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3 years ago

Translate triangle ABC 3 units right and 2 units down what are the coordinates for point A?

Mathematics

1 answer:

-BARSIC- [3]3 years ago

7 0

Answer:

Step-by-step explanation:

The coordinates of A(- 2, 1 )

3 units right → + 3

2 units down → - 2

Add 3 units to the x-coordinate of A and subtract 2 from the y- coordinate

A' = (- 2 + 3, 1 - 2 ) = (1, - 1 ) → C

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What is the 37th term of the arithmetic sequence with the first term -39 and the common difference of 8.

Mrrafil [7]

Answer:

$a_{37}=249$

Step-by-step explanation:

A sequence that has a common difference is an <em>arithmetic sequence</em>:

$a_n=a_1+(n-1)d$

where aₙ is the nth term, n is the index, and d is the common difference.

In your question:

n = 37
a₁ = -39
d = 8

Plug those into the formula:

$a_{37}=-39+(37-1)8$

Then solve:

$a_{37}=-39+(36)8\\a_{37}=-39+288\\a_{37}=249$

8 0

3 years ago

Calen is comparing the prices per child for hosting a birthday at Mr. Bob’s Buffet and Sally’s Pizza Safari.

Bas_tet [7]

Answer:

The cost per child is $2.50 more at Mr. Bob’s Buffet than it is at Sally’s Pizza Safari

Step-by-step explanation:

<u><em>The missing table in the attached figure</em></u>

step 1

Find the cost per child at Mr. Bob’s Buffet

we know that

The cost per child or unit rate is the same that the slope of the linear equation

From the graph take two points

(0,0) and (4,60)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{60-0}{4-0}$

$m=\$15\ per\ child$

step 2

Find the cost per child at Sally’s Pizza Safari.

From the data in the table

we have

(4,50) and (6,75)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{75-50}{6-4}$

$m=\$12.5\ per\ child$

step 3

<u><em>Verify each statement</em></u>

case A) The cost per child is $2.50 more at Mr. Bob’s Buffet than it is at Sally’s Pizza Safari

The statement is true

Because

The cost per child is $15 at Mr. Bob’s Buffet

The cost per child is $12.50 at Sally’s Pizza Safari

The difference is $2.50 per child

case B) The cost per child is $10.00 more at Mr. Bob’s Buffet than it is at Sally’s Pizza Safari

The statement is false (see the explanation)

case C) The cost per child is $15.00 more at Mr. Bob’s Buffet than it is at Sally’s Pizza Safari

The statement is false (see the explanation)

case D) The cost per child is $5.00 more at Mr. Bob’s Buffet than it is at Sally’s Pizza Safari.

The statement is false (see the explanation)

7 0

3 years ago

Ralph sold brownies for $0.27 a piece in order to earn money to buy baseball cards. If the cards cost $0.54 per pack, and if

qwelly [4]

Ha must have sold at least 2 pieces of brownies.

8 0

3 years ago

Read 2 more answers

8x -(-5) = 29 To make the equation true, what is the value of x?

olchik [2.2K]

Answer:

Step-by-step explanation:

Because you just have to replace and what would it give = 8(3) -(-5) = 29

6 0

3 years ago

Read 2 more answers

Use the substitution method to solve the following system of equations> y = - x - 4 - x + 2y = 13

Anon25 [30]

<h3>Answer:</h3>

(x, y) = (-7, 3)

<h3>Explanation:</h3>

The idea of substitution is that you write an expression for one of the variables in terms of the other variable(s), then use that expression in the place of the variable in all the other equations.

Here, your first equation gives and expression for y in terms of x. Use that expression in place of y in the second equation.

... y = -x-4 . . . . your first equation, defining y

... -x +2(-x-4) = 13 . . . . the above expression for y is put where y was in the second equation

Now, this is solved like any one-variable equation.

... -x -2x -8 = 13 . . . . eliminate parentheses

... -3x = 21 . . . . . . . . collect terms, add 8

... x = -7 . . . . . . . . . . divide by -3

... y = -(-7) -4 = 7 -4 = 3 . . . . use the expression for y to find the value of y

The solution is (x, y) = (-7, 3).

_____

<em>Comment on substitution</em>

Substitution works the same in equations as it does anywhere else in life. (Perhaps the only difference is that in equations, the substituted quantity must be <em>exactly equal</em>.) For example, in many vending machines, a dollar can be substituted for 4 quarters, and vice versa. In cooking, a small egg plus some additional liquid can be substituted for a large egg (in many cases).

The idea is that if two things are declared equivalent, either can be used in place of the other. For solving equations, this is a useful way to reduce the number of variables in an equation.

8 0

3 years ago