The acronym CPCTC stands for “corresponding parts of congruent __________ are congruent.”
Answer: Triangles
Step-by-step explanation:
The CPCTC property of congruent triangles says that is two triangles are congruent then their corresponding angles and sides are congruent.The acronym CPCTC basically stands for Corresponding Parts of Congruent Triangles are congruent.
It generally used two show any two corresponding segments or angles of two congruent triangles congruent.
Which expression is equivalent to
The equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
Logarithms and indicesTo get the equivalent expressions for the given logarithmic function, we will use the following laws of logarithm:
Laws of logarithm[tex]logab=loga+logb\\ log(\frac{a}{b} )=loga -logb[/tex]Given the logarithmic function:
[tex]log_{12}(\frac{1/2}{8w}) [/tex]
This can be further expressed as:
[tex]log_{12}(\frac{1/2}{8w} )[/tex][tex]log_{12}(\frac{1/2}{8w} )=log\frac{1}{2}-log8w [/tex]
Using the product law of logarithm
[tex]log_{12}(\frac{1/2}{8w}) =log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
Hence the equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
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A video rental store charges $4 per day to rent a movie and $3 per day to rent a video game. During one summer, Tony paid a total of $140 to rent movies and video games from this store. If he rented twice as many video games as movies, how much did he spend on movie rentals during the summer?
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which has more people a car that is 3/4 full or a car that is 1/4 full
£600 is put in a bank. after a year the money has increased by 8% how much is now in the bank
Set A is the set of all positive multiples of 2 that are less than or equal to 20. Set B is the set of all positive multiples of 4 that are less than or equal to 20. How many elements are positive multiples of 4 that are less than or equal to 20, but are not positive multiples of 2?
Evaluate the polynomial when x=4 y=-4
x^2-3y^2+2xy
A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
A line segment with endpoints (-4,5) and (-2,2) is reflected about the y-axis. Write the coordinates of the endpoints after the segment has been reflected.
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.
Two functions are represented in different ways. Function 1: y = 32x + 45 Function 2: x y 0 65 1 85 2 105 3 125 Which statements are true? Select each correct answer. Function 1 has a greater rate of change than function 2. Function 2 has a greater rate of change than function 1. Function 1 has a greater y-intercept than function 2. Function 2 has a greater y-intercept than function 1.
Answer:
Step-by-step explanation:
Function 1: y = 32x + 45 <- 45 is y-intercept
Function 2: x y 0 65 <- 65 is y-intercept
So Function 2 has a greater y-intercept than function 1.
Function 1: y = 32x + ... <- 32 is rate of change
Function 2: x y 0 65 1 85
rate of change = 85 - 65 = 20
So Function 1 has a greater rate of change than function 2.
Part I: Angle Sum Relationships
Arrange the three congruent triangles so that angles 1 and 3 are adjacent to one another, and angle 2 is adjacent to angles 1 and 3.
B. What do you notice about the three angles?
C. What do they appear to form?
D. What can you conclude about the sum of the angles in a triangle?
Answer with explanation:
→→The three Angles form a Linear pair.That is
⇒∠1+∠2+∠3=180°
→→When these three congruent triangles are joined they form a Trapezoid.
→→Sum of angles in a trangle is given by Angle sum property Axiom of triangle which states that sum of the angles in a triangle is 180°.
An experienced roofer can work twice as fast as her helper. working together, they can shingle a new section of roof in 4 hours. how long would it take the experienced roofer, working alone, to complete the same job?
The problem solves for the time it would take the roofer to work alone, by first determining the shared work rate. The helper works at rate x and the roofer at rate 2x (twice as fast). They complete 1 roof in 4 hours working together, thus their combined rate is 1/12 roof per hour. So, the roofer’s individual rate is 1/6 roof per hour, meaning she can finish the job alone in 6 hours.
Explanation:To solve this problem, we'll use the equation for work which is work = rate x time. Let's say the helper's rate of work as 1x and the roofer's rate as 2x, because the roofer can work twice as fast as the helper.
Bearing in mind that the total time it takes both of them to shingle the roof is 4 hours, according to the problem, we can represent this relationship as this equation: (2x + x) * 4 = 1 roof. This simplifies to 12x = 1, meaning the rate at which they work together is x = 1/12 roof per hour.
Thus, the roofer’s individual rate of work is 2x = 2/12 roof per hour = 1/6 roof per hour. Therefore, to calculate how much time it would take for the roofer to do the job alone, we simply divide the total task (1 roof) by the roofer’s rate of work, 1/(1/6) = 6 hours.
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By setting up and solving an algebraic equation based on the given conditions in the problem, we find that it would take the experienced roofer alone 3 hours to complete the same job.
Explanation:The problem is related to work rate and could be solved using algebra. Let's denote by X the time (in hours) it takes for the helper to complete the job alone. Considering that an experienced roofer can work twice as fast as her helper, the roofer could complete the same job alone in X/2 hours. From the problem, we know that when working together, they can complete the job in 4 hours. This means that the amount of work they do together in one hour (1/4) is equal to the sum of the amounts of work done by each in one hour (1/X + 2/X). By solving this equation, we get X = 6. So, it would take the helper 6 hours to complete the job, which means it would take the experienced roofer half of this time, which is 3 hours.
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what is the gcf of 12 78 and 90
the ratio of keiths age to Jared's ages 3 to 5 if Keith is 24 years old how old is Jared please show how many you got this answer I will mark brainiest
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stumpy the skeleton goes for a bike ride every night in the cemetery. He rides 1/2 way around the cemetery and stops. Stumpy then bikes 3/4 of the way around before stopping again. he finishes his ride by biking another 3/8. how far around the cemetery does stumpy bike?
use matrix method to solve x+4y=8 2x+y=9
[tex]12 \times 778 [/tex]
Final answer:
To multiply 12 by 778, one needs to perform the standard multiplication process. Multiplying each digit of 12 by 778 individually and then adding the results provides the final answer, which is 9336.
Explanation:
The student's question involves performing a multiplication operation, specifically 12 multiplied by 778. To solve this without a calculator, one can use a standard multiplication technique as follows:
Write down the two numbers, with 778 above 12.
First, multiply 2 (the rightmost digit of the lower number) by 778 to get 1556.
Next, multiply 1 (the leftmost digit of the lower number) by 778 and remember to add a zero at the end (because it represents the tens place), which gives us 7780.
Add the two results, 1556 and 7780, to get the final answer, which is 9336.
The result of 12 times 778 is 9336.
The value of (a-1)+a^2-b^2/1-ab+2(a-b)/2b when a=2 and b=-1 is ?
Final answer:
The value of the expression (a-1) + a^2 - b^2 / (1-ab) + 2(a - b) / (2b) when a=2 and b=-1 is -5/3.
Explanation:
To calculate the given expression when a=2 and b=-1, we first plug these values into the expression, which is (a - 1) + a^2 - b^2 / (1 - ab) + 2(a - b) / (2b). After substitution, it simplifies as follows:
The term (a - 1) becomes (2 - 1), which equals 1.
The term a^2 - b^2 becomes 2^2 - (-1)^2, which simplifies to 4 - 1 = 3.
The denominator 1-ab becomes 1 - (2)(-1), which equals 1 + 2 = 3.
The term 2(a - b) becomes 2(2 - (-1)), which is 2(3) = 6.
The denominator 2b becomes 2(-1), which is -2.
Now, the full expression simplifies to (1 + 3) / 3 + 6 / -2. Simplifying further, we get 4 / 3 + (-3), which equals to 4/3 - 3/1. After finding a common denominator, the expression simplifies to (4 - 9) / 3, which is -5/3.
Therefore, the value of the expression when a=2 and b=-1 is -5/3.
Suppose there is exactly one index k such that a[k] = x. what is the expected number of indices into a that we must pick before we find x and random-search terminates?
Morgan uses 1/4 of her supply of raisins to make trail mix and 3/8 of her supply of raisins to make cookies. If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply?
There are 8 pounds of raisins in Morgan's supply.
Let us say there are 'a' pounds of raisins in her supply.
What is a fraction?Fraction is a manner to represent part of a whole.
Raisins used to make trail mix = 1/4 of a = 1/4 a
Raisins used to make cookies = 3/8 of a = 3/8 a
It is given that:
Morgan uses 5 pounds of raisins,
[tex]\frac{1}{4} a+\frac{3}{8} a=5[/tex]
[tex]\frac{5}{8} a = 5\\\\a=8[/tex]
Therefore, there are 8 pounds of raisins in Morgan's supply.
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Morgan's total supply of raisins is 8 pounds.
Let's denote the total supply of raisins by R. According to the problem, Morgan uses 1/4 of her supply to make trail mix and 3/8 of her supply to make cookies. Together, this amounts to a total of five pounds of raisins used.
We set up the equation to represent the total amount of raisins used:
1/4 R + 3/8 R = 5
We need to find a common denominator to combine the fractions. Here, the common denominator is 8:
(2/8) R + (3/8) R = 5
Combining the fractions gives:
(5/8) R = 5
To isolate R, we multiply both sides of the equation by the reciprocal of 5/8, which is 8/5:
R = 5 * 8/5
When we simplify, we get:
R = 8
So, Morgan's total supply of raisins is 8 pounds.
A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 45°, what is the area of the opening?
A. 4.8 in2
B. 20.8 in2
C. 19.3 in2
D. 9.0 in2
Answer:
19.3
Step-by-step explanation:
took the test
factor :
x^4 (x+4) + 9 (x+4)
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A school table has 8 sides of equal lengths. if one side is 4 feet, what is the perimeter of the table?
What number is 8.0007 • 10 ^6 in scientific notation?
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The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results. Which compares the means of the data in the dot plots?
The mean for Mr. McIntyre’s class is about 2 more than the mean for Mrs. Ramos’s class.
The mean for Mrs. Ramos’s class is about 2 more than the mean for Mr. McIntyre’s class.
The mean for Mr. McIntyre’s class is about 1 more than the mean for Mrs. Ramos’s class.
The mean for Mrs. Ramos’s class is about 1 more than the mean for Mr. McIntyre’s class.
*The first picture is Mr. McIntyre’s Class
*The second picture is Mrs. Ramos’s Class
Answer:
If you are lazy like me the answer is B
Step-by-step explanation:
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Find the lowest common multiple of 28 and 210
Answer:
420
Step-by-step explanation:
210 = 14×15
28 = 14×2
The LCM wil be the product of unique factors;
... LCM = 14×15×2 = 420