All of the given options are incorrect.
The correct solution is:
To solve the area formula for b, we need to isolate b on one side of the equation.
Starting with the formula: A = 1/2 * h * b
Multiply both sides of the equation by 2 to cancel out the denominator: 2A = h * b
Divide both sides of the equation by h to isolate b: b = 2A / h
The area of a triangle can be found using the formula: A=1/2hb
Solve the area formula for b.
b=2(A−h)
b=A/2h
1/2b=A/h
b=2A/h
13 answers
Jason is collecting coins from different countries around the world. He currently has coins from 99 countries and plans to add 4 new countries to his coin collection each week. At this rate how many weeks (w) will it take Jason to have coins from all 195 countries?
Equation:
Solution:
Final Answer:
Equation:
Solution:
Final Answer:
Equation: w * 4 + 99 = 195
Solution:
Subtract 99 from both sides of the equation:
w * 4 = 195 - 99 = 96
Divide both sides of the equation by 4:
w = 96 / 4 = 24
Final Answer: It will take Jason 24 weeks to have coins from all 195 countries.
Solution:
Subtract 99 from both sides of the equation:
w * 4 = 195 - 99 = 96
Divide both sides of the equation by 4:
w = 96 / 4 = 24
Final Answer: It will take Jason 24 weeks to have coins from all 195 countries.
7−(13−5)=(13−5)−7
true false or open
true false or open
True
4x−2=6
true
false
open
true
false
open
True
2(x+7)=2x+14
true
false
open
true
false
open
True
Two buses start at the same point and travel in opposite directions. The first bus travels 10 miles per hour faster than the second bus. In 3 hours, the buses are 282 miles apart. Use the formula below to determine the rate of the second bus.
3(r + 10) + 3r = 282
r = 30 mph
r = 42 mph
r = 45 mph
r = 21 mph
3(r + 10) + 3r = 282
r = 30 mph
r = 42 mph
r = 45 mph
r = 21 mph
To solve the problem, we'll need to rearrange the equation and solve for r.
The equation given is 3(r + 10) + 3r = 282.
First, distribute the 3 to both terms inside the parentheses: 3r + 30 + 3r = 282.
Combine like terms: 6r + 30 = 282.
Next, subtract 30 from both sides: 6r = 252.
Lastly, divide both sides by 6 to solve for r: r = 42 mph.
So, the rate of the second bus is 42 mph.
The equation given is 3(r + 10) + 3r = 282.
First, distribute the 3 to both terms inside the parentheses: 3r + 30 + 3r = 282.
Combine like terms: 6r + 30 = 282.
Next, subtract 30 from both sides: 6r = 252.
Lastly, divide both sides by 6 to solve for r: r = 42 mph.
So, the rate of the second bus is 42 mph.
Solve the equation 12=bY−3 for Y. Show each step used to solve for Y and justify by giving the property used for each step.
To solve the equation 12 = bY - 3 for Y, we'll need to isolate Y on one side of the equation. Here are the steps:
Step 1: Add 3 to both sides of the equation. This is done to isolate the term containing Y.
12 + 3 = bY - 3 + 3
15 = bY
Step 2: Divide both sides of the equation by b. This is done to solve for Y.
15/b = bY/b
15/b = Y
So, Y = 15/b is the solution to the equation.
Justification:
Step 1: Adding 3 to both sides of the equation is using the Addition Property of Equality. It states that if a = b, then a + c = b + c.
Step 2: Dividing both sides of the equation by b is using the Division Property of Equality. It states that if a = b, then a/c = b/c, as long as c is not equal to zero.
Step 1: Add 3 to both sides of the equation. This is done to isolate the term containing Y.
12 + 3 = bY - 3 + 3
15 = bY
Step 2: Divide both sides of the equation by b. This is done to solve for Y.
15/b = bY/b
15/b = Y
So, Y = 15/b is the solution to the equation.
Justification:
Step 1: Adding 3 to both sides of the equation is using the Addition Property of Equality. It states that if a = b, then a + c = b + c.
Step 2: Dividing both sides of the equation by b is using the Division Property of Equality. It states that if a = b, then a/c = b/c, as long as c is not equal to zero.
1 answer