1)
B. x2 = 40 (y + 6)
C. 20y = x2 - 20
D. 40y = (x + 6)2
E. 40y = x2 – 240
Answer:
B and E
Step-by-step explanation:
The equations that represent a parabola with the focus (0,4) and the vertex (0, -6) are 40y = [tex]x^{2}[/tex] - 240 and [tex]x^{2}[/tex] = 40 (y + 6)
What is parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The general equation of a parabola is:
[tex](y -k)^{2}[/tex] = 4a(x − h) for horizontal parabola
[tex](x - h) ^{2}[/tex]= 4a(y − k) for vertical parabola
where (h,k) denotes the vertex
a = point of focus
According to question
focus of parabola :(0,4)
vertex of parabola (h,k): (0, -6)
now, form points given
a = 4 − (-6) = 10 as x coordinates are the same.
Since the focus lies to the left of vertex, a = 10
By The general equation of a parabola :
[tex](x - h) ^{2}[/tex]= 4a(y − k) for vertical parabola
[tex](x - 0)^{2}[/tex] = 4*10(y-(-6))
[tex]x^{2}[/tex] = 40 (y + 6) --------------------- (1)
or
[tex]x^{2}[/tex] = 40y + 240
40y = [tex]x^{2}[/tex] - 240 ---------------------------(2)
Therefore , parabola can be represented by equation (1) and (2).
Hence, the equations that represent a parabola with the focus (0,4) and the vertex (0, -6) are 40y = [tex]x^{2}[/tex] - 240 and [tex]x^{2}[/tex] = 40 (y + 6)
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A healthcare company surveys customers to determine whether each customer
would be willing to pay an additional $35 monthly for extra coverage. The results
of the survey are shown.
Would you pay extra?
Yes
No
Age
Below 50
50 or older
38
55
45
22
What is the probability a customer below the age of 50 would be willing to pay an
extra $35 monthly?
Answer : 59%
Step-by-step explanation:
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? *
Answer:
I'm going to say 24. I'm 97% sure I'm correct
How do you find an area of an object?
Answer:
Step-by-step explanation: The easiest territory computations are for squares and square shapes. To discover the space of a square shape, duplicate its tallness by its width. For a square, you just need to discover the length of one of the sides (as each side is a similar length) and afterward duplicate this without anyone else to discover the region.
What’s the answer show work
Answer:
68°
Step-by-step explanation:
This triangle is isosceles triangle, so RQS and QSR are equal,
SRQ= 180-56-56=68
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student is in sports.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P(Sports) = [?]
Round to the nearest hundredth.
Answer:
0.65
Step-by-step explanation:
The probability that a randomly selected student is in sports is 0.65.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, the number of students = 100.
Total number of outcomes =100
Number of favorable outcomes =65
Now, P(Sports) = 65/100
= 0.65
The probability that a randomly selected student is in sports is 0.65.
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Please Help!!!!!
You will be deeply appreciated
I need this for a test!
Answer:
C. 99
Step-by-step explanation:
The number are all less than 50 and then there is only one number that is greater than 50. The number is 99. Because it is a number that is not close to the average numbers at all, it is the outlier.
If this answer has helped you, please mark as brainliest
Answer:
C. 99
Step-by-step explanation:
an outlier is a number that is dralastically diffrent then the rest
which is equivalent to the polynomial
Answer:
The correct solution is "[tex]10g^3+2g^2+17g-14[/tex]".
Step-by-step explanation:
The given expression is:
= [tex](10g^3-8g^2+5g-14)+(10g^2+12g)[/tex]
By opening the brackets, we get
= [tex]10g^3-8g^2+5g-14+10g^2+12g[/tex]
By applying addition and subtraction, we get
= [tex]10g^3+2g^2+17g-14[/tex]
Or,
The expression isn't a perfect cube.
What is the area of the following circle?
Either enter an exact answer in terms of 7 or use 3.14 for and enter your answer as a decimal.
C
r= 1
Answer:
area: 3.14
Step-by-step explanation:
because the radius is one, one squared is the same as itself, then by multiplying one by pi, you simply get pi. Therefore making 3.14 your answer.
the answer should be 3.14 or 3.14159
A number n decreased by 18 is 3
Answer:
-36
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
A number n decreased by 18 is 3
This can be though of as:
N subtracted by 18 equals 3
And put into a solvable form:
N-18=3
Now lets solve for N:
N-18=3
+18 +18
=
N=21
So this is your answer!
Hope this helps!
Find the measure of angle b. PLZ HELP AND SHOW WORK
Answer:
1) A because of vertical angle theorem (VAT), which means that b=37 degrees
2) C because a right angle is= to 90 degrees. Take away 23, you get 67 degrees
3) B because the image shows a full angle, which is equal to 360 degrees. Take away 207 and 58, you get 95 degrees
4) D because a right angle is= to 90 degrees. Take away 44, you get 46 degrees
5) A because a right angle is=to 90 degrees. Take away 58, you get 32 degrees
Identify the constant of proportionality from the table.
X Y
3 21
5 35
6 42
8 56
O A. 3
O B. 21
C. 1/7
D. 7
Answer:
the correct answer is option D
Kyona opened a savings account with $500. Her account grew at a rate of 3% per year compounded
annually. She made no deposits or withdrawals on the account. At the end of 4 years, what was the
account worth, to the nearest dollar?
Answer:
560.00
Step-by-step explanation:
Answer:
560 dollars
Step-by-step explanation:
3%×4×500=60
60+500=560
Can someone help me with this? Right answer gets brainliest!! :)
Answer:
7 times (*) 8
Step-by-step explanation:
Product in this case means multiplication
The graph of a linear function is shown.
A coordinate plane with a straight line passing through (negative 4, 2), (0, 0), and (4, negative 2).
Which word describes the slope of the line?
positive
negative
zero
undefined
Zeros can be observed graphically or solved for algebraically. A linear function can have none, one, or infinitely many zeros. If the function is a horizontal line ( slope = [latex]0[/latex]), it will have no zeros unless its equation is [latex]y=0[/latex], in which case it will have infinitely many.
Answer:
answer is negative
Step-by-step explanation:
2021 edge :)
a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?
FYI THE PHONE COSTS 300$
Answer:
Step-by-step explanation:
Find the height, x, of the tree. 20 points for this question
79.03 ft
111.80 ft
124.74 ft
70.83 ft
Answer:
70.83
Step-by-step explanation:
srr if incorrect
Find the volume of the cone in the attached image.
