Final answer:
The solution set of the polynomial equation can be found by testing the given sets of roots and verifying which set satisfies the polynomial equation.
Explanation:
To find the solution set of the polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0, we need to factor the polynomial or use numerical methods to find roots. Polynomial equations of higher degrees such as quartics can often be simplified into quadratic equations or factored based on known roots or rational root theorem. Once a root is found, it can be used for polynomial division to reduce the degree of the polynomial and find other roots. One simple numerical method to guess and check roots would be to use synthetic division with possible rational roots.
However, since the question provides the sets of the roots, we only need to verify which set of roots satisfy the equation. We can use these sets as potential solutions and substitute the roots back into the equation to see if it satisfies the equation. Since complex roots always come in conjugate pairs for polynomials with real coefficients the only possible sets of roots that can be correct are {2 + i, 2 - i, -3, -1} or {2 + i, 2 - i, 3, -1}. Now we can substitute these roots into the original polynomial to determine which set is the actual solution
Round 2342 to the nearest hundred.
Answer:
2300
Step-by-step explanation:
The answer is 2300: first we need to know what we need to round the answer up to, because we need to round it up to hundred, we need to look at the number in the unit below it. So because we need it to the nearest hundred we look at the number in the tens. If the number is 0-4 we round down, if the number is between 5-9 we round up, because the number is 4 we round 2342 down to 2300. When we round down the number stays the same, if we round up we increase the number by 1. So the answer is 2300.
factorise x squared - 4x
Answer:
[tex]x(x-4)[/tex]
Step-by-step explanation:
Factor [tex]x[/tex] out of [tex]x^2[/tex]
[tex]x[/tex]·[tex]x[/tex] [tex]-4x[/tex]
Factor [tex]x[/tex] out of [tex]-4x[/tex]
[tex]x[/tex]·[tex]x[/tex]+[tex]x[/tex]·[tex]-4\\[/tex]
Factor [tex]x[/tex] out of [tex]x[/tex]·[tex]x[/tex]+[tex]x[/tex]·[tex]-4\\[/tex]
[tex]x(x-4)[/tex]
If you have any questions feel free to ask in the comments - Mark
Also when you have the chance please mark me brainliest.
What is the y-intercept of the line perpendicular to the line y = _~x+ 5 that includes the point (-3, -3)?
Slope-intercept form: y = mx + b
[m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]
For lines to be perpendicular, their slopes have to be negative reciprocals of each other. [basically changing the sign (+/-) and flipping the fraction/or switching the numerator and the denominator]
For example:
m = 2 or [tex]\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]-\frac{1}{2}[/tex]
m = [tex]-\frac{1}{4}[/tex]
Perpendicular line's slope = [tex]\frac{4}{1}[/tex] or 4
Since you know the slope of the line is:
y = -3/4x + 5
m = [tex]-\frac{3}{4}[/tex]
The perpendicular line's slope is [tex]\frac{4}{3}[/tex], so plug it into the equation
y = mx + b
[tex]y=\frac{4}{3} x+b[/tex] To find b, plug in the point (-3, -3) into the equation
[tex]-3=\frac{4}{3} (-3)+b[/tex]
-3 = -4 + b Add 4 on both sides to get "b" by itself
1 = b
The y-intercept is 1
A little girl stands on a carousel and rotates around the ride 6 times. if the distance between the little girl and the center of the carousel is 8 feet, how many feet did the little girl travel?
Answer:
301.44 feet.
Step-by-step explanation:
Given: Distance between the girl and the center of the carousel is 8 feet.
Girl stands in a carousel and rotates around the ride 6 times.
We know the radius if carousel is 8 feet.
Now, finding the circumference of carousel to find the area covered in one rotation of carousel.
Circumference= [tex]2\pi r[/tex]
⇒ Circumference= [tex]2\pi \times 8[/tex]
∴ Circumference= [tex]16\pi[/tex]
As given, carousel rotated 6 times.
Length covered in 6 rotation of carousel= [tex]6\times 16\pi[/tex]
⇒ Length covered in 6 rotation of carousel= [tex]96\pi[/tex]
Taking, π = 3.14
⇒ Length covered in 6 rotation of carousel= [tex]96\times 3.14[/tex]
∴Length covered in 6 rotation of carousel= [tex]301.44\ feet[/tex]
Hence, 301.44 feet travelled by little girl in a Carousel.
The little girl traveled approximately 301.62 feet.
To find the distance the little girl traveled on the carousel, we need to calculate the circumference of the circle and then multiply by the number of rotations.
The formula for the circumference of a circle is:
C = 2 × π × r
where r is the radius. Here, the radius r is 8 feet.
C = 2 × π × 8
C = 16π
So, the circumference is approximately 50.27 feet (since π ≈ 3.14).
Since the girl rotates around the carousel 6 times:
Total Distance = Number of Rotations × Circumference
Total Distance = 6 × 50.27
Total Distance ≈ 301.62 feet
Therefore, the little girl traveled approximately 301.62 feet.
the jellybean jar has a radius of 4.8 cm and a height of 11.8 cm. what would be a reasonable lower limit for the number of jelly beans in the jar
Answer:
[tex]\large\boxed{\large\boxed{100}}[/tex]
Explanation:
This question comes with four answer choices:
10,000100,0001001You just need to find a rough estimate of the volume of the jar and the volume of one jelly bean. This is called magnitude order.
The jellybean jar is cylindrical, Thus, its volume is [tex]\pi \times radius^2\times height[/tex]
To find the order of magnitude, you just use the numbers rounded to one signficant figure: round π to 3, the radius to 5, cm, and the height to 10:
[tex]Volume\approx 3cm\times (5cm)^2\times10cm=750cm^3\approx1,000cm^3[/tex]
The order of magnitude for the radius of a jellybean is 1 cm. And the order of magnitude of the volume of a sphere with a radius of 1 cm is the cube of the diameter (2cm):
[tex](2cm)^3=8cm^3\approx10cm^3[/tex]
Hence, a reasonable lower limit for the number of jellybeans in the jar is:
[tex]1,000cm^3/10cm^3=100[/tex]
To find a reasonable lower limit for the number of jelly beans in a jar with a radius of 4.8 cm and height of 11.8 cm, you can calculate the volume of the jar to be approximately 272 cm^3. Assuming the volume of a jelly bean to be approximately 1 cm^3, you can estimate the jar might hold at least 272 jelly beans.
Explanation:To calculate a reasonable lower limit for the number of jelly beans in the jar, a good starting point could be to calculate the volume of the jar and then consider the volume of a single jelly bean. Let's assume a jelly bean has an approximate volume of 1 cm^3 (though they can be bigger or smaller).
Given that the jar is cylindrical, we can calculate its volume using the formula for the volume of a cylinder: πr^2h, where r is the radius and h is the height. Here, radius = 4.8 cm and height = 11.8 cm.
Applying the values, we have: volume = π(4.8)^2 *11.8 = ~271.64 cm^3.
Dividing this volume by the volume of a single jelly bean gives us a rough estimate of the number of jelly beans that can fit in the jar. So, 271.64 cm^3 /1 cm^3 = 271.64, so roughly 272 jelly beans could be a reasonable lower limit, but you might be able to fit more depending on their actual size and how tightly they can pack together.
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Terri brought 1.74 meters of rope. Gracie brought 1.64 meters of rope. Who brought more rope
Answer: Terri brought 10 more centimeters of rope than Gracie.
Step-by-step explanation:
Plot the following points on the coordinate plane
(4 1/2, -2 1/2), (-3.5, 0.5), ( 0,-4)
Anyone have an answer this is study island Coordanate planes
Answer:
The points are plotted in the graph attached.
Step-by-step explanation:
The points are plotted in the graph attached.
16. Ramiro has $21. He wants to buy a skateboard that costs $47. How much
more money does he need to have at least $47? Write an inequality that
represents the situation. Solve the inequality and graph your solution.
really need help ASAP!
Answer:
x>26
Step-by-step explanation:
Subtract 47 from 21.
Now that you have 26, that is the least amount needed because in the question it says "at least". (The inequality sign is suppose to be greater than or equal to)
Answer:
The answer is x>26
Step-by-step explanation:
to graph this inequality you would have to put an open circle on 26 and go right.
Solve for x.
x + 0.60(15) = 0.80(x + 15)
Answer:
x = 15
Step-by-step explanation:
Find the area of the figure. If needed, round to the nearest tenth.
Isosceles trapezoid
7ft
6
ft
14 t
a. 63 sq.ft
b. 27 sq.ft
49 sq.ft
d. 126 sq.ft
Answer:
63 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (a + b)
where a and b are the parallel bases and h the perpendicular height
Here a = 7, b = 14 and h = 6, thus
A = [tex]\frac{1}{2}[/tex] × 6 × (7 + 14) = 3 × 21 = 63 ft²
please help me i’m confused
Yo sup??
SA of the composite figure=SA of all the faces
=2*20*5+6*20+(6*20-6*12)+2*6*5+2*12*4+6*12+2*4*6
=200+120+120+60+96+48
=644 cm^2
Hope this helps.
Cindy bought a new lamp for $40.00. She later saw the lamp on sale for 25% less than what she had originally paid. What was the lamp selling for the second time she saw it?
Answer: $30
Step-by-step explanation:
The lamp was selling for $30 which is 25% less than what Cindy bought.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Cindy bought a new lamp for $40.00.
She later saw the lamp on sale for 25% less than what she had originally paid.
∴ The discounted price of the lamp is 75% of the price for which Cindy bought which is,
= (75/100)×40.
= $30.00
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A technician charges $25 per hour plus $50 for a house call to repair home computers. Make a table and a graph to show the cost for one, two, three, and four hours of home computer repair service. Is there a direct variation?
Answer:
Step-by-step explanation:
1= 75
2=100
3=125
4=150
For every extra computer repair they have to pay an extra 25$
Which graph represents this equation -3x + 4y = 12
A hybrid car can drive 53 miles in the city on l gallon of gas.
How many gallons of gas will it use to drive a total of 371 city.mil
Enter the correct answer in the box.
gallons
Answer:
7 gallons of gas
Step-by-step explanation:
because the car can drive 53 miles on 1 gallon and your trying to find the amount of gallons needed for 371 miles you would divide 371 by 53 and you get 7.
Final answer:
To find out how many gallons of gas are used to drive 371 miles in a hybrid car with a fuel economy of 53 miles per gallon, divide 371 by 53, resulting in 7 gallons of gas needed.
Explanation:
To determine how many gallons of gas a hybrid car will use to drive a total of 371 city miles when the car can drive 53 miles on 1 gallon of gas, you can set up a simple division problem. The formula to calculate gallons used is:
Total miles driven ÷ Miles per gallon = Gallons of gas used
In this case, we divide 371 miles by 53 miles per gallon to find the total gallons of gas used:
371 miles ÷ 53 miles/gallon = 7 gallons
So, the hybrid car will use 7 gallons of gas to drive 371 city miles.
PLZZZZ HELP ASAP! Identify the LIKE terms and constants, if any, in the following expression: 8x - 3y + 5x - 2 *
Answer:
8x and 5x are like terms and the constant is 2 because it is by itself.
Step-by-step explanation:
Hope my answer has helped you and if not I am sorry.
A rectangle has vertices at (0,0),(3,0) and (0,6). What is the area of the rectangle
Area of the rectangle is 18 units.
Step-by-step explanation:
The distance between the points (0,0) and (0,6) gives the length of the rectangle.The distance between the points (0,0) and (0,3) gives the width of the rectangle.Area of the rectangle = length[tex]\times[/tex]width
Substitute length = 6 units and width = 3 units.Area of the rectangle = 6[tex]\times[/tex]3 = 18 units.Write a cosine function for the graph.
a.
y= 4 cos 2theta
c.
y= -4 cos 2theta
b.
y= 4 cos theta/2
d.
y= -4 cos theta/2
Answer:
Correct answer: y= 4 cos 2theta
Step-by-step explanation:
The Cosine Function
The general form of the cosine is
[tex]Y=A.cos(w\theta+B)[/tex]
where A is the amplitude, w is the angular frequency and B is the phase shift
The amplitude is the positive top value of the sinusoid or the most negative value. Since the sinusoid goes from -4 to 4, the amplitude is 4, thus
[tex]Y=4cos(w\theta+B)[/tex]
To find B and w, we use two points from the graph (0,4) and [tex](\pi/4,0)[/tex]:
[tex]4=4cos(w\times0+B)[/tex]
Simplifying
[tex]1=cosB[/tex]
Thus B=0
Now for the second point
[tex]0=4cos(w\times \pi/4)[/tex]
Or equivalently
[tex]\displaystyle \frac{\pi w}{4}=\frac{\pi}{2}[/tex]
Thus
w=2
Then, the cosine function is
[tex]Y=4cos2\theta[/tex]
Correct answer: y= 4 cos 2theta
V= 512^2/3* 19683^1/3*256^1/4
Answer:
V=512^2/3* 19683^1/3*256^1/4 = 6912
Step-by-step explanation:
V= [tex](512^{\frac{2}{3} } ) \times (19683^{\frac{1}{3} } )\times (256^{\frac{1}{4} } )\\[/tex]
As
[tex]2^{9} = 512\\2^{8} = 256\\19683^{\frac{1}{3} } = 27\\[/tex]
putting values in equation
V= [tex]2^{9(^{\frac{2}{3} } )} \times 27 \times 2^{8^({\frac{1}{4}) } } \\[/tex] let it be equation 1
As
[tex]2^9^{\frac{2}{3} } = 2^6 according\,to\,exponential\,rule\\2^8^\frac{1}{4} = 2^2 according\,to\,exponential\,rule\\\\[/tex]
putting values in equation 1
[tex]V= 2^6\times 27\times 2^2[/tex]
According to exponential rule [tex]2^6 \times 2^2 = 2^8[/tex]
V=[tex]2^8 \times 27\\[/tex]
[tex]V=256\times 27\\V=6912[/tex]
So
V= 6912
Keywords: Algebra
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Earl hates taking out the garbage and he hates washing the dishes, so he decides to make a deal
with his parents: He will flip a coin once for each chore and will perform the chore if the coin lands on
heads. What he doesn't know is that his parents are going to use a weighted coin that lands on heads
80% of the time!
Answer:
The question is incomplete. The complete question is shown below
1. What is the probability that Earl will have to do both chores?
Ans. (0.8 * 0.8 = 0.64)
2. What is the probability that Earl will have to take out the garbage but will not need to wash the dishes
Ans.( 0.8 * 0.2 = 0.16)
Step-by-step explanation:
1. The probability that Earl will have to do the chores is 0.8
Therefore the probability that Earl will have to do both chores is 0.8 * 0.8 = 0.64
2.The probability that Earl will have to take out the garbage but not need to wash the dishes
0.8 * 0.2 = 0.16
What is the measure of angle b?
36 degrees
63 degrees
117 degrees
56 degrees
Answer: 36 degrees
Step-by-step explanation:
The angle a is 63 degrees because 177 and a are supplementary and equal 180 degrees. Because there are 180 degrees in a triangle, 63+ 81 is 144. 36 and 144 is 180, therefore b is equal to 36.
Hope this helped!
An exterior angle of a triangle equals the sum of its opposite interiors.
The measure of b is 36 degrees
To calculate angle b, we use the following equation
[tex]b + 81 = 117[/tex] ------- because b and 81 are opposite interior angles to 117
Solving further, we have:
[tex]b = 117 - 81[/tex]
Evaluate like terms
[tex]b = 36^o[/tex]
Hence, the measure of b is 36 degrees
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you and four of your nine classmates received an A on your math test. what is the simplest fraction of students that scored an A on the test?
Answer:
5/9
Step-by-step explanation:
What is the sum of 2/5 and 1/3
Answer:11/15
Step-by-step explanation:
Most common denominator is 15 multiply 2/5 by 3 and 1/3 by 5 and that’s what you get
A store makes a profit of $15 on a wallet, after a mark up of 60%, what is the selling priceof the wallet?
To find the selling price of the wallet after a 60% markup and a profit of $15, we need to calculate the original price of the wallet and add the profit to it. The original price of the wallet is $25 and the selling price is $40.
Explanation:To find the selling price of the wallet, we need to first find the original price of the wallet before the markup. Let's call the original price 'x'. Given that the store makes a profit of $15 on a wallet after a markup of 60%, we can write the equation:
x + 0.6x = x + $15
Simplifying the equation, we get:
1.6x = x + $15
0.6x = $15
x = $15 / 0.6
So, the original price of the wallet is $25.
The selling price of the wallet is the original price plus the profit, which is $25 + $15 = $40.
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Ann thought of a number N, multiplied it by 5 and added 7. Then she told the result R to Jim. Write a formula that will tell you the value of R for any value of N. Using the previous formula, write the formula that could help Jim guess Anne’s number N as soon as he is given the value of the result R
Answer:
[tex]R=5N+7[/tex]
[tex]\displaystyle N=\frac{R-7}{5}[/tex]
Step-by-step explanation:
Equations
The relation between the number thought by Ann (N) and the final result (R) can be expressed as
[tex]R=5N+7[/tex]
So if for example, Ann thought in the number N=12, then
[tex]R=5\times 12+7=67[/tex]
If we know the value of R, it's easy to find back the value of N by solving the equation
[tex]R=5N+7[/tex]
subtracting 7 on each side
[tex]R-7=5N[/tex]
Dividing by 5
[tex]\displaystyle N=\frac{R-7}{5}[/tex]
So, if Ann tells Jim that R = 52, he can guess her number is
[tex]\displaystyle N=\frac{52-7}{5}[/tex]
[tex]N=9[/tex]
The formula for r, the value Jim hears, for any given value of n (Ann's number) is: r = 5n + 7
This formula breaks down as follows:
5n: This represents Ann multiplying n by 5.
+ 7: This represents Ann adding 7 to the result of multiplying n by 5.
r: This represents the final value, which Jim hears.
Therefore, by plugging any value of n into this formula, you can calculate the value of r that Jim would hear.
what is the answer?
Answer: It’s A
Step-by-step explanation:
If you reflect over the y axis your point changes
Simplify: Log3 27 = x can anybody help me with this?? Thank you!!
Answer:3
Step-by-step explanation:
3 ^x= 27
X=3
Find the sum and difference of 147, 167 and 204, 107.
To find the sum, add the numbers together. To find the difference, subtract the smaller numbers from the larger numbers.
Explanation:To find the sum of 147, 167, 204, and 107, simply add the numbers together:
147 + 167 + 204 + 107 = 625
To find the difference, subtract the smaller numbers from the larger numbers:
204 - 147 = 57
167 - 107 = 60
Therefore, the sum is 625 and the differences are 57 and 60.
Bobby has a piece of rope measuring 4 yards. How many 1-inch strips can be cut from the rope?
Answer:
144
Step-by-step explanation:
Step 1: Convert 4 yards into feet
1 yard = 3 feet
4 * 3 = 12 feet
Step 2: Convert 12 feet into inches
1 foot = 12 inches
12 * 12 = 144 inches
Answer: Bobby can cut 144 1-inch strips.
Answer:
144
Step-by-step explanation:
All you would need to know is that there is 36 inches in one yard and then you would just multiply the 36 by four to make the four yards total
what is (-100)a×56 and thanks