Answer:
b = 55°
Step-by-step explanation:
The angle at the centre is twice the angle on the circle subtended by the same arc, then
a = 0.5 × 110° = 55°
Angles on the circumference subtended by the same arc are congruent, so
b = a = 55°
Answer:
3.73 hours
Explanation:
In 1 hour, Lisa does 1/7th of the order while Bill does 1/8th of the order in an hour. To find out how long it will take them to fill the order, we have to:
Step 1:
Add the rate of both Lisa and Bill together
1/7 + 1/8
Step 2:
Since both denominators of the fractions are different, you have to find the least common multiple of 7 and 8
7·8= 56 8·7= 56
which is 56.
Step 3:
Then, you have to multiply the numerator of 1/7 with 8 and the numerator of 1/8 with 7.
1·8= 8 1·7= 7
The fractions would now have equal denominators:
Lisa: 8/56 Bill: 7/56
Step 4:
Now, you can add them together
8/56 + 7/56
which equals to 15/56. Both Lisa and Bill together completes 15/56th of the order in 1 hour.
Step 5:
15/56 is not the final answer as it is the RATE of them working together. To find how long it will take them total to complete the order, you must divide 56 with 15.
56/15
which is 3.73 hours in decimal form (rounded).
Answer:
We conclude that (4, 2) is NOT a solution to the system of equations.
Step-by-step explanation:
Given the system of equations


Important Tip:
- In order to determine whether (4, 2) is a solution to the system of equations or not, we need to solve the system of equations.
Let us solve the system of equations using the elimination method.

Arrange equation variables for elimination

Subtract the equations




Now, solve -2x = 6 for x

Divide both sides by -2

Simplify

For y - x = -2 plug in x = -3


Subtract 3 from both sides

Simplify

The solution to the system of equations is:
(x, y) = (-3, -5)
Checking the graph
From the graph, it is also clear that (4, 2) is NOT a solution to the system of equations because (-3, -5) is the only solution as we have found earlier.
Therefore, we conclude that (4, 2) is NOT a solution to the system of equations.