Answer:
A B D
Step-by-step explanation:
The solutions of the given cubic equation are (x = -8), (x = -4), and (x = 6) and this can be determined by using the factorization method.
Given :
Equation is \(x^3+6x^2-40x=192\).
The following steps can be used in order to determine the solution(s) to the given equation:
Step 1 - Write the given equation.
\(x^3+6x^2-40x=192\)
Step 2 - Rewrite the above equation.
\(x^3+6x^2-40x-192=0\)
Step 3 - Now, factorize the above equation.
\(\begin{aligned}\\x^3-6x^2+12x^2-72x+32x-192&=0\\(x^2+12x+32)(x-6)&=0\\\end{aligned}\)
Step 4 -Again factorize the above equation.
\(\begin{aligned}\\(x-6)(x^2+8x+4x+32)&=0\\(x-6)(x+8)(x+4)&=0\\\end{aligned}\)
Therefore, the correct options are A), B), and C).
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An Olympic runner set a record for the 100m event. The time was ten and sixty two hundredths seconds. Express the decimal form of the given time
please help me
PLS ANSWER THISHEHDNDJDJ
9514 1404 393
Answer:
1/12
Step-by-step explanation:
The slope of a ramp (or anything else) is the ratio of its "rise" to its "run."
The rise is the vertical change. Here, that is shown as 3 m.
The run is the horizontal change. Here, that is shown as 36 m.
Then the slope is ...
\(\text{slope }=\dfrac{\text{rise}}{\text{run}}=\dfrac{3\text{ m}}{36\text{ m}}=\boxed{\dfrac{1}{12}}\)
__
Additional comment
If this were a line on a graph, the slope would be calculated the same way. When the rise is positive to the right, the slope is positive. On a graph, if the rise is negative as you go to the right, the slope is negative.
2.) Vito uses 9 liters of water to water 20 flower pots. He is wondering how many liters of water (w) it
would take to water 40 flower pots. He assumes he will use the same amount of water on each pot.
How many liters of water does it take to water 40 flower pots?
Answer:
18 liters of water to water 40 flower pots
Step-by-step explanation:
Because you doubled the amount of flower pots and you just do the same thing with the water
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thabo rounded the number of marbles to the nearest 5. His answer was 340. write down 2 possible numbers for the actual number of marbles.
Answer:
338 or 335 they both get rounded of to the nearest 5
2 possible numbers for the actual number of marbles 338 and 335, are rounded to the nearest 5.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, Thabo rounded the number of marbles to the nearest 5 and his answer was 340.
Therefore, 2 possible numbers for the actual number of marbles could be
Whether it's 338 or 335, both numbers are rounded to the nearest 5.
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A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4 6 5 7 3 5 What is the best explanation of how to find the experimental probability of rolling a 3? To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary
The best explanation of how to find the experimental probability of rolling a 3:
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have the Data as:
Number Frequency Probability
1 4 0.13
2 6 0.20
3 5 0.17
4 7 0.23
5 3 0.10
6 5 0.17
total 30 1.00
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
= 5/30
= 1/6
= 0.166
= 16.6% or 17%.
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an airplane is 58 m long. a scale model of the plane is 40.6 cm long.
determine the scale factor used to create the model as a decimal rounded
to the nearest thousandth
If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:
58 m / 40.6 cm
To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:
58 m = 58 × 100 cm = 5800 cm
Now we can divide:
5800 cm / 40.6 cm = 142.857...
Rounding to the nearest thousandth, we get:
142.857... ≈ 142.857
Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
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(9,−7) after a dilation by a scale factor of 4 centered at the origin?
The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:
Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).
In conclusion, the coordinates of the image after a dilation are (36, -28).
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2x-y=5
2x-5y=-31
elimation method
Answer:
y=9, x=7
Step-by-step explanation:
2x-y=5 --> equation 1
2x-5y=-31 --> equation 2
change signs of equation 1
-2x+y=-5
solving method
-2x+y=-5 (cut -2x and 2x because -2x+2x =0)
2x-5y=-31 (likewise +y-5y and -5-31)
-4y= -36 (since -4 is multiplying on right side it will divide)
y= -36/-4 (cut negative with negative and simplify equation)
y= 9
put value of y in equation 1
2x-y=5
2x-9=5
2x= 14
x=14/2
x=7
Why is a data point with an x-coordinate of 0 a good point to use when creating a trend line for a data set? Select all that apply.
A. It is easy to compute the slope using this point.
B. The y-coordinate of this point is the y-intercept.
C. The y-coordinate of this point is always positive.
D. The coordinates of this point are both 0
This point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.
A. It is easy to compute the slope using this point.
B. The y-coordinate of this point is the y-intercept.
A data point with an x-coordinate of 0 is a good point to use when creating a trend line for a data set because it is easy to compute the slope using this point. The y-coordinate of this point is also the y-intercept, which is the point at which the line crosses the y-axis. Additionally, the coordinates of this point are both 0, making it easy to locate on a graph. While this point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.
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Entrywise eigenvector analysis of random matrices with low expected rank (Abbe, Fan, Wang, Zhong).pdf
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others.
While a large variety of bounds are available for average errors between empirical and population statistics of eigenvectors, few results are tight for entrywise analyses, which are critical for a number of problems such as community detection.
This paper investigates entrywise behaviors of eigenvectors for a large class of random matrices whose expectations are low-rank, which helps settle the conjecture in Abbe et al. (2014b) that the spectral algorithm achieves exact recovery in the stochastic block model without any trimming or cleaning steps. The key is a first-order approximation of eigenvectors under the ℓ∞ norm:
\(u_{k }\)≈1/ λ (\(\frac{A u^*_{k}}{*k}\))
where {uk} and {u∗k} are eigenvectors of a random matrix A and its expectation EA, respectively. The fact that the approximation is both tight and linear in A facilitates sharp comparisons between uk and u∗k. In particular, it allows for comparing the signs of uk and u∗k even if ∥uk−u∗k∥∞ is large. The results are further extended to perturbations of eigenspaces, yielding new ℓ∞-type bounds for synchronization (Z2-spiked Wigner model) and noisy matrix completion.
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Rewrite the following equation in slope-intercept form. 14x − y = –15
y = 14x + 15 would be the slope-intercept form
hello good day
can you help me please:(
Answer:
35. D
36. A
37. D
38. D
PLSS HELP YALLLLLLLLL
Which equation shows the correct use of the Distributive Property?
−4(3/2x−1/2)=−15
A- 6x + 4 = –15
B- 2x – 1/2 = –15
C- –6x – 2 = –15
D- –6x + 2 = –15
Answer:
D
Step-by-step explanation:
Hope this helped!
Happy Halloween!
6> z(10-z)
Which number is a solution of the inequality?
Answer:
6 > z(10 - z)
6 > 10z - z^2
z^2 - 10z^2 + 6 < 0
z > 9.36, z < 0.64
Therefore, option (0) is the correct answer.
Step-by-step explanation:
HOPE IT HELP
Which of the following describe -1 4/6? Select all that apply.
rational number
irrational number
whole number
integer
Answer:
rational number
Step-by-step explanation:
as the denominator is not zero
2.
Peter's salary last week was $80. This week he received $90. What percent of increase does this represent?
Answer:
The increase is $90 - $80 = $10.
Step-by-step explanation:
To find the percent of increase, we start by finding the amount of increase as a fraction or proportion of the original amount. In this case, the amount of increase is:
$10 / $80 = 0.125
To convert this to a percentage, we multiply by 100:
0.125 × 100 = 12.5%
Therefore, Peter's salary increase represents a 12.5% increase from last week's salary.
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The school chess club has 6 girls and 4 boys. Two students are to be selected at random to represent their school in a statewide tournament. The coordinator of the club writes each student’s name on a card and places the cards in a paper bag.
What is the probability that the coordinator will draw the name of a girl followed by the name of another girl, if the first name is not returned to the bag? Express your answer as a percent.
Answer:
33.3%
Step-by-step explanation:
6/10 x 5/9 which equals 1/3 when simplified, or 33.3%
What does y equal?
Will Give Brianlest!
Answer:
\(\boxed{\tt y=48}\)
Step-by-step explanation:
\(\tt \cfrac{3}{16}=\cfrac{9}{y}\)
Cross multiply:-
\(\tt 3 \times y=(9)\times (16)\)
\(\tt 3y=144\)
Divide both sides by 3:-
\(\tt \cfrac{3y}{3}=\cfrac{144}{3}\)
Simplify:-
\(\tt y=48\)
_________________
Hope this helps!
Answer:y=48 I hope this is helpful good luck have a good day
Step-by-step explanation:
3/16 = 9/y
Determine the defined range
3/16=9/y y=0 cross out the equal sign y=0
Simplify the equation using cross-multiplication
3y=144
Divide both sides of the equation by 3
y=48
Check if the solution is in the defined range
How many fourths are in 3/4?
4/16
1/2
3
4
Answer:
3 because I just answered in the thing
The number of fourths in fraction 3/4 is 3.
The correct option is 3.
To determine how many fourths are in 3/4, we can divide 3/4 by 1/4, as dividing by a fraction is equivalent to multiplying by its reciprocal.
So, 3/4 divided by 1/4 can be written as (3/4) x (4/1):
(3/4) x (4/1)
= (3 x 4) / (4 x 1)
= 12/4
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 4:
12/4
= (12/4) / (4/4)
= 3/1
Therefore, there are 3-fourths (3/4) in 3/4. This means that 3/4 is equivalent to 3 times 1/4.
Out of the provided options, the correct answer is 3.
Hence, the number of fourths in 3/4 is 3.
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Find the area enclosed by the circle (x-2)^2 + y^2 = 4 and the line x = 3.
Step-by-step explanation:
(3-2)^2+y^2=4
(9-4)+y^2=2^2
the power of y and 2 should be cut now
5+y=2
5-2=y
3=y
y=3
:. the area of enclosed by a circle is 3 cm
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
Answer:
\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)
\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)
So the equation of the circle is
\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)
Sydney described a ruler as a length of plastic that starts at 0 and continues on to 12 inches. The geometric term that best describes Sydney's description is a
Answer:
Line segment because it is part of a line that has two endpoints which are the 0 inch mark and the 12 inches mark.
What is the square number of 13?
Answer: If you wanted to know what 13x13, or the square of something is, then the value is 169. Or if you wanted to know the square root of 13, it would be about 3.606.
Step-by-step explanation: A square number is any number multiplied by itself = that number. For example, 12x12 = 144, which means the square root of 144 is 12, and the square number of 12 is 144.
One angle of a parallelogram measures 45°. What are the measures of the other three angles
in the parallelogram?
Answer: 135, 45, and 135 are the three other angles
==================================================
Explanation:
For a parallelogram, we'll have opposite angles with the same measure. So if one angle is 45 degrees, then the opposite angle is also 45 degrees. The other two angles are 180-45 = 135 degrees each. Adjacent angles in a parallelogram add to 180 degrees.
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an rock is thrown upward from a platform that is 154 feet above ground at 35 feet per second. use the projectile formula h = − 16 t 2 v 0 t h 0 to determine when the rock hit the ground.
The rock hits the ground approximately 4.215 seconds after it was thrown upward from the platform.
To determine when the rock hits the ground, we can use the projectile formula for height,
which is given as h = -16t^2 + v0t + h0,
where h represents the height,
t represents time,
v0 is the initial velocity,
and h0 is the initial height.
In this case, the rock is thrown upward from a platform 154 feet above the ground, so h0 = 154.
The initial velocity is given as 35 feet per second, so v0 = 35.
We need to find the value of t when the height h becomes 0.
Setting h = 0 in the projectile formula, we get:
0 = -16t^2 + 35t + 154
This is a quadratic equation that can be solved using various methods such as factoring, completing the square, or using the quadratic formula.
Solving this equation, we find two values of t:
t = 4.215 and t = -2.94.
Since time cannot be negative in this context, we discard the negative value.
Therefore, the rock hits the ground approximately 4.215 seconds after it was thrown upward from the platform.
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find minimum number of coins that make a given value
The given coins [1, 2, 5] and the value 11, the minimum number of coins needed is 2.
Here are the steps to find the minimum number of coins:
1. First, we create an array of size equal to the given value, initialized with a very large number. This array will store the minimum number of coins needed to make each value from 0 to the given value.
2. We set the first element of the array to 0, as it doesn't require any coins to make a value of 0.
3. Next, we iterate through all the coins available and for each coin, we iterate through all the values from the coin value to the given value.
4. For each value, we calculate the minimum number of coins needed by taking the minimum of the current minimum and the value obtained by subtracting the coin value from the current value and adding 1 to it.
5. Finally, we return the value stored in the last element of the array, which represents the minimum number of coins needed to make the given value.
Let's consider an example to better understand the process:
Given coins: [1, 2, 5]
Given value: 11
1. Initialize the array with [INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF] (INF represents infinity).
2. Set the first element of the array to 0, so it becomes [0, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF].
3. For the first coin (1), iterate through the array from index 1 to 11.
- For index 1, the minimum number of coins needed is 0 + 1 = 1.
- For index 2, the minimum number of coins needed is 0 + 1 = 1.
- For index 3, the minimum number of coins needed is 0 + 1 = 1.
- ...
- For index 11, the minimum number of coins needed is 0 + 1 = 1.
The array becomes [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
4. For the second coin (2), iterate through the array from index 2 to 11.
- For index 2, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
- For index 3, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
- For index 4, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).
- ...
- For index 11, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).
The array becomes [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2].
5. For the third coin (5), iterate through the array from index 5 to 11.
- For index 5, the minimum number of coins needed is 2 (minimum of 2 and 0 + 1 = 1).
- For index 6, the minimum number of coins needed is 2 (minimum of 2 and 1 + 1 = 2).
- ...
- For index 11, the minimum number of coins needed is 2 (minimum of 2 and 2 + 1 = 3).
The array becomes [0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2].
6. The minimum number of coins needed to make the given value (11) is 2.
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estoy conduciendo pro la carretera durante un viaje a través del país, avanzas a una velocidad constante de 60 millas por hora ¿cuál es la pendiente de la recta que representa esta relación?
\(60\)
Answer:
Tu intiendo engles? Me inteindo poquito espanol but me no inteindo mas/
Frank typed four pages in 24 minutes. Rosetta typed six pages in 30 minutes. Who typed more pages per minute? Show your work.
Answer:
type is takes 80 minutes to type 24 pages in how long will he take to type 87 feet pages? Look into the solution. 24 pages are done in 80 minutes will write it down. Then 87 pages are is equals to X. So X is equals to 87 in 280 divided by 24. Then the answer will be to 290 minutes. In 290 minutes A type is will complete 87 pages.
Solution:
For typing 24 pages, time is required = 80 minutes
For typing 1 page, time is required = \frac{80}{24}\min utes
And for typing 87 pages , time is required
=\frac{80\times87}{24}=290\min utes