Solve the system x+y=54
x-5y=0
A. (-45, -9)
B.(45, 9)
C. (9, 45)
D. (45, 9)

Answers

Answer 1

Answer:
$\displaystyle \n \begin{cases} x+y = 54 \n x-5y = 0~~~~~| \cdot (-1) \end{cases} \n \n \n \begin{cases} x+y = 54 \n -x+5y = 0 \end{cases} \n \texttt{-------------- gather equations} \n .~~/~~~~~6y = 54 \n \n y = (54)/(6) = \boxed{9} \n \n x = 54 - y = 54 - 9 = \boxed{45} \n \n \texttt{Problem solution: } \boxed{x = 45 ~~ and ~~ y = 9 }$

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What is the 12th term in the sequence?an=−16+2n

Enter your answer in the box.

Answers

What is the 12th term in the sequence?

an=−16+2n
n =term
n=12

Sub n=12
a(12)=-16+2(12)
a(12)=-16+24
a(12)=8

a12=-16+(2×12)=

-16+24=8

Apples sell 5 for a $1.00 how much will 2 1/2 dozen cost

Answers

1 dozen=12

2 and 1/2 dozen means 12 times 2.5=24+6=30 apples

5sellfor1

we know that 5 times 6=30

5 for 1
times 6 both sides
30 for 6

$6 for 2 and 1/2 dozen

$6.00

An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster?

Answers

Given:
volume of the block = 576 cubic inches
Square pyramid = base area : 3 square inches ; height = 4 inches

Volume of square pyramid = a² * h/3
V = 3 square inches * 4inches/3
V = 4 cubic inches

volume of block / volume of square pyramid
576 cubic inches / 4 cubic inches = 144

She can make 144 square pyramids.

Answer:

144 square pyramids

Step-by-step explanation:

The Red Line Below is Parallel To which of the following?A. The x-axis
B. The origin
C. the y-axis
D. None of those

Answers

Answer:

C. y axis

Step-by-step explanation:

y axis is the answer

The red line is parallel to the middle line which is the x -axis
Answer =A

A couple just had twin boys, but they can’t decide between the names Mike, Mark, Peter, Paul, Sam, and Sonny. If the couple randomly chooses names for the 2 boys from the names listed, what is the probability that the first boy born will be named Sam and the second boy born will be named Mark? Assume that the boys will not have the same name.

Answers

Answer:

The probability is 1/30 or 0.0333

Step-by-step explanation:

For calculating the probability we need to make a division between the number of ways in which the first boy born is named Sam and the second boy born is named Mark and the total number of ways in which the couple can name their children.

To calculate the total number of ways in which the couple can name their children, we can use the rule of multiplication as:

6 * 5 = 30

First boy Born 2nd Boy Born

Because we have 6 options for the name of the first boy and 5 options for the name of the second boy.

Additionally, In just one option from this 30, the first boy is named Sam and the second is named Mark.

So, the probability is calculate as the division between 1 and 30 as:

$P=(1)/(30) = 0.0333$

Final answer:

The probability that the first boy born will be named Sam and the second boy born will be named Mark is 1/15.

Explanation:

To find the probability that the first boy born will be named Sam and the second boy born will be named Mark, we need to determine the total number of possible outcomes and the number of favorable outcomes.

There are a total of 6 names to choose from and the couple needs to choose 2 names without repetition. So, the total number of possible outcomes is given by the combination formula C(6,2) which evaluates to 15.

Out of these 15 possible outcomes, there is only 1 favorable outcome where the first boy is named Sam and the second boy is named Mark.

Therefore, the probability that the first boy born will be named Sam and the second boy born will be named Mark is 1/15.