Triangle ABC was rotated to form triangle A'B'C'. Triangle A'B'C' was reflected across the x-axis to form Triangle A"B"C".

Which of the following statements correctly describes the relationship between Triangle ABC, Triangle A'B'C', and Triangle A"B"C"? Select all that apply.

Group of answer choices

Triangle ABC has greater angle measurements than Triangle A"B"C".

Triangle ABC is congruent to Triangle A"B"C".

Triangle A'B'C' has greater angle measurements than Triangle A"B"C".

Triangle ABC has greater side lengths than Triangle A"B"C".

Triangle A'B'C' is congruent to Triangle A"B"C".

Answer:

[tex](x,y)\rightarrow(0,2)[/tex]

Step-by-step explanation:

[tex]\displaystyle \left \{ {{x+y=2} \atop {y-x=2}} \right.\\[/tex]

Combine system of equations on both sides:

[tex](x+y)+(y-x)=2+2\\2y=4\\y=2[/tex]

Thus,

[tex]x+y=2\\x+2=2\\x=0[/tex]

(x, y) <=>(0, 2)

Step-by-step explanation:

[tex]x + y = 2 \\ y - x = 2 \\ \\ x + (x + 2) = 2 \\ y = x + 2 \\ \\ 2x + 2 - 2 = 2 - 2 \\ y = x + 2 \\ \\ 2x = 0 \\ y = x + 2 \\ \\ x = 0 \div 2 \\ y = x + 2 \\ \\ x = 0 \\ y = 0 + 2 \\ \\ x = 0 \\ y = 2[/tex]

a) A function w(t) to represent the amount of water in the pool using the two functions is w(t) = -3t + 5.

b) The pool will leak out the water when w(t)=0.

c) It will take 1.67 hours to leak out all the water from the pool.

d) Yes, functions f(t) and d(t) will intersect on the graphs when the pool stops leaking all the water out.

e) The domain of the functions  f(t), d(t) and w(t) are 0 ≤ t ≤ 1.67.

What are functions?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Subtract the amount flowing into the pool by the amount being drained out the pool to get the amount of water in the pool .

The given functions are -

Flowing: f(t) = t² + 8t + 9.

Draining: d(t) = t² + 11t + 4.

The amount of water in the pool is -

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Therefore, the function obtained is w(t) = -3t + 5.

When the condition is w(t) = 0 then, the pool will have leaked all the water.

Plugging in the values -

-3t + 5 = 0.

3t = 5

t = 1.67.

Therefore, the pool will leak all the water in 1.67 hours.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked. The graph is shown below.

The domain of a function is the set that contains all input values of the function. The input is the time in the given situation, so -

Time cannot be negative, hence t ≥ 0.

When all the water has been drained, everything stops, hence t ≤ 1.67.

Therefore, the domain of the function is 0 ≤ t ≤ 1.67.

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According to question we can say that the approximate percentage of the increase is 13.2352%.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

Based on the given conditions, formulate: (77 —68)/ 68

e sum or difference:9/68 = 0.132352

0.132352 x100/100

=13.2352%

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Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.

Lines (line segments) and points make up the forms we perceive (vertices). To create a shape, these line segments are connected at their vertices. These lines' sides are what they are known as. The line segment that connects two vertices of a form or two-dimensional object is referred to as a side in geometry.

The sine of an angle can never be greater than 1 because the sine function maps an angle to the y-coordinate of the point on the unit circle that corresponds to that angle. The y-coordinate of any point on the unit circle is always between -1 and 1, inclusive. Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

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Answer:

24 WEEKS

BECAUSE IF U MULTIPLY 24X25.50 U WILL GET 612 ADD 42.50 AND U WILL GET 654.50

To find the nature of the roots of a given quadratic equation, use the quadratic formula, which is [tex]x= \frac{(-b±\sqrt{b^2-4ac} )}{2a}[/tex].

Substitute the values of a, b, and c from the given equation into the formula and solve for x. The nature of the roots can then be determined by examining the sign of the discriminant, b² - 4ac.

If the discriminant is positive, the quadratic equation will have two real roots; if the discriminant is zero, the quadratic equation will have one real root; and if the discriminant is negative, the quadratic equation will have two complex roots.

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The Truth Table in logic gate is  used to specify the output of the logic gate for all possible combinations of the input signals. , it is the breakdown of all the possible truth values returned by the logical expression.

What is Truth Table ?

The truth table is a tabular representation of all combinations of values for inputs and their respective outputs.

It can be called as a mathematical table which shows all possible outcomes that would occur from all the possible scenarios that are considered as  factual.

Truth tables are generally used for the logic problems as in Boolean algebra and electronic circuits.

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Answer:

Step-by-step explanation:

A truth table for a logic gate is the table that specifies the logic value/state of the output of the gate for all possible combinations of the logic states of all inputs.

Let's take the example of the AND gate with two logic inputs A and B and one output Y.

A    B    Y

0    0    0

0    1     0

1     1     1

1    0     0

This is the truth table for the AND gate.

Answer:

(2) y = -2x² + 6x - 6

Step-by-step explanation:

Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.

Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.

Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Here,

we use the z-score algorithm to answer this query.

Score Z = x - μ/σ

x = the raw score

 population mean= μ 

Population standard deviation is σ

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability based on the Z-Table:

P(x<258) = 0.89736

Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.

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Answer:

analysis (i got to put a bunch of random stuff here cs the limit)

If you double the amount of fluid ounces, the amount of cups also double

There is proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.

The donation is proportional to the dinner bill

The donation for a dinner bill of $50 is $9

If there are 8 fluid ounces in one cup

8 : 1 = 16 : x

8/1 = 16/x

8 × x = 16 × 1

8x = 16

x = 16/8

x = 2

The difference between weight = 1

The difference between cost = $0.68 - $0.47

= $0.21

$0.89 - $0.68

= $0.21

$1.10 - $0.89

= $0.21

Cost of mailing 6-ounce letter

1 : 0.47 = 6 : x

1/0.47 = 6/x

1 × x = 6 × 0.47

x = $2.82

The donation for a dinner bill $50 is

Dinner bill : donation

25 : 4.50 = 50 : x

25/4.50 = 50/x

25 × x = 50 × 4.50

25x = 225

x = 225/25

x =$ 9

Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.

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Answer:

[tex]f(g(-3))=-25[/tex]

Step-by-step explanation:

[tex]g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25[/tex]

Answer:

we get a required sample size of 122.

Step-by-step explanation:

We can use the following formula to calculate the required sample size:

n = (Z * sigma / e)^2

where:

n is the required sample size

Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)

sigma is the standard deviation of the population

e is the maximum error allowed

Plugging in the given values, we get:

n = (1.96 * 0.6 / 0.08)^2 = 121.6

Rounding up to the next integer, we get a required sample size of 122.

The schedule of her course in 120 ways.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

According to the question there are five spaces for different subjects which are arranged in different order so the number of ways are

2(5,4)

= 5 * 4 * 3 *  2

=120 ways

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Answer:

Step-by-step explanation:

To solve this equation, we can start by using the logarithm property that states: log(a) - log(b) = log(a/b).

Then, we can apply this property to the left side of the equation:

log (7x+5) - log(x - 1) = log((7x+5)/(x - 1)) = 1

Next, we can rewrite the right side of the equation as:

log((7x+5)/(x - 1)) = log(7x+5) - log(x - 1) = 1

Now, we can use the inverse property of logarithms, which states: log(a) = b, then a = 10^b, to solve for x.

This gives us: (7x+5)/(x - 1) = 10

We can then cross-multiply and simplify to get: 7x+5 = 10x - 10

This equation simplifies to: 3x = -5

Dividing both sides by 3 gives us: x = -5/3

Therefore, the solution to the equation is x = -5/3.

The values of the variables are n = -17/31 and m = 23/93

From the information given, we have the equations;

To solve the simultaneous equation, we have to take the following steps

Make 'm' the subject from equation 1

9m = 1 + 4n

Divide both sides by 9, we get;

m = 1 -4n/9

Substitute the value into equation (2), we have;

11(1 -4n/9) - 2n = 5

expand the bracket

11 - 44n/9 - 2n = 5

find the LCM

11 - 44n - 18n  /9 = 5

cross multiply

11- 62n = 45

collect like terms

-62n = 45 - 11

-62n = 34

Make 'n' th subject

n = -34/62

n = - 17/31

Substitute the value into equation (3)

m = 1 - 4(-17/31)/9

m = 1+68/31 ÷9

m = 69/31 × 1/9

m = 69/279

m = 23/93

Hence, the values are n = -17/31 and m = 23/93

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7th interval is not perfect

7th interval is not perfect

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤1. The group of numbers such that 0 < x< 1 and the group of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Real intervals are the simplest sets whose "length" (or "measure" or "size") is straightforward to define, making them significant in the theory of integration. The Borel measure and ultimately the Lebesgue measure can subsequently be produced by applying the concept of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing method that automatically generates assured enclosures for all formulas, even in the presence of errors, approximations in mathematics, and arithmetic roundoff.

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Answer:

Step-by-step explanation:

The solution is the point where the 2 lines intersect.

If they intersect where x = 1 and y = 2 the solution is (1, 2).

12.57 cm is the length of the label on bottle.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that a  bottle of Buckley's has a radius of 2cm

You need to create a label for this product

We need to find the length of this label.

Means we need to find the circumference of the bottle.

The formula for circumference is

C=2πr

Given radius is 2cm

C=2×3.14×2

C=12.57 cm

Hence, 12.57 cm is the length of the label on bottle.

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Answer:

Step-by-step explanation:

Let the speed be x km/h

Let the time be t

In △ADC,

tan30°=

h

xt

​

3

​

1

​

=

h

xt

​

h=  xt

In △ABD,

tan60°=

h

x(6+t)

h=  

x(t+6)

3​

xt=

x(t+6)

3t=6+t

t=3 seconds

∴ total time taken=6+3=9 seconds

The coeficient of y² in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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Answer:37.68

Step-by-step explanation:

given:

diameter of cylinder =4in.

radius of cylinder=2in.

height of cylinder =3in.

Volume of cylinder=πr^2h

. = 3.14×2×2×3

. = 37.68 in Cube

Answer:

113.1

Step-by-step explanation:

If π= 3.14 And The Equation For This Type Of Problem Is V=πr2h then all you do is do 3.14 times 9 times 4

Where Your Multiplying 3 To Square Of 2 To Get 9, So Take that 3.14 Multiply It By 9 And Then 14, Thus the answer is 113.1

Hope This Helps

answer:

b+24

step-by-step explanation:

it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!

Answer:

- [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

Change in y over the change in x.

(3,2)(-4,1)

The y values are 1 and 2.

The x values are -4 and 3.  

You find the change by subtracting.

[tex]\frac{1--2}{-4-3}[/tex] = [tex]\frac{1+2}{-7}[/tex] = [tex]\frac{3}{-7}[/tex]

Can be written - [tex]\frac{3}{7}[/tex]

Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

Answer:

Step-by-step explanation:

-1 divided by x

1 - x

X - 1

Tim received 8 SMS on Monday, 4 emails on Thursday, and 0.52 of the communications were emails, which is the solution to (a), (b), and (c).

When two sets of data are joined and their frequencies are combined, a composite bar chart is utilized. Two pieces of data—emails and texts—are included in this inquiry, but they both fall under the same heading, "messages." With regard to question (a), it is clear from the diagram that Tim got 8 texts on Monday. In order to answer question (b), we must determine how many emails Tim received on Thursday. To do this, we must look at the bar for Thursday and divide the total number of texts by the total number of messages to determine the number of emails received. 15-11=4, indicating that Tim received 4 emails on Thursday.

given

Tim for five days, total the emails received, and then determine the percentage of emails relative to messages.

Total messages: 14+16+14+15+14=73.

Emails totaled: 6 + 10 + 10 + 4 + 8 = 38

Email to message ratio is equal to 0.52.

Emails made up 0.52 of the messages, therefore.

Tim got 8 texts on Monday, 4 emails on Thursday, and 0.52 of the messages were emails, according to an analysis of the composite bar chart we used to determine the answers to the three questions.

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The complete question is :- The composite bar chart Messages received shows the number of messages Tim received each day for five days.

a) How many texts did Tim receive on Monday?

b) How many emails did Tim receive on Thursday?

c) In total, what fraction of the messages were emails?

Give your answer in its simplest form.

There are 24 ,5-digit palindromes with different neighboring .

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

No, it is always between 0 t0 1.

Such a palindromic number should be  abcba  

2a+2b+c=14

Thus  c has to be even and we need

a+b=14−c/2 and we can choose for  a any value from  1 to  (14−c)/2

Thus the number of such palindromic numbers is

7+6+5+4+3=25

starting from  c=0 up to  c=8

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If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)

Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

F = P(1+rt), formula for simple rate of interest

Here,

=> Future value is F

Present value is P

=> Rate is R

=> Time is t

Substituting x for r

And, n for t

Also, 10,000 in for P

F = 10,000(1+xn)

The formula tells us principal + interest,

F = 10,000(xn)

Now, to get the x into terms of a percentage,

F = 10,000(n * x/100)

F = 10,000n(x/100)

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Answer:

  ln(x²y⁵/(5z⁷))

Step-by-step explanation:

You want to condense the logarithmic expression 2 ln(x) + 5 ln(y) - 7 ln(z) - In (5).

The relevant rules of logarithms are ...

  a·ln(b) = ln(b^a)

  ln(ab) = ln(a) +ln(b)

  ln(a/b) = ln(a) -ln(b)

  [tex]2\ln{(x)}+5\ln{(y)}-7\ln{(z)}-\ln{(5)}=\boxed{\ln\left(\dfrac{x^2y^5}{5z^7}\right)}[/tex]