If AB = PQ, BC=RQ, AC=PR and ∠ACB = ∠PRQ = 90˚. Write two congruency rules which can’t be applied to prove △ABC ≅ △PQR.

There are 5 11 pointer questions and 15 3 pointer questions

We are given that total points of the test is 100

The test contains questions of two markings 3 points and 11 points

It is given that the total number of questions is 20

Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'

Thus total number of questions=x + y =20

Now the total sum of all the points comes to 100

Therefore,

3x+11y =100

x + y =20

x= 20-y

Now putting the value of x in the other question,

3(20-y) +11y =100

60-3y +11y=100

8y=100-60

8y=40

y=5

Thus x=20-y=20-5=15

Thus there are 5 11 pointer questions and 15 3 pointer questions

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F(2) is equal to 17 for the given Function f(x) = 2(3)^x-1.

The f(2) for  function f(x) = 2(3)^x-1, we substitute x = 2 into the function and evaluate the expression.

Let's calculate f(2) step by step:

f(2) = 2(3)^2-1

First, we evaluate the exponent

3^2 = 9

Next, we substitute this value back into the expression:

f(2) = 2(9) - 1

Now, we perform the multiplication:

2 * 9 = 18

Finally, we subtract 1:

f(2) = 18 - 1

Simplifying further:

f(2) = 17

Therefore, f(2) is equal to 17 for the given function f(x) = 2(3)^x-1.

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Answer: \(f(2)=17\)

Step-by-step explanation:

        To solve, we will substitute 2 for x into the given function by raising to the power of 2, multiplying, and subtracting.

\(f(x)=2(3)^x-1\)

\(f(2)=2(3)^2-1\)

\(f(2)=18-1\)

\(f(2)=17\)

So, Tracy paid $12.50 for the encyclopedia and $45.50 for the math book.

In mathematics, an equation is a statement that shows the equality between two expressions. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An equation usually has an equals sign (=) between the two expressions. The equals sign indicates that the two expressions have the same value.

Here,

Let's use variables to represent the prices of the math book and the encyclopedia.

Let x be the price of the encyclopedia.

According to the problem, the price of the math book is 8 dollars more than 3 times the price of the encyclopedia. So, the price of the math book can be represented as:

=3x + 8

The total cost of the two books is given as 58 dollars. Therefore, we can write the equation:

x + (3x + 8) = 58

Simplifying and solving for x, we get:

4x + 8 = 58

4x = 50

x = 12.50

So, the price of the encyclopedia is $12.50.

To find the price of the math book, we can substitute x = 12.50 into the expression we derived earlier:

=3x + 8

= 3(12.50) + 8

= 37.50 + 8

= 45.50

Therefore, the price of the math book is $45.50.

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Answer:

34

Step-by-step explanation:

34*34=(30+4)^2=900+16+240=1156

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

The correct answer is option (D) "The graph shifts 7 units right and 8 units down".Explanation:To solve the given question, we need to use the rules for vertical and horizontal shifts, which are as follows:

Vertical Shift: y=f(x)+a moves the graph of f(x) upward if a > 0 and downward if a < 0.Horizontal Shift: y=f(x+a) moves the graph of f(x) left if a > 0 and right if a < 0.Now, let's transform the function f(x) into function g(x) and determine the shift required.The transformation of f(x) to g(x) is: g(x) = f(x - a) + bwhere a = horizontal shift and b = vertical shiftThe equation of the given functions is:f(x) = 1/(x − 2) and g(x) = 1/(x^(5/9))Let's set the equation of function f(x) in the standard form:y = 1/(x - 2)and the equation of function g(x) in the standard form:y = 1/(x^(5/9))

Now, we can observe that:To transform the graph of f(x) onto the graph of g(x), we need to shift the graph of f(x) right by 7 units and down by 8 units, which is given in option (D).Hence, the correct option is (D) "The graph shifts 7 units right and 8 units down".

The graph shifts 7 units right and 8 units down is the statement that describes the transformation of the graph of function f onto the graph of function g.Conclusion:Thus, we have determined the correct answer with an explanation and concluded that the correct option is (D) "The graph shifts 7 units right and 8 units down".

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Answer:

the answer is 24. 891 + 6. 588 - 16. 965 is14.514

Answer: 14.514

Step-by-step explanation:

24.891 + 6.588 = 31.479

31.479 - 16.965 = 14.514

Happy to help; have a great day! :)

The answer choice A, which is 75.87°C, is the correct answer. Boiling point is the temperature at which a liquid becomes a gas or vapor. It varies depending on the pressure in the surrounding environment. The boiling point of water at a pressure of 0.4 bar is 75.87°C.

As pressure affects the boiling point of water, water boils at a lower temperature as pressure drops, and at a higher temperature as pressure increases. Water boils at different temperatures depending on its pressure; therefore, when the pressure decreases, the boiling point of water decreases.

The boiling point of water is 100°C at standard atmospheric pressure of 1 bar or 1 atm. At a pressure of 0.4 bar, the boiling point of water decreases to 75.87°C. The decrease in boiling point is due to the lower atmospheric pressure.

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If the length of of a square increases from 3 inches to 7inches,the perimeter will increase from 12 inches to 28 inches. The perimeter will increase by 16inches

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The perimeter of a square is determined by adding all the sides together.

Therefore the perimeter of square = 4l

when the length is 3 inches, the perimeter = 4×3 = 12inches

when the length is 7inches , the = 4× 7 = 28inches

Therefore the perimeter increased from 12inches to 28inches. It increases by 16 inches

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When the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

The perimeter of a square can be represented as follows:

The perimeter of a square is the sum of the whole sides of the square.

perimeter of a square  = 4l

where

l  = side length

Recall the whole sides of a square is equal.

Therefore,

The side of the square is formally 3 inches.

Hence,

perimeter of a square = 4 × 3

perimeter of a square = 12 inches.

When the side length is increased to 7 inches.

Hence,

perimeter of a square = 4 × 7

perimeter of a square = 28 inches

Therefore, when the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

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Answer:

(x+3)*3=3x+9

Step-by-step:

Answer:

0.3495.

Step-by-step explanation:

............................

To find the 75th percentile of X is A. 1.00, we need to find the value of x such that the probability of X being less than or equal to x is 0.75.

Let f(x) be the density function of X. We know that f(x) is proportional to (1+x^2)^(-1), which means we can write:
f(x) = k(1+x^2)^(-1)
where k is a constant of proportionality. To find k, we use the fact that the total area under the density function is 1:
∫f(x)dx = 1
Integrating both sides, we get:
k∫(1+x^2)^(-1)dx = 1
The integral on the left-hand side can be evaluated using a substitution u = x^2 + 1:
k∫(1+x^2)^(-1)dx = k∫u^(-1/2)du = 2k√(u)
Substituting back for u and setting the integral equal to 1, we get:
2k∫(1+x^2)^(-1/2)dx = 1
Using a trigonometric substitution x = tan(t), we can evaluate the integral on the left-hand side:
2k∫(1+x^2)^(-1/2)dx = 2k∫sec(t)dt = 2kln|sec(t) + tan(t)|
Substituting back for x and simplifying, we get:
2kln|1 + x^2|^(-1/2) = 1
Solving for k, we get:
k = √(2/π)
Now we can write the density function of X as:
f(x) = (√(2/π))(1+x^2)^(-1)
To find the 75th percentile of X, we need to solve the equation:
∫(-∞, x) (√(2/π))(1+t^2)^(-1) dt = 0.75
This integral does not have a closed-form solution, so we need to use numerical methods to approximate the value of x. One way to do this is to use a computer program or a graphing calculator that has a built-in function for finding percentiles of a distribution. Using a graphing calculator, we can enter the function y = (√(2/π))(1+x^2)^(-1) and use the "invNorm" function to find the x-value corresponding to the 75th percentile (which is the same as the z-score for a standard normal distribution).
Doing this, we get:
invNorm(0.75) ≈ 0.6745
Therefore, the 75th percentile of X is approximately:
x = tan(0.6745) ≈ 0.835

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The cumulative distribution function (CDF) of X is\(F(x) = 1 - e^(-4x).\)

The cumulative distribution function (CDF) of a continuous random variable X gives the probability that X takes on a value less than or equal to a given value x. In this case, the CDF of X, denoted as F(x), is calculated as 1 minus the exponential function \(e^(-4x)\). The exponential term represents the probability density function (PDF) of X, which is given as \(f(x) = 4e^(-4x)\). By integrating the PDF from 0 to x, we can obtain the CDF.

The cumulative distribution function (CDF) is a fundamental concept in probability theory and statistics. It provides a way to characterize the probability distribution of a random variable by indicating the probability of observing a value less than or equal to a given value. In this case, the CDF of X allows us to determine the probability that X falls within a certain range. It is particularly useful in calculating probabilities and making statistical inferences based on continuous random variables.

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Answer:

C) 7 minutes

Step-by-step explanation:

start with formula

g(x) = x^4 - 3x^2 + 4x - 5

substitute x with number of stops (2)

g(2) = 2^4 - 3(2^2) + 4(2) - 5

simplify using p.e.m.d.a.s: start with exponents

g(2) = 16 - 3(4) + 4(2) - 5

multiply

g(2) = 16 - 12 + 8 - 5

subtract/add

16 - 12 = 4

4 + 8 = 12

12 - 5 = 7

input: 2

output: 7

ordered pair: (2,7)

Answer:

The range of the function should be:

-9 ≤ y ≤ 5

Hence, option D is true.

Step-by-step explanation:

We know that the set of values of the dependent variable for which a function is defined.

From the given function, we can easily observe that the graph is kind of oscillating between the y-value y = 5 and y = -9.

i.e.

at y = 5, the graph gets its maximum value

at y = -9, the graph gets its minimum value

Thus, the range of the function should be:

-9 ≤ y ≤ 5

Hence, option D is true.

Answer:

Step-by-step explanation:

The the terms be x and y

The sum of the terms = x+y

Difference of terms = x-y

Product of the sun and differences will be expressed as:

(x-y)(x+y) = x²-xy+xy-y²

(x-y)(x+y) = x²-y²

Hence the product of the terms is equivalent to the difference of two squares of the terms

Answer:

x=2.2

Step-by-step explanation:

11%5=2.2 so x=2.2

Answer:

x= 11/5

Step-by-step explanation:

5x=11 .     Divide each side by 5

5x/5 = 11/5 .  Cancel terms

x= 11/5

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The measure of the angle is x = 42.71°

In the right triangle we know the hypotenuse and the adjacent cathetus to angle x, so we can use the trigonometric relation:

cos(x) = (adjacent cathetus)/hypotenuse

Here we have:

adjacent cathetus = 12

Hypotenuse = 13

Then:

tan(x) = 12/13

x = Atan(12/13)

x = 42.71°

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Answer:

7. adjacent (next to each other)

8. vertical (right across from each other)

9. vertical (right across from each other)

10. neither

11. adjacent (right next to each other)

12. neither

Before I go on: all these angles have the same measure as the one across, so ∠SYX has the same measure as ∠UYV (76°), ∠XYW has the same measure as ∠TYU (40°), and ∠WYV has the same measure as ∠SYT (64°)...

13. ∠SYX = 76°

14. ∠XYW = 40°

15. ∠WYV = 64°

These last three are angles added together. They look tricky, but you just note the endpoints and add the measures of the included angles together.

16. ∠SYW = ∠SYX + ∠XYW = 76° + 40° = 106°

    ∠SYW = 106°

17. ∠TYX = ∠SYX + ∠SYT = 76° + 64° = 140°

    ∠TYX = 140°

18. ∠VYX = ∠WYV + ∠XYW = 64° + 40° = 104°

    ∠VYX  = 104°

I hope this helps you understand the concept! Have a great day!

Answer:

(-7,-3)

Step-by-step explanation:

step one) solve one equation for x.

y=-3x

-3x/-3=y/-3

x=(-y/3)

step two) plug in x for the other original problem.

y=x-4

y=(-y/3)-4

step three) solve for y.

y=(-y/3)-4

y+4=(-y/3)-4+4

3*(y+4)=(-y/3)*3

3y+12=-y

(3y+12)-3y=-y-3y

12/-4=-4y/-4

y=-3

step four) plug in -3 for y and solve for x.

y=x-4

-3=x+4

-3-4=x+4-4

-7=x

I am in algebra two so you can trust my answer. if you need more help lmk in the comments. happy holidays and stay safe!

Answer:

0.7874 inches

Step-by-step explanation:

divide

2 / 2.54

Answer:

0.8 in (nearest tenth)

Step-by-step explanation:

\(\sf Given \ 2.54 \ cm \approx 1 \ in\)

\(\sf \implies 1 \ cm \approx \dfrac{1}{2.54}=\dfrac{50}{127} \ in\)

\(\sf \implies 2 \ cm \approx \dfrac{50}{127}\cdot 2= \dfrac{100}{127} =0.8\ in \ (nearest \ tenth)\)

We have intercepts at (0, 0) and (18/5, 0), a local maximum at (3.6, f(3.6)), and the function is decreasing on (-∞, 3.6) and increasing on (3.6, ∞). The curve is a downward-facing parabola with a maximum at (3.6, f(3.6)).

To analyze the function f(x) = -2x² - 3x² + 36x, we first find its intercepts by setting y = 0:

x(-2x - 3 + 36) = 0

This gives us x = 0 and x = 18/5. Therefore, the x-intercepts are (0, 0) and (18/5, 0).

Next, we find the critical points by finding where f'(x) = 0 or does not exist:

f'(x) = -4x - 6x + 36 = -10x + 36

-10x + 36 = 0 => x = 3.6

So the critical point is (3.6, f(3.6)).

To determine whether this critical point is a maximum or minimum, we need to use the second derivative test. We have:

f''(x) = -10

Since f''(3.6) < 0, the critical point is a local maximum.

Next, we look at the intervals of increasing and decreasing. The derivative f'(x) is negative for x < 3.6 and positive for x > 3.6, so f(x) is decreasing on (-∞, 3.6) and increasing on (3.6, ∞).

To find any inflection points, we look at the concavity of f(x). We have:

f''(x) = -10

Since f''(x) is constant, there are no inflection points.

Finally, we can sketch the curve. We have intercepts at (0, 0) and (18/5, 0), a local maximum at (3.6, f(3.6)), and the function is decreasing on (-∞, 3.6) and increasing on (3.6, ∞). The curve is a downward-facing parabola with a maximum at (3.6, f(3.6)).

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Therefore, When ratios have the same units, we call that ratio a unit ratio.

When ratios have the same units, we call that ratio a unit ratio. An explanation of what is meant by the term ratio would be helpful. A ratio compares the relative sizes of two or more quantities. If the numbers being compared have the same units, then it is called a unit ratio. Unit ratios are ratios that relate to each other in terms of the same measurement unit. They are also sometimes known as unit rates or unit fractions. They are frequently used to compare the relative size of one quantity to another when they are measured in the same units. For example, when we say that there are two apples for every five oranges, we are expressing a ratio between apples and oranges. However, when we say that there are two apples per five oranges, we are using a unit ratio.

Therefore, When ratios have the same units, we call that ratio a unit ratio.

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The probability of having two years with high sales in a row for Apple Inc. is 0.16 or 16%.

To find the probability of two independent events happening in succession, you multiply their individual probabilities together. In this case, the probability of high sales in a given year is 40%, or 0.4.

Step 1: Convert percentages to decimal form.
High sales: 40% = 0.4

Step 2: Multiply the probabilities of high sales for two consecutive years.
Probability of two high sales years in a row = 0.4 * 0.4

Step 3: Calculate the result.
Probability = 0.4 * 0.4 = 0.16

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Answer:

122

Step-by-step explanation:

To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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