Answers
Answer: fourth choice 6, - 3+3√3 i, and -3 - 3√3 i
Solution:
1) Factor x^3 - 216 as a difference of cubes:
(x)^3 - (6)^3 = (x - 6) (x^2 + 6x + 6^2) = (x - 6) (x^2 + 6x + 36) = 0
3) first factor = 0 => x - 6 = 0 => x = 6
4) second factor = 0 => x^2 + 6x + 36 = 0
Using the quadratic formula:
x = [ - 6 +/- √(6^2 - 4*1*36) ] / (2)
=> x = [ - 6 +/- √ (-108) ] / 2 = -3 +/- 3√3 i
=> x = - 3 + 3√3 and x = - 3 - 3√3 i
Answer: 3, - 3+3√3 i, and -3 - 3√3 i
2) Which is equivalent to (2p^2 + 5pq - q^2) + (p^2 + 3pq - 2q^2) ?
Answer: first option 3p^2 + 8pq - 3q^2
Solution:
1) eliminate parenthesis:
2p^2 + 5pq - q^2 + p^2 + 3pq - 2q^2
2) combine like terms:
2p^2 + p^2 = 3p^2
5pq + 3pq = 8pq
-q^2 - 2q^2 = - 3q^2
3) The result is 3p^2 + 8pq - 3q^2, which is the first option.
Related Questions
Factor ab + bc + b2 + ac.
Answers
(b² + bc)+(ab + ac) =
b(b+ c)+a(b + с) =
(b + c)(b + a)
{So we can get the terms with the same variables together}
Factoring out the GCF from each term:
b(a + b) + c(a + b).
Then, factoring out a + b yields:
(a + b)(b + c).
I hope this helps!
in the diagram, the areas of ADC and DCB are in a ratio of 3:4. what are the coordinates of point C
Answers
the complete question in the attached figure
we know that
dAB=dAC+dCB
dAC=√((8-1)²+(-2+9)²)=√98
Area triangle ADC=dAC*CD/2
Area triangle DCB=dCB*CD/2
Area triangle ADC/Area triangle DCB=3/4
[dAC*CD/2]/[dCB*CD/2]=3/4
dAC=(3/4)*dCB-----------------------> equation (1)
dAB=dAC+dCB=√98
dAC=√98-dCB------------------------ > equation (2)
(1)=(2)
(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98
dCB=(4/7)√98
dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98
dAC=(3/7) )√98
find the slope point A (1.-9) and point B (8,-2)
m=(-2+9)/(8-1)=7/7=1-------------- > 45°
dAC=(3/7)√98
the component x of dAC is
dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3
the component y of dAC is
dACy=dACx=3
the coordinates of the point C are
point A(1.-9)
Cx=Ax+dACx----------> 1+3=4
Cy=Ay+dACy----------> -9+3=-6
the coordinates C(4,-6)
the answer is C(4,-6)
Answer:
C(4,-6) is correct on plato
Step-by-step explanation:
Anybody have the proper answer to this
Answers
A = π * 5.5 * 5.5
A = 30.25 π
3025 / 100 π mm^2
.. r = d/2
.. r = (11 mm)/2 = (11/2) mm
The area is given by
.. A = π*r^2
.. = π(11/2 mm)^2
.. A = (121/4)π mm^2
The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.
Answers
the std deviation of the sample will be:
σ/√n
plugging the values we obtain:
15/√36
=15/6
=2.5
hence the z-score when x=264 will be:
z=(264-264)/2.5
z=0
thus:
P(x<264)=P(z<0)=0.5
the z-score when x=266 will be:
z=(266-264)/2.5
z=0.8
hence
P(x<266)=P(z<0.8)=0.7881
thus
P(264<x<266)=P(0.5<z<0.7881)
=0.7881-0.5
=0.2881
Answer: 0.2881
The probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is 0.2881. The percentage is 28.81%.
The correct probability that the mean pregnancy length of 36 randomly selected women falls between 264 days and 266 days is given by the cumulative distribution function (CDF) of the normal distribution with a mean of 264 days, a standard deviation of 15 days, and a sample size of 36.
To find this probability, we first need to determine the standard error of the mean (SEM), which is calculated by dividing the standard deviation by the square root of the sample size:
[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{36}} = \frac{15}{6} = 2.5 \][/tex]
To find the z-scores corresponding to the mean pregnancy lengths of 264 days and 266 days. The z-score for a value x is calculated by:
[tex]\[ z = \frac{x - \mu}{SEM} \][/tex]
For 264 days:
[tex]\[ z_{264} = \frac{264 - 264}{2.5} = 0 \][/tex]
For 266 days:
[tex]\[ z_{266} = \frac{266 - 264}{2.5} = \frac{2}{2.5} = 0.8 \][/tex]
Now, we look up these z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities.
The probability of a z-score less than 0 is 0.5, and the probability of a z-score less than 0.8 is approximately 0.7881.
The probability that the mean pregnancy length is between 264 days and 266 days is the difference between these two probabilities:
[tex]\[ P(264 < \bar{x} < 266) = P(z < 0.8) - P(z < 0) \] \[ P(264 < \bar{x} < 266) = 0.7881 - 0.5 \] \[ P(264 < \bar{x} < 266) = 0.2881 \][/tex]
Therefore, the probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is approximately 0.2881.
To express this as a percentage, we multiply by 100:
[tex]\[ 0.2881 \times 100 \approx 28.81\% \][/tex]
The answer is: 28.81%.
Can someone help me?
Answers
There are 4+3+2 = 9 people who scored exactly 85 points (look at column 2)
So there are 4+9 = 13 people who are from brazil or scored exactly 85 points. Subtract out those who fit both criteria. So we'll subtract off 3 people
13-3 = 10
There are 10 people who fit the criteria out of 19 total. The 19 is from adding up all the values in the table.
Divide the two values to get 10/19
Answer: 10/19
How do you write
2/4
as a percentage?
Answers
Solve the system of equations. 2.5y + 3x = 27 5x – 2.5y = 5 What equation is the result of adding the two equations? –8x = 328x = 325y + 8x = 328x – 5y = 32 What is the solution to the system? (–4, 6)(–2.75, 8.6)(2.75, 3.5)(4, 6)
Answers
.. (2.5y +3x) +(5x -2.5y) = (27) +(5)
.. 8x = 32 . . . . . . . . . . . . . . . . . . . . . . . your 2nd selection
b) The solution to the system is (4, 6), your 4th selection.
.. This is the only choice with x=4, the solution to part (a).
Answer:
8x=32
(4,6)
Step-by-step explanation:
The heights (in inches) of 13 plants are 6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, and 17. What is the interquartile range of this data set? A) 3.5 B) 6 C) 10.5 D) 11
Answers
6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, 17.
The first step is to find Median in order to divide the above series into lower and upper quartiles.
To find the median, just cross out the first and the last value until you left with the single value, as the number of elements is odd.
Like first 6 would cancel the last 17,
second number 9 would cancel the second last number 16,
and so on.
By doing above exercise, we are left with 11.
So the median = 11.
Now any number below the median 11 would be in lower quartile series, while other half would be in upper one.
To find the lower quartile, find the median of 6, 9, 10, 10, 10, 11:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:
The two elements are: 10, 10.
Take average = (10 + 10) / 2 = 10
So lower quartile = 10
To find the upper quartile, find the median of 12, 12, 13, 14, 16, 17:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:
The two elements are: 13, 14.
Take average = (13 + 14) / 2 = 13.5
So Upper quartile = 13.5
The interquartile range = Upper Quartile - Lower Quartile = 13.5 - 10.0 = 3.5
So the correct option is (A) 3.5
-i
Let's first find the second quartile. This is also known as the Median. It is the middle value in your list of numbers. The middle number in your data is 11.
6, 9, 10, 10, 10, 11, (11 = Median), 12, 12, 13, 14, 16, 17
There are six numbers to the left of the middle number and six to the right. We have divided the data into two groups.
The first quartile is the middle number of the first group. Since there are 6 numbers there technically isn't a middle number, so we take the average of the two numbers closest to the middle. These are in parenthesis below:
6, 9, (10), (10), 11
Since the two number are the same (10) their average is also 10. The first quartile (denoted q1 = 10).
Now let's look at the numbers to the right of the median. Again there are 6 numbers here so none is technically in the middle but I have put in parenthesis the two closest to the middle.
12, 12, (13), (14), 16, 17.
The third quartile q3 is the average of 13 & 14. This is found by adding 13 + 14 and dividing the sum by 2. The third quartile is 13.5
Going back to our original list of data we have now split the data into four groups of 3 numbers each as follows:
6, 9, 10, (q1= 10), 10, 10, 11, (Median = 11), 12, 12, 13, (q3=13.5), 14, 16, 17
The interquartile range is the third quartile minus the first quartile. Here it is 13.5 - 10 = 3.5. It gives the range (the distance) between the first and third quartiles.
helppppppppppppppppppppppppppppppppppppp
Answers
The expression x²-14x+31=63 is a quadratic equation. To solve it, you must order it:
x²-14x+31-63=0
x²-14x-32=0
Then, you must apply the quadratic formula, which is shown below:
x=(-b±√(b^2-4ac))/2a
So you have the values of a,b and c:
:
a=1
b=-14
c=-32
When you substitute those values in the quadratic formula, you obtain:
x=(-(-14)±√((-14)^2-4(1)(-32))/2(1)
x1=-2
x2=16
So, the correct option is the third one: x=-2 or x=16
What is the area of this trapezoid? 44 in² 64 in² 168 in² 192 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 2 inches, F E is 14 inches, E C is 2 inches, A B is 14 inches., and E B is 12 inches.
Answers
we know that
[the area of the trapezoid]=[area rectangle]+2*[area triangle]
[the area of the trapezoid]=[14*12]+2*[12*2/2]=192 in²
the answer is 192 in²
Answer:
the answer is 192in
Step-by-step explanation:
Michaela uses measuring tape to measure a piece of paper. The measuring tape has an accuracy to the nearest centimeter. She uses her measurements to calculate the area of the piece of paper. Which of the answer choices show the degree of precision she can use to report the area?
Answers
You asked your classmates to name their favorite type of music. You found that 12 students like rock, 8 like rap, 6 like R&B, and 4 like jazz. Suppose you made a pie chart to display the data. How many degrees of the circle should represent rock music?
Answers
12+8+6+4=30
then we should divide the number 30 by 360(because the pie chart is 360 degrees):
[tex]360 \div 30 = 12[/tex]
now we should multiply 12(the number of students who likes rock) by 12
[tex]12 \times 12 = 144[/tex]
the answer is 144 degrees
What is the sum of 36 ounces and 4 pounds? 6 lb. 6 lb., 4 oz. 96 oz. 98 oz.
Answers
Answer:
6 lb 4 oz
Step-by-step explanation:
Since, 1 lb = 16 oz,
Here, the given phrase,
The sum of 36 ounces and 4 pounds,
[tex]= 36\text{ oz}+4\text{ lb}[/tex]
[tex]=36\text{ oz}+64\text{ lb}[/tex]
[tex]=100\text{ oz}[/tex]
Again,
1 oz = 1/16 lb,
[tex]100\text{ oz}=\frac{100}{16}=6.25\text{ lb} = 6\text{ lb}+0.25\text{ lb}=6\text{ lb }4\text{ oz}[/tex]
Hence, The sum of 36 ounces and 4 pounds is 6 lb 4 oz
Second option is correct.
The temperature of a liquid during an experiment can be modeled by the function f(x)=3.8cos(πx20)+2.2 , where f(x) is the temperature in °C and x is the number of minutes into the experiment.
What is the lowest temperature the liquid reached during the experiment?
Answers
the function is f(x)=3.8cos(πx20)+2.2
using a graph tool
see the attached figure
the answer is
the lowest temperature the liquid reached during the experiment is -1.6 °C
What is the point called where the perpendicular bisectors of the sides of a triangle intersect
Answers
This is the center of the circle that goes through the three vertices of the triangle. This circle is known as the circumcircle. It is the smallest circle possible in which the circle encompasses the triangle and none of the triangle spills outside the circle.
Which statement best describes the polynomial 2x + 8?
A. first degree polynomial with two terms
B. first degree polynomial with eight terms
C. second degree monomial
D. second degree binomial
Answers
Selection A is appropriate.
What is the perimeter of this equilateral triangle?
Equilateral triangle with one side labeled 13 meters.
Answers
The graph of y=|x|y=∣x∣y, equals, vertical bar, x, vertical bar is reflected across the xxx-axis and then scaled vertically by a factor of \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. What is the equation of the new graph?
Answers
Justification:
The statement is confusing, so I will re-write it to avoid confusions:
"The graph of y=|x| is reflected across the x-axis and then scaled vertically by a factor of 1/4. What is the equation of the new graph? "
Answer
Solution:
1) Reflection acros the x-axis means (a,b) transforms into (a, -b). That is for the given x the reflected function will return the negative of the original value, that is:
y = - |x|
2) Scaling by a factor of 1/4 means that the new function is multiplied by 1/4
=> y = - (1/4) |x| which is the answer
Trapezoid RSTV∼trapezoid WXYZ .
What is the scale factor of a dilation from RSTV to WXYZ ?
a. 14/25
b. 4/5
c. 7/8
d. 7/10
Answers
Answer:
Correct option is D
Scale factor of dilation is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
Given the two similar figures
Trapezoid RSTV∼trapezoid WXYZ
We have to scale factor of dilation from RSTV to WXYZ.
As the two trapezoid are similar therefore their ratio of corresponding sides gives the scale factor of dilation.
Hence, [tex]\text{scale factor of dilation is=}\frac{WX}{RS}=\frac{WZ}{RV}[/tex]
i.e [tex]\frac{28}{40}=\frac{35}{50}=\frac{7}{10}[/tex]
Hence, scale factor of dilation is [tex]\frac{7}{10}[/tex]
Jermaine did this work to solve an equation. Did he make an error?
Answers
The solution for the below equation is required:
4x + 6 - x = 2x + 3
The work done by the Jermaine is presented below :
4x + 6 - x = 2x + 3
5x + 6 = 2x + 3
Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.
So, the correct option is
Jermaine did make an error. He should have combined 4x and -1x to make 3x
3x + 6 = 2x + 3
Hope it helps..!!
Answer:
Step-by-step explanation:
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th
helpppppppppppppppppp
Answers
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
the trig unit circle
[tex]tan \frac{3π}{4} [/tex] = [tex] - tan \frac{π}{4} [/tex]
= -1
Remember,
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
= 1 ÷ -1
= -1
Then, when you substitute the values, you obtain:
Cot(3π/4)=-(√2/2)/(√2/2)
When you simplify the expression, you have the following result:
Cot(3π/4)=-1
What is the exact value of Cot(3π/4)?
The answer is: The exact value of Cot(3π/4) is -1
13) Suppose a coffee cup has a diameter of 8 cm and a height of 9 cm. What is the volume of the cup? (to nearest whole number)
Answers
Radius is 4 cm (half of diameter)
Height = 9 cm
Volume of cylinder = pi x r^2 x h
The answer is 452.16 or can be rounded to 452 cubic cm
Answer:
[tex]452\ cm^{3}[/tex]
Step-by-step explanation:
we know that
the volume of a cylinder (coffe cup) is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=8/2=4\ cm[/tex] -----> the radius is half the diameter
[tex]h=9\ cm[/tex]
substitute
[tex]V=\pi (4^{2})(9)=452.4\ cm^{3}[/tex]
Round to the nearest whole number
[tex]452.4\ cm^{3}=452\ cm^{3}[/tex]
Solve the system of equations using the linear combination method. {5m+3n=41 {3m−6n=9 Enter your answers in the boxes. m = n =
Answers
5m+3n=41
3m-6n=9 (multiplying the first equation by 3 and the second by 5)
15m+9n=123
15m-30n= 45 (subtracting the two equations)
39n = 78
n = 2,
and for m, 3m = 9+6(2)
= 21
m = 7
Therefore, n=2 and m=7
Answer:
n=2 m=7
Step-by-step explanation:
The gum you like to is on sale. it is regularly priced at $1.59. Write and equation that will help determine how much you’ll save if you buy the pack today.
S=sale price
C=cost savings
Answers
Classify the number as natural, whole, integer, rational, and/or irrational. Select all terms that are correct. 7√
Answers
PLEASE HELP!!!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x^2 + 2x +2
Answers
We are given this equation
[tex] y=-2x^{2} +2x+2 [/tex]
The vertex form is given by:
[tex] y=a(x-h)^{2} +k [/tex]
Now let us try to convert our equation into vertex form:
[tex] y=-2x^{2} +2x+2 [/tex]
Vertex form is given by:
[tex] y=-2(x-0.5)^{2} +2.5 [/tex]
comparing our equation with vertex form ,
The vertex (h,k) is (0.5, 2.5)
Next we have to find y when x=6, plugging x as 6 in the given equation,
[tex] y=-2(6)^{2} +2(6)+2 [/tex]
y=-58
So at x=6, y=-58.
Find two positive real numbers who's product is a maximum and whose sum is 156.
Answers
The sum of two numbers is 156, so we can write:
x+ y = 156
or
y = 156 - x
The product of two numbers = xy
Using the value of y in previous equation we can write:
Product = x(156 - x) = - x² + 156x
The above equation is a quadratic equation and results in a parabola. The maximum value of parabola with negative coefficient of x² lies at its vertex.
The x component of vertex will be = [tex] \frac{-b}{2a} [/tex]
Here b is the coefficient of x term, and a is the coefficient of x² term.
So,
a = -1
b = 156
Using the values in the formula we get the x component of vertex x = [tex] \frac{-156}{-2}=78 [/tex]
So x = 78
and
y = 156 - x = 156 - 78 = 78
Thus, the two numbers whose sum is 156 and which result in maximum product are 78, 78
Final answer:
To maximize the product of two numbers with a fixed sum of 156, we set up an equation for the product, differentiate, and find that the maximum product is obtained when both numbers are 78.
Explanation:
To find two positive real numbers whose product is a maximum and whose sum is 156, we need to use the concept of optimization in calculus. This involves taking the derivative of the function representing the product of the two numbers and setting it equal to zero to find the critical points. Since the sum of the numbers is fixed at 156, we can express one number in terms of the other, for example, x and 156 - x. The product of these two numbers is x(156 - x). To find the maximum product, we differentiate this function with respect to x:
[tex]\frac{d}{dx} [x(156 - x)] = 156 - 2x[/tex]
Setting this derivative equal to zero gives us 156 - 2x = 0, solving for x we find-
x = 78.
This gives us the two numbers as 78 and 78, because the sum must be 156 and the other number would be 156 - 78. To confirm that this gives a maximum, we would test the second derivative or use the first derivative test. However, by symmetry, when the sum of two numbers is fixed, their product is maximized when the two numbers are equal. In this case, both numbers are 78.
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
4x + 5 = 37
4x + 5 (-5) = 37 (-5)
4x = 32
4x/4 = 32/4
x = 8
It will take Bob ~8 seconds to reach 37 feet*
*Problem & answer
hope this helps
What is the answer to this problem?
Answers
To start, an isosceles triangle is any triangle with two sides of the same length.
In this case, you are given two measurements: 20 and 30.
This means that the third side of the triangle can either be 20 or 30, since two of the sides must equal one another.
Because the question is asking for the greatest possible perimeter of the triangle, it would only make sense that the third side would have to be 30 units in length to make the greatest possible perimeter since it is the possible length that is greatest in value (20 < 30).
Therefore, knowing that the sides of the triangle are now 20, 30, and 30, add the lengths up to find the perimeter:
20+30+30
=80
Therefore, the largest possible value of the perimeter would be 80 units.
Hope this helps and I hope you have a marvelous day! :)
Suria has x apples and oranges.how many apples and oranges does suria have altogether? Give your answer in terms of x
Answers
Answer:
It is given that Suria has x apples and Oranges.
Which means ,total number of fruits which includes apple and Orange is equal to x.
Suppose, number of Oranges Suria has = A
And, Number of Apples Possessed by Suria= B
→Number of Oranges +Number of Apple=x
→ A + B =x
So,total number of apples and Oranges does Suria have altogether = x