Given: , ∠DAC ≅ ∠BCA Prove: ∆ADC ≅ ∆CBA Look at the proof. Name the postulate you would use to prove the two triangles are congruent. SAS Postulate SSS Postulate AAA Postulate

Answer:

a. [tex]g(x)=f(x+3)+2[/tex]

b. [tex]g(x)=f(x-5)-4[/tex]

Step-by-step explanation:

Como f(x) no está especificada correctamente, vamos a tratarla genéricamente.

Las transformaciones que se proponen son traslaciones en el eje x y en el eje y.

Cuando se traslada'la función en el eje x, la variable independiente se reemplaza por una variable auxiliar u que es equivalente a la variable original x mas el valor desplazado hacia la izquierda.

Cuando se traslada la función en el eje y, simplemente se suma una constante a la función con un valor equivalente a las unidades que la función se traslado hacia arriba (si es hacia abajo, este valor es negativo).

Entonces, para trasladar f(x) 3 unidades a la izquierda u 2 unidades hacia arriba, empezamos por reemplazar la variable independiente por u=x+3 y luego agregar una constante igual a 2:

[tex]g(x)=f(x+3)+2[/tex]

Si queremos trasladar f(x) 5 unidades a la derecha y 4 unidades hacia abajo, empezamos por reemplazar la variable independiente por u=x-5 y luego agregar una constante igual a -4:

[tex]g(x)=f(x-5)-4[/tex]

En la figura se puede ver un ejemplo de la transformación para f(x)=x^2.

Greetings from Brasil...

The equation is:

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

Answer:

A. True

Step-by-step explanation:

Since it is lesser, it will also bring in lesser profit :)

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:

The cost of the paper book= $12

Step-by-step explanation:

Hardcover books costs $21

But paper book cost only a fraction of the hardcover book.

The paper book cost 4/7 of the hardcover book.

The cost of paper book= 4/7* paper book

The cost of paper book = 4/7*$21

The cost of the paper book= 4*3

The cost of the paper book= $12

Answer:

Answer B) (2 times )

Step-by-step explanation:

Let's start with the person that shook hands more (Dora), so we already know how four of this connections took place See attached image.

step 1:

D is connected to A, B, C, and E

Step 2:

Now proceed with the connections for the second greatest (C who shook hands with 3 people). Notice that C is already connected with D, and can connect with B and with E, but NOT with A (since this person shook hands only once - with D. So C is connected to B, D, and E completing the three handshakes.

step 3: Now just corroborate that B is already connected to two people (C and D).  So just count the number of connections that E is left with: 2 handshakes.

Answer:

( E ) 0

Step-by-step explanation:

Solution:-

- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.

- We will use an intuitive way of tackling this problem.

- We have a total of 5 people who greeted each other at the party.

- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".

- We will define our event as shaking hands. It takes 2 people to shake hands.

- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.

- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:

                            5C2 = 10 possible ways.

- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.

- We are already given the data for how many handshakes were made by each person as follows:

                      Name                 Number of handshakes

                       Alan                                   1

                       Bella                                  2

                       Claire                                 3

                       Dora                                   4

               =======================================

                      Total                                  10

               =======================================

- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.

Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.

Answer:

Step-by-step explanation:

If  x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;

2/x = y/3 ... 1 and;

y/3 = x/y... 2

From equation 1, 2y = 3x ... 3

and from equation 2; y² = 3x ... 4

Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;

2y = y²

2 = y

y = 2

Substituting y = 2 into equation 3 to get the value of x;

2y = 3x

2(2) = 3x

4 = 3x

x = 4/3

The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27

Answer:

-1

Step-by-step explanation:

Thanks

The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

We have to given that,

An expression to simplify,

⇒ (2 + √5) (2 - √5)

Now, We can simplify it by using formula,

⇒ (a - b) (a + b) = a² - b²

Hence, We get;

⇒ (2 + √5) (2 - √5)

⇒ (2² - √5²)

⇒ 4 - 5

⇒ - 1

Therefore, The product of expression (2 + √5) (2 - √5) is,

⇒ (2 + √5) (2 - √5) = - 1

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Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Distribute

8x +4 = 4x - 12x +12

Combine like terms

8x + 4 = -8x +12

Add 8x to each side

8x+4+8x = -8x+12 +8x

16x+4 = 12

Subtract 4 from each side

16x +4-4 = 12-4

16x = 8

Divide by 16

16x/16 =8/16

x = 1/2

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Expand brackets.

8x + 4 = 4x - 12x + 12

Subtract 4 on both sides.

8x = 4x - 12x + 12 - 4

Subtract 4x and add 12x on both sides.

8x - 4x + 12x = 12 - 4

Combine like terms.

16x = 8

Divide both sides by 16.

x = 8/16 = 1/2

Answer:

A. x <= 2

Step-by-step explanation:

The domain of a real function should be all real numbers. In

f(x) = sqrt(2-x)

we need 2-x to be non-negative, therefore

2-x >= 0

which implies

x <= 2

Answer:

[tex]\Huge \boxed{{x\leq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]f(x)=\sqrt{2-x}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.

[tex]2-x\geq 0[/tex]

[tex]-x\geq -2[/tex]

[tex]x\leq 2[/tex]

The domain of the function is x ≤ 2.

Answer: 0.388 m

Step-by-step explanation:

Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:

h1 = (3/5)*1.8m = 1.08m

now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:

h2 = (3/5)*1.08m = 0.648m

Now, using the same method as before, the height after the third bounce will be:

h3 = (3/5)*0.648m = 0.388 m

Notice that we can write this relation as:

h(n) = 1.8m*(3/5)^n

where n is the number of bounces.

if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:

h(3) = 1.8m*(3/5)^3 = 0.388 m

Answer:

3/7

Step-by-step explanation:

The prime numbers that lie between 1 and 21 are 2,3,5,7,11,13,17, and 19. These 8 balls, plus the 10-ball comes to a total of 9 balls that could be picked out of the 21. Therefore, the probability of picking one of these balls is 9/21 or 3/7

Answer:

[tex]\frac{9}{21}[/tex]

Step-by-step explanation:

→ List the prime numbers between 1 and 21

2, 3, 5, 7, 11, 13, 17 and 19

→ Count how many ball that is

8 balls

→ Remember in the question it says "what is the probability of selecting a ball with a prime number on it or a 10"

8 balls + 1 ball (the one with the number 10)

→ 9 balls overall over a total of 21

Answer: 16500(.65)^3 =4531.31

Step-by-step explanation:

Answer:

3.87

Step-by-step explanation:

The computation is shown below:

Data provided in the question

mean distance = [tex]\bar x[/tex] = 188 meters

Standard deviaton = [tex]\sigma = 14[/tex]

Hits drivers = 15

The distance = 174 meters

H_0: μ≤174;

H_a: μ>174

Based  on the above information, the test statistic z-score is

[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]

= 3.87

Hence, the test statistic is 3.87

Note:

We take the μ≤174 instead of μ=174;

Answer:

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

Step-by-step explanation:

Given that:

60% of the batteries are from manufacturer 1

90% of these batteries last for over 40 hours

Let the number of the battery duration be n = 0.90

Therefore n' = 1 - 0.90 = 0.10

Let p = manufacturer 1  and q = manufacturer 2

q = 1 - p

q = 1 = 0.6

q = 0.4

Thus ; 40% of the batteries are from manufacturer 2

However;

Only 75% of the batteries from manufacturer 2 last for over 40 hours.

Let number of battery duration be m = 0.75

Therefore ; m' = 1 - 0.75 = 0.25

A battery in a critical tool fails at 32 hours.

Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:

[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]

[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]

[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]

[tex]=\dfrac{0.1}{0.16}[/tex]

= 0.625

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

The probability that the battery was from manufacturer 2 is 62.5%.

Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:

Therefore, the probability that the battery was from manufacturer 2 is 62.5%.

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Answer:

Easiest way to do this is to get the X's on one side of the equals sign and the Y's on the other. Then, you can choose the one with the negative sign in it.

When you do that,

First one is 2x=0+y, or y = 2x

Second one is 2y=0+x, or 2y = x (weird right)

Third one is x=0+2y, or 2y = x (again, weird right)

Final one is 2y=0-x, or 2y = -x

The final one is the answer. Cheers, but don't forget to remember this for next time bro.

The slope would be 4/3 and the y-intercept is 1

Create a table x and y and in x there is -3/4 and 0 and for the y side is 0 and 1. The line would be in the 2 quadrant with 2 points on on the y axis 1 and the other on the x axis 0.9 and that would be the graphed description of the line. Sorry if this is hard to understand i don’t have a access to draw or insert an image.

The graph of the linear equation is on the image at the end.

To do it, we need to find two points on the line, so let's evaluate it.

When x = 0

y = (4/3)*0 + 1 = 1 ----> (0, 1)

When x = 3

y = (4/3)*3 + 1 = 5 ---> (3 , 5)

Now just graph these two points and connect them with a line, that will be the graph of the linear equation.

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Answer: 1/5

Step-by-step explanation:

given data;

chances of winning = 1/3

chances of losing = 1/3

chances of tying in a given round = 1/3

solution:

probability that you would win atleast 2 in any 3 matches without a tied match is

1/3 /  ( 2 - 1/3 )

= 1/3 / 5/3

= 1/5

the probability of winning 2 of 3 games without a tie is 1/5

Answer:

Cricket only= 30

Volleyball only = 15

Hockey only = 25

Explanation:

Number of students that play cricket= n(C)

Number of students that play hockey= n(H)

Number of students that play volleyball = n(V)

From the question, we have that;

n(C) = 50, n(H) = 50, n(V) = 40

Number of students that play cricket and hockey= n(C∩H)

Number of students that play hockey and volleyball= n(H∩V)

Number of students that play cricket and volleyball = n(C∩V)

Number of students that play all three games= n(C∩H∩V)

From the question; we have,

n(C∩H) = 15

n(H∩V) = 20

n(C∩V) = 15

n(C∩H∩V) = 10

Therefore, number of students that play at least one game

n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)

= 50 + 50 + 40 – 15 – 20 – 15 + 10

Thus, total number of students n(U)= 100.

Note;n(U)= the universal set

Let a = number of people who played cricket and volleyball only.

Let b = number of people who played cricket and hockey only.

Let c = number of people who played hockey and volleyball only.

Let d = number of people who played all three games.

This implies that,

d = n (CnHnV) = 10

n(CnV) = a + d = 15

n(CnH) = b + d = 15

n(HnV) = c + d = 20

Hence,

a = 15 – 10 = 5

b = 15 – 10 = 5

c = 20 – 10 = 10

Therefore;

For number of students that play cricket only;

n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30

For number of students that play hockey only

n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25

For number of students that play volleyball only

n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15

Answer:

Cricket only= 30

Volleyball only = 15

Hockey only = 25

Explanation of the answer:

Number of students that play cricket= n(C)

Number of students that play hockey= n(H)

Number of students that play volleyball = n(V)

From the question, we have that;

n(C) = 50, n(H) = 50, n(V) = 40

Number of students that play cricket and hockey= n(C∩H)

Number of students that play hockey and volleyball= n(H∩V)

Number of students that play cricket and volleyball = n(C∩V)

Number of students that play all three games= n(C∩H∩V)

From the question; we have,

n(C∩H) = 15

n(H∩V) = 20

n(C∩V) = 15

n(C∩H∩V) = 10

Therefore, number of students that play at least one game

n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)

= 50 + 50 + 40 – 15 – 20 – 15 + 10

Thus, total number of students n(U)= 100.

Note;n(U)= the universal set

Let a = number of people who played cricket and volleyball only.

Let b = number of people who played cricket and hockey only.

Let c = number of people who played hockey and volleyball only.

Let d = number of people who played all three games.

This implies that,

d = n (CnHnV) = 10

n(CnV) = a + d = 15

n(CnH) = b + d = 15

n(HnV) = c + d = 20

Hence,

a = 15 – 10 = 5

b = 15 – 10 = 5

c = 20 – 10 = 10

Therefore;

For number of students that play cricket only;

n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30

For number of students that play hockey only

n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25

For number of students that play volleyball only

n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15

▬▬▬▬▬▬▬▬▬▬▬▬

The correct answer is 180 oranges

Explanation:

In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:

[tex]\frac{9}{40} = \frac{x}{800}[/tex]   - 1. Multiply  9 x 800 and 40 x x (cross multiplication)

[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40

[tex]\frac{7200}{40} = x[/tex]

[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which   can be expressed as 180: 800

Answer:

$153

Step-by-step explanation:

Since she claimed two exemptions, Grace Kelly income's tax will only be $153, and $1847 being the yearly take home.

Effective tax rate is set at 7.65%

Look at the attached image (credit to Desmos graphing calculator)

To graph the equation y=4x+1, we just find two points that exist, plot them, and draw a straight line that goes through them.

Let's try x=0:

[tex]y=4(0)+1=1[/tex]

One point on the line is (0,1)

Let's try x=1:

[tex]y=4(1)+1=5[/tex]

Another point is (1,5).

Now, plot these two points and draw a line through them.

The graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

To plot the graph of the equation y=4x+1 by plotting points, we need to choose some values of x and then calculate the corresponding values of y using the equation.

Let's choose some values of x and calculate the corresponding values of y:

When x = 0, y = 4(0) + 1 = 1, so one point on the graph is (0, 1).

When x = 1, y = 4(1) + 1 = 5, so another point on the graph is (1, 5).

When x = -1, y = 4(-1) + 1 = -3, so another point on the graph is (-1, -3).

We can continue this process to find more points, or we can use these three points to draw a straight line through them.

Thus, the graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.

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Answer:

Option d: n = 36, p = 0.97, x = 36.

Step-by-step explanation:

We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.

We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.

Let X = Number of cans that are properly filled

The above situation can be represented through binomial distribution;

[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]

where, n = number of trials (samples) taken = 36 cans

            x = number of success = all cans are properly filled = 36

            p = probabilitiy of success which in our question is probability that

                  can have the correct amount, i.e. p = 97%

So, X ~ Binom (n = 36, p = 0.97)

Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.

Answer:

Question (2). Option (D)

Question (3). (a). 56

                     (b). 84

Step-by-step explanation:

Question (2).

Since, a% of b = [tex]\frac{a}{100}\times b[/tex]

42% of 350 = [tex]\frac{42}{100}\times 350[/tex]

Therefore, Option (d) is the correct option.

Question (3).

Total number of people who attended the music concert = 700

a). Percentage of people who arrived late in the concert = 8%

Therefore, number of people who attended the concert = 8% of 700

= [tex]\frac{8}{100}\times 700[/tex]

= 56

b). Percentage of people who bought the shirt = 12%

Number of people who bought the shirt = 12% of 700

= [tex]\frac{12}{100}\times 700[/tex]

= 84

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

Answer:

17 lanterns.

Step-by-step explanation:

There are 13 campers with one lantern each, so that will be 13 * 1 = 13 lanterns.

The company supplies 4 extra lanterns for the whole group.

So, they will bring 13 + 4 = 17 lanterns.

Hope this helps!

Answer:

Mars

Step-by-step explanation:

America

Answer:

$41,999

Step-by-step explanation:

Annual income = 45000

monthly income = $45000/12 months = $3750

mandatory expense at 38% rule = $3750 x 0.38 = 1425

other debt = 790

tax and insurance = 340

= 1425 - 790 - 340

= 295

balance left = 295

mortgage payment = (295/8.78) x 1000

= $33,599

purchase price = monthly payment/ 1- % of down payment

= $33599/1 - 0.20

= 33599/0.80

= $41,999

Answer:A

Step-by-step explanation: