<h2>A.</h2>
So let's break down this sentence (Let n = unknown number):
- "A number is doubled and then 1 is added to it"; Remember that double means multiplied by 2. With this sentence, we can determine that "2n + 1" is a part of the equation.
- "The answer is divided by 5, and then increased by 16"; The "answer" they refer to is "2n + 1" from the prior sentence. Since this is divided by 5 and <em>then</em> added by 16, we can determine that
is a part of our equation. - "The final result is 18"; This means that the prior part of the equation is equal (=) to 18. <u>With this info, our full equation is
</u>
<h2>B.</h2>
Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:
Next, multiply both sides by 5 to cancel out the division on the left side:
Next, subtract both sides by 1 to cancel out the + 1:
Lastly, divide both sides by 2 to cancel out the multiplication:
<u>In short, the number is 9/2 or 4.5.</u>
Answer:
0.75 or 3/4 cups
Step-by-step explanation:
Make a proportion
We need 1 1/4, or 1.25 cups of sugar for 20 cookies, and we need x cups of sugar for 12 cookies
1.25/20=x/12
To solve, we need to get the variable,x, by itself. It is being divided by 12. To reverse this, multiply both sides by 12.
12(1.25/20)=(x/12)12
The 12s on the right will cancel, and we are left with
0.75=x
0.75 is equivalent to 3/4
So, 0.75 or 3/4 cups of sugar is needed to make 12 cookies
Answer:
No solution
Step-by-step explanation:
Step 1: Write out equations
y = -1/4x + 2
3y = -3/4x - 6
Step 2: Substitution
3(-1/4x + 2) = -3/4x - 6
Step 3: Distribute
-3/4x + 6 = -3/4x - 6
From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.
Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.
Answer:
The correct answer is x = -8.
Step-by-step explanation:
To solve this equation, we want to get the variable x alone on the left side of the equation. To do this, we should first add 2 to both sides of the equation.
x/8 - 2 = -3
x/8 -2 + 2 = -3 + 2
x/8 = - 1
Next, we should multiply both sides of the equation by 8 to isolate the variable x.
x = -8
Therefore, the correct answer is x = -8.
If we want to check our answer, we can plug -8 back into the original equation.
-8/8 - 2 = -3
-1 -2 = -3
-3 = -3
Since the two sides match, we know that we got the correct answer.
Hope this helps!
