Answer: Angle B measures 70 degrees
Step-by-step explanation: One angle is given as 40 while the other two angles are yet unknown.
Remember that the sum of the interior angles in a triangle equals 180 degrees. In other words
Angle A + Angle B + Angle C = 180
Therefore
40 + (2x - 30) + (x + 20) = 180
40 + 2x - 30 + x + 20 = 180
By collecting like terms we have
40 - 30 + 20 + 2x + x = 180
30 + 3x = 180
Subtract 30 from both sides of the equation
3x = 150
Divide both sides of the equation by 3
x = 50
Having calculated x = 50 we can now compute the value of angle B as follows;
When x = 50,
2x - 30 becomes
2(50) - 30
= 100 - 30
= 70.
Angle B measures 70 degrees
For the first one,
294 + 30 + x- 37 = 360
add like terms
287 + x = 360
subtract 287 from both sides
x = 73
for the second one
4x +3 = 63
subtract 3 from both sides
4x = 60
divide both sides by 4
x = 15
Answer:
Step-by-step explanation:
Answer: it would take 20 weeks before the amount in both accounts would be the same.
Step-by-step explanation:
Let x represent the number of weeks that it will take either Ruben and Shawna to have the same amount of money in their account.
Let y represent the total amount that would be in Shawna's account after x weeks
Let z represent the total amount that would be in Ruben's account after x weeks
Shawna has $750 in the bank. She deposits $37.50 each week. This means that the total amount after x weeks would be
y = 37.5x + 750
Ruben has $850 in the bank. He deposits his paycheck of $102.75 every Monday,and he spends about $70.25 each week.. This means that the total amount after x weeks would be
z = 850 + 102.75x - 70.25x
z = 850 + 32.5x
To determine the number of weeks before the amount in both accounts will becomes the same, we would equate y to z. It becomes
37.5x + 750= 850 + 32.5x
37.5x - 32.5x = 850 - 750
5x = 100
x = 100/5 = 20
5. If a = b, and b = c then a = c is the transitive property.
6. The converse is switching the order of the statement.
The answer would be If A <15, then a <10: true
7. You have RS + ST = RT
Using subtraction property solve for RS by subtracting ST from both sides to get: RS = RT-ST
8. The addition property would be adding the same thing to both sides:
So. If p=q, then p+s = q+s
9. Vertical angles are the same:
6x-22 = 4x+2
Subtract 4x from both sides:
2x-22 = 2
Add 22 to both sides:
2x = 24
Divide both sides by 2:
x = 12
7x+5y=-24 (1)
4x+y=42 (2)
multiply equation (2) by 5 to get
20x+5y=210 (3)
then calculate (3)-(2) which gives you
13x=234 hence x=18
then substitute for x in either equation to get y=-30
