The acronym CPCTC stands for " Corresponding parts of congruent triangles are congruent. "
Step-by-step explanation:CPCTC--
It is a rule which states that if any of the two triangles are congruent by any of the congruency such as ASA, RHS , SAS or SS then the remaining sides and the remaining angles which were not covered in the congruency are also congruent.
Also, the acronym is:
Corresponding parts of congruent triangles are congruent.
algebra 2 function operations (link)
If four friends can eat four cakes in four days, then how many cakes can 10 friends eat in 10 days?
Which expressions are completely factored? Select each correct answer. 30a6−24a2=3a2(10a4−8) 16a5−20a3=4a3(4a2−5) 12a3+8a=4(3a3+2a) 24a4+18=6(4a4+3)
When factoring an expression, we need to identify the Greatest Common Factor of the expression (GCF). By definition, GCF is the product of prime factors involved with its Lowest Exponent.
We need to divide each term by the GCF to get the expression inside the parenthesis.
[tex] 30a^6-24a^2\\ GCF\; is \; 6a^2\\ \\ 30a^6-24a^2=6a^2(\frac{3a^6}{6a^2} -\frac{24a^2}{6a^2} )=6a^2(5a^4-4)\\ ---------------------\\ \\ 16a^5-20a^3\\ GCF \; is \; 4a^3\\ \\ 16a^5-20a^3=4a^3(\frac{16a^5}{4a^3} -\frac{20a^3}{4a^3})=4a^3(4a^2-5) \\ ---------------------\\ \\ 12a^3+8a\\ GCF \; is \; 4a\\ \\ 12a^3+8a=4a(\frac{12a^3}{4a}+\frac{8a}{4a})=4a(3a^2+2)\\ ---------------------\\ 24a^4+18\\GCF \; is \; 6\\\\24a^4+18=6(\frac{24a^4}{6} +\frac{18}{6})=6(4a^4+3) \\ --------------------- [/tex]
Conclusion:
From above we can conclude that the below expressions are factored completely
[tex] 16a^5-20a^3=4a^3(4a^2-5)\\ \\ 24a^4+18=6(4a^4+3) [/tex]
Bryan purchases a new boat. The expression below represents the value of the boat after x years. 22000(.88)^(x+2) Which statement is true?
A.The price of the boat decreases by 88% every year.
B.The price of the boat increases by 88% every year.
C.The price of the boat decreases by 12% every year.
D.The price of the boat increases by 12% every year.
The formula for the growth rate is given by
[tex] y=a(b)^x [/tex]
Now when b is greater than 1 , then it is increasing function
and when b is less than 1 , then it is decreasing function.
Now in the function
[tex] 22000(.88)^{(x+2)} [/tex]
here value of b is 0.88 , which is less than 1 , so it is decreasing function
And decay rate is given by
1-r = 0.88
Subtract 1 from both sides
-r = 0.88-1
-r = -0.12
r = 0.12
or r= 12%
It means it is decreasing at a rate of 12%
Hence Option C is correct
C.The price of the boat decreases by 12% every year.
Solve for a.
(a+6)^2=49
A −13 and 1
B −3 √6 and 3 √6
C −1 and 13
D −√43 and √43
The solutions for a are a=1 and a=−13. So the correct answer is A. -13 and 1.
To solve the equation [tex]\( (a+6)^2 = 49 \)[/tex], follow these steps:
1. Take the square root of both sides:
[tex]\[ \sqrt{(a+6)^2} = \sqrt{49} \][/tex]
2. Consider both positive and negative roots:
[tex]\[ a + 6 = \pm 7 \][/tex]
3. Solve for ( a ):
For ( a + 6 = 7 ):
[tex]\[ a = 7 - 6 = 1 \][/tex]
For ( a + 6 = -7 ):
[tex]\[ a = -7 - 6 = -13 \][/tex]
So, the solutions for ( a ) are ( a = 1 ) and (a = -13).
Therefore, the correct answer is A. -13 and 1.
Explain how to translate the statement into an equation. Use n for the variable. Sixty-three is the product of nine and a number.
Answer:
Sample Response: Replace the word "is" with an equals sign. Replace the word "product" with a multiplication sign. Replace the words "a number" with the variable n, to represent the unknown value. The equation is 63 = 9n.
The statement 'Sixty-three is the product of nine and a number' translates to the equation 63 = 9 × n. The variable n represents the unknown number that, when multiplied by nine, equals sixty-three.
To translate the statement "Sixty-three is the product of nine and a number" into an equation using n for the variable, we can use the following steps:
1. Identify the unknown number: Let's denote the unknown number as n
2. Express the known quantities: We know that "Sixty-three" is equal to the product of "nine" and the unknown number n .
3. Write the equation: The statement can be translated into the equation:
[tex]\[ 63 = 9 \times n \][/tex]
In this equation:
- 63 represents the product of 9 and n .
- 9 represents the known quantity.
- n represents the unknown number we are trying to find.
So, the equation [tex]\( 63 = 9 \times n \)[/tex]expresses the statement "Sixty-three is the product of nine and a number" using the variable n .
The name of a triangle whose angles are all more that 90 degrees?
Acute
Obtuse
Right
Isosceles
None of the above
Answer:
Option B is correct.
Obtuse triangle.
Step-by-step explanation:
Acute triangle:
In acute triangle, all angles are less than 90 degree.
Obtuse triangle:
In obtuse triangle, the triangle has an angle more than 90 degree.
Right triangle.
In right triangle, it has a right angle 90 degree.
Isosceles triangle.
In isosceles triangle, it can be acute, right or obtuse depends only on the apex angle.
Therefore, the triangle whose angles are all more that 90 degree is, Obtuse triangle.
Easy question, decent amount of points! 25 points, if you're curious!
Be quick or it is gone.
The length of a football field is 100 yards and the width is 53 yards. in the first game of the season, joe don catches the opening kickoff at the corner of the goal line and runs straight as a string the diagonal length of the field to score a touchdown. the next day, the local paper credits joe for a 100 yard touchdown run, but how far did he actually run?
Answer:
Joe Don actually ran 113.2 yards
Step-by-step explanation:
Length of the football field = 100 yd
Width of the football field = 53 yd
The football field is rectangular in shape. So in order to find the diagonal of the field, we need to split it up into two right triangles.
In one of the right triangles, the length and width becomes the two sides of it and diagonal is the third side.
In order to find the third side (diagonal), we need to apply the Pythagoras theorem.
So,
Diagonal² = 100² + 53²
Diagonal² = 10000 + 2809
Diagonal² = 12809
Taking square root on both sides
[tex]\sqrt{Diagonal^{2} } =\sqrt{12809}[/tex]
Diagonal = 113.17 yd
Diagonal = 113.2 yd (approx)
Thus Joe Don actually ran 113.2 yards
True or false: when comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. choose the correct answer below.
a. false, because the larger the standard deviation is, the less dispersion the distribution has.
b. true, because the standard deviation is the difference between the largest and smallest observation. when the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution.
c. true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
d. false, because the standard deviation measures the spread of the distribution, not the dispersion of the distribution.
The larger the standard deviation, the more dispersed the distribution is, because the standard deviation measures how far each observation is from the mean value of the distribution.
The correct option is C. The typical value being referred to in the option is the mean. The standard deviation measures how far each observation in a distribution is to the mean value of the distribution. Option D is wrong, because, the spread is also the degree of dispersion. The difference between the largest and smallest value in a distribution is the range and not the standard deviation . Hence, option B is wrong. The larger the standard deviation, the greater the dispersion. Hence, option A is wrong.Learn more : https://brainly.com/question/12402189?referrer=searchResults
1. Billy had 40 songs on his MP3 player. If he deleted 8 songs, what is the ratio of songs he kept to songs he deleted?
1 point
8:40
32:40
40:32
40:8
2. A vendor sold 63 hotdogs during a football game. If the ratio of hotdogs to hamburgers sold was 9:5, how many hamburgers did the vendor sell? *
1 point
Your answer
3. Paul had sold 24 orange fish. If the ratio of blue fish to orange fish is 3:8, how many fish did he sell in total?
1 point
Your answer
4. Jack has a collection of toy cars. If there are 2 blues, 5 black, 7 red and 3 purple cars, what is the ratio of purple to all the cars?
1 point
3:14
3:17
5. At an ice cream shop the ratio of sugar cones to waffle cones sold is 2:1. If there are 15 cones altogether, how many sugar cones are there?
1 point
3
5
15
10
6. There is a total of 72 total students. If the ratio of boys to girls is 4 to 5, how many of the students are girls?
1 point
32
40
8
7. Paul can walk 15 steps in 5 minutes. How long does it take Paul to walk 75 steps?
1 point
25
225
3
8. If the ratio of pink flower to blue flower is 2 to 7 and there are 12 pink flowers, how many blue flowers are there?
1 point
6
12
42
36
Other:
9. If the ratio of white pens to green pens is 1 to 4 and there are 6 white pens, how many are green?
1 point
6
20
24
36
10. Jennifer and Melissa are both making lemonade. Melissa uses 3 cups water to 1 cup lemon juice. Jennifer uses 5 cups water to 2 cups lemon juice. Which mixture will have more lemon flavor?
1 point
Jennifer's
Melissa's
11. Nicholas has a collection of pens. He has 4 red, 9 blues, 2 white and 3 black pens. What is the ratio of black to the total amount of pens in simplified form?
1 point
1:3
1:6
3:1
6:1
Michelle has read 0.05625 percent of a book. If she has read 18 pages, how many total pages are in the book?
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
There are 10 different ways to select a committee of 2 people from a group of 5 candidates.
Explanation:To calculate the number of ways to select a committee of 2 people from a group of 5 candidates, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
Here, n is the total number of candidates (5) and r is the number of people to be selected for the committee (2). Plugging in the values, we get:
5C2 = 5! / (2!(5-2)!)
Simplifying this expression:
5C2 = (5 * 4) / (2 * 1)
Therefore, there are 10 different ways to select the committee.
A parking lot charges $1.50 for the first hour of parking, and 55 cents for each additional half hour . how much would it cost to park a car from 12:45 pm to 6:15 pm
The parking cost for the specified duration would be $6.70.
Explanation:The parking fee consists of a base charge of $1.50 for the first hour. In this case, the car is parked for 5.5 hours (from 12:45 pm to 6:15 pm). The first hour is covered by the base charge, and the remaining 4.5 hours are billed as subsequent half-hours. For each half-hour, there is an additional charge of 55 cents. So, for the subsequent 4.5 hours, the additional charge is calculated as follows:
[tex]\[4.5 \times \$0.55 = \$2.475.\][/tex]
Adding this to the base charge:
$1.50 + $2.475 = $3.975.
Therefore, the total parking cost for the specified duration is $1.50 (for the first hour) + $2.475 (for the subsequent 4.5 hours), resulting in a final cost of $6.70.
This calculation ensures that the parking fee is accurately determined based on the initial hourly rate and subsequent half-hourly charges. The approach allows for a clear breakdown of the cost structure, providing transparency for users and ensuring fairness in the billing process.
A parking lot implements a fee structure of $1.50 for the first hour of parking and an additional charge of 55 cents for each subsequent half-hour. If a car is parked from 12:45 pm to 6:15 pm on the same day, how much would the parking cost for this duration?
What are the solutions to the equation x² = 625?
Select EACH correct answer.
A. -312.5
B.-25
C.25
D. 312.5
You purchase an item to sell in your store. The item costs you $6.45. You mark the item up 20%, but later run the item on sale at 5% off the marked price.If your customer must pay 6% sales tax, what will be the total amount paid by the customer for the item?
Which of the numbers is rational? A) π B) 25 C) 2 D) 3
Answer:
25, 2, & 3 are rational numbers
π is a irrational number.
Explanation:
I think we need to find out the irrational number.
Here we learn main difference between rational and irrational number.
Rational Number:
All numbers whose written in fraction form where numerator and denominator are whole number.
All the whole numbers are rational number.
For example: 2 (because we can write 2 as [tex] \frac{2}{1} [/tex]), [tex] \frac{5}{6} [/tex] etc
0.666666.... (endless repeating digits)
In given question: 25, 2 and 3 are rational numbers
Irrational Numbers:
All numbers that are not rational are considered irrational. An irrational number can be written as a decimal form, but not as a fraction form.
An irrational number has endless non-repeating digits to the right of the decimal point.
π = 3.141592...... (endless non repeating digits)
√2 =1.414213... (endless non repeating digits)
Answer:
25, 2, 3
Step-by-step explanation:
A rational number is a terminating decimal or a non-terminating, repeating decimal.
25, 2, and 3 are terminating decimals, so they are rational.
Which graph shows the solution to the inequality -x + 2 > 1
elise took out a payday loan for $500 due in 2 weeks that charged an $80 fee. what the periodic interest rate of the loan?
Answer:
16%Step-by-step explanation:
The periodic interest rate refers to the rate that it's charged after certain fixed period, can be yearly, monthly, daily. In this case, the periodic interest rate is due in 2 weeks.
Now, to find this interest rate, we just have to divide the fee by the loan and see what percentage represents
[tex]\frac{\$80}{\$500}=0.16[/tex]
Then, we multiply by 100 to obtain the percentage
[tex]0.16(100)= 16\%[/tex]
Therefore, the interest rate is 16%
riangle ABC is a right triangle. What is the relationship between angles A and B? They are congruent. They are complementary. They are supplementary. There is no relationship between them.
Answer:
50 square units.
Step-by-step explanation:
Eng2021
Gina paints beach scenes on notecards. She sells packages of 8 notecards for $8 for one package, $16 for 2 packages, and $24 for 3 packages. Which equation is the rule for the pattern if n is the number of packages and d is the selling price in dollars?
A 45° sector in a circle has an area of 13.75π cm². What is the area of the circle? Use 3.14 for pi.
Enter your answer as a decimal in the box.
cm²
Area of circle is 345.4 cm²
Area of sector:Given that;
Angle of sector = 45°
Area of sector = 13.75π cm²
Find:
Area of the circle
Computation:
Area of sector = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75π = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
43.175 = 0.125[Area of circle]
Area of circle = 345.4 cm²
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Find the following.
a. The side length of a cube with a volume of 125 units^3.
b. The volume of a cube with a side length of 4 units.
Solve (4 - x ≤ -1) ∩ (2 + 3x ≥ 17). Click on the graph until the solution set appears.
The solution set appears at x ≥ 5 for (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
The symbol ∩ represents an intersection or common between them.
Given, (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
( x ≥ 5) ∩ ( x ≥ 5).
So, x ≥ 5.
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How many ways can you choose the 5 cards out of a 52 card deck?
There are 2,598,960 ways to choose 5 cards out of a 52-card deck.
Explanation:To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. In this case, order doesn't matter, so we use the formula for combinations. The formula is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from and r is the number of items to be chosen.
For this question, n = 52 (number of cards in the deck) and r = 5 (number of cards to choose). We can plug these values into the formula to calculate the number of ways:
C(52, 5) = 52! / (5!(52-5)!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52-card deck.
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The number of ways to choose 5 cards from a deck of 52, irrespective of order, is 2,598,960. This number is calculated using the combination formula in combinatorics.
Explanation:This question relates to the field of Mathematics known as combinatorics, specifically the concept of combinations. When we choose 5 cards out of a 52-card deck, we're not interested in the order in which the cards are drawn, so we use combinations. We use the notation C(n, k), where n is the total number of items, and k is the number of items to choose.
The formula for finding combinations is C(n, k) = n! / [k!(n-k)!]. In this case, n=52 (the total number of cards in the deck) and k=5 (the number of cards we are selecting). Plug these values into the formula to get C(52, 5) = 52! / [5!(52-5)!] = 52! / (5!47!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52 card deck. This number takes into account all possible combinations of cards, without consideration of order or repetition.
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The function f(x)=-√-x is shown on the graph. Which statement is correct? The range of the graph is all real numbers greater than or equal to 0. The domain of the graph is all real numbers greater than or equal to 0. The range and domain of the graph are the same. The domain of the graph is all real numbers.
The correct option is: The range and domain of the graph are the same.
Explanation
Given function is: [tex]f(x) = -\sqrt{-x}[/tex]
The inside term of a square root can't be negative, it will be always 0 or positive. That means, [tex]-x \geq 0[/tex] or [tex]x\leq 0[/tex]
So, the Domain of the function is : "All real numbers such that [tex]x\leq 0[/tex]"
Now, if x=0, then f(x) =0 and if x is any negative number, then f(x) will be also negative.
That means, the Range of the function: "All real numbers such that [tex]f(x)\leq 0[/tex]"
So, the range and domain of the function are the same.
How might your life insurance premiums depend upon when you initially purchase the policy?
Answer:
The age you are when you purchase life insurance is the biggest factor in how much you will have to pay. The premium amount typically increases about 8% to 10% for every year of age. The older you are, the more expensive you are to insure. When you are in your 40s, your rates increase from 5%-8% and when you are over 50, your rates increase by 9%-12% each year.
Step-by-step explanation:
Answer:
The Life insurance premium totally depends on your age when you will be purchasing it.
Step-by-step explanation:
Age is a significant factor in purchasing the policy. Age can be directly related to the rate of premium in the term plan or in the insurance. The average increase in the rate when it is calculated per year is about 8 to 10 percent. {Told by Ted Bernstien}.
According to the common theories, when you are in your 40's, then the rate will be increased around 5 to 8 percent, and when you are in your 50's it will be about 9 to 12 percent if you calculated it yearly.
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Convert 59 degrees in Fahrenheit to Celsius temperature using the formula . 27°C 15°C 12°C 8°C
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
We have,
To convert a temperature in Fahrenheit to Celsius, you can use the formula:
°C = (°F - 32) x (5/9)
Let's apply this formula to convert 59 degrees Fahrenheit to Celsius:
°C = (59 - 32) x (5/9)
Simplifying the equation:
°C = 27 x (5/9)
°C = 135/9
°C = 15
Therefore,
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
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Isabella is solving the equation 4x^2=13x−3 with the quadratic formula.
Which values could she use for a, b, and c?
A. a = 4, b = −13, c = 3
B. a = 4, b = 3, c = −13
C. a = 4, b = 13, c = −3
D. a = 4, b = −3, c = 13
values could she use for a, b, and c a = 4 b = -13 c = 3
Step-by-step explanation:
We have been given the equation
4x²=13x-3
Subtract 4x² to both sides of the equation
0=-4x²+13x-3
Multiply both sides of the equation by -1
4x²-13x+3=0
The general equation of a quadratic equation is ax²+ bx +c=0
Comparing this equation with above equation 4x²-13x+3=0
a = 4
b = -13
c = 3
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devise a plan for simplifying th fourth root of a number that is not a perfect fourth power.
Final answer:
To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.
Explanation:
Simplifying the Fourth Root of Non-Perfect Powers
When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.
To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.
If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.