What are the roots of the polynomial equation x^3-10x=-3x^2+24? Use a graphing calculator and a system of equations.
a. -24, -3, 12
b. -12, 3, 24
c. -4, -2, 3
d. -3, 2, 4
Answers
simplifying the above we get
x^3+3x^2-10x-24=0
next we use the graphing tool to solve the expression above:
This will give us:
x=-4,x=-2, x=3
The answer is c] -4,-2,3
Answer : C
the roots of the polynomial equation x^3-10x=-3x^2+24
We use a graphing calculator
Graph the left hand side expression using graphing calculator
We graph [tex]y=x^3 - 10x[/tex]
Then we graph the right hand side expression using graphing calculator
[tex]y=-3x^2+24[/tex]
so we got two system of equations
The intersection of two graphs is our solution
The graph is attached below
We can see that the graph intersects at 3 points
(-4, -24) (-2,12) and (3,-3)
So the roots are -4, -2 , 3
Related Questions
A baker has 34 cup of sprinkles to spread on cupcakes. Each cupcake needs 18 cup of sprinkles.
The baker uses the fraction model that is partially shown to find the number of cupcakes that will have sprinkles.
mediaIMG7358611486128321.jpg34=6
Which is the correct division equation that describes the model?
A. 18 ÷
B. 34÷18=8
C. 34÷18=6
D. 18÷34=332
Answers
3/4 divided by 1/8 is actually 6/8 broken into groups of 1/8. That is why your answer is 6.
Dylan is wrapping a birthday present for his sister. The box the gift is in has a length of 6 inches, a width of 5 inches, and a height of 3 inches. What is the minimum amount of wrapping paper Dylan will need to completely cover the box?
Answers
To compute for the minimum amount of wrapping paper Dylan will need to completely cover the box, you have to compute the surface area of the box. The formula in getting the surface area of a rectangle is:
A = 2WL + 2LH + 2HW
Substituting the given measurements to the formula:
A = 2(5)(6) + 2(6)(3) + 2(3)(5)
A = 60 + 36 + 30
A = 126 square inches
Therefore, Dylan needs to purchase at least 126 square inches of wrapping paper to completely cover the box.
whats the slope of this graph??
Answers
By counting on the graph the slope is -1/2
By using the slope formula:
-2-0/4-0 = 4/-2 = 1/-2
Hence, the slope is same the both ways :)
Look at this prism and its net. Rectangular prism with length labeled 5 meters, width labeled 7 meters, and height labeled 12 meters. Net of the same rectangular prism with the same dimensionsn labeled. What is the surface area of this rectangular prism? cm²
Answers
Answer:358
Step-by-step explanation:just because it is
Which of these number words represents the numeral 4,056? four thousand, five hundred six four thousand, five hundred fifty-six four thousand, fifty-six four thousand, sixty-five
Answers
Solution:
we have been asked to find
Which of the given number words represents the numeral 4,056?
Its about the counting.
On unit place we have 6.
on Tenth place we have 5.
on hundredth place we have 0.
On Thousand place we have 4.
so in our number word representation there will be no "Hundreds".
So it will make
Hence the given number words representing the numeral 4,056 is Four thousands and fifty six
Why is 25 mg lighter than 25 cg
Answers
A particularly long traffic light on your morning commute is green on 20% of the mornings. assume that each morning represents an independent trial. (a) what is the probability that the first morning that the light is green is the fourth morning?
Answers
p=0.2
independent Bernoulli trials (green=success)
Need to find: probability that first three trials are failures, and the fourth one is a success.
Method: The conditions given fit the requirements of the geometric distribution, where for k failures before the first sucess
P(k)=(1-p)^k*p
=(1-0.2)^3*0.2
=0.8^3*0.2
=0.1024
Define the following terms. a. Dividend b. Divisor c. Quotient d. Remainder
Answers
Answer:
Dividend is the number which we divide. Divisor is the number by which we divide. Quotient is the quantity produced by the division of two numbers. Remainder is an amount left over after division.
Step-by-step explanation:
Need help in geometry!!!
Answers
JKLM: J(8,4) ; K(4,10) ; L(12,12) ; M(14,10)
I'll just use the first vertex of every quadrilateral in comparison with J(8,4)
A(-8,-4) ; B(-4,-10) ; C(-12,-12) ; D(-14,-10) → a sequence of reflections across the x and y-axes, in any order. This is easy because each vertex has the same number but different signs.
E(11,2) ; F(7,8) ; G(15,10) ; H(17,8) → a translation of 3 units left and 2 units up. As you can envision with a graph, from 11 to 8, you need to move to the left of the x-axis. from 2 to 4, you need to move up of the y-axis.
O(6,7) ; P(2,13) ; Q(10,15) ; R(12,13) → a translation 2 units right and 3 units down. From 6 to 8 of the x-axis and from 7 to 4 of the y axis.
S(4,16) ; T(10,20) ; U(12,12) ; V(10,10) → This one has no pair but it seems as though this is rotated along the point U.
W(11,7) ; X(7,13) ; Y(15,15) ; Z(17,13) → a translation 3 units down and 3 units left.
Use the number line. What fraction of 1 foot is 3 inches? What fraction of 1 yard is 3 inches?
Answers
The fraction of 1 foot is 3 inches is, 1/ 4
And, The fraction of 1 yard is 3 inches is, 1 / 12
What is Measurement unit?A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
To find the fraction of 1 foot is 3 inches.
And, The fraction of 1 yard is 3 inches.
We know that;
As shown on the number line,
⇒ 1 foot = 12 inches.
Hence, To find fraction of a foot 3 inches is,
we have to compare 3 inches to 12 inches as;
3 / 12
1 / 4
Thus, The fraction of 1 foot is 3 inches is, 1/ 4
And, We know that;
1 yard = 36 inches
Hence, We get;
The fraction of 1 yard is 3 inches is,
⇒ 3 / 36
⇒ 1 / 12
Learn more about the measurement unit visit:
https://brainly.com/question/777464
#SPJ3
the temperature outside is -5°F name the temperature that would make the sum of the two temperatures 0°F
Answers
The area of a trapezoid is 69.6 in2 and its altitude is 8.7 in. Find the perimeter of the trapezoid if the sum of its legs is equal to the sum of its bases.
Answers
A = 1/2h(b1 + b2)
69.6 = 1/2 x 8.7(b1 + b2)
69.6 = 4.35(b1 + b2)
16 = (b1 + b2) - the sum of the bases
16 in = the sum of the legs and the sum of the bases
16 + 16 = 32 inches
The perimeter is 32 inches.
A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other. The perimeter of the trapezoid is equal to 32 inches.
What is a trapezoid?A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is necessary.
As is mentioned that the area of the trapezoid is 69.6 in², while its altitude is 8.7 inches. Therefore, the sum of the bases of the trapezoid can be written as,
[tex]\rm \text{Area of trapezoid} = \dfrac{1}{2} \times (Base_1 + Base_2) \times Altitude[/tex]
[tex]69.6 = \dfrac{1}{2} \times (b_1 + b_2) \times 8.7\\\\(b_1 +b_2) = 16\rm\ inches[/tex]
Now, it is mentioned that the sum of the legs of the trapezoid is equal to the sum of its bases. Therefore, the perimeter of the trapezoid is,
[tex]\text{Perimeter of Trapezoid} = (\text{Sum of its bases}) +(\text{Sum of its legs})\\\\\text{Perimeter of Trapezoid} = 16+16 = 32\rm\ inches[/tex]
Hence, the perimeter of the trapezoid is equal to 32 inches.
Learn more about Trapezoid:
https://brainly.com/question/4758162
Add -4 + 2/3 . A) -52/3 B) -42/3 C) -32/3 D) -31/3
Answers
If D is supposed to be -3 1/3, that choice is the correct one.
___
As written, none of the answer choices are correct.
Rewrite 5
16 + 6
20 with a common denominator.
Answers
16: 16, 32, 48, 64, 18
20: 20, 40, 60, 80, 100
As we can see, they both have the number 80 in common. That number will be our LCD. Let's convert. 16 goes into 80 five times and 5 * 5 is 80. 5/16 is 25/80. 20 goes into 80 four times and 6 * 4 is 24. That makes 24/80. The expression is 25/80 + 24/80. Add both of those numbers and the sum is 49/80.
The access code for a gym lockergym locker consists of three digits. each digit can be any number from 00 through 77, and each digit can be repeated. complete parts (a) through (c). (a) find the number of possible access codes. (b) what is the probability of randomly selecting the correct access code on the first try? (c) what is the probability of not selecting the correct access code on the first try?
Answers
.. 8 * 8 * 8 = 512
b) The probability that a randomly selected code is correct is 1/512.
c) The probability it is not correct is 1 -1/512 = 511/512.
,
1) the number of possible access codes is 512.
Solution:
8 x 8 x 8 = 512
,
2) the probability of randomly selecting the correct access code on first try is 1/512.
.
sample space = 512
there is only 1 correct combination of numbers on the 512 possible codes so the answer is 1/512.
,
3) the probability of not randomly selecting the correct access code on first try is 511/512.
.
sample space = 512
there are 511 incorrect codes on the 512 possible codes so the answer is 511/512.
:)
Algebra 2 semester 1
Answers
Please make brainliest, I worked really hard:)
The school band had 2 shows last week. The first show had 400 people attending. The second show had 100 people attending. Which ratio correctly compares the number of people at the second show to the number of people at the first show?
Answers
Answer: 1/4
Step-by-step explanation:
Number at Second Show 100 100 ➗100
—————————————- = ———— = — — ———- = 1/4
Number at First show 400 400➗100
Hoped it help.
Which rule describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E"?
Answers
The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is the transformation composition rule. This involves applying a translation followed by a reflection in a specific order.
Explanation:The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is the transformation composition rule.
Transformation composition involves applying multiple transformations in a specific order. In this case, we need to determine the sequence of transformations that would result in the mapped figure.
By applying these transformations in the given order, we can map figure ABCDE to figure A"B"C'D"E".
The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" could involve a sequence of translations, reflections, rotations, or dilations, applied in a specific order. The specific transformations and their order would depend on the given figures and the desired outcome.
The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is called a sequence of transformations.
A sequence of transformations involves applying multiple transformations in a specific order to transform one figure into another. In this case, the figure ABCDE is transformed into A"B"C'D"E".
Let's break down the possible transformations that could be involved in this sequence:
1. Translation: A translation moves a figure without changing its size or shape. It involves sliding the figure in a specific direction. For example, if figure ABCDE is translated 3 units to the right and 2 units up, it would result in figure A"B"C'D"E".
2. Reflection: A reflection involves flipping a figure over a line called the line of reflection. The line of reflection acts as a mirror, with each point on the figure reflecting across the line. If figure ABCDE is reflected over a line, it would result in figure A"B"C'D"E".
3. Rotation: A rotation involves turning a figure around a fixed point called the center of rotation. The figure is rotated by a specific angle in a clockwise or counterclockwise direction. If figure ABCDE is rotated 90 degrees counterclockwise around a given point, it would result in figure A"B"C'D"E".
4. Dilation: A dilation involves changing the size of a figure while maintaining its shape. The figure is either enlarged or reduced by a scale factor. If figure ABCDE is dilated with a scale factor of 2 centered at a specific point, it would result in figure A"B"C'D"E".
Solve for z.
[tex]z {}^{4} - 65z {}^{2} + 64 = 0[/tex]
Answers
From their office, Cathy drives due west while John drives south. When John is 7 mi from the office, the distance between them is 1 mi more than Cathy’s distance from the office. Find the distance between Cathy and John.
Answers
.. x^2 = (x -1)^2 +7^2 . . . . Pythagorean theorem
.. 0 = -2x +1 +49 . . . . . . . eliminate parentheses and subtract x^2
.. 2x = 50 . . . . . . . . . . . . . simplify and add 2x
.. x = 25 . . . . . . . . . . . . . . divide by 2
The distance between Cathy and John is 25 miles.
A dog that weighs 15 pounds should eat 2 1/8 cups of a certain type of dog food per day. How much of the same type of dog food should be fed, per day, to a dog who weighs 34 pounds?
Answers
Final answer:
To determine how much the 34-pound dog should eat, set up a proportion based on the 15-pound dog's food intake. After setting up the proportion 15 pounds / 2 1/8 cups = 34 pounds / x cups and solving it, we find that the 34-pound dog should eat approximately 4.82 cups per day.
Explanation:
The question deals with proportional relationships and mathematics, specifically in finding out how much dog food to feed a dog based on its weight. To solve this problem, we need to establish a ratio or proportion from the information provided and then use it to find out how much food the 34-pound dog should eat.
A 15-pound dog eats 2 1/8 cups of dog food per day. We convert 2 1/8 cups to an improper fraction which is 17/8 cups. Now, we set up the proportion:
15 pounds / (17/8 cups) = 34 pounds / x cups
By cross-multiplying we have:
15 * x = 34 * (17/8)
x = (34 * 17) / (8 * 15)
x = (578) / (120)
After simplifying the fraction, we obtain x = 4.8166 which we can round to 4.82 cups per day for a 34-pound dog.
Find the 8th term in the arithmetic sequence An=-2x+4
Answers
Answer:
a(8) = -12
Step-by-step explanation:
The 8th term in the sequence is when n = 8. Substitute x = 8 into the rule An=-2x+4.
a(8) = -2(8) + 4
a(8) = -16 + 4
a(8) = -12
Two teams of interns are wrapping donated gifts at a hospital. if the teams work alone, team a can wrap all of the gifts in 7 hours, and team b can wrap all of the gifts in 5 hours. how many hours will it take the interns to wrap all of the gifts if both teams work together? round the answer to the nearest half hour.
Answers
Team A can wrap all gifts in 7 hours; thus they can wrap 1/7 of the gifts in 1 hour.
Team B can wrap all gifts in 5 hours; thus they can wrap 1/5 of the gifts in 1 hour.
1/7h + 1/5h = 1, where h is the number of hours; it equals 1 because it is 100% of the gifts;
Find a common denominator. 35 is the first thing 7 and 5 will both divide into. Convert the fractions:
5/35h + 7/35h = 1
12/35h = 1
Divide both sides by 12/35:
12/35h ÷ 12/35 = 1 ÷ 12/35
h = 1/1 ÷ 12/35
h = 1/1 × 35/12
h = 35/12
h = 2.9
h ≈ 3
Final answer:
When both teams work together, they can wrap the gifts with a combined rate of 12/35 of the work per hour. It would take them 35/12 hours, which is approximately 2.92 hours. Rounded to the nearest half-hour, both teams will take about 3 hours to wrap all of the gifts.
Explanation:
To determine the time it would take for both teams of interns to wrap the gifts when working together, we need to add their work rates. Team A can wrap the gifts in 7 hours, which means their rate is 1/7 of the work per hour. Team B can wrap the gifts in 5 hours, giving them a rate of 1/5 of the work per hour.
When combined, the rate at which they can wrap the gifts together is the sum of their individual rates:
Team A's rate: 1/7
Team B's rate: 1/5
Combined rate: 1/7 + 1/5 = 5/35 + 7/35 = 12/35 of the work per hour.
To find out how many hours it will take them to wrap all of the gifts together, we divide the entire job (1) by their combined rate (12/35):
1 / (12/35) = 35/12 hours = 2.9166... hours.
Rounded to the nearest half hour, they would take approximately 3 hours to wrap all of the gifts.
Imelda needs to convert 440 centimeters per minute to meters per hour. Which conversion factors should she use?
Answers
[tex] = 440 \dfrac{cm}{min} \times \dfrac{60~m \times min}{100~cm \times hr} [/tex]
[tex] = 440 \dfrac{cm}{min} \times \dfrac{3~m \times min}{5~cm \times hr} [/tex]
Multiply cm/min by 3/5 to get m/hr.
find the limit of the function by using direct substitution. lim(x^2-1) x->0
Answers
lim_(x->0) (x^2 - 1)
lim_(x->0) (x^2 - 1) = 0^2 - 1 = -1:
Answer: -1
Answer:
-1
Step-by-step explanation:
Direct substitution is just filling in the limit for x then solving. So in this case the limit is 0.
x^2-1
0^2-1
-1
Based on the table of values below, find the slope between points where x = 3 and where x = 7. x y 3 1 4 6 7 9
Answers
.. (9 -1)/(7 -3) = 8/4 = 2
Answer: The required slope is 2.
Step-by-step explanation: We are given to find the slope between the points where x = 3 and x = 7 from the following table :
x 3 4 7
y 1 6 9
We know that
the slope of a line between the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
At x = 3, y = 1 and at x = 7, y = 9.
Therefore, the slope between the points (3, 1) and (7, 9) is given by
[tex]m=\dfrac{9-1}{7-3}=\dfrac{8}{4}=2.[/tex]
Thus, the required slope is 2.
The shampoo you like to use is on sale. But you only get the lower price if you buy 3 bottles. You want to know how much you'll save.
Write a formula that will help you determine how much you'll save by buying 3 bottles
on sale.
Let's let
s = sale price per bottle
r = regular price per bottle
c = cost savings
Answers
The equation to this is going to be : c = 3r - 3s
If you want to get the lower price down you are going to have to buy 3 shampoo bottles in order to get a lower price. The cost you save is the main difference from a regular price. And the answer is c = 3r - 3s
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches, what is the area of the object?
A.33 square inches
B.40 square inches
C.20 square inches
D.60 square inches
Answers
B is the answer
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches. Then the area of the given figure is 40 inches.
What is area?"The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc."
What is the area of the square ?The area of the square is side times side i.e., a^2.
What is area of the rectangle ?The area of the rectangle is length times width i.e., l*b.
Here,
x = 3 inches, y = 10 inches, w = 5 inches, z = 5,
In the given figure:
Area of the square BCDE is a^2 = 5^2 = 25
Area of the rectangle ABFG is l*b = 5*3 = 15
Total area of the figure is = area of the square + area of the rectangle = 25+15 = 40.
Hence, the answer is option B.
To learn more about area here
https://brainly.com/question/27683633
#SPJ2
Please help will be pleasured:)
Answers
Harry's fitness trainer recommends that Harry drink 8 fluid ounces of water 8 times a day. Harry has a water bottle that holds 1 1/4 pints of water when filled. Today he has filled the water bottle three times and drank all of the water each time. Harry claims that he drank the total amount of water recommended by his fitness trainer. Explain why hair is claim is not true
Answers
and
8 oz x 8=64 oz
60<64
therefore he was 4 oz short of the total recommended amount.
Amount of fluid recommended by Harry's fitness trainer =8 fluid ounces of water 8 times a day = 8x8=64 fluid ounces.
Amount of fluid Harry water bottle holds= [tex] 1\frac{1}{4}=1.25 pints [/tex]
Amount of fluid Harry drinks when he fills the bottle 3 times = 1.25x3=3.75 pints.
1 pint = 16 fluid ounce
3.75 pint =16x3.75 =60 fluid ounces.
Harry drank only 60 fluid ounce compared to 64 fluid ounce his trainer recommended.
Harry claims that he drank the total amount of water recommended by his fitness trainer is not true.