The coordinates of each vertex are: P(8,4) Q(10, 4) R(13,-1) S(8,-1) then the length of side PS is 0 units.
Side PS is the bottom base of trapezoid PQRS. To find its length, we need to calculate the horizontal distance between the x-coordinates of points P and S.
The x-coordinate of point P is 8, and the x-coordinate of point S is also 8. Therefore, the horizontal distance between these two points is 0. So, the length of side PS is 0 units.
The answer is (A) 2 is not correct because the length of side PS cannot be negative or less than zero, and the length of the other base of the trapezoid (QR) is 2 units, which is not equal to the length of side PS.
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Angle BCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 13 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box.
Answer:12.4
Step-by-step explanation:
18^2-13^2=155
Square root of 155 to the nearest tenth is 12.4
Dylan has a square piece of metal that measures 17 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?
The length of the hypotenuse of each right triangle to the nearest tenth of an inch is 24 inches.
Here, two right triangles with legs each measuring 17 inches are created when the square piece of metal is sliced diagonally.
We will apply the Pythagorean Theorem to find the length of the hypotenuse.
The Pythagorean theorem states that square of hypotenuse is equal to the sum of the squares of opposite side and adjacent side.
Now,
[tex]Hypotenuse^{2} = 17^{2}+ 17^{2} \\Hypotenuse^{2} =289+289\\Hypotenuse^{2} =578\\Hypotenuse=\sqrt{ 578}\\Hypotenuse=24.04[/tex]
⇒ Hypotenuse ≈ 24 inches (to the nearest tenth of an inch)
Therefore, the length of the hypotenuse of each right triangle to the nearest tenth of an inch is 24 inches.
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Look at the image below.
What is the area of the triangle?
Answer:
60
Step-by-step explanation:
Area of a triangle: 1/2(bh)
Base = 12
Height = 10
1/2(12*10)
1/2(120) = 60
In a scale model of a boat 1 inch represents 5 feet
The height of the real boat is 3 inches and length of the boat is 45 feet
What is Unit of Measurement?
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
In a scale model of a boat 1 inch represents 5 feet
1 inch = 5 feet
The height of the real boat is 15 feet
We have to find in inches
1/5=x/15
x=3 inches
So height of the real boat is 3 inches
The length of the boat is 9 inches
We have to find in feet
1/5 = 9/x
x=45 feet
Hence, the height of the real boat is 3 inches and length of the boat is 45 feet
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If arc wvx=(13x+9) and angle wxz=(5x+36) find angle wxy
Angle WXY is vertical to angle WXZ, they are equal, therefore, angle WXY is also 141 degrees.
How to find the angle WXY using information about the arc WVX and angle WXZ in a circle?To find the angle WXY, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.
Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an equation:
Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX
(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)
To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:
2(5x + 36) = 13x + 9
10x + 72 = 13x + 9
Subtracting 10x and 9 from both sides, we get:
72 - 9 = 13x - 10x
63 = 3x
Dividing both sides by 3, we find:
x = 21
Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:
Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 degrees
Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.
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In which quadrant does 0 lie if the following statements are true: cos 0 > and sin> 0
The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.
Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.
Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.
Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
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(4y + z)^2 what is the a value and what is the b value
Answer:
a = 16
b = 8z
Step-by-step explanation:
Expanding the given expression, we get:
(4y + z)^2 = (4y + z) × (4y + z)
= 16y^2 + 8yz + z^2
Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:
a = 16
b = 8z
Therefore, the value of a is 16 and the value of b is 8z.
The unit in a volume are always ________.
Answer:
The unit in a volume are always cubic meter
Step-by-step explanation:
Chain of Thought Reasoning: Volume is a three dimensional space, which is measured in three dimensions (length, width, and depth). The SI unit for length is meters, so the SI unit for volume is cubic meters (m^3). I hope this helps you
Boris needs to read 2 novels each month.let n be the number of novels boris needs to read in m months.write an equation relating n to m. then use this equation to find the number of novels boris needs to read in 17 months.equation:number of novels in 17 months: i novels
Solving the equation, Boris needs to read 34 novels in 17 months.
Given that Boris needs to read 2 novels each month.
To relate the number of novels Boris needs to read (n) to the number of months he has to read them (m), we can use the equation:
n = 2m
This equation states that the number of novels (n) is equal to two times the number of months (m) since Boris needs to read 2 novels each month.
Now, to find the number of novels Boris needs to read in 17 months, we can substitute m = 17 into the equation:
n = 2m
n = 2(17)
n = 34
Therefore, Boris needs to read 34 novels in 17 months to meet his goal of reading 2 novels each month.
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1. If Cos A = 1/4, what is Sin B?
2. Simplify Sin A + Cos B ÷ 2
3. If Tan B = 1/5, what is Tan A? Which angle is bigger, angle A or angle B?
Please answer all 3
a. Sin A = opposite/hypotenuse = √15/4
b. (Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2
c. Tan A = 1/5
The both angle could be of same size
How do we calculate?Since Cos A = adjacent/hypotenuse,
Applying the Pythagorean theorem,
we can find the opposite side:
opposite^2 + 1^2 = 4^2
opposite^2 = 16 - 1
opposite = √15
Now we can find the value of Sin A:
Sin A = opposite/hypotenuse = √15/4
b.
Sin A + Cos B = (Sin A) + (Cos B)
(Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2
c. Since Tan B = opposite/adjacent,
we use Pythagorean theorem to find the hypotenuse:
hypotenuse^2 = 5^2 + 1^2
hypotenuse = √26
Tan A = opposite/adjacent = 1/5
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A number greater than 9 is called cute if when we add the product of the digits to
the sum of the digits, the result is the original number. For example 29 is cute since
2 + 9 + 2 × 9 = 29, but 513 isn’t cute since 5 + 1 + 3 + 5 × 1 × 3 6= 513. How many
cute numbers are there?
There are 6 cute numbers in total which are 14, 19, 49, 55, 79, 85.To find the cute numbers, we need to check all numbers greater than 9 and see if they satisfy the cute condition.
Let's start by analyzing the digits of a number. Suppose the number has two digits, x and y. The cute condition requires:
x + y + xy = 10x + y
Rearranging this equation, we get:
xy - 9x = y - x
xy - x - y = -9x
(x - 1)(y - 1) = 9x - 1
For a number to be cute, the right-hand side of the equation must be divisible by the left-hand side. Since 9x - 1 is odd, the left-hand side must also be odd, which means one of the factors (x - 1) or (y - 1) must be odd and the other even.
We can now check all possible pairs of (x,y) that satisfy this condition. We find that the cute numbers are:
14, 19, 49, 55, 79, 85. Therfore, there are total 6 cute numbers.
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how do you know when to use the Rule of Sum or Fundamental Counting Principle for probability problems?
If the events are exclusive, use the Rule of Sum. If the events are independent, use the Fundamental Counting Principle.
The Rule of Sum and the Fundamental Counting Principle are two common methods used in probability to calculate the total number of possible outcomes. Knowing which method to use depends on the nature of the problem and the type of events involved.
The Rule of Sum is used when we have two or more exclusive events. This means that only one of the events can happen at a time. For example, when rolling a die, the events of rolling a 2 or a 4 are exclusive because you cannot roll both at the same time.
The rule of sum states that the total number of possible outcomes is the sum of the number of outcomes for each event.
On the other hand, the Fundamental Counting Principle is used when we have a sequence of events that are independent of each other. This means that the outcome of one event does not affect the outcome of the next event.
For example, when flipping a coin, the outcome of the first flip does not affect the outcome of the second flip. The fundamental counting principle states that the total number of possible outcomes is the product of the number of outcomes for each event.
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Of 125 students attending a college orientation session, 18 are criminal justice majors. If 4 students at the orientation are selected at random, determine the probability that each of the 4 is a criminal justice major. Assume that selection is to be done without replacement Set up the problem as if it were to be solved, but do not solve. P(4 criminal justice majors selected) N
The probability that each of the 4 is a criminal justice major is equal to 0.0003 (rounded to four decimal places).
The probability of selecting 4 criminal justice majors from a group of 125 students, without replacement,
Using the hypergeometric probability distribution.
Start by calculating the total number of ways to choose 4 students from the group of 125.
C(125,4) = 125! / (4! (125-4)!)
= 125 x 124 x 123 x 122 / (4 x 3 x 2 x 1)
= 9,691,375
Next, calculate the number of ways to choose 4 criminal justice majors from the group of 18.
C(18,4) = 18! / (4! (18-4)!)
= 18 x 17 x 16 x 15 / (4 x 3 x 2 x 1)
= 3060
Finally,
Probability of selecting 4 criminal justice majors
= number of ways to choose 4 criminal justice majors / total number of ways to choose 4 students:
P(4 criminal justice majors selected) = C(18,4) / C(125,4)
⇒P(4 criminal justice majors selected) = 3060 / 9,691,375
= 0.0003157
Therefore, probability that each of the 4 students selected at random from the group of 125 students are criminal justice majors, without replacement is 0.0003 (rounded to four decimal places).
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Engineers built an arch bridge across a river. The arch bridge
makes a parabola shape that has the equation
y=-0. 1(x – 5)2 + 12, where x and y are measured in
meters. If the bridge makes contact with both banks at a height
of 4 meters, how long is the distance between the two banks
of the river where the bridge is? Round your answer to the
nearest whole number.
To find the distance between the two banks of the river where the arch bridge is, we first need to determine the points where the bridge makes contact with the banks at a height of 4 meters.
We are given the parabola shape of the arch with the equation y = -0.1(x - 5)^2 + 12.
1. Set the height y equal to 4 meters:
4 = -0.1(x - 5)^2 + 12
2. Subtract 12 from both sides:
-8 = -0.1(x - 5)^2
3. Divide both sides by -0.1:
80 = (x - 5)^2
4. Take the square root of both sides:
sqrt(80) = x - 5
5. Now, we find the two x-values where the bridge contacts the banks:
x1 = sqrt(80) + 5
x2 = -sqrt(80) + 5
6. Calculate the distance between the two banks by subtracting x2 from x1:
Distance = x1 - x2 = (sqrt(80) + 5) - (-sqrt(80) + 5)
7. Simplify the expression:
Distance = 2 * sqrt(80)
8. Round your answer to the nearest whole number:
Distance ≈ 18 meters
The distance between the two banks of the river where the arch bridge is, is approximately 18 meters.
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1, 3 solve find each vault of measure. assume all segments that appear to be tangent are tangent
Hi! To solve the problem and find each vault of measure, please provide more information or a diagram, as it is unclear which geometric figure you are referring to. The terms "vault," "measure," "segments," and "tangent" can be included in the answer once more context is given.
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help pls rlly fast i will give good points
Answer: less than
Step-by-step explanation:
2.
A painting company will paint this wall of a building. The owner gives them the following dimensions:
Window A is 6-ft x 5
6 ft x 5 ft.
Window Bis 3 ft x 4 ft.
Window Cis 9ft?
Door D is 4 ft x 8 ft.
33 ft
What is the area of the painted part of
the wall?
577 square feet is the area of the painted part of the wall.
To calculate the area of the painted part of the wall, you'll first need to find the total area of the wall and then subtract the areas of the windows and door. Let's assume the wall has a height of 33 ft and a width of 20 ft (since the other dimensions aren't provided).
1. Calculate the total area of the wall:
Area of wall = Height x Width = 33 ft x 20 ft = 660 sq ft
2. Calculate the areas of the windows and door:
Window A = 6 ft x 5 ft = 30 sq ft
Window B = 3 ft x 4 ft = 12 sq ft
Window C = 9 sq ft (already provided)
Door D = 4 ft x 8 ft = 32 sq ft
3. Subtract the areas of the windows and door from the total wall area:
Painted area = Wall area - (Window A + Window B + Window C + Door D) = 660 sq ft - (30 sq ft + 12 sq ft + 9 sq ft + 32 sq ft) = 660 sq ft - 83 sq ft = 577 sq ft
The area of the painted part of the wall is 577 square feet.
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Find the midpoint of the segment with the following endpoints.
(8,4) and (2,7)
Answer:
( 5 , 5½ )
Step-by-step explanation:
It's simple actually, use the midpoint formula,
[tex] \frac{x1 + x2}{2} ... \frac{y1 + y2}{2} = ( \frac{8 + 2}{2} ... \frac{4 + 7}{2} ) = (5..5 \frac{1}{2} )[/tex]
Take the ... as a comma.
So the final answer is ( 5 , 5.5 )
Suzie paid a total of $324 for c tickets to a rock festival. How much does each ticket cost
If for "c" tickets, Suzie paid an amount of $324, then the cost of each ticket is represented by "324/c".
The number of tickets that Suzie bought is = c tickets, and
Let "x" be the cost of "each-ticket for "rock-festival".
The total amount spent for "c" tickets is = $324,
Therefore, we can write the cost-equation as;
⇒ c × x = 324,
To find the value of "x", we solve for it by dividing both sides of the equation by "c":
⇒ x = 324/c,
So, the cost of each ticket is $324 divided by the number of tickets "c" that Suzie bought.
Therefore, Each tickets cost is 324/c.
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The dot plot shows the number of magazines bought in a month by 21 people in a office:
Dot plot labeled Number of Magazines Bought shows 10 dots over 0, 7 dots over 1, 2 dots over 2, 1 dot over 3, and 1 dot over 9
Is the median or the mean a better center for this data and why?
Median; because the data is not normally distributed and clusters on the left
Mean; because the data is not normally distributed and clusters on the left
Median; because the data is symmetric with an outlier
Mean; because the data is symmetric with an outlier
The median is a better center for this data because the data is not normally distributed and clusters on the left.
Median; because the data is not normally distributed and clusters on the left. The dot plot shows that the data is skewed to the left with most people buying fewer magazines. The median is less sensitive to outliers and gives a better representation of the center of this skewed distribution. The mean would be affected by the outlier (1 person bought 9 magazines), which would pull the mean to the right and give a misleading representation of the center of the data.
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13. the area of a rhombus is 484 square millimeters. one diagonal is one-half as long
as the other diagonal. find the length of each diagonal.
The length of each diagonal whose area is 484 square millimeters is 22 and 44.
Area of rhombus = 484 square millimeters
Let one diagonal of rhombus = p
other diagonal of rhombus = q
The length of one diagonal of rhombus is one-half as long as the other diagonal of rhombus
p = q/2
Area of diagonal = [tex]\frac{1}{2}d_{1}d_{2}[/tex]
Area of diagonal = [tex]\frac{1}{2}pq[/tex]
Area of diagonal = [tex]\frac{1}{2}\frac{q}{2}q[/tex]
484 = [tex]\frac{1}{4}q^{2}[/tex]
q² = 1936
q = 44 millimeter
p = q/2
p = 44/2
p = 22 millimeter
The length of each diagonal p and q is 22 mm and 44 mm respectively
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5-|p+6|=8
2 answers
NOT 19
There's a roughly linear relationship between the length of someone's
femur (the long leg-bone in your thigh) and their expected height.
Within a certain population, this relationship can be expressed using
the formula h = 2. 46f + 60. 6, where h represents the expected
height in centimeters and f represents the length of the femur in
centimeters. What is the meaning of the f-value when h 128?
This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters
When h is 128, we can use the formula h = 2.46f + 60.6 to solve for the corresponding value of f.
128 = 2.46f + 60.6
Subtracting 60.6 from both sides:
67.4 = 2.46f
Dividing both sides by 2.46:
f ≈ 27.4
Therefore, when h is 128, the f-value (length of the femur) is approximately 27.4 centimeters. This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters.
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What is the measure of an angle that goes through 2/8 of a circle?
The measure of an angle that goes through 2/8 of a circle is 90°
A circle is a 2-dimensional shape that is round in shape it is equidistant from the center.
A circle has a total angle of 360°
That is the whole complete angle of the circle = 360°
The 2/8 th of the complete angle of the circle = 360 * 2/8
= 360 * 1/4
= 360/4
=90°
Thus, the 90° of the circle is given as 2/8th of an angle of the circle or we can say that the quarter angle of a circle comes out to 90°.
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If Wendy is 63 inches tall and her hand is 6. 5 inches long, what is the residual if the formula to predict h, height in inches, from x, hand length in inches?
If the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches
A residual is the difference between the predicted value of a variable (in this case, height) and the actual value of that variable. Residuals are often used in statistical analysis to assess the accuracy of a prediction or model.
In this case, if we were given the formula for predicting height from hand length, we could use it to predict Wendy's height and compare that to her actual height of 63 inches. The residual would be the difference between the predicted height and her actual height. If the prediction overestimated her height, the residual would be negative. If it underestimated her height, the residual would be positive.
For example, if the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches (predicted height minus actual height). If the formula predicted her height to be 61 inches, the residual would be +2 inches.
Overall, residuals are a useful tool for assessing the accuracy of predictions or models, but the specific calculation of a residual depends on the formula being used to make the prediction.
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Determine the values of a, b, and c in the following matrix equation.
4 a
[34]
30
52
[3
2 b5
1 8
LC
a.
b.
C.
54=
16.
The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8
Determining the values in the matrix equation.To determine the values of a, b, and c in the matrix equation:
4 a + 3 0 = 7 3
3 4 5 b c 5
By addition operation, we have
a + 0 = 3
3 + 5 = c
4 + b = 5
When the equations evaluated, we have
a = 3
c = 8
b = 1
The above are the values of a b and c
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Complete question
Determine the values of a, b, and c in the following matrix equation.
4 a + 3 0 = 7 3
3 4 5 b c 5
If (x+1/x)² = 3, find x³+1/x³.
The value of the algebraic expression from the given parameters is:
x³ + 1/x³ = 0
How to solve Algebraic Expressions?The given problem is simply based on the expansion.
In expansion, what we do is that we expand the mathematical terms by first of all removing all the brackets that are in that mathematical expression.
In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one binomial with the another one and then this type of identities are called as Standard Identities.
For example:
(x + a)(x + b) = x² + (a + b)x + ab
Thus:
(x + 1/x)² = 3
x + 1/x = √3
(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)
√3³ = x³ + 1/x³ + 3(√3)
x³ + 1/x³ = 3√3 - 3√3
x³ + 1/x³ = 0
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Solve the following problems:
given: circle k(o), diameter us, mru=50°, mut=30°
find: m
The measure of angle M is 20°.
To solve the problem, we need to find the measure of angle M, given the information about Circle K with center O, diameter US, angle MRU = 50°, and angle MUT = 30°.
Step 1: Determine the relationship between angles MRU and MUT.
Since MRU and MUT are both inscribed angles in Circle K, they share the same intercepted arc, which is arc MU.
Step 2: Calculate the measure of arc MU.
The measure of an intercepted arc is twice the measure of the inscribed angle. Since angle MRU = 50°, the measure of arc MU will be 2 * 50° = 100°.
Step 3: Find the measure of angle M.
We know that angle MUT = 30°, and the measure of an intercepted arc is twice the measure of the inscribed angle. Therefore, the measure of arc MT = 2 * 30° = 60°. Now, since arc MU = 100°, we can determine the measure of arc MS (arc MS = arc MU - arc MT) which is 100° - 60° = 40°.
Step 4: Calculate the measure of angle M.
Finally, the measure of angle M can be found using the intercepted arc MS. Since the measure of an intercepted arc is twice the measure of the inscribed angle, angle M = 1/2 * arc MS = 1/2 * 40° = 20°.
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Given the following information about two triangles, triangle CAT and triangle DOG:
Which postulate can be used to prove triangle CAT and triangle DOG are congruent?
SSS Postulate
SAS Postulate
SSA Postulate
ASA Postulate
AAS Postulate
Choose all that apply
To determine which postulate can be used to prove that triangle CAT and triangle DOG are congruent, we need information about the side lengths and angles of each triangle. Unfortunately, the given information about triangles CAT and DOG is not provided in your question.
However, I can briefly explain each of the mentioned postulates to help you understand how they can be applied to prove congruence:
1. SSS (Side-Side-Side) Postulate: If all three sides of one triangle are equal in length to the corresponding sides of another triangle, the triangles are congruent.
2. SAS (Side-Angle-Side) Postulate: If two sides and the included angle of one triangle are equal to the corresponding sides and included angle of another triangle, the triangles are congruent.
3. SSA (Side-Side-Angle) Postulate: This is not a valid postulate for proving triangle congruence.
4. ASA (Angle-Side-Angle) Postulate: If two angles and the included side of one triangle are equal to the corresponding angles and included side of another triangle, the triangles are congruent.
5. AAS (Angle-Angle-Side) Postulate: If two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.
Once you have the necessary information about triangles CAT and DOG, you can apply the appropriate postulate to prove their congruence.
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A circle is placed in a square with a side length of 8 m, as shown below. Find the area of the shaded region.
Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the shaded region is the expression 16(4 - π) square metres.
How to evaluate for the shaded regionThe shaded region is the remaining area in the square which is outside the circle, so it is derived by subtracting the area of the circle from the area of the square as follows:
area of the square = 8 m × 8 m
area of the square = 64 m²
area of the circle = π × 4 m × 4 m
area of the circle = 16π m²
area of the shaded region = 64 m² - 16π m²
area of the shaded region = 16(4 - π) m²
Therefore, the area of the shaded region is the expression 16(4 - π) square metres.
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