#5
57.8 can be rounded to 60 because 57.8 is closer to 60 than 50 and 81 is relatively close to 80. if we had to estimate the quotient, we would have
60 ÷ 80 = 0.75
#8
2.8 can be rounded to 3 because 2.8 is closer to 3 than it is to 2 and 6 can be left alone because it will make our division easier.
3 ÷ 6 = 0.5
#11
737.5 can be rounded to 700 and 9 can be rounded to 10.
700 ÷ 10 = 100
Factor
7
x
7
x
out of
14
x
2
14
x
2
.
7
x
(
2
x
)
−
21
x
7
x
2
x
-
21
x
Factor
7
x
7
x
out of
−
21
x
-
21
x
.
7
x
(
2
x
)
+
7
x
(
−
3
)
7
x
2
x
+
7
x
-
3
Factor
7
x
7
x
out of
7
x
(
2
x
)
+
7
x
(
−
3
)
7
x
2
x
+
7
x
-
3
.
7
x
(
2
x
−
3
)
Answer:
The following measurements are:
(Option #4)
(Option #7)
(Option #5)
(Option #2)
Step-by-step explanation:
To begin, we can find the measure of
by applying the inscribed angle theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
Since the intercepted arc (RS) is 46 degrees, we have:

Next, we can find the measure of arc QT using the same theorem. So,

Notice that the chord RT is actually a diameter. From the theorem about the inscribed angle including a diameter, we know that the intercepted arc will have a measure of
. Since the arc ST is part of the arc RST, and we know RS is
, we can set up and solve this equation:

We can use the same idea to find RQ. We know that RQT is
and QT is
, so:

Answer:
25
Step-by-step explanation:
x = (20/28) * 35
x = 25