The values of a,b,c,d for \(2x^3-6x^2-36x=2x(ax+b)(cx+d)\) are given by 1, -6, 1, 3 respectively.
Given the equation is,
\(2x^3-6x^2-36x=2x(ax+b)(cx+d)\)
factorizing the left hand expression we get,
\(2x^3-6x^2-36x\\=2x(x^2-3x-18)\\=2x(x^2-6x+3x-18)\\=2x[x(x-6)+3(x-6)]\\=2x(x+3)(x-6)\)
So, 2x(x-6)(x+3) = 2x(ax+b)(cx+d)
So, a=1, c=1, b= - 6, d=3
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(a) how many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (note: 062 is not a legit three-digit number)
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. Thus, 6 x 5 x 4 = 120, and 120 x 6 = 720.
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. This is because you can have 6 different choices for the first digit, 5 choices for the second digit, and 4 choices for the third digit. This means that for each of the 6 choices for the first digit, you can have 5 choices for the second digit, and for each of those 5 choices, you can have 4 choices for the third digit. This results in 6 x 5 x 4 = 120 possible combinations for each of the 6 choices for the first digit. Since there are 6 choices for the first digit, 120 x 6 = 720 possible three-digit numbers in total.
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what is .072 divided by 345.00 rounded to the nearest tenth?
Answer:
.072 / 345.00 = 0.0002086956
the tenth place is the first digit to the right of the decimal point so it would round to 0.0
Round to the nearest tenth of the number is 0.
We need to round it to the nearest tenth.
Write the above expression in fractional form.
{0.072}{345} = 0.00028
the Round to the nearest tenth of the number is 0.
HOPE THIS HELP
PLEASE HELP AND EXPLAIN! :)
WORTH 48 POINTS!
Is (2, 6) a solution to this system of equations?
y = x + 4
y = 9x + 10
Answer:
x=-1/5
y=41/5
I am not able to explain to you how I achieved these results, but at least you can try and see if you can solve the equation.
Answer:
No, (2,6) is not a solution to this system of equations.
Explanation:
Okay so lets restate the question:
Is (2, 6) a solution to this system of equations?
y = x + 4
y = 9x + 10
First, you find the x and y intercepts from the equations stated above.
y=x+4
x intercept(s): (-4,0)
y intercept(s): (0,4)
So for the first equation, (2,6) is not a solution.
Now, we find the x and y intercepts for the second equation.
y=9x+10
x intercept(s): (-10/9,0)
y intercept(s): (0,10)
So for the second equation, (2,6) is not a solution.
Both equations do not have (2,6) involved.
And its 24 points not 48 :((((
john went from weighing 140 pounds to 155 pounds. what is the percent of change and is it an increase or decrease?
Weight of the John increased by 10.71 percent as he is weighing 140 pounds to 155 pounds.
As given in the question,
Original weight of John is equal to 140 pounds
John's changed weight is equal to 155 pounds
155 is greater than 140 pounds
Increase in John's weight.
Change in weight = Increased weight - actual weight
Percent of change in John's increased weight
= [ | change in weight| / Actual weight ] × 100
= [(155 - 140 ) / 140] × 100
= (15 / 140)× 100
= 10.71%
Therefore, the percent of change in John's weight is increased by 10.71%.
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Factor to write an equivalent expression
36a - 16
Answer:
4(9a-4)
Step-by-step explanation:
36a - 16
We can factor 4 from each expression.
4*9a - 4*4
4(9a-4)
what is the term for the value that occurs most often in a series of numbers?
The term for the value that occurs most often in a series of numbers is called the mode.
The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.
To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.
The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.
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What is the tangent ratio of angle xº?
Answer:
option number 2
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Here's the Solution :
Using Trigonometry,
\( \tan(x) = \dfrac{6}{8} \)A school club sold 300 shirts. 31% were sold to fifth-graders, 52% were sold to sixth graders, and the rest were sold to teachers. How many shirts were sold to each group -- fifth graders, sixth graders, and teachers? Explain or show your reasoning.
Answer:
Fifth graders= 93 shirts
Sixth graders= 156 shirts
Teachers= 51 shirts
Step-by-step explanation:
31% of 300 is 93
52% of 300 is 156
The total number of shirts sold to fifth graders and sixth graders is:
156+93= 249
The number of shirts sold to teachers is:
300-249= 51
Can someone help me with this please?
Answer:
16.49
Step-by-step explanation:
21^2 - 13^2 = 272
square root 272 = 16.49
3(y - 10) + 1 = x(y - 8)
pls help asap
Answer:
x=3y-29/y-8
Step-by-step explanation:
3(y-10)+1=x(y-8)
xy-8x=3y-29
x(y-8)=3y-29
/y-8 /y-8
x=3y-29/y-8
HELP ME PLEASEEE!!!!
don’t use for points or i’ll report and get ur info.
Find the measure for the unknown angle.
Answer:
49°
Step-by-step explanation:
Right angled triangle:
This is a type of triangle with one of the angle as 90°
Sum of angles in a Right angled triangle is 90°
Therefore,
y + 41° = 90°
collecting like terms
y = 90 - 41 = 49°
Therefore,
y = 49°
Find the area of the composite figure to the nearest hundredth.
55 mm
32. 5 mm
12. 5 mm
12. 5 mm
The area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.
To find the area of the composite figure, we need to divide it into simpler shapes and then find their areas separately. The composite figure is made up of a rectangle and two semicircles.
First, let's find the area of the rectangle. The length of the rectangle is 55 mm and the width is 32.5 mm, so the area of the rectangle is:
\($$A_{rect} = length \times width = 55 \text{ mm} \times 32.5 \text{ mm} = 1787.5 \text{ mm}^2$$\)
Next, let's find the area of each semicircle. The diameter of each semicircle is equal to the width of the rectangle, which is 32.5 mm. Therefore, the radius of each semicircle is:
\($$r =\) \(\frac{32.5 \text{ mm}}{2} = 16.25 \text{ mm}$$\)
The formula for the area of a semicircle is:
\($$A_{semicircle} = \frac{1}{2} \pi r^2$$\)
So, the area of each semicircle is:
\($$A_{semicircle} = \frac{1}{2} \pi (16.25 \text{ mm})^2 \approx 329.97 \text{ mm}^2$$\)
To find the total area of the composite figure, we add the area of the rectangle to the area of the two semicircles.
\($$A_{total} = A_{rect} + 2 \times A_{semicircle} \approx 2447.43 \text{ mm}^2$$\)
Therefore, the area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.
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7. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function shown in the graph.
A. y = 5/4x - 2
B. y = -4/5x + 2
C. y = 4/5x + 2
D. y = –5x – 2
Answer:
B. y=-4/5x+2\(\frac \frac\)
-2-2/5-0=-4/5 slope
2 is y-intercept
Step-by-step explanation:
Answer:
B. y = -4/5x + 2
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
4
5
y-intercept:
(
0
,
2
)
x
y
0
2
5
2
0
if (5,y) is a solytion tobthe equation y = 2x - 11, what is the value of y?
the value of y is -1
suppose that from a standard deck, you draw three cards without replacement. what is the expected number of face cards (not including aces) that you will draw?
To solve this problem, we first need to determine the probability of drawing a face card (not including aces) on the first draw. There are 12 face cards in a standard deck, and 32 non-face, non-ace cards. So the probability of drawing a face card on the first draw is 12/44.
Next, we need to determine the probability of drawing a face card on the second draw, given that we did not draw a face card on the first draw. There are now 11 face cards left in the deck, and 43 cards total (since we removed one card on the first draw). So the probability of drawing a face card on the second draw, given that we did not draw a face card on the first draw, is 11/43.
Finally, we need to determine the probability of drawing a face card on the third draw, given that we did not draw a face card on the first or second draw. There are now 10 face cards left in the deck, and 42 cards total (since we removed two cards on the first and second draws). So the probability of drawing a face card on the third draw, given that we did not draw a face card on the first or second draw, is 10/42.
To find the expected number of face cards (not including aces) that we will draw, we need to multiply the probabilities of each draw and sum the results. So:
Expected number of face cards = (12/44) * (11/43) * (10/42) * 3
Expected number of face cards = 0.038
Therefore, the expected number of face cards (not including aces) that you will draw when drawing three cards without replacement from a standard deck is approximately 0.038.
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What is the inverse of the function
f
(
x
)
=
−
1
2
(
x
+
3
)
f(x)=−
2
1
(x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis?
The inverse function of the function f(x) = 12(x+3) is f(x) = -2x - 3
A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.
The function given is:
To find the inverse, we must perform the following procedures.
y takes the place of f(x);
y = -(x+3)/2
Change the x and y variables.
x = -(y+3)/2
Calculate y
2x = - (y + 3)
2x = -y - 3
y = -2x - 3
We get the following in inverted notation:
f(x)⁻¹ = -2x - 3
Thus the obtained inverse function is f(X) = -2x - 3
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You currently owe $12,500 on your VISA credit card. With an APR of 28%, how long will it take for you to pay off the balance if your monthly payment is $860 ? 31.48 years no solution 18 months 31.48 months
To calculate the time it will take approximately 31.48 to pay off the balance on your VISA credit card, we can use the formula for the number of periods (months) required to repay a loan with a fixed monthly payment. The correct answer is 31.48 months.
The formula is:
n = -(1/30) * log(1 - ((r * P) / A))
First, let's calculate the monthly interest rate (r):
r = 0.0233333
n = -(1/30) * log(1 - ((0.0233333 * 12500) / 860))
Therefore, it will take approximately 31.48 months to pay off the balance on your VISA credit card with a monthly payment of $860.
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suppose nine pairs of similar-looking boots are thrown together in a pile. what is the minimum number of individual boots that you must pick to be sure of getting a matched pair? why? since there are 9 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . it follows that if a minimum of boots are chosen, at least two must be from the same pair.
the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.
Since there are 9 pairs of boots in the pile, we can determine that each pair has two boots. If at most one boot is chosen from each pair, the maximum number of boots chosen would be 18.
To guarantee that a matched pair of boots is chosen, we must pick at least two boots from the pile, one from each boot of the same pair. Therefore, the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.
Number of pairs of boots in the pile = 9
Number of boots in each pair = 2
Maximum number of boots that can be chosen = 9 x 2 = 18
Minimum number of boots required to guarantee a matched pair = 2
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What is the general solution to the the differential equation 3y′′−y′−2y=0 ?
Therefore, the general solution to the given differential equation is: \(y(t) = c1e^{(-2t/3)} + c2e^t\) where c1 and c2 are arbitrary constants.
To find the general solution to the given differential equation, we can solve the associated characteristic equation. The characteristic equation for the given differential equation is:
\(3r^2 - r - 2 = 0\)
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the equation, we have:
(3r + 2)(r - 1) = 0
Setting each factor equal to zero, we get:
3r + 2 = 0 --> r = -2/3
r - 1 = 0 --> r = 1
The roots of the characteristic equation are r = -2/3 and r = 1.
\(y(t) = c1e^{(-2t/3)} + c2e^t\)
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a sample of 158 college students asked them if they liked statistics. 93% said yes. calculate a 89% confidence interval for the true population proportion of those who like statistics
We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.
For P, what is the confidence interval at 95 percent?
Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.
What is the 95 percent confidence interval for the population's proportion of smokers?
Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.
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suppose the probability that maya is home is 1/3 and the probability that jim is home is 1/4. but the probability that jim is home given that maya is home is 1/2. what's the probability that they're both home?
The probability that they're both home is 1/12.
In the given question,
Probability of Maya at home P(A) = 1/3
And probability of Jim at home P(B) = 1/4
The probability that Jim is home given that maya is home P(A∪B) = 1/2
We have to find the probability when they both are at home P(A ∩ B).
As we can see that the probability of both the events are independent
So, we can use
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Therefore,
1/2 = 1/3 +1/4 – P(A ∩ B)
P(A ∩ B) = 7/12 – 1/2
P(A ∩ B) = 1/12
Hence, the probability that they're both home is 1/12.
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the base of a triangle is eight less than twice it’s height, if the area of the triangle is 5cm^2 find the length of the base
Answer:
the height = 5cm
the base = 2cm
Step-by-step explanation:
.If Julie’s average art test scores are 85, what would you
predict her average math test scores to be?
Do you think your prediction is going to be accurate given
this data? Explain your answer
Answer:
no the 85 will not be accurate percentage for math test because you don't have any previous math test scores to even get a average grade.
An adult takes 400mg of vitamin c.
Each hour, the amount of vitamin c in
the person's system decreases by about
29%. How much vitamin c is left after 6
hours?
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Answered A right cylinder has a radius of 2 units and a height of 5 units. What is the volume of the cylinder? Round to the nearest tenth. 31.4 cubic units. 62.8 cubic units 157.1 cubic units 314.2 cubic units.
Answer:I believe the answer is b (62.8 cubic units)
Step-by-step explanation:
Answer:
62.8
Step-by-step explanation:
What is the answer for this
Answer: 4units^2
Step-by-step explanation:
B*H/2
4*2/2= 4
So 4units^2 is the area
Answer:
4 unit²
Step-by-step explanation:
Here,
base = 2
height = 4
Area of the triangle = 1/2 x base x height
= 1/2 x 2 x 4
= 4 unit²
The formula to find the volume of a sphere is V=3.14r^3 where r is the
radius of the sphere. What is the formula in terms of r?
PLEASE HELP!
divide by 3.14 on both sides first.
V/3.14 = r^3
Now cube root both sides.
3√(V/3.14) = r
r = 3√(V/3.14)
r is the cube root of v/3.14.
ow many incongruent primitive roots does 13 have? find a set of this many incongruent primitive roots modulo 13.
There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.
There are 12 elements of the group \(U_{13}\) , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are \(\phi (\phi (n))\) of them. So we must compute \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\) . There are 4 incongruent primitive roots.
To find them, take the powers each element in turn:
1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1 (2 has order 12, it is a primitive root)
Of course, the higher powers of 2 cannot be.
Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.
For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.
Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.
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When Iris subtracted-16-(-16), she got a difference of 32. Is her answer
correct? If not, what mistake did she make? Explain
Answer:
Hope this helps
Step-by-step explanation:
-16 - (-16) cab also be written as -16 + 16 which is 0. Iris was not correct because she didn't realize that the first 16 was negative.