The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let R represent the number of Regular gallons, P represent that of Premium and D represent that of Diesel.
A total of 800 gallons was sold, hence:
R + P + D = 800 (1)
Also:
$2910 was sold combined, therefore:
3.5R + 4.25P + 4D = 2910 (2)
440 more gallons of regular was sold, hence:
R = P + D + 440 (3)
The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
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See the attached two problems, one is consider the augmented matrix and the other is consider the matrix.
The row operations on the augmented matrix are
R₂ → 4R₂R₃ → R₃ + 3What is an augmented matrix?An augmented matrix is a matrix in which the coefficient matrix and the column matrix are written together.
Since we have the augmented matrix
[tex]\left[\begin{array}{ccc}1&3&5\\0&\frac{1}{4} &-1\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\1&\\10&\end{array}\right][/tex]
To determine the next row operations, we proceed as follows.
Since we want to convert the second element in the second row to 1, we multiply row 2 by 4,
So, R₂ → 4R₂
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\10&\end{array}\right][/tex]
Now, since we want to convert the first element in the third row to 0, the row operation we perform is we add 3 to row 3
So, R₃ → R₃ + 3
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\0&9&-8\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\13&\end{array}\right][/tex]
So, the row operations are
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Simplify and then evacuate by plugging in the vaules of A, B, C, and/or D
A = 8
B = 10
C =16
D = 11
Evaluating the expression results to
A - 2(B - A) - 3B simplifies to --18C(4 - D) + 2CD simplifies to 240How to evaluate the expressionsTo simplify the given expressions, we substitute the values of A, B, C, and D into the expressions and perform the necessary calculations.
A - 2(B - A) - 3B:
Substituting the values:
8 - 2 * (10 - 8) - 3 * 10
Simplifying the expression inside parentheses
8 - 2(2) - 3 * 10
8 - 4 - 30
Performing subtraction
8 - 4 - 30
-18
Therefore, A - 2(B - A) - 3B simplifies to --18
evaluate the second expression C(4-D)+2CD:
C = 16
D = 11
Substituting the values:
16(4 - 11) + 2(16)(11)
Simplifying
16(-7) + 2(16)(11)
-112 + 352
240
Therefore, the value of the expression C(4-D)+2CD, when C = 16 and D = 11, is 240.
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What is the length of side s of the square shown below?
45
90°
OA. 1
OB. 2
OC. 2.2
OD. 4
OE. E
F. 4.2
Answer:
E
Step-by-step explanation:
using Pythagoras' identity on the lower right triangle , with legs s and hypotenuse 2 , then
s² + s² = 2²
2s² = 4 ( divide both sides by 2 )
s² = 2 ( take square root of both sides )
s = [tex]\sqrt{2}[/tex]
{-2, 3, 2, 4, -3} what is the range?
Answer: 7
Step-by-step explanation:
The range of a set of numbers is the difference between the highest and lowest numbers in that set.
For the given set, the highest number is 4 and the lowest number is -3.
So, the range is 4 - (-3) = 7.
The relation of a line graph is visualized by drawing
lines between all of the points on a grid.
The relation of a line graph is visualized by drawing lines between all of the points on a grid is false.
What is a line graph?A line graph is a type of graph that uses lines to connect data points. The points are typically plotted on a grid, but the lines do not need to connect all of the points. In fact, it is often more helpful to only connect the points that are relevant to the data that you are trying to visualize.
For example, when graphing temperature over time, there is only need to connect the points that represent the temperature at each hour. There is no need to connect the points that represent the temperature at midnight, 2am, 4am, etc.
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Complete question:
The relation of a line graph is visualized by drawing lines between all of the points on a grid. Is this true or false? Explain your answer.
Find the coordinates for the midpoint of the segment with the endpoints given.
(5, 6) and (8, 2)
please see photo thank you
Answer:
look below
Step-by-step explanation:
formula A=1/3 Bh
1/3 ×8×5×5
8x5x5=200
200/3=66.66666 round to 66.77cubic metets
A 16 ounce bottle of spring water is $2.08. A 20 ounce bottle of fresh water is $2.40. Which statement is true ?
A 16 ounce bottle of spring water is $2.08. A 20 ounce bottle of fresh water is $2.40 Therefore, this statement "A 20 ounce bottle of fresh water is $2.40" is true.
To determine which statement is true, let's compare the prices of the two water bottles:
16 ounce bottle of spring water: $2.08
20 ounce bottle of fresh water: $2.40
To find the price per ounce for each water bottle, we can divide the total price by the number of ounces:
Price per ounce of spring water: $2.08 / 16 ounces = $0.13 per ounce
Price per ounce of fresh water: $2.40 / 20 ounces = $0.12 per ounce
Comparing the prices per ounce, we can see that the price per ounce of fresh water ($0.12) is less than the price per ounce of spring water ($0.13).
Therefore, the statement "A 20 ounce bottle of fresh water is $2.40" is true.
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The graph represents the piecewise function: f (x) ={ , if -3
The domain and the range of the function are
Domain = (-∝, ∝)Range = (0, ∝)How to determine the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph is a piecewise function
When combined gives an absolute function
The rule of a function is that
The domain is the set of all real numbers
This means that the input value can take all real values
However, the range is greater than the constant term
In this case, it is 0
So, the range is y > 0
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Question
The graph represents the piecewise function:
f(x) =
What is the domain and range of the function
Solve 3x + 6 = 34
Answers:
−2
4
6
10
Answer:
To solve the equation 3x + 6 = 34, we need to isolate x on one side of the equation.
First, we can start by subtracting 6 from both sides of the equation to get:
3x + 6 - 6 = 34 - 6
Simplifying this, we get:
3x = 28
Next, we divide both sides by 3 to isolate x:
3x/3 = 28/3
Simplifying this, we get:
x = 28/3
This is not one of the answer choices listed. However, we can approximate the answer to the nearest integer. Using a calculator, we get:
x ≈ 9.333
Rounding to the nearest integer, we get:
x ≈ 9
Therefore, the answer closest to the solution of the equation 3x + 6 = 34 is 10.
Dilation D was performed on a rectangle. How does the image relate to the pre-image? Select three options
v.²/
The image is a reduction because 0
The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
The angles of the image are two-fifths the size of the angles of the pre-image.
O The center of dilation is at point Q.
The base of the image is two-fifths the size of the base of the pre-image.
The true statements are
The base of the image is two-fifths the size of the base of the pre-image.The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The image is a reduction because 0 < n < 1How to get the true statementsDilation was performed on a rectangle with a center of dilation at point V. We will evaluate the given options to determine their accuracy:
Option 1: The image is a reduction because 0 < n < 1 (True)
Explanation: Since the dilation factor is 2/5, this is less than 1, the resulting image will be smaller than the original rectangle. Therefore, this option is true.
Option 2: This is true. Dilation preserves the proportional relationship between corresponding sides of similar shapes. Since the dilation factor is 2/5, the side lengths of the image will be two-fifths the length of the corresponding side lengths of the pre-image. Therefore, this option is true.
Option 5: is true Since the dilation factor is 2/5, the base of the image will be two-fifths the length of the base of the pre-image. This is in line with the proportional relationship preserved by dilation. Therefore, this option is true.
In summary, options 1, 2, and 5 are true, while options 3 and 4 are false.
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question
Dilation D Subscript V, two-fifths was performed on a rectangle. How does the image relate to the pre-image? Select three options. The image is a reduction because 0 < n < 1. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The angles of the image are two-fifths the size of the angles of the pre-image. The center of dilation is at point Q. The base of the image is two-fifths the size of the base of the pre-image.
Is triangle fgh similar to triangle jkl? If so, identify the similarity postulate or theorem that applies. (Please help!!!)
The similarity of the triangles cannot be determined
How to identify if the triangles are similarFrom the question, we have the following parameters that can be used in our computation:
The triangles (see attachment)
The triangles are given as
FGH and JKL
Where we have
A pair of corresponding angle
Also, we have
A pair of similar side
There are no other parameters to determine if the triangles are similar or not
This means that the similarity cannot be determined
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4,, and C represent three different numbers from 2 through 5. What is the SMALLEST possible value of the entire expression below?
Show your work.
10 - A B/C
The smallest possible value of the entire expression is 7.5, which occurs when A = 5, B = 2, and C = 4.
We are given the three different numbers 4, and C represent three different numbers from 2 through 5 and we have to find out the smallest possible value of the entire expression 10 - A B/C.
To find the smallest possible value, we need to take the greatest value of A, the smallest value of B, and the smallest value of C.
The given number 4 is in between 2 and 5, so it cannot be the greatest value.
Therefore, A must be 5. Now, the other two numbers must be chosen from the remaining three numbers 2, 3, and 4.
We need to choose the smallest possible value of B and C to make the entire expression the smallest. The smallest value of B is 2.
Now, we need to choose the smallest possible value of C. If C is 4, then the entire expression becomes:10 - 5(2/4) = 10 - 2.5 = 7.5If C is 5, then the entire expression becomes:10 - 5(2/5) = 10 - 2 = 8
Thus, the smallest possible value of the entire expression is 7.5.
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Alex Murphy purchased a TV with surround sound and remote control on an installment plan with a 60 down payment and 12 payments of $104.63. Find the installment price of the TV.
The installment price of the TV is $1,195.56.
To find the installment price of the TV, we need to calculate the total amount paid over the installment period.
The down payment is $60, and there are 12 monthly payments of $104.63 each.
Total amount paid over 12 months = Monthly payment x Number of payments
= $104.63 x 12
= $1,255.56
Now, we can calculate the installment price by subtracting the down payment from the total amount paid:
Installment price = Total amount paid - Down payment
= $1,255.56 - $60
= $1,195.56
Therefore, the installment price of the TV is $1,195.56.
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A rectangular piece of paper measures 280 cm by 140 cm . How many circles of radius 7 cm can be cut out from it?
Take pie = 22/7
Answer ASAP
Work Shown
rectangle area = length*width = 280*140 = 39,200 square cm
circle area = pi*r^2 = (22/7)*(7)^2 = 154 square cm
Divide the two areas
39200/154 = 254.54545 approximately
That rounds down to 254
Rounding to 255 will not work because there won't be enough paper for that 255th circle
3. Set up and solve an equation to
find the missing angle
measurements in the following:
H
4x - 20
G
2x
2G=
ZH=
21=
||
2x
I
The missing angle measurements are:
Angle G = 66.67 degrees
Angle H = 113.32 degrees
Angle Z = 66.68 degrees
Angle I = 66.68 degrees
Let's analyze the given information and solve for the missing angle measurements:
From the diagram, we can see that angle H and angle G are adjacent angles, and the line segment HG acts as a transversal. We are given that the measure of angle G is 2x, and we need to find the missing angle measurements, which are the measures of angle H, angle Z, and angle I.
Since angle G and angle H are adjacent angles, their measures add up to 180 degrees. So we can set up the equation:
2x + (4x - 20) = 180
Simplifying the equation:
6x - 20 = 180
Next, we solve for x:
6x = 200
x = 200/6
x = 33.33
Now that we have found the value of x, we can substitute it back into the original equation to find the measures of the missing angles:
Angle G = 2x = 2(33.33) = 66.67 degrees
Angle H = 4x - 20 = 4(33.33) - 20 = 133.32 - 20 = 113.32 degrees
Angle Z = 180 - Angle H = 180 - 113.32 = 66.68 degrees
Angle I = Angle Z = 66.68 degrees
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A point (3, 4) is the point of intersection of the diagonals of the parallelogram, two of whose consecutive corners are at the points (3, 2) and (5, 10). Find the co-ordinates of the remaining corners
The coordinates of the remaining corners are (2, 2) and (2, 10).
To find the coordinates of the remaining corners of the parallelogram, we can use the fact that the diagonals of a parallelogram bisect each other.
Let's call the point of intersection of the diagonals as (3, 4). The midpoint of one diagonal is the same as the midpoint of the other diagonal.
First, let's find the midpoint of the diagonal connecting (3, 2) and (5, 10). The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this formula, we find the midpoint as (4, 6).
Since the point (3, 4) is the midpoint of the other diagonal, we can use this information to find the coordinates of the remaining corners.
If we reflect the point (4, 6) across the point of intersection (3, 4), we will obtain the coordinates of the remaining corners.
Reflecting (4, 6) across (3, 4), we get:
(4 - 2, 6 - 4) = (2, 2)
Therefore, the remaining corners of the parallelogram are (2, 2) and (2, 10).
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The area of a kindergarten classroom is 972 square feet. How many square yards is that? (There are 9 square feet in a square yard.)
Answer:
972 ft²(1 yd²/9 ft²) = 108 yd²
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Given statement solution is:- The statement that best explains whether the data in the table represents a linear or nonlinear function is:
The table represents a nonlinear function because the graph does not show a constant rate of change.
When x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.
The statement that best explains whether the data in the table represents a linear or nonlinear function is:
The table represents a nonlinear function because the graph does not show a constant rate of change.
In the given table, the values of y do not change at a constant rate as x increases or decreases. For example, when x increases from -4 to -1, y changes from 4 to 2.5, which is a rate of change of -1.5. However, when x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.
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Statements
1
Quadrilateral ABCDwith m/A= (10z), m/B= (8x), m/C= (10z)",
and m/D= (8x)".
2 m/A+m/B+m/C+m/D=360°
3 (10x)+(8x) + (10x) + (8x) = 360°
4
5 x=10
Reasons
Given
Substitution Property
Combine like terms
We can solve for x:
20z + 16x = 360°
16x = 360° - 20z
x = (360° - 20z)/16
Quadrilateral ABCD is given with the measures of angles:
m∠A = 10z
m∠B = 8x
m∠C = 10z
m∠D = 8x
The sum of the measures of the angles of a quadrilateral is 360°:
m∠A + m∠B + m∠C + m∠D = 360°
Substituting the given angle measures:
(10z) + (8x) + (10z) + (8x) = 360°
Combine like terms:
20z + 16x = 360°
Given the equation from step 4, we can solve for x:
20z + 16x = 360°
16x = 360° - 20z
x = (360° - 20z)/16
Reasons:
Step 1: The given angles are labeled with their corresponding measures.
Step 2: The sum of the measures of the angles of a quadrilateral is a geometric property.
Step 3: Substitution of the given angle measures into the equation for the sum of angles.
Step 4: Combining like terms by adding the coefficients of z and x.
Step 5: Solving the equation for x by isolating it on one side.
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( MAKE YOUR OWN COMIC AND SOLVE IT SHOWING WORK) THE COMIC HAS TO BE ALIKE TO THE EXAMPLE NOT THE SAME THING BUT DIFFERENT CHARATER DIFFERENT TRIG PROBLEMS
To create another comic out of the scenario is as follows: An eagle is chasing a bird and spots it on top of a 10ft tree and is looking at it at an angle of elevation of 30° degrees.
How to calculate the distance the eagle needs to catch the bird?To calculate the distance, the trigonometric sine law needs to be obeyed and the formula is written below as follows.
a/sinA = b/sinB
where;
a= 10ft
A= 30°
b= ?
B= 90°
That is;
10/sin30° = b/sin90°
make b the subject of formula;
b = 10×sin90°/sin30°
= 10×1/0.5
= 20ft
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Rewrite each fraction with a denominator of 12.
3
4
5
3
The equivalent fractions with a denominator of 12 are
3/4 = 9/125/3 = 20/12How to rewrite the fractionsTo rewrite each fraction with a denominator of 12, we need to find an equivalent fraction that has 12 as its denominator.
3/4 can be rewritten as (3/4) * (3/3) = 9/12.
5/3 can be rewritten as (5/3) * (4/4) = 20/12.
Therefore, the fractions with a denominator of 12 are:
3/4 = 9/12
5/3 = 20/12
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complete questions
Rewrite each fraction with a denominator of 12.
3/4
5/3
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
.
The maximum number of tables the restaurant can have is 37. This ensures that the total number of people seated at the tables (37 * 4 = 148) is less than the legal limit of 150 people in the restaurant at one time.
To find the maximum number of tables the restaurant can have, we need to solve the inequality 4t < 150.
Dividing both sides of the inequality by 4, we have:
t < 150/4
Simplifying the right side, we get:
t < 37.5
Since the number of tables must be a whole number, we can conclude that the maximum number of tables the restaurant can have is 37.
Let's verify this by substituting t = 37 into the original inequality:
4t < 150
4(37) < 150
148 < 150
Since 148 is less than 150, the inequality holds true. However, if we increase the number of tables to 38, we get:
4(38) < 150
152 < 150
In this case, 152 is not less than 150, so the inequality is no longer satisfied.
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PLEASE HELP!
See the image below!
Answer:
A ≈ 199.98
Step-by-step explanation:
the area (A) of Δ ABC can be calculated as
A = [tex]\frac{1}{2}[/tex] ab sinΘ ( substitute values for a, b and Θ )
= [tex]\frac{1}{2}[/tex] × 25 × 33 × sin29°
= 12.5 × 33 × sin29°
≈ 199.98 ( to 2 decimal places )
-1
-2
The lengths of movie files that are available for streaming are modeled using the normal distribution shown below.
The mean of the distribution is 170.8 min and the standard deviation is 19.7 min.
100
in the figure, Vis a number along the axis and is under the highest part of the curve.
And, U and Ware numbers along the axis that are each the same distance away from V.
Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W.
Continue
3
0
U
120
Percentage of total area shaded: (Choose one)
140
160
180
V
Time (in min)
200
220
0 240
W
3
Answer:
the best value for the percentage of the area under the curve that is shaded is 68%.
Step-by-step explanation:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 170.8 min and the standard deviation is 19.7 min, we can calculate the values of U, V, and W.
U: U is one standard deviation below the mean.
U = Mean - 1 * Standard Deviation
U = 170.8 - 1 * 19.7
U ≈ 151.1
V: V is the mean.
V = Mean
V = 170.8
W: W is one standard deviation above the mean.
W = Mean + 1 * Standard Deviation
W = 170.8 + 1 * 19.7
W ≈ 190.5
Now, let's determine the best value for the percentage of the area under the curve that is shaded. Based on the empirical rule, the highest percentage that can be shaded is approximately 68% since it represents the data within one standard deviation of the mean.
Therefore, the best value for the percentage of the area under the curve that is shaded is 68%.
Write an algebraic expression to represent the given phrase. Use x as the variable to
represent the unknown quantity.
8. The sum of a number and 20
9. The product of a number and 20
10. The quotient of 20 and a number
11. The difference of a number and 20
Choices for 8-11:
A) 20-x
D) x + 20
B) 20x
20
X
E)
C) X-20
X
20
AB)
Answer:
8) x + 20
9) 20x
10) 20/x
11) x-20
Step-by-step explanation:
8) x + 20
9) 20x
10) 20/x
11) x-20
Given the points A(-2, 1) and B(3, 4), what are the coordinates of point C in the fourth
quadrant such that mZCAB= 90 degrees and AB = AC? Express your answer as an ordered pair.
degree
The coordinates of C are (121/6, -47/15).Therefore, the answer is (121/6, -47/15 )Answer: (121/6, -47/15)
The given points are A (-2, 1) and B (3, 4).
We need to determine the coordinates of point C in the fourth quadrant such that m∠CAB=90° and AB=AC.
In order to determine the coordinates of point C,
The slope of ABThe slope of the line passing through A(-2, 1) and B(3, 4) is given bym = (y₂ - y₁) / (x₂ - x₁)m
= (4 - 1) / (3 - (-2))m
= 3 / 5
The mid-point of A and BMid-point of A and B is given by the following formula:
Mid-point = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Mid-point of AB is: ((-2 + 3) / 2, (1 + 4) / 2)
= (1/2, 5/2)
The slope of the line perpendicular to AB
The slope of the line perpendicular to AB is given by the following formula: m₁ * m₂ = -1
Where m₁ is the slope of AB and m₂ is the slope of the line perpendicular to ABm₁ = 3 / 5m₂ = - 5 / 3 (as the line is perpendicular to AB and the product of slopes of two perpendicular lines is -1)
The mid-point and the slope of the line perpendicular to AB to find the coordinates of C
Let the coordinates of C be (x, y)We know that AC = AB and we know the coordinates of A (-2, 1) and mid-point of AB (1/2, 5/2).
Simplifying this equation, we get:
15b = 47b = 47 / 15
Substituting this value of b in the equation we got earlier:
a = (70 + 20b) / 8
= (70 + 20(47/15)) / 8
= 121 / 6
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Find the enclosed area within the boundaries defined by the equations
x = 2y^2− 6, x = 2 − 1/3y, y= 7 and y= −3. Can someone help me plss
Answer: sorry I can't help you
Step-by-step explanation:
The enclosed area can be found by plotting the given equations, finding the points of intersection, establishing the boundaries, and then calculating the integral of the difference between the two functions within these boundaries.
∫7-3[ (2-1/3*y) - (2y² - 6) ] dy
Explanation:
To find the enclosed area within the boundaries defined by the equations x = 2y²- 6, x = 2 – 1/3y, y= 7 and y= -3, you would firstly have to plot these equations on a plane, observe their intersection points and identify the boundaries of the area enclosed.
Then, the enclosed area can be calculated by integrating the difference between the two functions within those points where y = -3 to y = 7. Once you've done that, you calculate the definite integral of each of the functions separately from y = -3 to y = 7 and subtract the results. Here's the computation:
∫7-3[ (2-1/3*y) - (2y² - 6) ] dy
Calculating this integration will give you the area enclosed within the boundaries defined by these equations.
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he square of 9 less than a number is 3 less than the number. What is the number? –12 or 7 –12 or –7 –7 or 12 7 or 12
Answer:
I thing its 7- 12 sorry if wrong
Step-by-step explanation:
Which description does NOT guarantee that a quadrilateral is a parallelogram?
a quadrilateral with consecutive angles supplementary
a quadrilateral with the diagonals bisecting each other
a quadrilateral with both pairs of opposite sides congruent
quadrilateral with two opposite sides parallel
The description that does NOT guarantee that a quadrilateral is a parallelogram is:
a quadrilateral with consecutive angles supplementary.Why the statement is not a guaranteeWhile it is true that consecutive angles in a parallelogram are supplementary (their sum is 180 degrees), the converse is not true. In other words, having consecutive angles that are supplementary does not necessarily imply that the quadrilateral is a parallelogram.
There are other types of quadrilaterals, such as trapezoids or irregular quadrilaterals, that can also have consecutive angles that are supplementary.
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