Complete the table for the function y = 0.1^x
The first step: plug values from the left column into the ‘x’ spot in the formula <u>y=0.1^x</u>.
* 0.1^-2 : We can eliminate the negative exponent value by using the rule a^-1 = 1/a. Keep this rule in mind for future problems. (0.1^-2 = 1/0.1 * 0.1 = 100).
* 0.1^-1 = 1/0.1 = 10
* 0.1^0 = 1 : (Remember this rule: a^0 = 1)
* 0.1^1 = 0.1
Our list of values: 100, 10, 1, 0.1
Now, we can plug these values into your table:
![\left[\begin{array}{ccc}x&y\\2&10\\1&10\\0&1\\1&0.1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%26y%5C%5C2%2610%5C%5C1%2610%5C%5C0%261%5C%5C1%260.1%5Cend%7Barray%7D%5Cright%5D)
The points can now be graphed. I will paste a Desmos screenshot; try to see if you can find some of the indicated (x,y) values: [screenshot is attached]
I hope this helped!
Answer:
50
Step-by-step explanation:
12x + 15 = 5x + 85 {Subtract 15 from both sides}
12x + 15 - 15 = 5x + 85 - 15
12x = 5x + 70 {Subtract 5x from both sides}
12x - 5x = 70
7x = 70 {Divide both sides by 7}
x = 70/7
x = 10
∠U = 5x = 5*10 = 50
Answer:
8
Step-by-step explanation:
x=pizza
y= breadsticks
3x+2y=30
2x+3y=25
first we myltiply the top equation with 3 and then w emultiply the lower equation with -2 so it is
9x+6y=90
-4x-6y= -50
now we can add them together and the y contracts
5x=40
now we divide it by 5
x=8
So pizza costs 8
Answer:
22
Sarah's age is best represented by M-24 or as the question used x-24 where the mother's age is best represented by M where the question used x.
Step-by-step explanation:
We are given that Sarah (S) is 24 years younger than her mother (M).
So S=M-24.
We are given that Sarah (S) and her mom's age adds up to 68.
So S+M=68.
We are going to solve this system by substitution since one of the variables is solved for. I'm going to plug first equation into second like so:
(M-24)+M=68 I replaced S with M-24.
M+M-24=68 Put like terms together.
2M-24 =68 Combined the like terms.
2M = 92 Added 24 on both sides.
M = 92/2 Divided 2 on both sides.
M = 46 Simplified the 92/2.
So her mother's age is 46.
We know that S=M-24 so S=46-24=22.
Sarah is 22 years old.
The answer is 110 adult tickets. Let x= student tickets and y= adult tickets.
We know that the total tickets sold was 440. That means the total number of student tickets (x) plus the total number of adult tickets (y) equaled 440. Putting it into an equation, you get:
x+y=440
Now we know that the amount of student tickets is equal to three times as many adult tickets, so in an equation that is seen as:
x=3y
In order to solve for one variable, plug in 3y for the x value of the first equation to get:
y+3y=440
then solve:
4y=440
y= 440/4
y=110
The total number of adult tickets sold was 110 tickets.
(This method used in math is technically called "Solving Systems of Equations", just fyi).
