Answers
The length of the line is given as follows:
B. 12 units.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The parameters for this problem are given as follows:
Length of the line is the hypotenuse.Horizontal change is of 10 units.Vertical change is of 6 units.Hence the length of the line is given as follows:
l² = 10² + 6²
[tex]l = \sqrt{10^2 + 6^2}[/tex]
l = 12 units. (rounded up).
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Related Questions
PLEASE HURRY!! Which angle is adjacent to DFE
Answers
The adjacent angle is BFD.
We are given to find the adjacent angle to angle DFE in the figure.
The two angles that have a common vertex and a common side are called adjacent angles.
We can see that angles DFE and AFB have a common vertex F but they do not have a common side. So, the angles are not adjacent.
We can see that angles DFE and AFC have a common vertex F but they do not have a common side. So, the angles are not adjacent.
We can see that angles DFE and BFD have a common vertex F and a common side FD. So, the angles are adjacent.
Hence,
∠BFD adjacent angle.
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4. a) Verify that DEF is a right triangle.
E(-2, 2)
D(1,4)
F(3,1)
b) Describe another method that you could
use to answer part a).
Answers
Answer:To verify whether triangle DEF is a right triangle, we can use the slope formula and the perpendicularity criterion.
a) Verification of DEF as a right triangle:
Calculate the slopes of the two sides:
Slope of DE = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - (-2)) = 2 / 3
Slope of EF = (y2 - y1) / (x2 - x1) = (1 - 2) / (3 - (-2)) = -1 / 5
Check if the product of the slopes is -1 (perpendicular lines):
(Slope of DE) * (Slope of EF) = (2 / 3) * (-1 / 5) = -2 / 15
Since the product of the slopes is not -1, the sides DE and EF are not perpendicular. Therefore, triangle DEF is not a right triangle.
b) Another method to determine if triangle DEF is a right triangle:
Another method to answer part a) is by calculating the lengths of the three sides DE, EF, and DF. Then, we can check if the Pythagorean theorem holds true.
Calculate the lengths of the sides:
Length of DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((1 - (-2))^2 + (4 - 2)^2) = sqrt(9 + 4) = sqrt(13)
Length of EF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - 1)^2 + (1 - 4)^2) = sqrt(4 + 9) = sqrt(13)
Length of DF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - (-2))^2 + (1 - 2)^2) = sqrt(25 + 1) = sqrt(26)
Apply the Pythagorean theorem:
If DF^2 = DE^2 + EF^2, then triangle DEF is a right triangle.
DF^2 = (sqrt(26))^2 = 26
DE^2 + EF^2 = (sqrt(13))^2 + (sqrt(13))^2 = 13 + 13 = 26
Since DF^2 equals DE^2 + EF^2, the Pythagorean theorem holds true, indicating that triangle DEF is a right triangle.
Therefore, the two methods of verification provide conflicting results. One method (using the perpendicularity criterion) suggests that DEF is not a right triangle, while the other method (using the Pythagorean theorem) suggests that it is a right triangle. In such cases, it is important to double-check the calculations and verify the accuracy of the given points to resolve the discrepancy.
Step-by-step explanation:
Se le dieron ocho esferas doradas a un rey, pero una de ellas era falsa, por lo que llamó al mejor matemático para demostrar que tenía razón. Dijo: te daré el balance, pero solo puedes usarlo dos veces. Si encuentras la esfera falsa, te doy el doble de recompensa.
Answers
The spheres into groups and testing the groups against each other The false Sphere,Now our findings to the king and claim our reward.
To identifying a false sphere using a balance with only two uses can be approached by dividing the spheres into groups and testing the groups against each other. Here's one possible solution to the problem:
First, divide the spheres into three groups of three, three, and two spheres each. Weigh the two smaller groups against each other on the balance. If they balance, then the false sphere must be in the larger group of three.
Next, take any two spheres from the larger group and weigh them against two spheres from one of the smaller groups. If they balance, then the false sphere must be the remaining sphere in the larger group. If they don't balance, then the false sphere must be one of the spheres being weighed.
Finally, take the two spheres that didn't balance and weigh them against each other. Whichever one is lighter is the false sphere.
Using this method, we have used the balance twice and identified the false sphere. Now, we just need to present our findings to the king and claim our reward.
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x and y intercept for x-2y=32
Answers
Answer:
The x-intercept is (32, 0),The y-intercept is (0, -16).------------------------
Set one variable to 0 and solve for the other.
For the x-intercept, set y = 0 and solve for x:
x - 2(0) = 32 x = 32For the y-intercept, set x = 0 and solve for y:
0 - 2y = 32 -2y = 32 y = -16The x-intercept is (32, 0) and the y-intercept is (0, -16).
Two angles, ∠A and ∠B, are complementary. If sin A = 4/7, what is cos B?
A. 74
B. 47
C. 37
D. √44/7
Answers
The Value of cos B is,
⇒ cos B = 0.64
We have to given that;
Two angles, ∠A and ∠B, are complementary.
And, sin A = 4/7
Now, We can simplify as;
sin A = 4/7
A = sin⁻¹ 4/7
A = 39.8°
Since, Two angles, ∠A and ∠B, are complementary.
Hence, We get;
∠A + ∠B = 90°
39.8° + ∠B = 90°
∠B = 90 - 39.8°
∠B = 50.2°
Thus, Value of cos B is,
⇒ cos B = cos 50.2° = 0.64
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Answer all these questions for ratio and rate
Answers
1. We can buy 15 cans of green beans for $10.
2. The jet could fly 959 miles in 7 hours at same speed.
3. Its take 4 days for the car manufacturer to produce 800 cars.
How many cans can be bought for $10?A proportion refers to an equation in which two ratios are set equal to each other.
To get how many cans of green beans you can buy for $10, we will set up a proportion:
9 cans / $6 = x cans / $10
By cross-multiplying, we get:
9*($10) = 6x
90 = 6x
x = 90 / 6
x = 15.
2. To get distance the jet can fly in 7 hours, we will use [tex]Distance = rate * time[/tex]
Rate = Distance / Time
Rate = 548 miles / 4 hours
Rate = 137 miles per hour
Now we will it to get how far the jet could fly in 7 hours:
Distance = Rate × Time
Distance = 137 miles per hour × 7 hours
Distance = 959 miles.
3. We will set up a proiportion.
1400 cars / 1 week = 800 cars / x days
To solve for x, we cross-multiply and divide
1400 * x = 800 * 7
1400x = 5600
x = 5600 / 1400
x = 4.
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Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?
Multiple Choice
a.5,734
b.8,000
c.4,601
d.4,050
Answers
when X = 3, Ŷ equals 4,601. The correct answer is (c) 4,601.
If the least squares regression equation is Ŷ = 1,202 + 1,133X, we can find the value of Ŷ when X = 3 by substituting X = 3 into the equation and solving for Ŷ:
Ŷ = 1,202 + 1,133(3)
Ŷ = 1,202 + 3,399
Ŷ = 4,601
what is equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=). The expressions on either side of the equals sign can be numbers, variables, or combinations of both, connected by arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.
An equation can be either true or false, depending on the values of the variables and constants involved. Equations are used in a wide variety of mathematical contexts, from basic arithmetic to advanced calculus, physics, and engineering.
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the slope of line that passes through the points (20,30) and (40,14) is
a) -5/4
b) -4/5
c) 4/5
d) 5/4
Answers
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (20, 30 ) and (x₂, y₂ ) = (40, 14 )
m = [tex]\frac{14-30}{40-20}[/tex] = [tex]\frac{-16}{20}[/tex] = - [tex]\frac{4}{5}[/tex]
Brainlest and 10 points!!!!!!!!!
Answers
Answer:
1. Yes, 90+45+45=180
2. Yes, adds to 180
3. No
4. No
Step-by-step explanation:
Express each of the following as a rational number: 7/12 - 5/6 + 1/8 - 5/8
Answers
Answer:
The answer is -0.75
Step-by-step explanation:
7/12-5/6+1/8-5/8
find Lcm of 12 and 8 is 24
7/12-5/6+1/8-5/8
-------------------------
24
2(7)-4(5)+3(1)-3(5)
-------------------------
24
14-20+3-15
-----------------
24
= -18
-----
24
=-3/4
= -0.75
i need help with my homework
Answers
The triangle drawn on the grid using the scaled dimensions is attached
Drawing the triangle on the grid
From the question, we have the following parameters that can be used in our computation:
Base = 10 meters
Height = 15 meters
The scale is given as
1 unit represents 2 meters
When represented on the grid, we have
Base = 10/2 units
Height = 15/2 units
Evaluate
Base = 5 units
Height = 7.5 units
Next, we draw the triangle on the grid using the above dimensions
See attachment for the triangle
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Find the value of x in the trapezoid below.
C
A
B
X
79° D
x = [?]°
Answers
The value of x in the trapezoid that is shown above is calculated as:
x = 101°.
How to Find the value of x in the Trapezoid?The trapezoid in the image shown is an isosceles trapezoid because the two lower base angles are indicated to be congruent to each other, therefore, any of the lower base angle and upper base angle would be supplementary or have a sum of 180 degrees when added together.
Given that angle A and angle D are congruent, therefore:
m<A = 79 degrees.
m<A + m<B = 180 [supplementary angles]
79 + x = 180
x = 180 - 79
x = 101°
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paperback books cost a total of $. How much change will Prakash get if he buys 3 hardcover books and 5 paperback books, and gives the clerk $20 bills?
Answers
If the cost of one paperback book is less than $1, he would receive even more change.
To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.
However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.
Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.
This is the maximum amount of change Prakash could receive if each paperback book costs $1.
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one way of solving systems of linear equations is by adding a multiple of one equation to the other. the multiplier for one equation is chosen so that one of the two variables will cancel out in the sum. what should you multiply the equation y
Answers
To eliminate one of the variables by adding a multiple of one equation to the other, you should multiply the equation containing the variable you want to eliminate by a suitable multiplier.
Let's assume you want to eliminate the variable y. In this case, you should multiply the equation containing y by a multiplier that will make the coefficient of y in one equation equal to the negative coefficient of y in the other equation. This will ensure that when you add the two equations, the y terms will cancel out.
For example, if the equation you want to eliminate y from is 2x + 3y = 7, and the other equation is 4x + 5y = 9, you would multiply the first equation by -5 and the second equation by 3 to obtain:
-5(2x + 3y) = -5(7) (equation 1 multiplied by -5)
3(4x + 5y) = 3(9) (equation 2 multiplied by 3)
This will result in:
-10x - 15y = -35 (equation 1 after multiplication)
12x + 15y = 27 (equation 2 after multiplication)
Now, when you add the two equations, the y terms will cancel out, and you can solve for the remaining variable x.
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Let event A = You roll an even number on the first cube.
Let event B= You roll a 4 on the second cube.
Are the events independent or dependent? Why?
A. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
B. Independent, because they have no outcomes in common.
C. Dependent, because 4 is an even number.
OD. Dependent, because both cubes have six sides.
Answers
Compare the rates of change of the following items.
y = 0.6z
6
8
00
2
4
OB. The rate of change of item I is equal to the rate of change of item II.
I
II
OA. The rate of change of item II is greater than the rate of change of item I
y
OC. The rate of change of item I is greater than the rate of change of item II
0.6
1.2
1.8
2.4
Answers
The rate of change of item I is greater than the rate of change of item II
The rate of change of item I is 0.6
Let us find the rate of change of item II
Rate of change = 1.2-0.6/4-2
=0.6/2
=0.3
So rate of change of item II is 0.3 which is lesser than rate of change of I
the rate of change of item I is greater than the rate of change of item II
Hence, the rate of change of item I is greater than the rate of change of item II
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a graph that uses images to symbolize the data that appears on the graph is known as a
Answers
A graph that uses images to symbolize the data that appears on the graph is known as a pictograph.
A pictograph is a type of chart that represents data using images or symbols. Each symbol on the pictograph represents a specific quantity, and the quantity is determined by the number of times the symbol appears on the chart. Pictographs are used to present data in a visually appealing and easy-to-understand manner, especially when the data is complex or there are multiple variables involved. Pictographs can be useful for a wide range of applications, from presenting sales figures to illustrating demographic information. They are often used in advertising, marketing, and educational materials to make data more engaging and memorable.
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A bakery makes cylindrical mini muffins that measure 2 inches in diameter and 1 and three fourths inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
103 and 5 over 7 in2
84 and 6 over 7 in2
66 and 1 over 7 in2
17 and 2 over 7 in2
Question 9(Multiple Choice Worth 2 points)
(Scale Factor MC)
The state of Colorado is 4 centimeters long and 3 centimeters wide on a map. A cartographer wants to use a scale factor of 2.5 to enlarge the map. What is the area of the enlarged map?
12 cm2
30 cm2
35 cm2
75 cm2
Question 10(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures LC)
An image of a rhombus is shown.
A rhombus with a base of 21 inches and a height of 19 inches.
What is the area of the rhombus?
160.5 in2
80 in2
399 in2
199.5 in2
Question 11(Multiple Choice Worth 2 points)
(Circumference MC)
A race car drove around a circular track that was 0.4 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.
107.11 feet
214.21 feet
336.31 feet
672.61 feet
Question 12(Multiple Choice Worth 2 points)
(Scale Factor MC)
The distance between two cities on a map is 25 inches. The actual distance between the two cities is 400 miles. How many miles would 35 inches be on the map?
560 miles
285 miles
16 miles
11 miles
Question 13(Multiple Choice Worth 2 points)
(Surface Area of Cylinders LC)
Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?
a cylinder with the diameter labeled 2.6 centimeters and the height labeled 3.8 centimeters
SA = 2π(1.3)2 + 1.3π(3.8)
SA = 2π(2.6)2 + 2.6π(3.8)
SA = 2π(2.6)2 + 1.3π(3.8)
SA = 2π(1.3)2 + 2.6π(3.8)
Question 14(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 6 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 5 centimeters.
What is the area of the tile shown?
34.5 cm2
45 cm2
54 cm2
57.5 cm2
Question 15(Multiple Choice Worth 2 points)
(Area of Circles LC)
A circle with a diameter of 36 inches is shown.
circle with diameter of 36 inches
What is the area of the circle using π = 3.14?
113.04 in2
452.16 in2
1,017.36 in2
4,069.44 in2
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Answers
The area of the circle with a Diameter of 36 inches, π = 3.14, is 1017.36 square inches.
The surface area of one mini muffin and multiply it by 6. The surface area of a cylindrical mini muffin can be calculated as 28 and 2/7 square inches. Multiplying by 6, we get a total of 169 and 1/7 square inches. Approximating the answer, we get 169 and 1/7 169.14 square inches. the correct answer is 169 and 1/7 square inches.
The area of the enlarged map, we need to scale up the dimensions of the state of Colorado by the scale factor of 2.5.
The length of the enlarged map would be 4 cm * 2.5 = 10 cm.
The width of the enlarged map would be 3 cm * 2.5 = 7.5 cm.
Area = length * width
Area = 10 cm * 7.5 cm
Area = 75 cm²
Therefore, the area of the enlarged map is 75 cm².
The area of a circle can be calculated using the formula:
Area = π * (radius)^2
the diameter of the circle is 36 inches, we can find the radius by dividing the diameter by 2:
Radius = 36 inches / 2 = 18 inches
Now, we can calculate the area using π = 3.14:
Area = 3.14 * (18 inches)^2
= 3.14 * 324 square inches
= 1017.36 square inches
the area of the circle with a diameter of 36 inches, using π = 3.14, is 1017.36 square inches.
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Please HELPP!!!!! I badly need this. Math, Geometry, circle unit.
Answers
Answer:
36 π and 12 π respectively.
Step-by-step explanation:
To find the area of a circle, we do πr^2. For circumference, we do 2πr, where r is the radius. Since we know the diameter of this circle is 12, and we know the radius is half the diameter, then:
12/2 = 6 = r
knowing r, we can find out the area and the circumference. The area is:
πr^2 = π 6^2, so it is 36π for the area. The circumference is:
2πr = 2 π 6 = 12π.
Triangle ABC has vertices at A(−3, 3), B(0, 4), and C(−3 , 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−3, −1), B′(0, 0), C′(−3, −4) A′(−3, 7), B′(0, 8), C′(−3, 4) A′(−7, 3), B′(−4, 4), C′(−7, 0) A′(1, 3), B′(4, 4), C′(1, 0)
Answers
The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.
So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:
A'(-3, 3 - 4) = A'(-3, -1)
B'(0, 4 - 4) = B'(0, 0)
C'(-3, 0 - 4) = C'(-3, -4)
Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).
So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).
To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
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The equation y = 5x + 50 shows the amount of money Emma has in her savings account. How much money will Emma have in her account after 30 weeks?
Answers
The amount of money that Emma would have in her account after 30 weeks is $200.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the amount of money Emma has in her savings account is given by;
y = mx + c
y = 5x + 50
By substituting the given parameter (x = 30 weeks), we have the following:
y = 5(30) + 50
y = $200
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Using the slope-intercept form of the linear equation, the amount in her account after 30 weeks is $200
What is a linear equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1.
In this problem, we are given an equation in the slope- intercept form and which is represented as y = mx + c
In the given equation;
y = 5x + 50
x = number of weeksThe amount in her account after 30 weeks is calculated as;
y = 5(30) + 50
y = 200
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In the parallelogram above, if DH = 13, find the length of DF.
Type your answer...
Answers
it will be 26 cm as diagonals bisect each other
3.1 Complete the following statements so that they are true: 3.1.1The angle between the tangent and chord is ... 3.1.2Opposite angles of a cyclic quadrilateral are ... 3.2In the diagram below, two circles have a common tangent TAB. PT is a tangent to the smaller circle. PAQ, QRT and NAR are straight lines. Let Q = 40°. N B 40° 3.2.1 Determine, with reasons, THREE other angles equal to 40°. 3.2.2 If P₁= A4 prove that PTRN is a parallelogram.
Answers
3.1.2 Opposite angles of a cyclic quadrilateral are supplementary.
3.2.1 Three other angles equal to 40° are:
- Angle APT: Since tangent PT is perpendicular to radius OA, angle APT is equal to angle OAP which is the same as angle QAT (alternate angles).
- Angle QAR: Since triangle QAR is isosceles (QA = QR), angle QAR is equal to angle QRA which is equal to 40°.
- Angle QPN: Angle QPN is the angle between the tangent PT and chord QN. Using the result from 3.1.1, angle QPN is equal to the angle subtended by chord QR in the alternate segment which is equal to angle QAR.
3.2.2 We know that angle QAR = 40° and angle QRT = 90° (since RT is a radius and hence perpendicular to tangent PT). Therefore, angle PRT = 50° (sum of angles in triangle PRT is 180°).
Since angles PRT and NRT are alternate angles, they are equal. Therefore, angle NRT = 50°.
Since angles QNR and QTR are alternate angles, they are equal. Therefore, angle QNR = 90° - 50° = 40°.
Since angle QNR = angle QAR, quadrilateral QNAR is cyclic. Therefore, angle QNA = 180° - angle QAR = 140° (opposite angles of a cyclic quadrilateral are supplementary).
Finally, since angles PTR and NRT are equal and opposite angles of a parallelogram, quadrilateral PTRN is a parallelogram.
Hence, we have proved that PTRN is a parallelogram.
Compute the following surface area.
A pyramid has base edges that measure 6 meters, and a slant height of 7.5 meters. What is its surface area?
__________sq. meters
Answers
Answer:
126 sq metres
Step-by-step explanation:
area of triangle = 0.5 X base length X height
surface area = base square + 4 (triangles)
= (6X6) + 4(0.5 X 6 X 7.5)
= 36 + 4(22.5)
= 36 + 90
= 126 (sq metres)
Mark
as
has
3 times
as
many marbles as
Sipho. If he
gives Sipho
17 marbles he will have
twice as many
marbles as
Sipho
Answers
Suppose Sipho has x marbles. According to the given information, Mark has 3 times more marbles than Sipho, so Mark has 3 times more marbles.
If Mark gives Sipho 17 marbles, Mark will be left with (3x - 17) marbles. And this will be twice as many Sipho particles, i.e. x.
Therefore, we can write the equation:
3x - 17 = 2x
To solve x, we subtract 2x on both sides of the equation:
3x - 2x - 17 = 0
Simplify the equation:
x - 17 = 0
Added 17 to both sides:
x = 17
So Sipho has 17 marbles. Since Mark has 3 times as many marbles as Sipho, Mark has 3 * 17 = 51 marbles.
So Sipho has 17 marbles and Mark has 51 marbles.
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Select the true statement about trend lines.
A. The distance between each point and the line is always the same.
B. The distance from the points to the line should be as small as
possible.
OC. A trend line connects the points.
D. A trend line goes through the first and last points.
Answers
The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.
What is a trend line?In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.
Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.
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a circle has radius 16 units and a central angle that defines an arc with length . a second circle has radius 5 units and a central angle that defines an arc with length . how do the measures of the 2 angles compare? explain or show your reasoning..
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In this problem, we have two circles with different radii and central angles defining arcs with specific lengths. We are asked to compare the measures of the two central angles.
Recall that the length of an arc (arc length) can be calculated using the formula: Arc Length = Radius × Central Angle (in radians). To compare the measures of the central angles, we'll first rearrange the formula to solve for the central angle: Central Angle = Arc Length / Radius.
For the first circle with radius 16 units and an arc length, let's denote the central angle as θ₁. Thus, θ₁ = Arc Length₁ / 16.
For the second circle with radius 5 units and an arc length, let's denote the central angle as θ₂. Therefore, θ₂ = Arc Length₂ / 5.
To compare the central angles θ₁ and θ₂, we can use the ratios of the respective arc lengths and radii. If the ratio of Arc Length₁ to Arc Length₂ is the same as the ratio of 16 to 5, then the central angles are equal. If the ratio is greater, then θ₁ is greater than θ₂, and if the ratio is smaller, then θ₁ is smaller than θ₂.
Without the specific arc lengths, we cannot determine the exact relationship between the central angles, but this method can be used to compare them once the arc lengths are provided.
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Given the functions f(x) = 2x −1 and g(x) = 2x + 4, which operation results in the largest coefficient on the x term? (1 point)
Addition
Subtraction
Multiplication
Two operations result in the same coefficien
Answers
Answer:
The answer is Multiplication.
Step-by-step explanation:
The coefficient of the x term in f(x) is 2, and the coefficient of the x term in g(x) is 2. When we add or subtract the two functions, the coefficient of the x term remains 2. However, when we multiply the two functions, the coefficient of the x term becomes 4. Therefore, multiplication results in the largest coefficient on the x term.
Here is the solution for each of the operations:
Addition: f(x) + g(x) = (2x −1) + (2x + 4) = 4x + 3
Subtraction: f(x) - g(x) = (2x −1) - (2x + 4) = -5
Multiplication: f(x) * g(x) = (2x −1) * (2x + 4) = 4x^2 + 6x - 4
As you can see, the coefficient of the x term in f(x) * g(x) is 4, which is larger than the coefficients of the x terms in f(x) + g(x) and f(x) - g(x). Therefore, multiplication results in the largest coefficient on the x term.
suppose at a certain college we know 80% of the students like chipotle and 65% of the students like papa john's pizza. moreover, of the students that like chipotle we know 69% like papa john's pizza. suppose we randomly select a student. what is the probability that a student likes papa john's, given they do not like chipotle?
Answers
Therefore, the probability that a student likes papa john's given they do not like chipotle is approximately 0.275 or 27.5%.
Bayes' theorem allows us to calculate conditional probabilities, which is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that a student likes Papa John's pizza given that they do not like Chipotle.
We start by using the given probabilities to calculate the probability that a student does not like Chipotle, which is the complement of the probability that they do like Chipotle. Then, we calculate the probability that a student likes both Papa John's and Chipotle, and use this to find the probability that a student likes Papa John's given that they do not like Chipotle.
Bayes' theorem is a powerful tool that is used in a wide range of fields, including statistics, probability theory, and machine learning. It provides a systematic way to update probabilities based on new information or evidence, which is a crucial aspect of many real-world applications.
P(B) = 1 - 0.8 = 0.2 (the probability that a student does not like chipotle)
P(A|B) = P(A and B) / P(B) = (0.65 - 0.69*0.8) / 0.2 ≈ 0.275
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