A.) Mark is correct as every increase in x of 2 equals a y increase of 4
Answer:
Length of arc AB = 1.57 yds
Step-by-step explanation:
Given:
Central angle (θ) = 30°
Radius (r) = 3 yds
Required:
Length of arc AB approximated to the nearest hundredths
Solution:
Length of arc = θ/360 * 2πr
Length of arc AB = 30/360*2*π*3
Length of arc AB = 1.57079633
Length of arc AB = 1.57 yds (nearest hundredths)
Answer:
x = 6
Step-by-step explanation:
These two angles make a complementary angle meaning the sum of the angles will be 90°. We can use this information to make an equation to solve for x.
10x + 30 = 90 (Given)
10x = 60 (Subtract 30 on both sides)
x = 6 (Divide 10 on both sides)
Answer:
6 bags
Step-by-step explanation:
The first gift is a box of 18 chocolate candy bars, and the second gift is a pack of 12 cookies. Destiny wants to use all of the chocolate candy bars and cookies to make identical snack bags for her cousins. What is the greatest number of snack bags that Destiny can make? Answer: 6 bags
You can simply collect terms, subtract the constant and divide by the x-coefficient. It is generally considered easier to do those steps if you eliminate fractions first (multiply by 12).
Multiply by 12
... 4(x -1) +3(x +5) = 6
... 4x -4 +3x +15 = 6 . . . . . eliminate parentheses
... 7x +11 = 6 . . . . . . . . . . . .collect terms
... 7x = -5 . . . . . . . . . . . . . . subtract the constant 11
... x = -5/7 . . . . . . . . . . . . . divide by the x-coefficient
_ _ _ _ _ _ _
Here it is the other way.
... x(1/3 +1/4) +(-1/3 +5/4) = 1/2
... (7/12)x + 11/12 = 1/2 . . add the fractions to finish collecting terms
... x + 11/7 = 6/7 . . . . . . . multiply by 12/7
... x = -5/7 . . . . . . . . . . . subtract 11/7
At the third step here, you could subtract 11/12 before doing the multiply. You get the same answer, but you have to do the extra conversion of 1/2=6/12.
