As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.
In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.
The intersection of two sets contains only the elements that are present in both sets. In this case,
R ∩ S = {x | x > 0 and x < 3}
The integers that are present in this set are 1 and 2.
Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
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Work out the length of x in the triangle below
If your answer is is decimal, give it to 1 d.p.
Answer:
8 m
Step-by-step explanation:
You want the length x that gives a triangle area of 26 m² when the angle between side x and side 13 m is 30°.
AreaThe area formula is ...
A = 1/2ab·sin(C)
26 = 1/2(13)(x)·sin(30°) = 13/4x . . . . . use given values
x = (4/13)(26) = 8 . . . . . . divide by the coefficient of x
The length x in the triangle is 8 m.
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In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (b) What is the probability that a subject would guess more than 20 correct in a series of 36 trials?
The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001
How to find the pobability that a subject would guess more than 20 correct in a series of 36 trialsIn a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.
Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.
The probability of guessing more than 20 correct is:
P(X > 20) = 1 - P(X ≤ 20)
Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).
Therefore: P(X > 20) = 1 - 0.9999 = 0.0001
So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).
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Given a and ß are the roots of the quadratic equation x² + 5x + 8 = 0. Form the quadratic equation which has the roots a - 2 and ß - 2.
The quadratic equation with roots a - 2 and b - 2 is x² + 9x + 22 = 0
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 5x + 8 = 0
On simplifying , we get
From the given quadratic equation x² + 5x + 8 = 0, we can identify that a = 1, b = 5, and c = 8.
So, the sum of the roots a and ß is -b/a = -5/1 = -5, and the product of the roots is a x b = c/a = 8/1 = 8.
Now, we need to find the quadratic equation with roots a - 2 and ß - 2.
By using the sum and product of the roots, we can write:
Sum of roots = (a - 2) + (b - 2) = a + b - 4
Product of roots = (a - 2) x (b - 2) = ab - 2a - 2ß + 4
From the given quadratic equation x² + 5x + 8 = 0, we know that:
a + b = -5
ab = 8
Substituting these values in the above equations, we get:
Sum of roots = -5 - 4 = -9
Product of roots = 8 - 2a - 2b + 4 = 12 - 2(a + b) = 22
So , the quadratic equation is given as x² + 9x + 22 = 0
Hence , the equation is x² + 9x + 22 = 0
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A test was given to a group of students. The grades and gender are summarized below
A B C Total
Male 3 10 12 25
Female 14 2 13 29
Total 17 12 25 54
If one student is chosen at random from those who took the test,
Find the probability that the student got a 'A' GIVEN they are male.
The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.
To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:
P(A | Male) = P(Male | A) × P(A) / P(Male)
We can find the values of the terms in the formula using the information given in the table:
P(Male) = (25/54) = 0.46 (the proportion of all students who are male)
P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')
P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')
Therefore, plugging these values into the formula:
P(A | Male) = 0.18 × 0.31 / 0.46
P(A | Male) ≈ 0.12
So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.
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Enter the mean absolute deviation of the data.
45, 48, 50, 42, 40
The mean absolute deviation of the data is
The mean absolute deviation of the data: 45, 48, 50, 42, and 40 comes out to be 3.2
The mean of the number is defined as the average of the numbers that is the sum of the number to the total number of numbers
= 45 + 48 + 50 + 42 + 40 / 5
= 225 / 5
= 45
The mean absolute deviation is defined as the measure of how much the values in the data set are different from the mean of the data.
MAD = [tex]\frac{1}{n}[/tex] * ∑ | x - mean |
where n is the number of data
x is the individual data
MAD = 1/5 * (|45-45| + |48-45| + |50-45| + |42-45| + |40-45|)
= 0.2 * (0 + 3 + 5 + 3 + 5)
= 0.2 * 16
= 3.2
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This answer will be marked as BRAINLIESTTTTTT
Step-by-step explanation:
All of the sides are equal so find 'x'
6x -10 = 4x + 5
2x = 15
x = 7.5
as a check : the the sides are 6(7.5) - 10 = 35 cm
4 ( 7.5) + 5 = 35
10 ( 7.5 - 4 = 35 cm
three sides of 35 cm = 3 x 35 = 105 cm = 1.05 m
so YES the perimeter is greater than one meter
NO LINKS!! URGENT HELP PLEASE!!!
Please help me with #3
Answer:
1.a.SAS axiom
b. ASA axiom
Step-by-step explanation:
There are five basic conditions for triangles to be congruent:
SSS:For Question:
1.
a. InΔABC and ΔBCD
AB=CD opposite sides of the parallel line are equal Side
∡BAC=∡BDA Given Angle
BC=BC Same side Side
It fulfills the condition of the SAS axiom,
InΔABC ≅ ΔBCD by SAS axiom
b. InΔABC and ΔCDE
∡ACB=∡DCE Vertically opposite angle Angle
BC=CD given Side
∡ABC=∡CDE right angle Angle
It fulfills the condition of the ASA axiom,
InΔABC ≅ ΔCDE by ASA axiom It may be R.H.S. axiom too.
The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.If Event A = freshman or sophomore, what is Event A'?
Event A' = freshman or junior
Event A' = sophomore or senior
Event A' = junior or senior
Event A' = freshman or senior
The probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.
We have,
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The conditional probability is the happening of an event, when the probability of occurring of other event is given. The probability of event A, given that the event B is occurred.
Students of high school who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. In this,
74% likely to tryout for softball;
27% likely to tryout for volleyball;
42% likely to tryout for tennis;
88% likely to tryout for swimming.
Let the tryout for volleyball is event A and tryout for swimming is event B. Thus,
P(A)=0.27
P(B)=0.88
Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.
Thus, probability of the union of trying out for either volleyball or swimming
P(A or B)=P(A)+P(B)-P(A and B)
P(A or B)=0.27+0.88-P(A)*P(B)
P(A or B)=0.27+0.88-0.27×0.88
P(A or B)=0.9
Hence, the probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.
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complete question:
The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?
a. 1. 15
b. 0. 61
c. 0. 91
d. 0. 24
.l want the solution
The absolute value equation that has these minimum and maximum heights as its solutions is 9=|x−45|
We have,
"The min is simply the lowest observation, while the max is the highest observation. Obviously, it is easiest to determine the min and max if the data are ordered from lowest to highest."
First, find the difference of both solutions.
54 - 36 = 18
Than, divide it by 2
18/2 = 9
9 = | x − 54+9 |
Either way: 9 =|x−45|
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compplete question:
For the Pony Ride, the minimum height is 36 inches and the maximum height is 54 inches. Write and solve an absolute value equation that has these minimum and maximum heights as its solutions.
Find all zeros of the function
f
(
x
)
=
3
x^3
-
9
x^2
-
18
x
+
24
.
Enter the zeros as a list separated by commas.
The zeros of the function are x = -2, x = 2, x = 3.
How to solveThe zeros of the function f(x) = [tex]3x^3 - 9x^2 - 18x + 24 = 0[/tex] are obtained by setting the function equal to zero and solving for x:
[tex]3x^3 - 9x^2 - 18x + 24 = 0[/tex]
These factors as:
3(x - 2)(x + 2)(x - 3) = 0
Setting each factor equal to zero gives the solutions:
x - 2 = 0 → x = 2
x + 2 = 0 → x = -2
x - 3 = 0 → x = 3
So, the zeros of the function are x = -2, x = 2, x = 3.
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I will give the BRAINIEST!
function, g(x), can be represented with the following set of ordered pairs:
{(-9, -14), (18, 40), (3, 10), (-15, -26)}
Which set of ordered pairs represents g¹ (x)?
A
B
C
D
{(2, 3), (4,4), (-2, 1), (−12, −4)}
{(2, -1), (14, 5), (18, 7), (25,5)}
{(12, 18), (2, 8), (16, 22), (6, 12)}
{(-2, 2), (6,2), (4,2), (-8, 2)}
Answer:
The set of ordered pairs that represents g¹(x) can be found by reversing the order of each pair in the original function g(x) and then solving for x. Therefore, g¹(x) would be:
{(-14, -9), (40, 18), (10, 3), (-26, -15)} with the x-coordinates being -9, 18, 3, and -15 respectively.
Step-by-step explanation:
Solve for area and perimeter in each of the following problems.
The perimeters and areas of the rectangles are listed below:
Case 1: p = 54 yd, A = 170 yd²
Case 2: p = 46 m, A = 120 m²
Case 3: p = 44 mm, A = 72 mm²
Case 4: p = 60 in, A = 209 in²
Cases 5 / 6: p = 32 mi, A = 55 mi
Case 7: p = 66 m, A = 242 m²
Case 8: p = 94 yd, A = 550 yd²
Case 9: p = 72 km, A = 320 km²
How to determine the perimeter and the area of a rectangle
In this problem we must determine the perimeter and the area of eight rectangles, whose formulae are introduced below:
Perimeter
p = 2 · (w + h)
Area
A = w · h
Where:
w - Widthh - HeightNow we determine the perimeter and the area for each case:
Case 1
p = 2 · (17 yd + 10 yd)
p = 54 yd
A = (17 yd) · (10 yd)
A = 170 yd²
Case 2
p = 2 · (15 m + 8 m)
p = 46 m
A = (15 m) · (8 m)
A = 120 m²
Case 3
p = 2 · (18 mm + 4 mm)
p = 44 mm
A = (18 mm) · (4 mm)
A = 72 mm²
Case 4
p = 2 · (11 in + 19 in)
p = 60 in
A = (11 in) · (19 in)
A = 209 in²
Cases 5 and 6
p = 2 · (5 mi + 11 mi)
p = 32 mi
A = (5 mi) · (11 mi)
A = 55 mi
Case 7
p = 2 · (22 m + 11 m)
p = 66 m
A = (22 m) · (11 m)
A = 242 m²
Case 8
p = 2 · (22 yd + 25 yd)
p = 94 yd
A = (22 yd) · (25 yd)
A = 550 yd²
Case 9
p = 2 · (16 km + 20 km)
p = 72 km
A = (16 km) · (20 km)
A = 320 km²
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Moore's law states that the maximum number of transistors that can fit on a silicon chip doubles every two years. The function f(x)= 42(1.41) to the X power model the number of transistors, in millions, that can fit on a chip, where X is the number of years since 2000. Using this model, in what year can a chip hold 1 billion transistors?
We can say that a chip can hold 1 billion transistors in the year 2007.
To solve for the year when a chip can hold 1 billion transistors, we need to set the function f(x) equal to 1000 (since 1 billion is 1000 million).
So,[tex]42(1.41)^x = 1000[/tex]
Divide both sides by 42:
[tex](1.41)^x = 23.81[/tex]
Take the logarithm of both sides (with base 1.41):
x = log(23.81)
Using a calculator, we find that x is approximately 5.98.
Since X represents the number of years since 2000, we add 5.98 to 2000 to get the year when a chip can hold 1 billion transistors:
2000 + 5.98 = 2006.98
Rounding to the nearest year, we can say that a chip can hold 1 billion transistors in the year 2007.
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Can someone help me with 6-10. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The volume of each figure would be given below as follows:
6.) = 11,253.76in³
7.) = 57,876.48 mm³
8.) = 3,744ft³
9.) = 297mm³
10.) = 34.54cm³
How to calculate the volume of the given shapes above?For question 6.)
The formula for the volume of the cylinder = πr²h
radius = diameter/2 = 32/2 = 16in
height = 14 in
volume = 3.14×16×16×14
= 11,253.76in³
For question 7.)
The formula for the volume of cylinder = πr²h
height = 32mm
radius = X² = 40²-32²
= 1600-1024
= 576
X = √576
= 24
Volume = 3.14×24×24×32
= 57,876.48mm³
For question 8.)
The volume of rectangular prism;
= length×width×height
= 12×8×39
= 3,744ft³
For question 9.)
The volume for triangular prism:
= 1/2×b×h×l
= 1/2 × 11×5.4×10
= 297mm³
For question 10.)
The volume of hemisphere ;= 2/3πr³
= 2/3× 3.14× 33/2
= 34.54cm³
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Please help!!! 100 Points!!!!
Answer:
r = 4
Step-by-step explanation:
The general form of the equation is y=mx + b where m is the slope and b is the intercept. The problem tells us that the slope is -3. So we know that y=-3x+b
Let's use the known coordinate (-5,13) to solve for b.
y=-3x+b
13 = -3(-5) + b
13 = 15 + b
b = -2
So now we have the equation:
y=-3x-2
Let's use the other coordinate (-2,r) and solve for the unknown "r" (which is y):
y = -3*-2 - 2
y = 6 - 2
y = 4
So the answer is 4.
what is 9+10 ?
free 10 points
it is 19 because maths says that 9+10 is 19
Answer:
the answer is 19......
Step-by-step explanation:
Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
A. (-7, -1), 36 units
B. (7, 1), 36 units
C. (7, 1), 6 units
D. (-7, -1), 6 units
Answer:
D
Step-by-step explanation:
To find the center and radius of a circle given its equation, we need to rewrite the equation in the standard form (x - a)^2 + (y - b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius.
So, let's complete square for x and y terms:
x^2 + 14x + y^2 + 2y + 14 = 0
x^2 + 14x + 49 - 49 + y^2 + 2y + 1 - 1 + 14 = 0
(x + 7)^2 + (y + 1)^2 = 36
Comparing this equation with the standard equation, we get the center at (-7, -1) and radius as sqrt(36) = 6 units.
So, the correct answer is option D: (-7, -1), 6 units.
what is a regression through the origin
A regression through the origin is a linear regression model where the intercept time period is assumed to be 0, meaning the regression line passes through the starting place.
This version is also referred to as zero-intercept regression or homogeneous regression.
It's far frequently used whilst there's a theoretical foundation to agree with that the relationship among the dependent and unbiased variable passes via the foundation or whilst the information propose that the intercept ought to be 0.
The slope coefficient represents the change within the structured variable for a one-unit increase inside the unbiased variable.
However, this kind of regression may not be appropriate in all cases, and a general linear regression version with an intercept term can be greater suitable.
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what equation is the blue line
Hello!
the equation of the blue line is 3y + 0.5x
What is the volume of this rectangular prism?
The volume of this rectangular prism given the base area and height is 385 cubic inches.
What is the volume of the rectangular prism?Volume of the rectangular prism = Base area × height
Base area = 35 square inches
h = 11 inches
Volume of the rectangular prism = Bh
= 35 square inches × 11 inches
= 385 cubic inches
Hence, 385 cubic inches is the volume of the rectangular prism.
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SOMEONE HELP PLEASE
Which of these values for P and a will cause the function f(x) = Pa* to be an exponential growth function?
O A. P=;a=
OB. P= ; a=
= 12
9
C. P = 9; a =
= 1/2/2
OD. P= 9; a = 1
4
The option that makes the function, f(x) = P·(a)ˣ, an exponential growth function is the option B
B. P = 1/9; a = 12
What is an exponential function?An exponential function is a function of the form; Y = a·bˣ
Where;
a = The y-intercept, (a, 0)
b = The growth or decay factor
x = The exponent
The function can be expressed as follows;
f(x) = P·(a)ˣ
An exponential growth function is one that increases in value as the value of the input variable increases, in which the growth or decay factor is a > 1
The option that therefore yields an exponential growth is one in which the value of the variable a is larger than 1.
The correct option is therefore, option B.
B. P = 1/9; a = 12
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What is the volume of the above figure ?
Step-by-step explanation:
Volume = length X width X height = 8 x 2 x 6 = 96 m^3
The sum of a number n and 8 is multiplied by -4 an the result is -12 what is the number
Answer:
-5
Step-by-step explanation:
Arranging the numbers
-4 (n+8) = -12
n+8 = -12/-4
n+8 = 3
n = 3-8
n = -5
Can u pleaseee answer all parts pleaseeeee <3333
please help meee
a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)
b. The increase in cost between 12 noon and 3 pm is $2.
c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
How do you express a data set in interval notations?Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.
The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.
We can represent it as (8am, 9am) U (11am, 12pm).
It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).
And stays constant at : (9am, 10am) U (10am, 11am)
Cost increase from 12 to 3pm,We simply deduct the 12pm's cost from 3pm's cost.
So, we have
Cost increase = $3.5 - $1.5
Evaluate the difference
Cost increase = $2
Hence, the cost increase is $2
The time interval where the cost is lowerWhen you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
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Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+b.
x= 1, 2, 3
y= 11, 22, 33
Answer:
y= 11x
Step-by-step explanation:
find the slope: 22-11/2-1= 11/1 or 11
To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x
The vertices of a rectangle are given in the column’s of the matrix R= [0,0,6,6,0,6,6,0] if 3X [0,1,-1,0] is found to perform a transformation what are the coordinates of the transformed rectangle
The coordinates of the forth corner point of the rectangle will be (-1, 3)
The point will be at (-1, 3).
Use the x value that has only been used once, -1, and the y value that has only been used once. (6,0) and (6, 3) are on the same side vertically of the rectangle because their x values are the same.
Because 6 > -1, you know that they make up the right side of the rectangle.
(-1,0) and (6, 0) both have the same y values, so they are on the same side horizontally, and are the bottom of the rectangle because 0<3.
This all means the fourth point is the rectangles top left corner.
Because it is a rectangle, its sides are parallel, so you know that it will have the same x value as the left bottom point (-1,0) and the same y value as the right top point, (6, 3).
Hence, the coordinates of the forth corner point of the rectangle will be (-1, 3)
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there vertices of a rectangle are (-1,0) (6,0), and (6,3) . What are the coordinates of the forth corner point of the rectangle?
janelle drove 60 km in 5/6 hours, and bernie drove 54 km in 2/3 hours. who drove faster? how many times as fast?
Bernie drove 1.125 times as fast as Janelle.
To determine who drove faster, we can calculate the average speed (in km/h) of each driver using the formula:
average speed = distance / time
For Janelle:
average speed = 60 km / (5/6 hours) = (60 km) x (6/5 hours) = 72 km/h
For Bernie:
average speed = 54 km / (2/3 hours) = (54 km) x (3/2 hours) = 81 km/h
Therefore, Bernie drove faster than Janelle. To determine how many times as fast, we can divide Bernie's average speed by Janelle's average speed:
81 km/h / 72 km/h = 1.125
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on a piece of paper graph this system of equations y=x-10 y=x^2-2x-3
The solution to the system is 6 and 11.
We have,
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation.
Given equation:
y=2x-1 .....(1)
y=x+5....(2)
Now solving equation 1 and 2, we get
2x -1 = x + 5
2x - x= 5 +1
x = 6
and, y= 2x-1
y= 2(6)-1
y= 12 -1
y= 11
Hence, the value of x is 6 and y is 11.
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complete question:
On a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5
c3m9 divided by cm2?
Answer:
c^2 m^7
Step-by-step explanation:
c^3 m^9 = cm^2 x c^2 m^7
c^m m^9 / cm^2
= (cm^2 x c^2 m^7)/cm^2
= c^2 m^7
a squared -16a-12 (factored)
The expression a² - 16a - 12 when factored is a(a - 16) - 12
From the question, we have the following parameters that can be used in our computation:
a² - 16a - 12
The above expression is a quadratic expression
It cannot be completely factored
This is because the roots of the expressions are irrational numbers
To partially factor the expression, we have
a² - 16a - 12 = a(a - 16) - 12
Hence, the expression a² - 16a - 12 when factored is a(a - 16) - 12
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