Mathematics, 13.10.2019 23:30 davistakeisha95

Abag of marbles contains only purple and yellow marbles. the bag has three times as many yellow marbles as purple. the bag contains 164 total marbles. write an equation or system of equations to find out how many of each color of marble is in the bag. define your variable(s) and expressions. show how you checked your answer.

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Write the expressions: $y+p=164
 \\ y=3p$
The variable y represents the number of yellow marbles. The variable p represents the number of purple marbles. The first expression is saying that when we add both the yellow and purple marbles together, there are 164 total. The second expression is saying for every one purple marble, there are three yellow, or that there are three times as many yellow marbles.

Lets find how many purple marbles there are:
First, substitute 3p for y in our first equation. (3p)+p=164

Combine like terms. 4p=164

Isolate the variable by dividing both sides by 4. p=41

There are 41 purple marbles.

Now, let find how many yellow marbles.
Because we already know there are 41 purple marbles, lets replace p with 41. y+(41)=164

Isolate the variable by subtracting 41 from both sides. y=123

There are 123 yellow marbles.

Now we should check.
Substitute the variables in the first expression. Is it true?
$123+41=164
 \\ 164=164$
Yes, because 41 plus 123 equals 164, it is true.

Substitute the variables in the second expression. Is it true also?
$123=3(41)
 \\ 123=123$
Yes, because 41 times 3 equals 123, it is true.

Answer from: Quest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

Answer from: Quest

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,

b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,

and solve for the variable

* lets solve the problem

∵ $7^{x}=77$

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴ $ln(7^{x})=ln(77)$

- use the rule $ln(a^{n})= nln(a)$

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴ $x=\frac{ln(77)}{ln(7)}=2.23$

* the solution of the equation is 2.23 to the nearest 2 decimal places

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