The values of the variables in the angles and measures of the side lengths of the quadrilaterals can be found using the properties of the quadrilaterals
8. z = 20
9. x = 18°
10. y = 12°
11. AB = 11
12. a = 10
13. b = 8
14. c = 18
15. d = 4
16. w = 6
17. x = 2
18. y = 31
19. z = 20
What is a quadrilateral?A quadrilateral is a four sided polygon.
8. The quadrilateral ABCD is a parallelogram, therefore;
The opposite sides have the same lengths;
z - 3 - 17
z = 17 + 3 = 20
z = 20
9. 4·x° and 108° are same side interior angles, therefore;
4·x° + 108° = 180°
4·x° = 180° - 108° = 72°
x = 72°/4 = 18°
x = 18°
10. 6·y° and 9·y° are same side interior angles, therefore;
6·y° + 9·y° = 15·y° = 180°
y = 180°/15 = 12°
y = 12°
11. The segment AB is congruent to segment CD, by the properties of a parallelogram
CD = 11
Therefore;
AB = CD (definition of congruency)
AB = CD = 11
AB = 11
12. The quadrilateral WPBH is a rectangle, therefore;
WH ≅ PB (properties of a rectangle)
WH = PB (definition of congruency)
WH = 12
PB = 2·a - 8
Therefore;
2·a - 8 = 12 (substitution property of equality)
2·a = 8 + 12 = 20
a = 20 ÷ 2 = 10
a = 10
13. The diagonals of a quadrilateral bisect each other;
The diagonals of a rectangle have the same length
Therefore;
WA = AH
WA = 16
AH = 2·b
Therefore b = 16/2 = 8
b = 8
14. 3·c° + 2·c° = 90°
5·c° = 90°
c = 90°/5 = 18
c = 18
15. WA = AP
Therefore;
4·d = 16
d = 16/4 = 4
d = 4
16. The quadrilateral is a square;
The length of the sides of a square are congruent, therefore;
20 = 3·w + 2
3·w = 20 - 2 = 18
w = 18/3 = 6
w = 6
17. The diagonals of a square bisect the interior angles, therefore;
22·x + 1° = 90°/2 = 45°
x = (45 - 1)°/22 = 2
x = 2
18. y - 11 = 20
Therefore;
y = 20 + 11 = 31
y = 31
19. The diagonals of a square are perpendicular to each other, therefore;
5·z - 10° = 90°
5·z = 90° + 10° = 100°
z = 100°/5 = 20°
z = 20°
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A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot.
A store is advertising a sale with 10% off all items in the store. The sales tax is 5%. A 55-inch
television is regularly priced at $855. What is the total price of the television, including sales tax,
if it was purchased on sale?
Answer:
$812.25
Step-by-step explanation:
Given data
Cost of TV= $855
Discount= 10%
Tax= 5%
Let us find the amount of the Discount
=10/100*855
=0.1*855
=$85.5
Let us find the amount of the Tax
=5100*855
=0.05*855
=$42.75
Hence the cost of the TV is
=855+42.75-85.5
=897.75-85.5
=$812.25
HElp pls :((((((((((((
Answer:Just add them all
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
First you have to find the percentage of pan crust to all the other crusts to do this you add all the crusts together:
397+220+167+196 = 980
Then divide 196 by 980:
196/980 = .2 or 20%
Then multiply 400 by 20%
400*20% = 80
How do I determine whether a graph is a function?
Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.
Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.
So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.
On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.
It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.
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If their meal cost 24.95 and there is a 7 sales tax. What will their total bill be?
Answer:
no lo se
Step-by-step explanation:
solo quiero punts
Since the area of the rectangle for a uniform probability distribution must equal one, what must the height equal, in general? Choose the correct answer below. range B. range 2. C. range D. More information is needed
The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Therefore the required answer for the question is Option D.
So, the Probability density function is portrayed graphically as a rectangle where (b-a) is the base and 1/(b-a) is the required height.
Probability density function refers to the method that helps to define the random variable's probability within a distinct range of values as opposed to taking one value.
then,
the height of the rectangle for a uniform probability distribution should be 1/(b-a)
The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Thus the correct answer is Option D.
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pls help, i have class rn :(
in how many ways can alice distribute 12 apples to 3 children (a child can have no apples)
A shell and tube exchanger is used to heat (6 kg/s of oil) (cp=2 KJ/kg °K), from 20°C to 48°C. The exchanger is single pass through the shell and multiple passes through the tubes in counterflow. Water enters the shell at 90°C and leaves at 55°C. The total global heat transfer coefficient is estimated to be (2000 W/m2°K). Calculate:
a) The amount of heat transferred [w]
b) The transfer area [m^2].
c) The efficiency of the I.C. [%]
d) Once the exercise has been solved, it is necessary to see how to improve its efficiency by modifying certain parameters that allow the objective to be achieved without altering the original proposed design to a large extent.
Modification to improve the efficiency of the heat exchanger, One way to improve the efficiency of the heat exchanger is by increasing the flow rate of the fluid (oil and water) without altering the overall design of the heat exchanger
Mass flow rate of oil (m1) = 6 kg/s,Specific heat of oil (cp) = 2 kJ/kg K,Initial temperature of oil (T1) = 20°C,Final temperature of oil (T2) = 48°C,Inlet temperature of water (Tw1) = 90°C,Outlet temperature of water (Tw2) = 55°C,Overall heat transfer coefficient (U) = 2000 W/m2 K.
The amount of heat transferred,Heat transfer rate (Q) = m1cp (T2 – T1)We know that,Q = UA (Tw1 – T2)
Therefore,m1cp (T2 – T1) = UA (Tw1 – T2)
Therefore,Q = 6 × 2 × (48 – 20) × 103= 86400 W= 86.4 kWThe transfer area,We know that,Q = UA (Tw1 – T2)
Therefore,A = Q / U (Tw1 – T2)
Therefore,A = 86,400 / (2000 × (90 – 55))
Therefore,A = 4.32 m2The efficiency of the heat exchanger,Heat transfer rate (Q) = m1cp (T2 – T1)
We know that,Heat input = m1 cp (T2 – T1) × 100Therefore,η = Q / (m2 × cp × (Tw1 – Tw2)) × 100Therefore,η = 86,400 / (1 × 4.18 × (90 – 55)) × 100
Therefore,η = 53.1%Modification to improve the efficiency of the heat exchanger, One way to improve the efficiency of the heat exchanger is by increasing the flow rate of the fluid (oil and water) without altering the overall design of the heat exchanger.
This increase in the flow rate will increase the rate of heat transfer, which will lead to an increase in the efficiency of the heat exchanger.
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Based on histogram above what is the average number of hours worked by 20 salesperson in company G
Answer:
\(Average = 38\)
Step-by-step explanation:
Given
The attached histogram
Required
The average work hours by 20 salespeople
First, we get the total hours worked as follows:
\(Hours = 3 * 30 + 5 * 34 + 9 * 40 + 2 * 45 + 1 * 50\)
\(Hours = 760\)
Divide by number of salespeople
\(Average = Hours/n\)
\(Average = 760/20\)
\(Average = 38\)
What is used to periodically check that a process is in statistical control?
a. sampling
b. scrap parts
c. the process is only measured in the beginning 100 percent inspection.
Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time
What is used to periodically check that a process is in statistical control?
a. sampling
b. scrap parts
c. the process is only measured in the beginning 100 percent inspection.
a. Sampling is used to periodically check that a process is in statistical control.
Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time. SPC involves collecting and analyzing data on the process, and using statistical methods to determine whether the process is in statistical control (i.e., producing consistent and predictable results) or is out of control (i.e., producing inconsistent or unpredictable results).
One way to monitor a process using SPC is to use sampling. This involves taking a sample of parts or products from the process at regular intervals, and measuring certain characteristics of the sample (such as dimensions, weight, or color). The data collected from the samples can then be analyzed using statistical methods to determine whether the process is in control or out of control.
If the data collected from the samples indicates that the process is out of control (i.e., producing inconsistent or unpredictable results), corrective action can be taken to bring the process back into control. By regularly monitoring and adjusting the process using SPC techniques like sampling, organizations can ensure that their processes are producing consistent and high-quality results.
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what’s the area and perimeter for this problem?
Answer:
Area=153.75 divdided by 2 = 76.88
permitere= 8 + 10.25+18.8=37.05
Step-by-step explanation:
would this be correct?
Answer:
Yes it is absolutely right.
A standard subdivision consists of subdivisions with ___________ parcels. ten or fewer four or fewer exactly two five or more
A standard subdivision consists of subdivisions with four or fewer parcels.
In a standard subdivision, the number of parcels is limited to four or fewer. This means that each subdivision within the standard subdivision will have a maximum of four parcels.
So, if you are looking for a standard subdivision, you can expect to find subdivisions with four or fewer parcels.
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Solve by completing the square 5x^2+7k+76=9x+4x^2
the solution to the equation by completing the square is: x = (9/2) ± √(-7k - 47/4).
To solve the given equation by completing the square, we need to rewrite the equation in the form of \((x + a)^2 = b\) , where a and b are constants. This can be done by following these steps:
1. Move all the terms to one side of the equation:
\(5x^2 + 7k + 76 - 9x - 4x^2 = 0\)
2. Combine like terms:
\(x^2 - 9x + 7k + 76 = 0\)
3. Rewrite the equation by completing the square for the x terms. To do this, take half of the coefficient of x (-9/2), square it, and add it to both sides of the equation:
\(x^2 - 9x + (-(9/2))^2 + 7k + 76 - (-(9/2))^2 = (-(9/2))^2\)
4. Simplify:
\((x - (9/2))^2 + 7k + 76 - (81/4) = 81/4\)
5. Combine constants:
\((x - (9/2))^2 + 7k + 47/4 = 0\)
6. Solve for x by taking the square root of both sides:
x - (9/2) = ±√(-7k - 47/4)
7. Add (9/2) to both sides:
x = (9/2) ± √(-7k - 47/4)
Therefore, the solution to the equation by completing the square is: x = (9/2) ± √(-7k - 47/4).
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If the number of equally likely sample outcomes of a single stage of an experiment is 4, what is the total number of elements in the sample space if the experiment has 3 stages?
Answer
64
Step-by-step explanation:
4 x 4 x 4
so it's like you take 4 and 3 stage = 4 x 4 x 4
Hope it helped !
Have a nice day studying ! Mark me as Brainliest too Ty !
The result of a vertical shift followed by a reflection in the x-axis would most naturally be denoted by__. The result of a reflection in the x-axis followed by a vertial shift would most naturally be denoted by__. Therefore, reversing the order__ change the final result
The terms that complete the three blanks are:
-f(x) + k-f(x) + kdoes notWhat is transformation?Transformation involves changing the position and the size of a shape, line or point
When a shape is shifted vertically, and then reflected across the x-axis;
The rule of transformation is: -f(x) + k
When a shape is reflected across the x-axis, and then shifted vertically;
The rule of transformation is: -f(x) + k
Notice that the rule of both transformations are the same.
Hence, reversing the order does not change the final result
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-14+u=50 I need help
Multiply 2 to the odd position number then adding -4 to the even position number stating 3. ( complete the number pattern
__,__,__,__,__,__,__,__,__,__
A complete list of the numbers in the pattern: 3, 6, 10, 14, 18, etc.
How to calculate the valueThe number pattern you described is as follows:
3,
(2*5)-4 = 6,
(2*7)-4 = 10,
(2*9)-4 = 14,
(2*11)-4 = 18,
The first number is 3, and then each subsequent number is found by multiplying the previous odd number by 2 and then subtracting 4.
For example, the second number is found by multiplying the first number by 2 and then subtracting 4, which gives us 6. The third number is found by multiplying the second number by 2 and then subtracting 4, which gives us 10.
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ument will3. Graph and investigate the following piecewise equation: (5points)f(x)={, ?for x < 2(-x + 10 for 2
We are given the following function:
\(\begin{gathered} f(x)=\lbrace x^2;\text{ x<2} \\ -x+10;2\le x\le6\} \end{gathered}\)The graph of this equation is a parabola for values of x < 2 and a line for values of 2<= x <= 6. The graph is the following:
Helppppp with this please
Answer:180
Step-by-step explanation:
hope this helps
Answer:
0.8 mm
Step-by-step explanation:
Given that you require the actual size.
The ant has been magnified by 15 X
To find the actual size divide magnified size by 15
actual size = 12 mm ÷ 15 = 0.8 mm
Triangle P Q R is shown. Angle Q P R is a right angle. The length of hypotenuse Q R is 14.1 and the length of P R is 12.7. What is the measure of ∠R in △PQR? Round to the nearest degree. 26° 42° 45° 64°
Answer:
<R = 26degrees
Step-by-step explanation:
Making <R as the reference angle
Adjacent side = 12.7
Hypotenuse = 14.1
Cos <R = adj/hyp
Cos <R = 12.7/14.1
Cos <R = 0.9007
<R = arccos(0.9007)
<R =25.7
<R = 26degrees
Answer:
A. 26°
Step-by-step explanation:
I took it on EDG
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Lee plans to attend the Sullivan County Fair and is trying to decide what would be a better deal. He can pay $33 for unlimited rides, or he can pay $17 for admission plus $2 per ride. If Lee goes on a certain number of rides, the two options wind up costing him the same amount. What is that cost? How many rides is that?
It will cost Lee $ ____
for both options if he goes on ____
rides.
for the demand function, q=-5p 1200, determine the price p, that maximizes revenue
The price that maximizes revenue is p = 120.
The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.
Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:
R = p × q
R = p × (-5p + 1200)
To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.
dR/dp = -10p + 1200 = 0
Solving this equation for p:
-10p + 1200 = 0
-10p = -1200
p = -1200 / -10
p = 120
Therefore, the price that maximizes revenue is p = 120.
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what is the term for the rotational movement of the nose of the plane
The volume of a cone can be calculated using the formula \(V = (1/3) * * r2 * h\), where V is a constant roughly equal to 3.14159, r is the radius, and h is the height.
When the required values are substituted, the answer is \(V = (1/3) * 3.14159 * (1.75 feet)2 * 2.1\) feet.
The assessment of this expression yields V = 5.6688 cubic feet. The cone has a radius of 1.75 feet, a height of 2.1 feet, and a volume of approximately 5.6688 cubic feet."Pitch" is the technical word for the rotating movement of an airplane's nose. Pitch describes the rotation of the aircraft's nose around its lateral axis, either upward or downward. A plane is said to be in a positive pitch attitude when its nose is pointing up, and a negative pitch attitude when it is pointing down. Pitch control is essential for maintaining the correct flying path and managing the aircraft's height.
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Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.
Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.
Let,
\(B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right]\)
Then,
\(AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right]\)
Therefore, Ab is reflection about y = x .
As U = Bx and T∘U
A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).
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A seven-question quiz has 4 true/false questions followed by 3 multiple choice questions. For each multiple choice question there are four possible answers. In how many different ways is it possible to answer the seven questions?
a. 28
b. 12
c. 80
d.1024
It is possible to answer in 1024 different ways the seven questions.
What is quiz?
A form of game or competition where knowledge is tested by asking question is called quiz.
There are 2 possible answers for each true/ false question.
Since there are 4 true/false questions, the total number of ways to answer them is 4² = 16.
for each multiple choice question, there are 4 possible answers.
Since there are numbers multiple choice questions are 3 and the total number of ways to answer them is 4³ = 64.
Therefore, the total number of ways to answer questions is the product of the number of ways to answer the true/false questions and the number of ways to answer the multiple choice questions:
16 × 64 = 1024
It is possible to answer in 1024 different ways the seven questions.
So the answer is (d).
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What are the vertical and horizontal components of A(-3,4) and B(2,-5)?
Answer: In physics, when you break a vector into its parts, those parts are called its components. For example, in the vector (4, 1), the x-axis (horizontal) component is 4, and the y-axis (vertical) component is 1. Typically, a physics problem gives you an angle and a magnitude to define a vector; you have to find the components yourself using a little trigonometry.
Suppose you know that a ball is rolling on a flat table at 15 degrees from a direction parallel to the bottom edge at a speed of 7.0 meters/second. You may want to find out how long the ball will take to roll off the edge 1.0 meter to the right.
Define your axes so the ball is at the origin initially and the x-axis is parallel to the bottom edge of the table (refer to the figure). Therefore, the problem breaks down to finding out how long the ball will take to roll 1.0 meter in the x direction. To find the time, you first need to know how fast the ball is moving in the x direction.
The solution to the system x + y=b and x−y=2b is (1, a). What is the value of a?
The solution to the system is (x, y) = (3b/2, b/2), which can be written as (1, a) by letting a = b/2. Therefore, the value of a in terms of b is a = b/2.
What is diagonal?The term "diagonal" usually refers to a line segment that connects two non- adjacent corners of a geometric shape, such as a square or a rectangle, and which lies inside the shape.
For example, in a square, the diagonal is the line segment that connects opposite corners of the square, and which passes through its center. The length of the diagonal can be calculated using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides of the square.
by the question.
Let's denote the acute angle of the rhombus as x degrees. Then, we know that the obtuse angle is twice as large, so it must be 2x degrees.
We also know that the diagonals of a rhombus are perpendicular bisectors of each other. Therefore, the shorter diagonal (which we'll call d1) divides the rhombus into two congruent right triangles, each with hypotenuse 13cm and one leg equal to half the length of d1, which is 5cm (since d1 is the perpendicular bisector of the other diagonal).
Using the Pythagorean theorem, we can find the length of the other leg of each right triangle:
a²+b² = c2
a²+52 = 132 a² = 144
a = 12
Therefore, the length of each half of the longer diagonal (which we'll call d2) is 12cm. The full length of d2 is twice this, or 24cm.
Now we can use the fact that the diagonals of a rhombus bisect each other at 90-degree angles to find the acute angle of the rhombus:
tan(x) = (d1/2)/(d2/2) = d1/d2
tan(x) = 10/24
x=tan 1(10/24) = 23.19degrees
x = 23.19°
To solve for the value of a in the system:
x + y = b ...(1)
x - y = 2b ...(2)
We can add equations (1) and (2) to eliminate y:
(x + y) + (x - y) = b + 2b
2x = 3b
x = 3b/2
Substituting x = 3b/2 into equation (1):
3b/2 + y = b
y = b/2
So the solution to the system is (x, y) = (3b/2, b/2), which can be written as (1, a) by letting a = b/2. Therefore, the value of a in terms of b is a = b/2.
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50 points
2.) A car barrels off a cliff and free-falls for 8 seconds before crashing
and burning on the shoreline below. How tall is the cliff? The acceleration
due to gravity is 9.81 m/s2. *
313.92 m
313.98 m
314.04 m
314.11 m
Answer:
i dunno i think its B
Rachel earns $6.25 each week for doing chores. Bob earns $5.50 each week for doing chores.
After 13 weeks, how much more will Rachel earn than Bob for doing chores?
$
Answer:
Rachel will have 9.25$ more than Bob after 13 weeks