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Combine like terms. What is a simpler form of the expression?
−3(−4y+3)+7y
To combine like terms and simplify the expression −3(−4y+3)+7y, we can follow these steps:
Step 1: Distribute the −3 to each term inside the parentheses:
−3 * (−4y) + (−3 * 3) + 7y
This gives us:
12y - 9 + 7y
Step 2: Combine the like terms:
(12y + 7y) - 9
This simplifies to:
19y - 9
Therefore, a simpler form of the expression −3(−4y+3)+7y is 19y - 9.
Solve the formula for the indicated variable.
A equals Start Fraction 1 over 2 End Fraction b h, for h
To solve the formula A = (1/2)bh for h, we need to isolate the variable h on one side of the equation. Follow these steps:
Step 1: Multiply both sides of the equation by 2 to eliminate the fraction:
2A = bh
Step 2: Divide both sides of the equation by b:
(2A)/b = h
Therefore, the formula A = (1/2)bh, when solved for h, becomes h = (2A)/b.
Solve the equation.
5 c minus 9 equals 8 minus 2 c
To solve the equation 5c - 9 = 8 - 2c, we can follow these steps:
Step 1: Combine like terms on each side of the equation:
5c + 2c = 8 + 9
This simplifies to:
7c = 17
Step 2: Divide both sides of the equation by 7 to solve for c:
c = 17/7
We can leave the answer as a fraction or approximate it as a decimal:
c ≈ 2.43 (rounded to two decimal places)
Therefore, the solution to the equation 5c - 9 = 8 - 2c is approximately c = 2.43.
Solve the equation.
6 left-parenthesis n minus 4 right-parenthesis equals 3 n
(1 point)
Responses
4
4
2
2
6.5
6.5
8
To solve the equation 6(n - 4) = 3n, we can follow these steps:
Step 1: Distribute 6 to each term inside the parentheses:
6n - 24 = 3n
Step 2: Subtract 3n from both sides of the equation to isolate the variable n:
6n - 3n - 24 = 0
Simplifying further:
3n - 24 = 0
Step 3: Add 24 to both sides of the equation:
3n - 24 + 24 = 0 + 24
Simplifying further:
3n = 24
Step 4: Divide both sides of the equation by 3 to solve for n:
(3n)/3 = 24/3
Simplifying further:
n = 8
Therefore, the solution to the equation 6(n - 4) = 3n is n = 8.
Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi/h. When will they be 400 mi apart?
(1 point)
Responses
4 hours
8 hours
10.5 hours
12 hours
To find out when the two buses will be 400 miles apart, we can use the formula:
Distance = Speed * Time
Let's calculate the time it takes for each bus to travel:
For the first bus with an average speed of 55 mi/h:
Distance = Speed * Time
400 = 55 * Time
Simplifying the equation:
Time = 400 / 55 ≈ 7.27 hours
For the second bus with an average speed of 45 mi/h:
Distance = Speed * Time
400 = 45 * Time
Simplifying the equation:
Time = 400 / 45 ≈ 8.89 hours
Now, since the buses are traveling in opposite directions, we need to add the times it took for each bus to find the total time it takes for them to be 400 miles apart:
Total Time = 7.27 hours + 8.89 hours ≈ 16.16 hours
Therefore, the buses will be approximately 400 miles apart after 16.16 hours.
–5y –9 = –(y – 1)
–one-half
– Image with alt text: one-half
–2
–2
–2
–2
–two-fifths
To solve the equation -5y - 9 = -(y - 1), we can follow these steps:
Step 1: Distribute the negative sign inside the parentheses on the right side of the equation:
-5y - 9 = -y + 1
Step 2: Remove the parentheses, being careful to distribute the negative sign to every term within:
-5y - 9 = -y + 1
-5y - 9 = -y + 1
Step 3: Combine like terms on each side of the equation:
-5y + y = 1 + 9
-4y = 10
Step 4: Divide both sides of the equation by -4 to solve for y:
y = 10 / -4
y = -5/2
Therefore, the solution to the equation -5y - 9 = -(y - 1) is y = -5/2 or -2.