What is SAS congruence rule of triangle?
The SAS (Side-Angle-Side) Congruence Rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
The SAS (Side-Angle-Side) congruence rule is a method used to determine if two triangles are congruent. This rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
To determine if two triangles are congruent using the SAS rule, we must first identify the two sides and the angle in one triangle that are congruent to the two sides and the angle in the other triangle. This means that they must have the same measures in terms of length and angle.
Once we have identified the corresponding sides and angles, we can use the SAS rule to determine if the two triangles are congruent. If the two sides and the angle of one triangle are congruent to the two sides and the angle of another triangle, then the two triangles are congruent.
However, if the two sides and the angle of one triangle are not congruent to the two sides and the angle of another triangle, then the two triangles are not congruent. The SAS rule is a simple and effective way to determine if two triangles are congruent.
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what is 45.5% of 132.24km ?
Answer:
60.1692 kilometers
Step-by-step explanation:
Percent Value: 45.5%
Number: 132.24
45.5% of 132.24...
... is equivalent to multiplying them:
45.5% × 132.24 ≈ 60.1692
Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 10 minutes, clock B every 15 minutes, and clock C every 20 minutes.The three clocks sound together every _minutes.
Answer:
Given that,
Calvin has three alarm clocks which sound at different intervals.
Clock A goes off every 10 minutes
Clock B every 15 minutes
Clock C every 20 minutes.
To find: the three clocks sound together every _minutes
The three clock sounds together for every least common minutes of the 3 clocks (A,B,C)
To find LCM of 10,15,20.
we get,
LCM of 10,15,20 is 60
Therefore we get that,
The three clock sounds together for every 60 minutes.
Answer is:
The three clock sounds together for every 60 minutes.
Graphical For the following exercises, graph the inequality. 20.x2 + 2y > 7 21.y2 – 2x2 > -3and x2 + y2 <9 Extensions For the following exercises, graph the inequality. 22.y 2 ()* 23. y < 302.X + 1 Real-World Applications For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. 24. Two numbers add up to 144. One number is half the square of the other number. What are the numbers? 25. The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number. What are the numbers?
The graph of the inequality y^2 > 0 represents all real numbers except y = 0.
The graph of the inequality y < 30 represents all real numbers less than 30.
The inequality y^2 > 0 represents all values of y where y squared is greater than 0. Since the square of any nonzero number is always positive, the solution is all real numbers except y = 0, which can be graphed as a number line with an open circle at y = 0.
The inequality y < 30 represents all values of y that are less than 30. This can be graphed as a horizontal line on the y-axis with an open circle at y = 30, indicating that 30 is not included in the solution set.
For the real-world applications, let's solve them step-by-step:
Two numbers add up to 144. One number is half the square of the other number.
Let's assume the two numbers are x and y. We have the following system of equations:
x + y = 144 (Equation 1)
x = (1/2)y^2 (Equation 2)
From Equation 1, we can solve for x in terms of y: x = 144 - y.
Substituting this into Equation 2, we get 144 - y = (1/2)y^2.
Rearranging the equation, we have: (1/2)y^2 + y - 144 = 0.
Now we can solve this quadratic equation for y. Once we find the value(s) of y, we can substitute them back into Equation 1 to find the corresponding values of x.
The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number.
Let's assume the two numbers are x and y. We have the following system of equations:
x^2 + y^2 = 1156 (Equation 1)
y = √(3x^2) (Equation 2)
Substituting Equation 2 into Equation 1, we get: x^2 + (√(3x^2))^2 = 1156.
Simplifying, we have x^2 + 3x^2 = 1156.
Combining like terms, we get 4x^2 = 1156.
Now we can solve this quadratic equation for x. Once we find the value(s) of x, we can substitute them back into Equation 2 to find the corresponding values of y.
Remember to leave a 1 line space between paragraphs in your answer.
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What are the similarities between the binary and decimal systems?
Similarities between binary and decimal systems -
Arithmetic operations can be carried out on numbers in both the binary ands decimal systemsValues of each bit and digit in binary and decimal numbers respectively depends on how close they are to the decimal pointInteger and fraction components are represented in both decimal and binary systems.The differences between the binary and decimal systems -
The decimal number system uses ten different digits (from 0 to 9); but the binary number system uses only two different digits (0 and 1). Decimal system is also called Hindu-Arabic or just Arabic number system. A bit (short for binary digit) is the smallest and basic unit of data in a computer.Learn more about decimal systems
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How do you solve quotients step by step?
We can Long Division method to solve quotients step by step
What is long division method and its steps ?
When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.
We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.
1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.
2. Next, divide it by the divisor, and write the result as the quotient on top.
3. Subtract the outcome from the digit, and then put the difference below.
Step 4: Decrease the dividend's subsequent digit (if present).
Step 5: Carry out Step 4 again.
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Joanne wants to put wallpaper in her daughter's room. Each wall measure 16.8 feet long by 12.9 feet wide. What is the area of one wall in her daughter's bedroom?
Explain the concept of extraneous solutions. Give examples with the different types of functions explored.
Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
What is a function ?
Function can be defined as a relation , which relates an input to output is called as function.
In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,
however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.
Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
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(3/8 + 3/4) - (1/3 + 1/6) thank you!
3. The mass m is less than 5 kilograms.
Answer:
5 minus m ( variable)
Step-by-step explanation:
np
I do not understand this. Can you please explain.
Answer:
E
Step-by-step explanation
y^(3/5) = \(\sqrt[5]{y{3}}\)
y^(-3/5) = 1/\(\sqrt[5]{y{3}}\)
In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute a the end vary from runner to runner according to the N(104,12.5) distribution. The heart rates for male nonrunners after the same exercise have the N(130,17) distribution. (a) What percent of the runners have heart rates above 140? Give your answer to two decimal places. percent of the runners: (b) What pereent of the nonrunners have heart rates above 140 ? Give your answer to two decimal places. percent of the nonrunners:
(a) Approximately 0.22% of the runners have heart rates above 140.
(b) Approximately 27.84% of the nonrunners have heart rates above 140.
(a) The percentage of runners with heart rates above 140 can be determined by calculating the cumulative probability of the normal distribution N(104, 12.5) beyond the value of 140. We subtract the cumulative probability from 1 and multiply by 100 to obtain the percentage.
Using statistical software or a standard normal distribution table, we can find the z-score for 140 in the N(104, 12.5) distribution. The z-score formula is given by: z = (x - μ) / σ, where x is the value (140 in this case), μ is the mean (104), and σ is the standard deviation (12.5).
Substituting the values, we get: z = (140 - 104) / 12.5 = 2.88 (approximately)
Looking up the z-score in the standard normal distribution table or using software, we find that the cumulative probability for z = 2.88 is approximately 0.9978.
To calculate the percentage of runners with heart rates above 140, we subtract this cumulative probability from 1: 1 - 0.9978 = 0.0022.
Converting this to a percentage, we get 0.0022 * 100 = 0.22%.
Therefore, approximately 0.22% of the runners have heart rates above 140.
(b) To calculate the percentage of nonrunners with heart rates above 140, we follow a similar process using the N(130, 17) distribution.
Using the same z-score formula, we find the z-score for 140 in the N(130, 17) distribution: z = (140 - 130) / 17 = 0.5882 (approximately).
Looking up the z-score in the standard normal distribution table or using software, we find that the cumulative probability for z = 0.5882 is approximately 0.7216.
To calculate the percentage of nonrunners with heart rates above 140, we subtract this cumulative probability from 1: 1 - 0.7216 = 0.2784.
Converting this to a percentage, we get 0.2784 * 100 = 27.84%.
Therefore, approximately 27.84% of the nonrunners have heart rates above 140.
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The length of a rectangular field is 24 meters this is 3 meters less than twice the width find the width
Answer:
The width is 5 meters
Step-by-step explanation:
The rectangular field is 24 meaning adding just one width and length of the rectangle would be 12.
x = width
2x - 3 + x = 12
3x - 3 = 12
3x - 3 + 3 = 12 + 3
3x = 15
x = 5
Use the diagram to write the ratio (as a fraction in lowest terms) for each trigonometric function.
sin X-
cos X-
tan X-
sin M-
cos M
tan M-
M
5
13
12
-X
The values of the trigonometric identities are:
Sin X = 5/13
Cos X = 12/15
Tan X = 5/12
Sin M = 12/13
Cos M = 5/13
Tan M = 12/5
We have,
Sin = Perpendicular / Hypotenuse
Cos = Base / Hypotenuse
Tan = Perpendicular / Base
Now,
Sin X = 5/13
Cos X = 12/15
Tan X = 5/12
And,
Sin M = 12/13
Cos M = 5/13
Tan M = 12/5
Thus,
The values of the trigonometric identities are:
Sin X = 5/13
Cos X = 12/15
Tan X = 5/12
Sin M = 12/13
Cos M = 5/13
Tan M = 12/5
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Which set of ordered pairs represents y as a function of x?
O {(-4, 0),(-2,2).(-4,-2), (-2, 4),(-4, - 4)}
{(0,4), (1,7),(1,10), (2, 13), (3, 16)}
{(3, 1), (3, 2), (3, 3), (3, 4), (3,5)}
{(3, 3), (-1,-1),(-2,-2), (4,4),(-4,-4)}
I need the answer ASAP!!!
a triangular window can only have an area of 120 square feet and the architect wants the base to be 4 feet more than twice the height. find the base and height of the window.
the base of the triangular window is 24 feet and the height is 10 feet.
Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.
The formula to calculate the area of a triangle is:
Area = (1/2) × base × height
In this case, we can write the equation as:
120 = (1/2) × base × h
Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:
base = 2h + 4
Substituting this expression for the base into the area equation, we have:
120 = (1/2) × (2h + 4) × h
Now we can solve this equation for the height.
Multiplying both sides of the equation by 2 to remove the fraction:
240 = (2h + 4) × h
Expanding the right-hand side:
240 = 2h² + 4h
Rearranging the equation and setting it equal to zero:
2h² + 4h - 240 = 0
Now we can solve this quadratic equation. Factoring out a 2:
2(h² + 2h - 120) = 0
Factoring the quadratic expression inside the parentheses:
2(h + 12)(h - 10) = 0
Setting each factor equal to zero:
h + 12 = 0 or h - 10 = 0
Solving these equations, we get:
h = -12 or h = 10
Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.
Substituting the height value back into the expression for the base:
base = 2h + 4
= 2(10) + 4
= 20 + 4
= 24
Therefore, the base of the triangular window is 24 feet and the height is 10 feet.
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99 is 0.9% of what number? Would you expect the answer to be a lot less than 99, slightly less than 99, slightly greater than 99, or a lot greater than 99 explain
Answer:
Question: 99 is 0.9% of what number?
Answer:11,000
Question: Would you expect the answer to be a lot less than 99, slightly less than 99, slightly greater than 99, or a lot greater than 99 explain.
Answer: I was honestly thinking that the number would be a lot bigger. Considering that 0.9 percent is 90/100 which is more than half.
Step-by-step explanation:
I hope this helps!!!!
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The equation (x + 9)^2 + (y - 4)^2 = 81 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals. Hint: position is the center of the circle and range is the radius of the circle.
Answer:
The position of the radio is (-9, 4).
The range of the radio is 9.
Step-by-step explanation:
The equation (x + 9)^2 + (y - 4)^2 = 81 is in the form of a circle, so we can use the standard equation for a circle to find the center and radius of the circle. The standard equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius of the circle
In the equation (x + 9)^2 + (y - 4)^2 = 81, we can see that:
h = -9 k = 4 r = 9Therefore, the center of the circle is at (-9, 4) and the radius of the circle is 9.
The position of the source of the radio signal is at the center of the circle, which is at (-9, 4). The range of the signal is the radius of the circle, which is 9. This means that the radio signal can be received by any device within a 9-unit radius of the source.
The source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.
The equation (x + 9)^2 + (y - 4)^2 = 81 represents the position and range of the source of a radio signal. By analyzing the equation, we can determine the position of the source and the range of the signals.
Position: The equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle. Comparing this with the given equation, we can see that the center of the circle is at (-9, 4). Therefore, the position of the source of the radio signal is at the coordinates (-9, 4).
Range: In the equation, the term 81 represents the radius of the circle, denoted as r. So, the range of the signals is equal to the radius, which in this case is √81 = 9 units. This means that the radio signals from the source can reach a maximum distance of 9 units from the center.
In summary, the source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.
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which properties can be used to solve 7y-15=-29? select all that apply.
a. identity property of multiplication
b. addition property of equality
c. distributive property
d. inverse property of multiplication
e. commutative property of addition
Answer:
e d and b
Step-by-step explanation:
just trust me
Find surface area of a rectangular prism 3 ft 2 ft 6 ft
Answer:
72 ft ^2
Step-by-step explanation:
Surface area = 2 * ( 3x6 + 6x2 + 2x3) = 72 ft^2
Work needs to be shown please someone help and don’t answer for your benefit with no intention to help
Answer:
\(\frac{x+3}{x+2}\)
Step-by-step explanation:
\(\frac{x^2+10x+21}{x^2+9x+14}\) Factor the expressions that are not already factored.
=
\(\frac{(x+3)(x+7)}{(x+2)(x+7)}\) Cancel out x+7 in both numerator and denominator.
=
\(\frac{x+3}{x+2}\)
PLSSS someone help me out
Evaluate (5n)^2 + (2n-3m)^2 for m=-3 and n=-2.
A) 269
B) 189
C) 125
D) 46
Please solve
(5n)^2 + (2n-3m)^2 = (5*(-2))^2 + (2*(-2)-3*(-3))^2
= (-10)^2 + (-4+9)^2
= 100 + (5)^2
= 100 + 25
= 125
(C) 125
what is the unit rate of 48 ounces for 5.76 $
This means that each ounce of the product costs $0.12.
The unit rate is a mathematical calculation that determines the cost per ounce of a particular product. In this case, we are given that 48 ounces of a product costs $5.76. To find the unit rate, we need to divide the cost by the number of ounces.
So, the unit rate for 48 ounces of this product would be:
$5.76 ÷ 48 ounces = $0.12 per ounce
It's important to note that unit rates can be useful when comparing the prices of different products or different sizes of the same product. By calculating the unit rate, we can determine which option offers the best value for our money.
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In the picture shown below, what proportion would NOT give the correct value of x?
Answer: (c)
Step-by-step explanation:
In the given figure, two triangles are similar namely \(\triangle ABC\) and \(\triangle ADB\)
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of \(x\) that is,
\(\Rightarrow x=\sqrt{81\times 45}\\\Rightarrow x=60.37\)
Option (c) does not give the correct value of \(x\)
Answer:
C
Step-by-step explanation:
In the given figure, two triangles are similar namely and
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of that is,
Option (c) does not give the correct value of
Find the value of a3 + 3b2 when a = 2 and b = -2
Given:
a = 2 and b = -2.
To find:
The value of \(a^3+3b^2\).
Solution:
We need to find the value of expression \(a^3+3b^2\) at a = 2 and b = -2.
Substituting a = 2 and b=-2 in \(a^3+3b^2\), we get
\((2)^3+3(-2)^2\)
\(=8+3(4)\)
\(=8+12\)
\(=20\)
Therefore, the value of expression \(a^3+3b^2\) at a = 2 and b = -2 is 20.
Crickets and math
Thanks for help
Answer:
the answer is A
Step-by-step explanation:
Help help help help help help
A magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the ​respondents, ​% chose chocolate​ pie, and the margin of error was given as percentage points. Describe what is meant by the statement that​ "the margin of error was given as percentage​ points."
The statement indicates that the interval 12%±5% is likely to contain the true population percentage of people that prefer chocolate pie.
According to the statement
we have a given that the Among the 1000 respondents,
12% chose chocolate pie, and the margin of error was given as
±5 percentage points.
and we have to explain the statement that the margin of error was given as ±5 percentage points.
We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.
And this statements also indicates the interval between the like and unlike respondents of chocolate pie.
So, this statement indicates that the interval 12%±5% is likely to contain the true population percentage of people that prefer chocolate pie.
So, The statement indicates that the interval 12%±5% is likely to contain the true population percentage of people that prefer chocolate pie.
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The sum of two numbers is 16 and their difference is 2 the big number between them is
hello
the answer to the question is:
A + B = 16
A - B = 2
----> A = 9, B = 7
and the number between them is 8