Answers
1. The values of x, y, and z are x = 15.5, y = 9.54, and z = 0. 2. The values of x and y are x = 1.4375 and y = 8. 3. The values of x and y are x = 6 and y = 52.5. 4. X can have any value and the triangles will still be similar
1. We are given that ΔPRS is congruent to ΔCFH.
From ΔPRS, we know that:
∠P = 180 - 28 - ∠R
∠P = 152 - 13y
From ΔCFH, we know that CH is the hypotenuse and CF is one of the legs. So, using the Pythagorean Theorem, we have:
CH^2 = CF^2 + FH^2
39^2 = 24^2 + FH^2
FH^2 = 39^2 - 24^2
FH = sqrt(39^2 - 24^2) = 30
Since ΔPRS is congruent to ΔCFH, their corresponding sides are equal. Therefore:
PS = CH = 39
2x - 7 = CF = 24
Solving for x and y:
2x - 7 = 24
2x = 31
x = 15.5
39 = 2x - 7
46 = 2x
x = 23
∠P = 152 - 13y
28 = 152 - 13y
124 = 13y
y = 9.54
Solving for z:
PS = 2x - 7
39 = 2(15.5) - 7
39 = 31
z = 0
Therefore, the values of x, y, and z are x = 15.5, y = 9.54, and z = 0.
2. We are given that ΔABC is similar to ΔDEF. Therefore, the corresponding sides are proportional:
AB/DE = BC/EF = AC/DF
Substituting the given values:
8/(y-6) = 19/(4x-1) = 14/DF
We can solve for x and y using any two of the three ratios.
Let's first solve for x and y using the first two ratios:
8/(y-6) = 19/(4x-1)
Cross-multiplying, we get:
8(4x-1) = 19(y-6)
Expanding the brackets, we get:
32x - 8 = 19y - 114
32x - 19y = -106
Now let's use the third ratio:
14/DF = 8/(y-6)
Cross-multiplying, we get:
14(y-6) = 8DF
Simplifying, we get:
y = (4/7)DF + 6
Substituting this into the equation we got earlier:
32x - 19y = -106
32x - 19[(4/7)DF + 6] = -106
32x - (76/7)DF - 114 = -106
32x - (76/7)DF = 8
Multiplying both sides by 7, we get:
224x - 76DF = 56
Using the equation we got from the third ratio:
14(y-6) = 8DF
14y - 84 = 8DF
14y = 8DF + 84
y = (4/7)DF + 6
Substituting this into the equation we just got:
14[(4/7)DF + 6] = 8DF + 84
8DF + 84 = (56/7)DF + 84
8DF = (56/7)DF
DF = 7
Substituting DF = 7 into the third ratio:
14/DF = 8/(y-6)
14/7 = 8/(y-6)
2 = y-6
y = 8
Now we can substitute y = 8 into the equation we got earlier:
32x - 19y = -106
32x - 19(8) = -106
32x - 152 = -106
32x = 46
x = 1.4375
Therefore, the values of x and y are x = 1.4375 and y = 8.
3. Since ΔZMK ≈ ΔAPY, we know that the corresponding angles are congruent:
m∠M = m∠A
m∠K = m∠Y
Therefore, we can write two equations:
m∠M = 2y + 7
m∠K = 41°
Also, we know that:
m∠M + m∠K + (13x - 37)° = 180°
Substituting the values we have:
112° + 41° + (13x - 37)° = 180°
13x + 116 = 180
13x = 64
x = 4.9231
Substituting x into the third equation:
112° + 41° + (13x - 37)° = 180°
13x + 116 = 180
13(4.9231) + 116 + m∠K = 180
m∠K = 41°
Substituting m∠K = 41° into the second equation:
m∠K = m∠Y
13x - 37 = 41
13x = 78
x = 6
Substituting x into the first equation:
m∠M = 2y + 7
112 = 2y + 7
105 = 2y
y = 52.5
Therefore, the values of x and y are x = 6 and y = 52.5.
4. Since ΔBTS ≈ ΔGHD, we know that the corresponding angles are congruent:
m∠S = m∠H
m∠B = m∠G
Therefore, we can write two equations:
m∠S = 7y + 5
m∠B = m∠G = 21°
Also, we know that:
m∠B + m∠T + m∠S = 180°
Substituting the values we have:
21° + m∠T + 56° = 180°
m∠T = 103°
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠G:
m∠B + m∠T + m∠G = 180°
21° + 103° + m∠G = 180°
m∠G = 56°
Since we have a pair of similar triangles, we can use their side lengths to set up a proportion:
BS/BT = GD/GH
Substituting the given values:
25/31 = (4x-11)/GH
Solving for GH:
GH = (31/25)(4x-11)
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠H:
m∠G + m∠H + m∠D = 180°
56° + m∠H + 90° = 180°
m∠H = 34°
Substituting the values we have:
m∠S = 7y + 5
56 = 7y + 5
51 = 7y
y = 7.2857
Substituting y into the first equation:
m∠S = 7y + 5
m∠S = 7(7.2857) + 5
m∠S = 59
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠T:
m∠B + m∠T + m∠S = 180°
21° + m∠T + 59° = 180°
m∠T = 100°
Now we can use the fact that we have a pair of similar triangles to find x:
BS/BT = GD/GH
25/31 = (4x-11)/GH
25/31 = (4x-11)/((31/25)(4x-11))
Simplifying:
25/31 = 25/31
Therefore, x can have any value and the triangles will still be similar.
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Related Questions
The first place sled team took 9 days, 15 hours, and 46 minutes to finish the Iditarod. The second place team took 9 days, 21 hours, and 39 minutes. How much faster was the first place team?
PLEASE PUT ANSWER AS HOURS AND MINUTES FASTER, Thank You!!!!
Answers
Answer: ur mom anyways jk
Step-by-step explanation:
6hrs and 7mins pls dont trust me on this answer and if u get it wrong im sorry
Fill in the missing value. 4:9 = ? : 36
Answers
i think it may be 16:36
explanation: if the 9 was multiplied by 4 which 9x4 is 36 it means that the 4 for the 4:9 will probably end up 16 hence 4x4 is 16 making the answer probably 16:36 to my own understanding
Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z
Answers
Using analyzing functions, The correct answer is B. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane.
What are the analyzing functions?Studying a mathematical function's characteristics and behavior is the process of doing an analysis of a function.
Telling a function's story involves detailing all of its attributes and features.
When you analyze a function, you are telling your side of the story and outlining how you came to your conclusions.
A thorough study involves global information from graphs and precise information from algebra. The graphical and algebraic data should be in agreement, so you may use either to support the other as you do the analysis.
The function [tex]g(x) = (x + 1)^2[/tex] is a vertical shift of the function [tex]f(x) = x^2[/tex]. The vertex of the parabola representing g(x) is shifted one unit to the left, and one unit up.
The graph for option X matches these specifications and passes through the given points, so it represents the function g(x) = [tex](x + 1)^2.[/tex]
Hence, The correct answer is B. X.
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The sum of two numbers is 54 and the difference is 2. What are the numbers?
Answers
Answer:
25, 27
Step-by-step explanation:
maybe ,,,,,,,,,hhy2u2u
Answer: Sum: 28 + 26 = 54
Difference: 28 - 26 = 2
Step-by-step explanation:
x + y = 54
x + 26 = 54
X = 28
Find the image vertices for a dilation with center (0,0) and scale factor of 4.
Answers
Let's say we have a triangle with vertices A, B, and C. The coordinates of these vertices are:
A = (2, 4)
B = (-3, 1)
C = (0, -2)
To find the image vertices after a dilation with a center of (0,0) and a scale factor of 4, we can multiply each coordinate by 4.
For vertex A:
A' = (4 * 2, 4 * 4) = (8, 16)
For vertex B:
B' = (4 * (-3), 4 * 1) = (-12, 4)
For vertex C:
C' = (4 * 0, 4 * (-2)) = (0, -8)
Therefore, the image vertices after a dilation with a center of (0,0) and a scale factor of 4 are:
A' = (8, 16)
B' = (-12, 4)
C' = (0, -8)
A company makes wax candles in the shape of a cylinder. Each candle has a radius of 3 inches and a height of 4 inches. How much wax will the company need to make 140 candles?
Use 3.14 for \pi , and do not round your answer.
Answers
Answer:
15825.6 [tex]in^3[/tex]
Step-by-step explanation:
using 3.14 for pi you follow the formula for volume of a cylinder which is [tex]\pi r^2 h[/tex] when we plug in it comes to [tex]3.14\cdot3^{2}\cdot4[/tex] and then you solve that to get 113.04, but since you need 140 candles, we multiply the volume of one candle by 140 to get 15825.6 [tex]in^3[/tex]
What is the value of x in the equation 8+4=2(x-1) brainly 5 11/2
Answers
The value of x in the equation 8+4=2(x-1) is 7
To solve for x in the equation 8+4=2(x-1), we can follow these steps:
Simplify the left-hand side of the equation by adding 8 and 4 to get 12:
8 + 4 = 12
Simplify the right-hand side of the equation by distributing the 2 to the expression inside the parentheses:
2(x-1) = 2x - 2
Set the left-hand side and the right-hand side equal to each other:
12 = 2x - 2
Add 2 to both sides of the equation:
12 + 2 = 2x
14 = 2x
Divide both sides of the equation by 2:
14/2 = x
x = 7
Therefore, the value of x in the equation 8+4=2(x-1) is 7.
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Line t is shown in the coordinate plane. -6-5 -6 5 -4 2 -1 -2-10 3 4 5 6 X A. What is the slope of line t? B. What is the y intercept? C. Line s (not shown) has the same slope and passes through the point (0,4).Draw a table representing points on line s? D. Which equation could represent line s? i.y = -x + 4 ii. y = -3x +4 iii. y= 3x + 4 iv. y=1/3x +4
Answers
The slope of line t is equal to 1/3.
The y-intercept of line t is equal to -1.
A table representing points on line s is shown below.
An equation that could represent line s is: IV. y = 1/3x +4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (0 - (-1))/(3 - 0)
Slope, m = 1/3
Based on the graph, the y-intercept of t is at point (0, -1)
Additionally, a table representing points on line s is given by;
x y
-6 2
-3 3
0 4
3 5
Since line s has the same slope and passes through the point (0, 4), an equation that represents it is given by;
y = mx + c
y = x/3 + 4.
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4^2 =2 x (----- + 3) complete this calculation
Answers
4^2 = 2 x (5 + 3) = 2 x 8 = 16
Step by step solved:
Starting with 4^2 = 2 x (----- + 3), we can work backwards to solve for the missing value:
4^2 = 2 x (----- + 3)
4^2 = 2 x (x + 3) (let x represent the missing value)
4^2 = 2x + 6
16 = 2x + 6 (evaluate 4^2 as 16)
10 = 2x
5 = x
Therefore, the missing value is 5, and the completed calculation is:
4^2 = 2 x (5 + 3) = 2 x 8 = 16
Do segments with lengths 11, 12, and 20 form a triangle? If so, classify the triangle as acute, right, or obtuse?
Answers
Answer:
Yes, the segments with lengths 11, 12, and 20 can form a triangle.
To check this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we can check that:
11 + 12 > 20
11 + 20 > 12
12 + 20 > 11
Since all three inequalities are satisfied, the segments can form a triangle.
To classify the triangle, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, for a triangle with sides a, b, and c and angle A opposite side a, we have:
c^2 = a^2 + b^2 - 2ab cos(A)
Using this formula, we can find the cosine of each angle and determine if the triangle is acute, right, or obtuse based on the values obtained.
For the given triangle, we have:
a = 11, b = 12, c = 20
cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) ≈ 0.714
Since cos(A) is positive and less than 1, the angle A is acute. Similarly, we can find the cosines of the other angles:
cos(B) = (c^2 + a^2 - b^2) / (2ca) ≈ 0.943
cos(C) = (a^2 + b^2 - c^2) / (2ab) ≈ -0.519
Since cos(B) and cos(C) are both positive and less than 1, angles B and C are also acute.
Therefore, the given triangle is acute.
Find the measurements of X
pt. 2
Answers
Answer:
45
Step-by-step explanation:
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer: x=-6
Step-by-step explanation:
8x+14=4x-10
-4x -4x
4x+14=-10
-14 -14
4x=-24
/4 /4
x=-6
Given:-
[tex] \tt \: 8x + 14 = 4x - 10[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 8x + 14 = 4x - 10[/tex][tex] \: [/tex]
[tex] \tt \: 8x - 4x = -10 - 14[/tex][tex] \: [/tex]
[tex] \tt \: 4x = -24[/tex][tex] \: [/tex]
[tex] \tt \: x = \cancel\frac{ - 24}{4} [/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \purple{ \: x = -6 \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
If the price of cocoa beans goes up, what will happen to the supply of chocolate?
Producers will produce more chocolate
The supply of chocolate will remain unchanged
Producers will offer less chocolate to the market
The demand for chocolate will immediately increase
Answers
Answer:
producers Will grow more chocolate.
The area of a classroom is 20 square meters. If the length is increased by 3 meters and the width is increased by 1 meter, the classroom will double in area. Determine the dimension of the new classroom.
Answers
The dimension of the new classroom is 8 meters of length and 5 meters of width.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given that,
Area of the classroom = 20 square meters
Let x be the length and y be the width of the classroom.
Area of a rectangular classroom = Length × Width.
So, we get an equation,
xy = 20
x = 20/y [Equation 1]
If length is increased by 3 meters and the width is increased by 1 meter, the classroom will double in area.
(x + 3) (y + 1) = 20 × 2
(x + 3) (y + 1) = 40 [Equation 2]
Substitute [Equation 1] in [Equation 2]
((20/y) + 3) (y + 1) = 40
Multiplying,
20 + 3y + (20/y) + 3 = 40
3y + (20/y) = 40 - 23
3y + (20/y) = 17
Multiplying throughout by y,
3y² + 20 = 17y
3y² - 17y + 20 = 0
3y² - 12y - 5y + 20 = 0
3y (y - 4) - 5 (y - 4) = 0
(3y - 5) (y - 4) = 0
3y - 5 = 0 or y - 4 = 0
y = 5/3 or y = 4
Let y = 4, then x = 20/4 = 5
Dimension of the new classroom is (x+3) = 8 meters and (y+1) = 5 meters
Hence the dimension of the new classroom is 8 meters and 5 meters.
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let ABC be a triangle. Determine the exact values of
the three angles A, B, C. if we know that A = 5x, B = 6x, and C =
7x
Answers
For the given triangle ABC, the exact values of the three angles are: A = 50°, B = 60°, and C = 70°.
Let ABC be a triangle. The angles A, B, and C can be determined using the fact that the sum of the angles in any triangle is 180°.
We know that
A = 5x, B = 6x, and C = 7x, so:
A + B + C = 5x + 6x + 7x = 18x
Since the sum of the angles in a triangle is 180°, we can set
18x = 180°
and solve for x:
18x = 180°, x = 10°
Therefore, A = 50°, B = 60°, and C = 70°.
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The CEO of Super Electronics asked customers to fill out a survey to win a $100 gift certificate. The customers were asked to list the products they purchased that day. 88 bought laptop computers. 52 bought desktop computers. 64 bought printers. What is the probability that the winner of the gift certificate bought a printer from Super Electronics? A.
Answers
Answer:
To calculate the probability that the winner of the gift certificate bought a printer from Super Electronics, we need to use the total number of customers who participated in the survey as the denominator and the number of customers who bought printers as the numerator.
The total number of customers who participated in the survey is:
Total Customers = Number of Customers who bought Laptops + Number of Customers who bought Desktops + Number of Customers who bought Printers
Total Customers = 88 + 52 + 64
Total Customers = 204
The number of customers who bought printers is 64.
Therefore, the probability that the winner of the gift certificate bought a printer from Super Electronics is:
P(Bought a Printer) = Number of Customers who bought Printers / Total Customers
P(Bought a Printer) = 64 / 204
P(Bought a Printer) = 0.3137 (rounded to 4 decimal places)
So, the probability that the winner of the gift certificate bought a printer from Super Electronics is 0.3137 or approximately 31.37%.
The real number
t
corresponds to the point
P(− 2
1
, 2
3
)
on the unit circle. Evaluate the six trigonometric functions of
t
. Write your answer as a simplified frection, if necessary, Part 2 of 6
cost=
Part 5 of 6
Answers
The real number t corresponds to the point P(-2/1, 2/3) on the unit circle. To evaluate the six trigonometric functions of t, we can use the coordinates of point P.
Part 2 of 6:
cost= x-coordinate of point P = -2/1 = -2
Part 5 of 6:
sect= 1/cost= 1/(-2)= -1/2
The other four trigonometric functions can be evaluated similarly using the coordinates of point P:
sint= y-coordinate of point P = 2/3
cott= x-coordinate/y-coordinate = (-2/1)/(2/3) = -3
csc t= 1/sint= 1/(2/3)= 3/2
tant= y-coordinate/x-coordinate = (2/3)/(-2/1) = -1/3
Therefore, the six trigonometric functions of t are:
sint= 2/3
cost= -2
tant= -1/3
csc t= 3/2
sect= -1/2
cott= -3
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Out of 12,14,15,16,18,20,22 and 24
What numbers have the sum of a prime number
Answers
Answer:14+15=19, 15+16=31, 15+22=37
Step-by-step explanation:
Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?
Answers
The final answer is 8*2=16 ways
Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?
There are a couple of steps to solving this problem.
Step 1: Consider the two people who insist on sitting next to one another as one unit. This means that there are now 7 units to be seated in the 8 chairs.
Step 2: Calculate the number of ways that the 7 units can be seated in the 8 chairs. This is done using the formula n!/(n-r)!, where n is the number of chairs and r is the number of units. In this case, n=8 and r=7, so the formula is 8!/(8-7)!, or 8!/1!, which simplifies to 8.
Step 3: Calculate the number of ways that the two people who insist on sitting next to one another can be seated within their unit. There are 2! or 2 ways that they can be seated.
Step 4: Multiply the number of ways that the 7 units can be seated in the 8 chairs by the number of ways that the two people can be seated within their unit. This gives us the total number of ways that the 8 people can be seated if two of them insist on sitting next to one another.
So the final answer is 8*2=16 ways.
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Factor the following complex matrices into unitary times upper triangular:
(i) i 1 , (ii) 1+i 2-1 , (iii) i 1 0 , -1 2i 1-i -1 1 i 1
0 1 i
(iv) 1 1 -i
1-i 0 1+i
-1 2+3i 1
Answers
The answer is calculated by elementary row operations
To factor the given complex matrices into unitary times upper triangular, you will need to use elementary row operations. Specifically, you can use scaling, addition, subtraction, and multiplication of rows.
(i) i 1:
Row 1: Scale by i
Result: i2 1 = -1 1
(ii) 1+i 2-1:
Row 1: Subtract Row 2
Result: 1 0 -1
Row 2: Scale by i
Result: i 1 -i
(iii) i 1 0 , -1 2i 1-i -1 1 i 1
Row 1: Subtract i times Row 2
Result: 0 1 0 , -1 2i 0 -i -1 0 i
Row 2: Scale by i
Result: 0 1 0 , i 0 -1 -i -1 0 1
Row 3: Subtract Row 1
Result: 0 0 0 , i 0 -1 -i -1 0 1
(iv) 1 1 -i
Row 1: Subtract Row 2
Result: 1 0 -i
Row 2: Scale by i
Result: i 0 1+i
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Use the compound interest formula \( A=P e^{\lambda t} \) to solve. Round to two decimal places. Find the accumulated value of an investment of \( \$ 5,000 \) at \( 9 \% \) compounded continuously for
Answers
The accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
The accumulated value of an investment of $\$ 5,000$ at 9% compounded continuously for 4 years is $7,311.12.
This can be calculated using the compound interest formula
\(A=P e^{\lambda t}\).
In this equation, A is the accumulated value of the investment, P is the principal investment amount (which is $\$ 5,000$), $\lambda$ is the interest rate per compounding period (which is 0.09) and t is the number of compounding periods (which is 4 years).
Therefore, the accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
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Who can help me please
Answers
The similarity statements are;
SV/RS = TV/TU
AC/AB = CE/ED
What are similar triangles?Formally, two triangles ABC and DEF are similar if and only if:
Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.
The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.
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use the table that shows air mail letter rates to greenland. weight 5.0, 6.0, 7.0, 80. Rate: 4.20, 5.05, 5.90, 6.75
Answers
The set of ordered pairs from the given table is: (5.0, 4.20), (6.0, 5.05), (7.0, 5.90), (8.0, 6.75).
What are ordered pairs?When two items are written inside parantheses and are separated by a comma, they create an ordered pair. For instance, the ordered pair (x, y) indicates an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables or constants, have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant. It implies that (x, y) may not always be equivalent to (y, x).
The set of ordered pairs from the given table is:
(5.0, 4.20)
(6.0, 5.05)
(7.0, 5.90)
(8.0, 6.75)
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The complete question is:
Find the determinant. \[ \left|\begin{array}{ccc} d+b & d & d \\ d & d+b & d \\ d & d & d+b \end{array}\right| \]
Answers
The determinant of a 3x3 matrix can be found using the following formula:
\[ \left|\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}\right| = a(ei - fh) - b(di - fg) + c(dh - eg) \]
In this case, we can substitute the values from the given matrix into the formula:
\[ \left|\begin{array}{ccc} d+b & d & d \\ d & d+b & d \\ d & d & d+b \end{array}\right| = (d+b)((d+b)(d+b) - d^2) - d(d(d+b) - d^2) + d(d^2 - d(d+b)) \]
Simplifying the expression gives:
\[ = (d+b)(d^2 + 2bd + b^2 - d^2) - d(d^2 + bd - d^2) + d(d^2 - d^2 - bd) \]
\[ = (d+b)(2bd + b^2) - d(bd) + d(-bd) \]
\[ = 2bd^2 + 2b^2d + b^3 - bd^2 - bd^2 \]
\[ = b^3 + 2b^2d \]
Therefore, the determinant of the given matrix is \[b^3 + 2b^2d\].
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What is the value of x in this triangle? Enter your answer in the box. x = A triangle with angle measures 39 degrees and 102 degrees. The third angle has an unknown measure, x degrees.
Answers
Answer:
39°
Step-by-step explanation:
You want to know the measure of the third angle in a triangle with two angles given as 39° and 102°.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
39° +102° +x = 180°
x = 39° . . . . . . . . . . . . subtract 141° from both sides
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Correct tion for the circle with the following properties. Center (4,8), passes through (-10,-5)
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The equation of a circle with center at (4, 8) and passing through (-10, -5) is [tex](x-4)^2 + (y-8)^2 = (6)^2.[/tex]
To find this equation, we need to use the distance formula: [tex]d = sqrt((x2-x1)^2 + (y2-y1)^2).[/tex]
We can substitute in the coordinates of the center of the circle and the point it passes through:
[tex]d = sqrt((-10-4)^2 + (-5-8)^2)[/tex]
[tex]d = sqrt( (6)^2 + (13)^2 )[/tex]
d = sqrt(36 + 169)
d = sqrt(205)
d = 14.2
Now, we have the radius of the circle. We can use this to form the equation of the circle:
[tex](x-4)^2 + (y-8)^2 = (14.2)^2[/tex]
[tex](x-4)^2 + (y-8)^2 = (6)^2[/tex]
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Make a table comparing a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with both descriptions and sketches, including markings for congruency. All work should be original
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We have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.
What is congruency?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
Parallelogram: A four-sided shape with opposite sides parallel. Opposite sides are parallel, opposite angles are congruent, diagonals bisect each other.
Rectangle: A four-sided shape with four right angles.
Opposite sides are parallel and congruent, all angles are right angles, diagonals are congruent and bisect each other.
Square: A four-sided shape with four congruent sides and four right angles.
All sides are congruent, all angles are right angles, diagonals are congruent and bisect each other.
Rhombus: A four-sided shape with four congruent sides. All sides are congruent, opposite angles are congruent, diagonals bisect each other, and are perpendicular bisectors of each other.
Kite: A four-sided shape with two pairs of adjacent sides congruent. Diagonals are perpendicular, one diagonal bisect the other, opposite angles are congruent.
Trapezoid: A four-sided shape with one pair of parallel sides.
One pair of opposite sides are parallel, non-parallel sides may or may not be congruent, and diagonals intersect at a point inside the trapezoid.
Hence, we have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.
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PLEASE HELP!!! I don’t have to show any work btw! <33
1) Which of the following are the coordinates of point B’ , the image of point B after a translation of (x-4, y-3)
A- B’(-1,2)
B- B’(-4,-3)
C- B’(1,5)
D- B’(1,-2)
2) The two figures are congruent. Describe the isometry that maps the original figure onto the new figure.
A- Translation (x-3,y-1)
B- Reflection over the line x = 1
C- 90 Degree Rotation
D- 270 Degree Rotation
3) The smaller figure is a dilation of the original figure. Which two statements below are true?
A- The dilation is an enlargement.
B- The dilation is a reduction.
C- The dilation has a scale factor of 1/2
D- The dilation had a scale factor of 2
E- The dilation has a scale factor of 1/4
4) Complete a glide translation (x-2,y) and then reflect over x axis. What would be the new ordered pairs for P’ and S’?
A- P’(1,-2) S’(2,5)
B- P’(5,-2) S’(6,-5)
C- P’(1,2) S’(2,5)
D- P’(3,2) S’(4,5)
5) Complete a dilation with scale factor of 1/2 around the origin and then reflect over the y-axis. What are the new ordered pair of A’?
A- A’(-4,-10)
B- A’(-1,-2.5)
C- A’(2,5)
D- A’(1,2.5)
Tysm
Answers
The coordinates of B' after the translation represented by (x - 4, y - 3) is (1, -2). See other solutions below
The coordinates of B' after the translationB is located at the point (5, 1) in the figure.
If we translate the point by (x - 4, y - 3), the new location of B, denoted by B', can be found by subtracting 4 from the x-coordinate and 3 from the y-coordinate.
Therefore, B' is located at (1, -2).
The isometry transformationThe given information provides us with a set of matching points, which are:
Preimage = (2, 1)
Image = (-1, 2)
These points can be represented by the equation:
(x, y) = (-y, x)
This equation indicates that the points have undergone a (d) clockwise rotation of 270 degrees.
The statements of the dilationHere, the smaller shape is created by scaling down a larger shape, the transformation is a dilation that results in a reduction.
The scale factor for this transformation could be either 1/2 or 1/4.
The glide transformatonGiven the points P = (3, -2) and S = (4, -5), we apply two transformations.
The first transformation (x - 2, y) is defined as shifting the x-coordinate of each point left by 2 units, while keeping the y-coordinate the same.
This results in new points P' = (1, -2) and S' = (2, -5).
The second transformation involves reflecting the new points across the x-axis, which changes the sign of their y-coordinates.
The resulting points are P'' = (1, 2) and S'' = (2, 5).
The new ordered pair of point AIn this context, we are given the coordinates of point A as (-2, -5).
This implies that if we scale down the original coordinates by a factor of 1/2, we get the new coordinates of point A, which become (-1, -2.5).
Therefore, the coordinates of point A' are (-1, -2.5).
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Big ideas 7.5 question
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Measure of angles ∠Q,∠T,∠R are 98°, 98°, 82° respectively.
What is isosceles trapezoid?An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid.
Given,
Isosceles trapezoid QRST
m∠S = 82°
Base angles are equal in Isosceles trapezoid
m∠R = m∠S
m∠R = 82°
and
m∠Q = m∠T
Sum of all interior angles of a quadrilateral is 360°
m∠Q + m∠T + m∠R + m∠S = 360°
m∠Q + m∠Q + 82° + 82° = 360°
2 m∠Q = 360° - 164°
2 m∠Q = 196°
m∠Q = 98°
m∠T = 98°
Hence, 98°, 98°, 82° are measure of angles ∠Q,∠T,∠R respectively.
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Suppose that a distribution is normal, with mean =10 and standard deviation =3. Two samples a and b, each of length N, are independently drawn from this distribution. For which of the following operations on a and b will the resulting distribution also be normal?
If the distribution is normal, state this and provide exact mathematical expressions (integer, fraction, radical, etc.) for the mean, median, and standard deviation of the new distribution (do not use a decimal). If the distribution is not normal, use R to numerically estimate the values and express the result as a decimal (at least 3 significant figures).
Summarize your results in a table similar to the one given below. (Note that some quantities may not be well-defined mathematically. You do not have to check for this, but you can mark possible cases with asterisks.)
Answers
Yes, the distribution of a and b is normal, with mean μ=10, median m=10, and standard deviation σ=3.
The resulting distribution of a+b, a-b, a*b, and a/b will also be normal, with the following values:
Operation
Mean
Median
Standard Deviation
a+b
μ=20
m=20
σ=√6
a-b
μ=0
m=0
σ=√6
a*b
μ=100
m=100
σ=30
a/b
μ=3
m=3
σ=1
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