Step-by-step explanation:
[tex]5 {x}^{2} - 4 {y}^{2} + 80 = 0[/tex]
[tex]5 {x}^{2} - 4 {y}^{2} = - 80[/tex]
[tex] - \frac{ 5{x}^{2} }{16} + \frac{ {y}^{2} }{20} = 1[/tex]
[tex] \frac{ {y}^{2} }{20} - \frac{5 {x}^{2} }{16} = 1[/tex]
To find foci,
[tex]c = \sqrt{ {a}^{2} + b {}^{2} } [/tex]
so
[tex]c = \sqrt{20 + 16} [/tex]
[tex]c = \sqrt{36} [/tex]
[tex]c = ±6[/tex]
Since the y term has a greater denomiator, our foci is
(0,6) and (0,-6)
Find a fourth degree polynomial equation with rational coefficients that has roots -1 multiplicity of 2 and 1-4i.
A. x^4-18x^2-32x-15
B. x^4+14x^2+32x+17
C. x^4+2x^3+6x^2+32x+40
D. x^4+4x^3+2x^2+12x+45
A polynomial of degree 4 will have 4 zeros. The zero of 3 with a multiplicity of 2 counts as two of these zeros. You've also been given a zero of -i. So it seems that we only have 3 of the 4 zeros. We need all 4 to be able to form the desired polynomial.
You didn't mention that the polynomial should have real coefficients. But I'm going to assume it because otherwise we can't solve the problem. If a polynomial with real coefficients has a complex zero, then the complex conjugate of that complex zero will also be a zero. This is how we will find the 4th zero.
A complex number in standard form is a + bi. Its complex conjugate is a + (-bi) or a - bi. The complex zero we were given is -i. In standard form this would be 0 + (-i). The complex conjugate of 0 + (-i) would be 0 - (-i) or 0 + i or just i.
So the four zeros of the desired polynomial are 3 (twice), -i and i. If a number "z" is a zero of a polynomial then (x - z) is a factor of that polynomial. Using this fact and the four zeros we can write a factored form of our desired polynomial:
f%28x%29+=+a%28x-3%29%28x-3%29%28x-%28-i%29%29%28x-i%29
Simplifying the 3rd factor we get:
f%28x%29+=+a%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29
where the "a" is any non-zero number. Since there are an infinite number of non-zero numbers, there will be an infinite number of possible correct solutions to this problem. To make things easy we will choose to make "a" be 1. This makes our factored polynomial:
f%28x%29+=+%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29
All we have to do now is multiply this out. We can simplify this process if we take advantage of some factoring patterns. The first two factors can be multiplied using:
%28a-b%29%5E2+=+a%5E2-2ab%2Bb%5E2
And the last two factors can be multiplied using:
%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2
With these patterns we get:
f%28x%29+=+%28%28x%29%5E2-2%28x%29%283%29%2B%283%29%5E2%29%28%28x%29%5E2-%28i%29%5E2%29
Simplifying inside each factor we get:
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-i%5E2%29
And since i%5E2+=+-1 this becomes:
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-%28-1%29%29
or
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2%2B1%29
We have one more multiplication. There are no shortcuts for this one. We have to multiply each term of one factor times each term of the other and then add like terms, if any:
f%28x%29+=+x%5E2%2Ax%5E2%2Bx%5E2%2A1%2B%28-6x%29%2Ax%5E2%2B%28-6x%29%2A1%2B9%2Ax%5E2%2B9%2A1
Simplifying...
f%28x%29+=+x%5E4%2Bx%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9x%5E2%2B9
f%28x%29+=+x%5E4%2B10x%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9
Re-ordering into standard form:
f%28x%29+=+x%5E4%2B%28-6x%5E3%29%2B10x%5E2%2B%28-6x%29%2B9
This is a polynomial function of degree 4 with the given zeros.
P.S. As mentioned earlier, this is not the only possible correct answer. This is the answer when you make "a" equal to 1. Other values for "a" give us different polynomial functions which also have the same zeros. For example, if we had chosen a = 2 we would have gotten f%28x%29+=+2x%5E4%2B%28-12x%5E3%29%2B20x%5E2%2B%28-12x%29%2B18.
If 1/3 gallon of paint covers 1/6 of a wall, then how many quarts of paint are needed for the entire wall?
Answer:
8 quarts
Step-by-step explanation:
1/3 of a gallon ---1/6 of a wall
x - 1 (all the wall)
x = (1 x 1/3) / 1/6
x = 1/3 / 1/6
x = 6/3
x = 2 gallons
1 gallons - 4 quarts
2 gallons - x
x = (2 x 4) / 1
x = 8 / 1
x = 8 quarts
find the probabaility of each event picking a blue marble from a bag of 4 red marbles 6, blue marbles and 1 white marble
Answer:
⁶/11
Step-by-step explanation:
total marbles = 4+6+1
=11
blue marble/total marbles : ⁶/11
If your state has a property tax rate of 0.056, and you pay $3,164.45 in property taxes every year, what is the assessed value of your property? a. $177,209 b. $21,265 c. $56,508 d. $48,684 please select the best answer from the choices provided a b c d
Answer:
C $56,508
Step-by-step explanation:
You take the property taxes of $3164.45 & divide by the tax rate of .056 & you get $56,508
To double check, $56,508 property value X the tax rate of .056 (5.6%) = $3,164.45
what are the answers
Answer:
I use app called math
way
Step-by-step explanation:
if you answer these question i chose 15 points
Answer:
5. angle A=40
6. angle C= 80
7. angle C= 110
Step-by-step explanation:
In all three questions, it says angle B= angle A+ angle C
So for each when it gives you angle B and one of the others, you just subtract either angle A or angle C from the total angle (B) to find the other. For example, for question 5, it asks for angle A saying that B is a right angle and c equals 50. Well, a right angle is 90 degrees. So to find angle A, you do 90-50.
please help 10pts each
dang im rlly givin away too much points lol
solve for x
3x=5x-4
Answer:
x = 2
Step-by-step explanation:
Given :
3x = 5x - 4Add 4 on each side
3x + 4 = 5x - 4 + 43x + 4 = 5xSubtract 3x from each side
3x - 3x + 4 = 5x - 3x4 = 2xDivide 2 from each side
4/2 = 2x/2x = 2A
D
N
4
1
B EK
к
10
Solve for N.
AABC - ADEC
8
4
N
N=1?
10
Enter
Answer: N = 5
ok done. Thank to me >:3
Jake and maddie each take the closest path from their homes to the store. based on the picture below, what is the approximate difference in the distance each person traveled to the store?
Answer:
we can't really answer the question without the pictue, but if the time count stays the say and the distance doen't, it would be (t=time/d=distance) (lets say time was an hour and you traveled 11 miles each hour,) then it would be 11t = d
But, if it is without multiplication, then just add all the numbers in each turn to get your answer.
Hope this saved your time. :)
Answer: 6.4 m
Step-by-step explanation:
A water tank holds 36 gallons
of water. A new water tank holds
25% more water. How many
gallons of water can the new
water tank hold?
Sasha's mom bought a container with 150
bracelet beads for Sasha's birthday party.
There were 8 girls at the birthday party to
equally share the beads. Between what two
amounts of beads should each girl receive?
Answer:
between 18 and 19
Step-by-step explanation:
150/8= 18.75
BRAINLIEST (If there are two answers) Which formulas can be used to find the surface area of a right prism where p is the perimeter of the base, h is the height of the prism, BA is the area of bases, and LA is the lateral area?
A. SA = BA + ph
B. SA = BA -LA
C. SA = BA + 1/2ph
D. SA = BA + 1/2ph
E. SA = BA + LA
Answer:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S.
Step-by-step explanation:
What is the value of x in the equation 2 – 11x = 4x + 17?
Answer:
-1=x
Step-by-step explanation:
2-11x=4x+17 Given
2(+11x)-11x=4x+(11x)+17 Subtract 11x from both sides
2=15x+17 Simplify
2 (-17)=15x (-17) +17 Subtract 17 from both sides
-15=15x Simplify
-15/15=15x/15 Divide both sides by 15 (isolate x)
-1=x Simplify
x=-1
Step-by-step explanation:
2-11x=4x+17-11x-4x=17-2-15x=15-15x÷-15=15÷-15x=-1What is 14 pounds in ounces
25) 3 NaHCO3
Na
H = C =_0 =
Find 1 rational number between -2/9 and 0
Answer:
Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.
Point A, B and C are given above. Give point D do make a parallelogram
I think D at (2,1) will do
hope it helps...!!!
Step-by-step explanation:
I think D at (2,1)
hope it will help
Please help I will give brainliest.
Answer:
a = 3 , b = 8 , c = 4
Step-by-step explanation:
the standard form of a quadratic equation is
ax² + bx + c = 0
3x² + 8x + 4 = 0 ← is in standard form
with a = 3, b = 8, c = 4
Mr. Silberman borrowed money for a computer for $1,500. He will pay $50 per month until it is paid off.
Ms. Washington also borrowed money for a computer. The equation D=-100m + 1,800 represents the amount Ms. Washington owes, D. in
dollars, after m months.
Which person will owe more money after 9 months? Move the correct words and dollar amount to the blanks to complete the sentence.
After 9 months.
will owe
more than
Mr. Silberman
Ms. Washington
$50
$100
$150
$200
$250
$300
Answer: Mr. Silberman has to pay $150 more than Ms. Washington.
Step-by-step explanation: First calculate how much tax Mr. Silberman will have to pay off after 9 months. 50x9=450, so $450 is how much tax he will have to pay. Add that to 1,500, which is the total cost of the computer, which equals $1,950.
Ms. Washington only has to pay $1,800. Mr. Silberman has to pay $1,950. So Mr. Silberman has to pay more. He has to pay $150 more than Ms. Washington.
Which expression is equivalent to
?
2
od
1
4
062
2
LN Leyla
o
Answer:
2nd one is correct.....
Which scenario most likely describes an example of plagiarism?
taking a photo of a photo in an art gallery and pasting it into a personal journal
taking a photo of another photo displayed in an art gallery and claiming it as your own
painting a landscape based on inspiration from a photo in a museum
digitally altering a photograph found online and crediting the original photographer
Answer: Taking a Photo of another photo displayed in an art gallery and claiming it as your own
Step-by-step explanation: Because you are claiming something as your own(when it's not) is considered plagiarism and no other situation is considered plagiarism but this one so really the process of elimination explains the answer to this question
Letters a, b, c, and d are angle measures.
Lines f and g are intersected by line n. At the intersection of lines n and g, clockwise from the top, the angles are: a, 75 degrees, blank, b. At the intersection of lines n and f, clockwise from the top, the angles are blank, blank, d, c.
Which should equal 105° to prove that f ∥ g?
a
b
c
d
Answer: d
Step-by-step explanation:
The 75 degree angle and angle d are same-side interior angles, meaning that if they were supplementary, the lines would be parallel by the converse of the same-side interior angles theorem.
Matching angles of two congruent figures
translation
corresponding
transformation
image
congruent figures
Answer:
Corresponding
Step-by-step explanation:
Matching angles of two congruent figures are called corresponding angles. The angles that are in the same position will have the same measurement.
Which of the following parallelograms is NOT similar to the others?
A
B
C
D
the answer is D
Step-by-step explanation:
Answer: C
Step-by-step explanation:
The height of the parallelogram for A is 3 units while the length the base is 6 units.
For D it follows this same pattern, the height is 1 which is half of the length of the base, 2.
B also follows this pattern, the height is 2 which is half of the length of the base, 4
C does not follow this pattern and is the odd one out.
How do you solve this question
Answer:
x = 8
Step-by-step explanation:
2(13x + 12) = 70 + 20x + 2
26x + 24 = 72 + 20x
-20x -20x
6x + 24 = 72
-24 -24
6x = 48
÷6 ÷6
x = 8
(please help me)
Amelie spins the following spinner, which has 10 equally sized spaces numbered 1 through 10. The numbers 1 and 7 are colored blue; the numbers 2, 4, and 6 are red; and the numbers 3, 5, 8, 9, and 10 are green.
A spinner as described in the text.
What is the probability that Amelie spins either an odd number or a red number?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
8/14
Step-by-step explanation:
there are 5 odd numbers and 3 numbers are coloured red
How many 1/2 scoops of rice can fit in a two-cup bowl
Answer:
4 (cooked)
Step-by-step explanation:
2 / 1/2 = 4
-4+x< or equal to 9
Solve for x
please
Answer:
13 through -infinity
or
13, -infinity
Step-by-step explanation:
if f(x)=(2x)^2 find f(-4)
Answer:
64
Step-by-step explanation:
1. Plug it in:
(2(-4))^2
2 times -4 is -8
(-8)^2 = 64
So there’s your answer
A right pyramid with a square base is shown. the length of the base is 8 inches and the slant height is 5 inches. kabir wants to know the volume of a solid right pyramid with a square base. he uses a ruler to measure the length of the base as 8 inches. he then measures the slant height to be 5 inches. the hypotenuse of the right triangle used to determine the height is inches. the leg of the right triangle that lies on the same plane as the base is inches. the height of the pyramid is inches. the volume of the solid pyramid is cubic inches.
The volume of the given pyramid comes to be 64 cubic inches.
Length of the square base a= 8 inches
Slant height l =5 inches
What is the volume of a pyramid?The volume of a pyramid is with base area A and height h is 1/3Ah.
So, base area A= 8*8 =64 square inches.
From Pythagoras theorem
[tex]l^{2} =(\frac{a}{2})^2 +h^{2}[/tex]
[tex]5^{2} =(\frac{8}{2})^2+h^{2}[/tex]
[tex]h=3[/tex] inches
So, volume of the pyramid = 1/3*A*h
=1/3*64*3
=64 cubic inches.
Hence, the volume of the given pyramid comes to be 64 cubic inches.
To get more about pyramids visit:
https://brainly.com/question/218706
Answer:
5, 4, 3, & 64
Step-by-step explanation:
i did it