Hello, there!
What's the answer to the equation 4(x + 7) = 9(x - 1) + 22
Answer: x = 3
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Explanation:
First, let's simplify this
4 * x = 4x
4 * 7 = 28
Now, we have 4x + 28 = 9(x - 1) + 22
Now, let's simplify the right side by using the distributive property as well.
9 * x = 9x
9 * -1 = -9
Now, we have 4x + 28 = 9x -9 + 22
Let's combine like terms on the right side
-9 + 22 = 13
Npw, we have 4x + 28 = 9x + 13
Let's isolate the x. To do this, we will first subtract 28 from each side.
4x + 28 = 9x + 13
-28 -28
4x = 9x - 15
Now, we will subtract 9x from each side.
4x = 9x - 15
-9x -9x
-5x = -15
Now, we will multiply each side by -1 to make x a positive number.
-5x = -15
*-1 *-1
5x = 15
Finally, we will simplify this completely. To do this, we will divide each side by 5.
5x = 15
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5 5
x = 3
Our final answer is x = 3
I hope I helped!
Let me know if you need anything else!
~ Zoe
Answer:
already put answer lol i just want points
Step-by-step explanation:
Answer:
The system if equation that can be used to derive this are
6x + 4y = 69 AND
12x + y = 96
The price of a drink is $7.5
Step-by-step explanation:
The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .
Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y
The first person made a purchase which led to the equation
6x + 4y = 69______ equation 1
And the second person also made a purchase that lead to the equation
12x + y = 96_____ equation 2
We make y the subject of the formula in equation 2 and apply it in 1
Y = 96 - 12x
Now apply the above in equation 1
6x + 4y = 69
6x + 4(96 - 12x)= 69
6x + 384 - 48x = 69
42x = 384 - 69
X = 315/42
X = 7.5
Substitute x= 7.5 in equation 2
12x + y = 96
12(7.5) + y = 96
90 + y = 96
Y = 6
Therefore, the price of a drink is $7.5
Answer:
Step-by-step explanation:
This is written in the standard form of a quadratic function:
where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:
where:
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:
Using your original equation, identify the a, b, and c terms:
Insert the known values into the equation:
Simplify. Two negatives make a positive:
X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:
Simplify using PEMDAS:
The value of y is -6 (3,-6). Insert these values into the vertex form:
Insert the value of a and simplify:
:Done
