Answer:
y=1/3x+4
Step-by-step explanation:
Answer:
a = 125°
b = 55°
c = 55°
d = 55°
e = 125°
f = 55°
Step-by-step explanation:
See the attached diagram.
The angles (x + 75)° and (2x + 25)° are the alternate angles and they are equal.
So, x + 75 = 2x + 25
⇒ x = 50
Hence, (x + 75)° = (50 + 75)° = 125°.
Now, from the given diagram it is clear that
a = (x + 75)° = (2x + 25)° = e = 125°
And, b = c = d = f = 55°
This is because, a and b are supplementary angles and their sum will be 180°.
So, a + b = 180°
⇒ 125° + b = 180°
⇒ b = 55°
So, b = c = d = f = 55° (Answer)
Answer:
B: 610; A: 202,000
D: 253; C: 2,007,000
Step-by-step explanation:
These are all expressions that can be calculated as is, or that can be simplified a little bit by taking advantage of the distributive property and other properties of addition and multiplication. The idea is to look for numbers that show up more than once, and rearrange the expression so they only show up once.
__
<h3>B = (597 -176) +(13 +176)</h3>
This is a straight addition problem. The two "176" values have opposite signs, so cancel when they are added. Using the associative and commutative properties of addition, we can rearrange this to ...
597 +13 +(-176 +176)
= 597 +13
This can further be rearranged to ...
= (597 +3) +(13 -3)
= 600 +10
= 610
__
<h3>A = 2020×173 -2020×73</h3>
The factor 2020 can be put outside parentheses using the distributive property:
= 2020(173 -73)
= 2020×100
= 202,000
__
<h3>D 17×15 -15 +13</h3>
The value 15 is repeated. Terms using it can be combined using the distributive property.
= 15(17 -1) +13
= 15(16) +13
= 240 +13
= 253
Another way to look at this one is to use the factoring of the difference of squares.
= (16 +1)(16 -1) +(-15 +13)
= 16² -1² +(-2)
= 256 -3
= 253
__
<h3>C 2019×890 -(12000 -2019×110)</h3>
Again, we can focus on rearranging so 2019 only needs to show up once.
= 2019(890 +110) -12000
= 2019×1000 -12×1000
= (2019 -12)×1000
= 2,007,000
A semi circle is half a full circle. Find the area of the full circle and divide it by 2.
Area of a circle = pi x r ^2
R is half the diameter
Area of full circle:
Area = 22/7 x 21^2
Area = 1386 sq. Ft
Area of stage = 1386/2 = 693 square feet
