What are the roots of the polynomial function x^4 +7x^2-144=0
Answer:
Step-by-step explanation:
[tex]x^4+7x^2-144=0\\x^4+16x^{2} -9x^{2} -144=0\\x^{2} (x^{2} +16)-9(x^{2} +16)=0\\(x^{2} +16)(x^{2} -9)=0\\(x^{2} -(-16))(x^{2} -3^2)=0\\(x^{2} -16 \iota^2)(x+3)(x-3)=0\\(x^{2} -(4\iota)^2)(x+3)(x-3)=0\\(x+4\iota)(x-4\iota)(x+3)(x-3)=0\\x=\pm4 \iota,\pm3[/tex]
Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply. Multiple select question. cross out A) (0, 0) cross out B) (1, −25) cross out C) (−2, 5) cross out D) (−1, 25) cross out E) (4, 10) cross out F) (−5, 2)
9514 1404 393
Answer:
A) (0, 0)
B) (1, −25)
D) (−1, 25)
Step-by-step explanation:
For the point to lie on the line, the y-value must be -25 times the x-value. That is the case for points A, B, D.
A piece of wire 22 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
9.56 m of the wire should be used for the square, to maximize the total area of the wire
Let x be the side length of the square.
So, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
Let y represent the side length of the equilateral triangle.
So, the perimeter of the triangle is:
[tex]\mathbf{P_t=3y}[/tex]
The length of the wire is given as:
[tex]\mathbf{P=22}[/tex]
This implies that:
[tex]\mathbf{P_s + P_t=22}[/tex]
Substitute values for Ps and Pt
[tex]\mathbf{4x + 3y=22}[/tex]
Make y the subject
[tex]\mathbf{y=\frac{22 -4x}3}[/tex]
For an equilateral triangle of side length y, the height (h) of the triangle is:
[tex]\mathbf{h =\frac y2\sqrt 3}[/tex]
The area of the triangle is then calculated as:
[tex]\mathbf{A_t = \frac 12 yh}[/tex]
This gives
[tex]\mathbf{A_t = \frac 12 y\times \frac y2\sqrt 3}[/tex]
[tex]\mathbf{A_t = \frac{y^2}{4}\sqrt 3}[/tex]
The area of the square is:
[tex]\mathbf{A_s = x^2}[/tex]
So, the total area is:
[tex]\mathbf{A = A_s + A_t}[/tex]
[tex]\mathbf{A = x^2 + \frac{y^2}{4}\sqrt 3}[/tex]
Substitute [tex]\mathbf{y=\frac{22 -4x}3}[/tex]
[tex]\mathbf{A = x^2 + (\frac{22 - 4x}{3})^2 \times \frac{\sqrt 3}{4}}[/tex]
Differentiate
[tex]\mathbf{A' = 2x + \frac{\sqrt 3}{4} \times \frac 19 \times 2(22 - 4x) \times (-4)}[/tex]
[tex]\mathbf{A' = 2x - \sqrt 3 \times \frac 19 \times 2(22 - 4x) }[/tex]
[tex]\mathbf{A' = 2x - \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Set to 0
[tex]\mathbf{2x - \frac{2\sqrt 3}9 (22 - 4x) = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Divide through by 2
[tex]\mathbf{x = \frac{\sqrt 3}9 (22 - 4x) }[/tex]
Multiply through by 9
[tex]\mathbf{9x = \sqrt 3 (22 - 4x) }[/tex]
Open bracket
[tex]\mathbf{9x = 22\sqrt 3 - 4x\sqrt 3 }[/tex]
Collect like terms
[tex]\mathbf{9x +4x\sqrt 3= 22\sqrt 3 }[/tex]
Factor out x
[tex]\mathbf{x(9 +4\sqrt 3)= 22\sqrt 3 }[/tex]
Solve for x
[tex]\mathbf{x= \frac{22\sqrt 3}{9 +4\sqrt 3} }[/tex]
Simplify
[tex]\mathbf{x= \frac{38.11}{9 +6.93} }[/tex]
[tex]\mathbf{x= \frac{38.11}{15.93} }[/tex]
[tex]\mathbf{x= 2.39 }[/tex]
Recall that, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
So, we have:
[tex]\mathbf{P_s=4 \times 2.39}[/tex]
[tex]\mathbf{P_s=9.56}[/tex]
Hence, 9.56 m of the wire should be used for the square
Read more about maximizing lengths at:
https://brainly.com/question/3433355
Add and simplify 4/9 + 3/7
Answer:
55/63
Step-by-step explanation:
1. Joseph bought 23 pineapples and 37 green mangoes. If he combined all the fruits and shared these equally to his 3 brothers, how many fruits did each of them get?
2. There were 130 persons invited in a festival. The venue has rectangular tables that can sit 6 persons each. The longer side can sit two persons while the shorter side can sit one. The host arranges 6 tables in a row placed shorter end to shorter end. How many rows of tables are needed to sit all the invited guests?
1. Each if them would get 20 fruits
[tex]23 + 37 = 60[/tex]
[tex]60 \div 3 = 20[/tex]
2. There should be 5 rows of tables needed to sit all the invited guests
On every row there would be 26 people, so then we need to divide 130 by 26 and we get 5. Then if we check, 26 times 5 equals 130.
Hope that helped:)
The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their squares is 293. What is the absolute difference between the greatest and the least of these three numbers in the arithmetic sequence?
We want to find the absolute difference between the greatest and the least of 3 consecutive terms of an arithmetic sequence that meet some given criteria. We will get that the difference is 3.88 or 12.88.
We know that the difference between any pair of two consecutive terms in an arithmetic sequence is a constant.
So if that difference is D, we can write 3 consecutive terms as:
A, A + D, A + 2*D
The sum must be equal to 27, then we have:
A + (A + D) + (A + 2*D) = 27
And the sum of their squares is equal to 293, then we have:
A^2 + (A + D)^2 + (A + 2*D)^2 = 293
If we simplify these two equations we get:
3*A + 2*D = 27
3*A^2 + 6*D*A + 5*D^2 = 293
To solve this, we just need to isolate one of the variables in the first equation and then replace that in the other one.
3*A = 27 - 2*D
A = (27 - 2*D)/3 = 9 - (2/3)*D
Replacing that on the other equation we get:
3*(9 - (2/3)*D)^2 + 6*(9 - (2/3)*D)*D + 5*D^2 = 293
Now we can solve this for D:
3*(81 - 2*9*(2/3)*D + D^2) + 54*D - 4*D^2 + 5*D^2 = 293
(243 - 293) + 18*D + 4*D^2 = 0
-50 + 18*D + 4*D^2 = 0
That is just a quadratic equation, the solutions are given by:
[tex]D = \frac{-18 \pm \sqrt{18^2 - 4*4*(-50)} }{2*4} \\\\D = \frac{-18 \pm 33.53}{8}[/tex]
Then we have two possible values for D, we take the positive one to get:
D = (-18 + 33.53)/8 = 1.94
And the difference between the greatest and least of these 3 numbers is twice the common difference, so is equal to 2*D = 2*1.94 = 3.88
If instead we take the other solution, we get:
D = (-18 - 33.53)/8 = -6.44
Then the absolute difference is -2*D = -2*-6.44 = 12.88
If you want to learn more, you can read:
https://brainly.com/question/25715593
Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes
Answer:
if you remember the bell curve 32 32 13.5 13.5 2.35 2.35 and .15 put the mean in the middle of the bell curve we find that 13.5 + 2.35 + .15 so
16% is your probablility
10.
Write an equation for the translation of y = |x|.
15.5 units down
A. y = |x| + 15.5
B. y = |–15.5x|
C. y – 15.5 = |x|
D. y = |x| – 15.5
Answer:
D
Step-by-step explanation:
Without writing the equation x^2 = 8y in the standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola.
A- parabola
B- ellipse
C- hyperbola
D- circle
Step-by-step explanation:
Given -
x
2
=
8
y
It is a parabola opening up.
The general form of the equation of a parabola opening up is -
x
2
=
4
a
y
In which pair can figure “a” take figure “b”
Answer:
2
Step-by-step explanation:
I need help with math. Brainiest will be yours. Tell me if the file is not loading.
How do you write 10 X 10 X 10 X 10 using exponents?
Answer:
104. Explanation: There are 4 10 s to multiply.
Step-by-step explanation:
-8x + 14y = -30
4x - 7y = 18
Answer:
I think you may have written it down wrong because no solution for that is possible.
Easy question:
Pump A can fill a tank of water in 6 hours. Pump B can fill the same tank in 10 hours. How long would it take the two pumps, working together, to fill the tank?
Answer:
3 hours and 45 minutes
Step-by-step explanation:
let's assume the tank has a volume of x liters.
let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.
the formula to calculate the time is:
time = volume / speed
If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x
So the time this takes is:
time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.
For the triangle shown on the left,
find the length of the side labeled x
find the measure of angle A in degrees
Answer:
See belowStep-by-step explanation:
For the shown triangle we use the tangent of 60° angle to find the value of x:
tan = opposite / adjacenttan 60° = x/14√3 = x / 14x = 14√3Angle A and 60° are complementary.
The measure of angle A:
m∠A = 90° - 60° = 30°Step-by-step explanation:
[tex] \tan(60) = \frac{x}{14} \\ \\ \sqrt{3} = \frac{x}{14} \\ \\ x = \sqrt[14]{3} [/tex]
the measure of angel A
m < a = 90-60 = 30
Can somebody help me as soon as possible
Answer:
It's decreasing quickest between 3:23 and 3:24 (where the steepest drop on the graph is)
Answer:
3:23-3:24
…………………..
write an equation for the red line.
Answer:
Its is the second one
Step-by-step explanation:
Remember: rise over run
The b of the equation is -2 because that is how far it goes down on the y axis.
The slope is 3x.
Put the slope like this 3/1= rise/run
Sorry for the delayed response!
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)
Answer: Choice C
(x, y) → (x – 3, y + 5)
=================================================
Explanation:
The "5 units up" portion means that each y value increases by 5. Therefore, we go from y to y+5. Going from x to x-3 means that we shift each point 3 units to the right.
For example, if the starting point is (1,7), then we have the following steps:
[tex](x,y) \to (x-3,y+5)\\\\(1,7) \to (1-3,7+5)\\\\(1,7) \to (-2,12)\\\\[/tex]
The point (1,7) moves 5 units up and 3 units to the left to arrive at (-2,12).
Note that the order doesn't matter. We could start moving 5 units up, then go 3 units left. Or we could start going 3 units left, then 5 units up. We'll arrive at the same destination.
Eric kept track of his days is a journal:
good or bad. If 5% of his days were bad
after 60 days had gone by, how many
good days did he have?
Answer:
3
Step-by-step explanation:
5 percent * 60 =
(5:100)* 60 =
(5* 60):100 =
300:100 = 3
Answer: 57
Step-by-step explanation:
5% of 60 is 3 and 60-3 is 57
How to place 5/3 on a number line
Step-by-step explanation:
the answer is in the image above
Answer:
Step-by-step explanation:
Convert improper fraction to mixed fraction.
[tex]\dfrac{5}{3}=1\dfrac{2}{3}[/tex]
1 2/3 is between 1 and 2. denominator is three. Divide into 3 parts.
If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?
Answer:
16/52 or 16/54
Step-by-step explanation:
2 blacks 2 reds
4 colours
4 kings
4 queens
4 jacks
4 ace
16 total of ‘em
and number of cards in Deck is 52, 54 if counted 2 jokers
Angelique buys 16 cans of lemonade for $8.80 Find the cost of each can. Give units with your answer.
Answer:
$0.55 for one can
Step-by-step explanation:
16 cans of lemonade = $8.80
1 can of lemonade = $8.80 / 16 = $0.55
What is the decimal equivalent of 40%?
Answer:
.40
Step-by-step explanation:
move the decimal over 2 times
Answer:
40%=0.4
Step-by-step explanation:
Wendy is conducting a marketing survey. She mailed 35,400 surveys and got 12,744 responses. What is the percentage
Answer:
0.036%
Step-by-step explanation:
Solve for this variable shown
Y=
Answer:
how is traffic to + 54 degree + 42 degree then that 96 degree - by 180 degree you get you will get 84 degree
Write the ratio in simplest form as a fraction.
32 inches to 1 foot
Answer:
8/3
Step-by-step explanation:
1 foot = 12 inches, so it would be 32/12. After simplifying and dividing 4 on both sides, you would get 8/3.
8.
Graph y = |x| – 5.
A. Graph a
B. Graph b
C. Graph d
D. Graph c
Answer:
D. Graph c
Step-by-step explanation:
I got this answer correct on Gradpoint
Help this is due today!!!!!
Answer:
D
Step-by-step explanation:
-1/2m=-18
m=36
answer is D
Answer:
m = 36
Step-by-step explanation:
[tex]\frac{1}{3} m+3-\frac{5}{6}m=-15[/tex]
Combine like terms:
[tex](\frac{1}{3} m+(-\frac{5}{6}m)[/tex]
[tex](\frac{2}{6} m+(-\frac{5}{6}m)[/tex]
[tex]-\frac{3}{6}m = -\frac{1}{2} m[/tex]
[tex]-\frac{1}{2}m+3=-15[/tex]
Subtract 3 from each side:
[tex]-\frac{1}{2}m=-18[/tex]
Multiply each side by -2:
[tex]m = 36[/tex]
a
. Bruce Banner buys a suit priced at $865.49. He
receives a 20% discount because he's a hero. After
that, a 7% tax is applied (yes, he must pay taxes,
despite being a hero). What is the final price of the
suit?
Answer:
$740.86
Step-by-step explanation:
Let me know if you need the steps.
a cars gas tank holds 15 gallons of gas. the car used up 9 gallons of gas. what percent of the gas in the tank is remaining?
9514 1404 393
Answer:
40%
Step-by-step explanation:
15 -9 = 6 gallons remain. The fraction remaining can be expressed as a percentage by multiplying it by 100%.
fraction remaining = (remaining gallons)/(capacity) = 6/15 = 2/5
percent remaining = 2/5 × 100% = 40%
