What is the missing statement in the proof? Scroll down to see the entire proof.

Given: ∆ABC with m∠ABC = 90°

A right triangle A B C.



Prove: AB2 + BC2 = AC2

Statement

Reason

1. Draw view diagram.

A right triangle A B C. Point D is at the midpoint of side A C. A line runs from D to B to form two right triangles A B D and D B C.



construction

2. ∠ ABC≅ ∠BDC

Angles with the same measure are congruent.

3.

Reflexive Property of Congruence

4. ∆ABC ~ ∆BDC

AA criterion for similarity

5.
Corresponding sides of similar triangles are proportional.

6. BC2 = AC × DC

cross multiplication

7. ∠ ABC ≅ ∠ADB

Angles with the same measure are congruent.

8. ∠ BAC ≅ ∠DAB

Reflexive Property of Congruence

9. ∆ABC ~ ∆ADB

AA criterion for similarity

10.
Corresponding sides of similar triangles are proportional.

11. AB2 = AC × AD

cross multiplication

12. AB2 + BC2 = AC × AD + AC × DC

addition

13. AB2 + BC2 = AC(AD + DC)

Distributive Property

14. AB2 + BC2 = AC × AC

segment addition

15. AB2 + BC2 = AC2

multiplication

A.
∠ BDC ≅ ∠ADB

B.
∠BCA ≅ ∠DCB

C.
∠ BAC ≅ ∠BAD

D.
∠ DBC ≅ ∠BAC

Answer:

(8.47,0) (-0.47,0)

Step-by-step explanation:

y = a(x - h)² + k

y = a(x - 4)² - 20

-4 = a(0 - 4)² - 20

16 = 16a

a = 1

y = (x - 4)² - 20

x-intercepts: y = 0

(x - 4)² = 20

x - 4 = +/- 4.47..

x = 4.47+4, -4.47+4

x = 8.47, -0.47

It is proved that [ [A, B]², C] = 0 for any 2 × 2 real matrices A, B, and C.

To prove or disprove the statement [ [A, B]², C] = 0, where A, B, and C are 2 × 2 real matrices, we need to evaluate the commutator [ [A, B]², C] and check if it equals zero.

First, let's calculate [A, B]:

[A, B] = A * B - B * A

Next, we calculate [ [A, B]², C]:

[ [A, B]², C] = [ (A * B - B * A)², C]

               = (A * B - B * A)² * C - C * (A * B - B * A)²

Expanding the square terms:

= (A * B - - B * A * A *

          B * C B * A) * (A * B - B * A) * C - C * (A * B - B * A) * (A * B - B * A)

= A * B * A * B * C - A * B * A * B * C - B * A * B * A * C + B * A * B * A * C

              - A * B * B * A * C + B * A * A * B * C + A * B * B * A * C

= 0

Therefore, we have proved that [ [A, B]², C] = 0 for any 2 × 2 real matrices A, B, and C.

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The Complete Question is:

We define the commutator, denoted by [ X , Y ], of two square matrices X and Y to be [ X , Y ] = X Y − Y X. Let A, B, and C be 2 × 2 real matrices. Prove or disprove: [ [A, B]², C] = 0

The number of permutations of 8 objects taken 3 at a time is 336.

To calculate the number of permutations, we use the formula for permutations of n objects taken r at a time, which is given by P(n, r) = n! / (n - r)!. In this case, we have 8 objects and we want to take 3 objects at a time. Therefore, the number of permutations is P(8, 3) = 8! / (8 - 3)! = 8! / 5!.

Simplifying further, we have 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 and 5! = 5 x 4 x 3 x 2 x 1. Canceling out common factors, we get (8 x 7 x 6) / (3 x 2 x 1) = 336.

Therefore, the number of permutations of 8 objects taken 3 at a time is 336.


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Answer:

3/4x + 12 =48

3/4x=36

x=48

If below assumptions are not met, then the validity of the confidence interval may be compromised, and alternative methods may need to be used to estimate the mean increase in blood pressure.

In statistics, sampling is the process of selecting a subset of individuals or objects from a larger population for the purpose of studying or estimating certain characteristics of the population. The subset of individuals or objects is known as a sample.

Sampling is often used when it is impractical or impossible to collect data on the entire population. By studying a representative sample, statisticians can make inferences about the population as a whole with a certain level of confidence.

In order for a 95% confidence interval for the mean increase in blood pressure to be valid, the following assumptions must be made:

If these assumptions are not met, then the validity of the confidence interval may be compromised, and alternative methods may need to be used to estimate the mean increase in blood pressure.

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Answer:

32 possible outcomes

Step-by-step explanation:

There are two options for each question (true or false).

Hence, according to the counting principle :

Question 1 = true or false = 2

Question 2 = true or false = 2

Question 3 = true or false = 2

Question 4 = true or false = 2

Question 5 = true or false = 2

2 * 2 * 2 * 2 * 2 = 2^5 = 32

Answer: 120 people

Step-by-step explanation:

First take $4100 - $500 = $3600

then you divide

3600/30 = 120

which equals

120 People are estimated to attend

Answer:

6 million

Step-by-step explanation:

50% = 1/2

1/2 + 1/3 = 5/6

5/6 people watched or listened, which means 1/6 people did not do either of them.

1/6 of 36 (million) = 6 (million)

So, the answer is 6 million.

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer:

Pumpkin seed has more grams of protein per ounce

216 grams of protein

Step-by-step explanation:

1 pound = 16 ounce

16 ounce of sunflower seeds = 96 grams of protein

6.5 ounce of pumpkin seeds = 58.5 grams of protein

Which type of seed has more grams of protein per ounce?

Sunflower seeds:

Protein per ounce = 96 grams / 16 ounce

= 6 grams of protein per ounce

Pumpkin seeds:

Protein per ounce = 58.5 grams / 6.5 ounce

= 9 grams of protein per ounce

Therefore,

Pumpkin seed has more grams of protein per ounce

How many more grams of protein are there in 24 ounces of the higher-protein seeds?

Quantity of protein = 24 ounces ×

9 grams of protein per ounce

= 216 grams of protein

Answer:

Step-by-step explanation: k = 25

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Given:

Using synthetic division we get,

Hence, the answer is,

Answer:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)

Step-by-step explanation:

Evaluate 13-0.75w+8x13−0.75w+8x13, minus, 0, point, 75, w, plus, 8, x when w=12w=12w, equals, 12 and x=\dfrac12x= 2 1 ​ x, equals, start fraction, 1, divided by, 2, end fraction.

For this case we have the following expression:

 \(13-0.75w + 8x\)

Evaluate for the following values:

 w = 12

 x = 1/2

 We Substituting the values we have:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)

Answer:

Business Process Mapping

Business process mapping refers to activities involved in defining what a business entity does, who is responsible, to what standard a business process should be completed, and how the success of a business process can be determined.

Answer:

11c−11.2

Step-by-step explanation:

Answer:

-11.2 + 11c

Step-by-step explanation:

PEMDAS

-2(5 - 4c) + 0.6(5c - 2)

-10 + 8c + 3c - 1.2 (Combine like terms)

-11.2 + 11c

Sorry if I'm wrong in advance!

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

If about 20% of British children are deficient in vitamin and doctors test a group of elementary school children, the probability that the first vitamin d-deficient child is the 8th one tested is 4.19% determined using geometric distribution formula.

In probability and statistics, geometric distribution refers to the probability that first success would occurs after n number of trials and is given by:

P(X)=q^(x-1)p

Where p is the probability of success and q is (1-p)

In this case,

p=probability of children deficient in vitamin= 0.2

q= probability of children not deficient in vitamin= 0.8

Hence,

P(8)=0.8^(8-1)*0.2= 0.0419

Hence, the probability that 8th child is deficient is 4.19%

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Answer:

b

Step-by-step explanation:

Answer:

3x - 6

Step-by-step explanation:

Let's call the number of coins Karen has "x".

According to the information given, Bill has 6 coins fewer than two times the number of coins Karen has, so we can write the following expression for the number of coins Bill has:

Bill: 2x - 6

To find the total number of coins Karen and Bill have, we simply add the number of coins each person has:

Karen + Bill: x + (2x - 6) = 3x - 6

So the total number of coins Karen and Bill have is 3x - 6.

Answer:  the total amount of coins Bill and Karen have can be found with the following equation: 3x-6

Step-by-step explanation:

Karen has x coins

Bill's coins are twice the x, so 2x, and he has 6 fewer than that.

The equation becomes x+2x-6 which can be simplified to 3x-6.

If Roselyn is driving to visit her family, who live 150 kilometers away.  the price for the amount of fuel that Roselyn will use for the entire drive is $15.

Roselyn  Driving time :

Time = 150 km / 60 km/h

Time  = 2.5 hours

Liters of fuel that Roselyn's can will use

Liters = 2.5 hours * 60 km/h / 6 km/l

Liters = 25 liters of fuel

Amount paid = 25 liters * 0.60 dollars/liter

Amount paid = $15

Therefore the price is $15.

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Answer:

this angle is 90°.

5x°+55°=90°

5x=90°-55°

5x=35°

x=35/5

x=7

It's not necessarily certain that a function's inverse is a function! It is necessary for the original function to be a one-to-one function in order to ensure that its inverse will likewise be a function.

What does a function's inverse mean with an example?

The original value for which a function produced its output is returned by the inverse function. In terms of functions, f and g are inverse, using the formula f(g(x)) = g(f(x)) = x. The initial value can be retrieved using a function that is its inverse. As a result, g(y) = (y-5)/2 = x is the inverse of f. (x).

                                A function that reverses the effects of another function is said to have an inverse. If y=f(x), then x must always equal g, then a function g is the inverse of a function f. (y). Application of f followed by application of g is equivalent to doing nothing, in other words.

y = x² is a function

but inverse y = +/- √x   is not

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Within-groups design compares the same subjects across time. In this design, participants are measured or observed on multiple occasions, such as before and after an intervention or at different time points.

The purpose of the within-groups design is to examine changes within individuals over time, allowing researchers to assess the impact of an intervention or the natural progression of a phenomenon within the same group of subjects.

By comparing the same subjects across time, within-groups designs help to control for individual differences and increase the internal validity of the study.

This design allows researchers to evaluate the effectiveness of an intervention by assessing changes within individuals and determining if those changes are statistically significant.

It also allows for a more precise assessment of the impact of an intervention or the stability of a phenomenon over time.

Within-groups designs are commonly used in fields such as psychology, education, and medicine to study changes in behavior, cognition, or health outcomes.

They provide valuable insights into individual responses to interventions or the natural course of development or disease progression within a specific group of subjects.

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The domain of this function is all real numbers are a. (fog)(2) = f(g(2)) = f(2²-4) = f(0) = 1

b. (gof)(2) = g(f(2)) = g(5(2)+1) = g(11) = 11²-4 = 117

c. (fog)(-5) = f(g(-5)) = f((-5)²-4) = f(21) = 106

d. (gof)(-5) = g(f(-5)) = g(5(-5)+1) = g(-24) = (-24)²-4 = 572

e. (fog)(x) = f(g(x)) = f(x²-4) = 5(x²-4)+1 = 5x²-19

a. (f+g)(x) = f(x) + g(x) = 5x+1 + x²-3x+2 = x²+2x+3

The domain of this function is all real numbers since there are no values that make the function undefined.

b. (f-g)(x) = f(x) - g(x) = 5x+1 - (x²-3x+2) = -x²+8x-1

The domain of this function is all real numbers since there are no values that make the function undefined.

c. (fg)(x) = f(x)g(x) = (5x+1)(x²-3x+2) = 5x³-14x²-x+2

The domain of this function is all real numbers since there are no values that make the function undefined.

d. (x)/(6(x²)) = 1/(6x)

The domain of this function is all real numbers except x=0, since 0 makes the denominator zero and the function undefined.

a. (f+g)(x) = f(x) + g(x) = 5x+1 + 5x²-4 = 5x²+5x-3

The domain of this function is all real numbers since there are no values that make the function undefined.

b. (f-g)(x) = f(x) - g(x) = 5x+1 - (5x²-4) = -5x²+5x+5

The domain of this function is all real numbers since there are no values that make the function undefined.

c. (fg)(x) = f(x)g(x) = (5x+1)(5x²-4) = 25x³+x²-20x-4

The domain of this function is all real numbers since there are no values that make the function undefined.

d. -6(x)/(2(x)) = -3

The domain of this function is all real numbers except x=0, since 0 makes the denominator zero and the function undefined.

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Answer:

Area of white circle = 346.36 cm²

Step-by-step explanation:

Area of a circle = πr² where r is the radius

r = diameter/s

For the green circle, d = 42, r = 21

A = π(21)² = 1,385.44 cm²

The white circle has a diameter half of the green circle = 42/2 = 21 cm
So radius of white circle = 21/2 = 10.5 cm

Area of white circle = π (10.5)² = 346.36 cm²

Answer:

270

Step-by-step explanation:

Since you have the value of x as 90

3x=3*90

3x=270

a. The function rule for f^−1 is: \(f^{-1} (y) = (y + 16)/6\)

b. The function rule for g^−1 is: \(g^{-1} (v) = (v - 30)/2\)

What is integral function?

A continuous counterpart of a sum, an integral is used to compute areas, volumes, and their generalizations. The method of computing an integral, known as integration, is one of calculus's two fundamental operations, the other being differentiation.

a. To find the function rule for \(f^{-1}\) we need to solve for x in terms of y using the given equation:

y = 6x - 16

First, we can add 16 to both sides of the equation:

y + 16 = 6x

Then, we can divide both sides by 6 to isolate x:

x = (y + 16)/6

Therefore, the function rule for f^−1 is:

\(f^{-1} (y) = (y + 16)/6\)

b. To find the function rule for \(g^{-1}\), we need to solve for u in terms of v using the given equation:

v = (2u + 85/5) + 13

First, we can simplify the expression in parentheses by multiplying 85/5:

v = (2u + 17) + 13

Then, we can subtract 13 from both sides of the equation:

v - 13 = 2u + 17

Next, we can subtract 17 from both sides:

v - 30 = 2u

Finally, we can divide both sides by 2 to isolate u:

u = (v - 30)/2

Therefore, the function rule for g^−1 is:

\(g^{-1} (v) = (v - 30)/2\)

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Place value of 432 is 400 +30+02 .

What is place value?

In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.

Main body:

The place value of a digit will increase by 10 times as we move  left on the place worth chart and reduces by ten times as we tend to move right.

The place of digit 4 will be hundreds.

The place of digit 3 will be tens.

The place of digit 2 will be ones.

Hence place value of 432 is  400 +30+02 .

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