Which rule explains why these triangles are congruent?

Which expression is equivalent to 27 + 63 ?

3(9 + 18)

9(3 + 7)

21(7 + 3)

7(21 + 9)

Answer:

y = 2(x-3)^2-2

Step-by-step explanation:

We can find the quadratic equation by using the vertex form.  The vertex form of a quadratic equation is:

[tex]y=a(x-h)^2+k[/tex], where x and y are any point on the parabola, a is the constant (indicating whether the parabola opens up or down), and h and k are the coordinates of the vertex.

Since we already have the y-int (an x and y coordinate lying on the parabola) and the vertex, we can plug in both to find a:

[tex]16=a(0-3)^2-2\\16=a(-3)^2-2\\16=9a-2\\18=9a\\2=a[/tex]

Thus, the equation is:

[tex]y=2(x-3)^2-2[/tex]

Answer:

The distance (mi) the car travels from the car rental lot for every 1 hour elapsed.

Step-by-step explanation:

Answer:

The first one is B

The second one is The y intercept is 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

he could buy 2 pounds of chocolates and save $1.

a. Your income on the 31st day is given as follows: $10,737,418.24

b. Your total income for working 31 days is of: $21,474,836.47

The definition of a geometric sequence is given as follows:

[tex]a_n = a_1(r)^{n - 1}[/tex]

In which the terms are given as follows:

In a geometric sequence, each term is the multiplication of the previous term by the common ratio.

The sequence in this problem is given as follows:

(0.01, 0.02, 0.04, ...).

Hence the first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 0.01, q = 2[/tex]

Thus the definition is of:

[tex]a_n = 0.01(2)^{n - 1}[/tex]

The income on the 31st day is of:

[tex]a_{31} = 0.01(2)^{30} = 10,737,418.24[/tex]

The sum of the first n terms of a geometric sequence is given as follows:

[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]

Then the sum of the first 31 terms is of:

[tex]S_{31} = 0.01\frac{1 - (2)^{31}}{1 - 2} = 21,474,836.47[/tex]

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-3^2+(-4+7)(2)

answer = 15

Answer:

15

Step-by-step explanation:

a negative number squared is positive, so its 9 + (-4 + 7)*2. 7-4 is 3, which we then multiply by 2 to get 6. Now add that to 9 to get 15.

Hope this helps!

The original number in the statement is 18.5

The statements in the question are given as:

Let the number be x

So, we have the following equation

2x + 11 = 47.7

Subtract 11 from both sides

2x = 36.7

Divide by 2

x = 18.35

Hence, the number is 18.35

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Answer:

-5

Step-by-step explanation:

y (4) need to times 2.5 to be 10

so, x (-2) needs to times 2.5 to be the answer

-2 * 2.5 = -5

The lower limit of the fifth class for the track of social interactions

for a week is 50.

Allow the class intervals to be 30 - 34, 35 - 39, 40 - 44, 45 - 49, 50 - 54, etc. for some aggregated data.

In this case, the distribution is continuous, and all of the class intervals overlap.

Fifth class ; 50 - 54,

The class boundaries of the range from 50 - 54, 50 is the lower limit while 54 is the upper limit.

Thus, the  lower limit of the fifth class for the track of social interactions

for a week is 50.

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Answer:56 days

Step-by-step explanation:8 weeks*7 days= 56 days total

Answer:

It will take him 10 days to get to 135 markers.

[tex]d=12m+15[/tex]

Step-by-step explanation:

(attached)

Answer: 1680. The answer is 1680 because 56% of 3000 is 1680 people.

Answer:

The suit orginally costed $160 dollars.

Step-by-step explanation:

The solution to the inequality is m < −1 13/15 . m is less than negative 1 and 7 over 15

In this question we have to solve for the inequality that is given as m + 1/5 < -1 2/3

We would have to rewrite the equation using the math tool

[tex]m +\frac{1}{5}\leq 1\frac{2}{3}[/tex]

The mixed fraction can be properly rewritten  as improper fraction

[tex]m +\frac{1}{5}\leq \frac{5}{3}[/tex]

subtract 1/5 from 5/3

[tex]m\leq -\frac{5}{3} -\frac{1}{5}[/tex]

we have to carry out the subtraction of the fraction

[tex]m < \frac{-25-3}{15}[/tex]

[tex]m < \frac{-28}{15}[/tex]

This can be written in mixed fraction as

[tex]m < -1\frac{13}{15}[/tex]

Hence the solution of m is D. m < −1 13/15

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Complete question

m + 1/5 < -1 2/3

Responses

A. m > −1 13/15

m is greater than negative 1 and 13 over 15

B. m > −1 7/15

m is greater than negative 1 and 7 over 15

C. m < −1 7/15

m is less than negative 1 and 7 over 15

D. m < −1 13/15

m is less than negative 1 and 7 over 15

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let's check all the options, then

A)  y ≤ (1/4)x - 1

At (-5, -7), we have

-7 ≤ (1/4)(-5) - 1

-7 ≤ -2.25

This is incorrect.

B)  x + y ≤ 3

At (-5, -7), we have

-5 + (-7) ≤ 3

-12 ≤ 3

This is correct.

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

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Answer:

4 ft

Step-by-step explanation

the combined length of the other three sides can be found with 54-6 is 48 inches

48 inches can be turned into feet by dividing by 12.

48in / 12=4ft

Equation:

5 x (2/12 + 7/12 + 7/12) = f                    f = amount of fabric needed

Solve:

10/12 + 35/12 + 35/12 = f

80/12 = f

Simplify:

6 8/12

Answer:

Tamara needs 6 ft and 8 inches of fabric to make five of each item.

The mean of the given sample data is 210, and the standard deviation is 7.937.

Given size 'n' = 300

The population proportion 'p' = 0.7

Let 'x' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 300 × 0.7

                                                              μ  = 210

b)  variance of the binomial distribution

⇒ n p q

⇒ 300 × 0.7 ×0.3

⇒ σ² = 63

The standard deviation of the binomial distribution:

⇒ √n p q = √63 = 7.937

Thus, the mean of the given sample data is 210, and the standard deviation is 7.937.

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The question seems to be incomplete the correct question would be:

describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7 a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution

Answer:

15:25 or 15 brownies

Step-by-step explanation:

25 / 5 = 5 (scale factor)

3 * 5 = 15

The slope of the given line, 3x - 5y = 15, is 3/5 and the y-intercept is -3

From the question, we are to determine the slope and y-intercept of the given line.

The given line is

3x - 5y = 15

To determine the slope, we will write the equation in the slope-intercept form of a line.

The slope-intercept form of a line is given as

y = mx + b

Where m is the slope

and b is the y-intercept

Now, we will express the given equation in this form

3x - 5y = 15

-5y = 15 - 3x

Divide through by - 5

y = -3 + 3/5x

y = 3/5x - 3

By comparing to the slope-intercept form of a line,

m = 3/5

and b = -3

Hence, the slope is 3/5 and the y-intercept is -3

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The interest on the bill will be calculated as follows:

Amount of Loan = $550

Sales Tax = 6% of $550 = $33

Total Loan = $550 + $33 = $583

Interest = 13.25% APR x $583 = $77.13

Late fee = $29

Total Interest = $77.13 + $29 = $106.13

Answer:2.25 or 9/4

first we need to add 6h and 2h together, and we get 8h, and we divide 8 both side will get the fraction 18/8 and we can simplify will get 9/4 if you want more simple and will become 2.25

Answer:  $8.64 and $7.79 respectively.

Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:

3p + 2c = 41.50

2p + 5c = 43.25

The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.

By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:

First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:

15p + 10c = 207.50

6p + 15c = 129.75

Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:

15p + 10c = 207.50

6p + 15c = 129.75

9p = 207.50 - 129.75

9p = 77.75

p = 77.75 / 9

p = 8.64

Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:

3p + 2c = 41.50

3(8.64) + 2c = 41.50

25.92 + 2c = 41.50

2c = 41.50 - 25.92

2c = 15.58

c = 15.58 / 2

c = 7.79

Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.

Answer:

Step-by-step explanation:

is times 43

The number of $ 5 bills = 3

The number of $ 10 bills = 6

The number of $ 20 bills = 15

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount be = $ 375

Let the total number of bills = 24

Let the number of $ 5 bills be = x

Let the number of $ 10 bills be = y

Let the number of $ 20 bills be = z

The total number of $ 5 bills x = ( 1/2 ) x number of $ 10 bills

So , x = y/2

Now , the equation will be

The total number of bills = x + y + z

So , x + y + z = 24   be equation (1)

And ,

The total amount = 5x + 10y + 20z

So , 5x + 10y + 20z = 375

Divide by 5 on both sides , we get

x + 2y + 4z = 75   be equation (2)

On simplifying equation (1) and equation (2) , we get

x + y + z = 24

Substituting the value of y , we get

x + 2x + z = 24

3x + z = 24   be equation (3)

And ,

x + 2y + 4z = 75

x + 4x + 4z = 75

5x + 4z = 75   be equation (4)

Multiply equation (3) with 4 , we get

12x + 4z = 96   be equation (5)

Subtract equation (4) from equation (5) , we get

7x = 21

Divide by 7 on both sides , we get

x = 3

Therefore , the number of $ 5 bills is 3

Substitute the value of x , we get

y = 2x

y = 6

Therefore , the number of $ 10 bills is 6

Substitute the value for x and y in equation (1) , we get

x + y + z = 24

3 + 6 + z = 24

z + 9 = 24

Subtract 9 on both sides , we get

z = 15

Therefore , the number of $ 20 bills is 15

Hence ,

The number of $ 5 bills = 3

The number of $ 10 bills = 6

The number of $ 20 bills = 15

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The greatest common factor will be 8.

We have three numbers 24, 56 and 72.

The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24

The factors of 56 are : 1, 2, 4, 7, 8, 14, 28, 56

The factors of 72 are : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Therefore, the greatest common factor will be 8.

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