Part 1) we know that
m∠5=44° m∠11=86°
m∠2=m∠5------> by vertical angles
m∠2=44°
m∠13=m∠11------> by vertical angles
m∠13=86°
m∠12+m∠13=180°-----> supplementary angles
m∠12=180-86-----> m∠12=94°
m∠14=m∠12----> by vertical angles
m∠14=94°
m∠1=m∠11----> by corresponding angles
m∠1=86°
m∠4=m∠1----> by vertical angles
m∠4=86°
m∠2+m∠1+m∠6=180
m∠6=180-(86+44)----> 50°
m∠6=50°
m∠3=m∠6----> by vertical angles
m∠3=50°
m∠8=m∠3----> by corresponding angles
m∠8=50°
m∠8+m∠7=180°-----> supplementary angles
m∠7=180-50----> 130°
m∠7=130°
m∠10=m∠6----> by corresponding angles
m∠10=50°
m∠10+m∠9=180°-----> supplementary angles
m∠9=180-50-----> 130°
m∠9=130°
the answers Part 1) are
m∠1=86°
m∠2=44°
m∠3=50°
m∠4=86°
m∠5=44°
m∠6=50°
m∠7=130°
m∠8=50°
m∠9=130°
m∠10=50°
m∠11=86°
m∠12=94°
m∠13=86°
m∠14=94°
Part 2)
a) what is m∠TPR?
in the right triangle PTR
m∠PTR+m∠TPR+m∠TRP=180° ( the sum of internal angles of triangle is equal to 180 degrees)
m∠PTR=30°
m∠TRP=90°
so
m∠TPR=180-(90+30)----> 60°
the answer Part 2a) is
m∠TPR=60°
b) what is the length in inches of segment PR?
in the right triangle PTR
sin 30=PR/TP-----> PR=TP*sin 30-----> PR=14*(1/2)----> 7 in
the answer Part 2b) is
PR=7 in
c) what is the length in inches of segment TR?
in the right triangle PTR
cos 30=TR/PT-----> TR=PT*cos 30-----> TR=14*(√3/2)---> TR=7√3 in
the answer Part 2c) is
TR=7√3 in
d) what is the length in inches of segment PQ?
in the right triangle PQR
PR=7 in
RQ=PR-----> by angle 45°
so
RQ=7 in
applying the Pythagoras Theorem
PQ²=RQ²+PR²-----> 7²+7²-----> PQ²=98-----> PQ=√98 in---> PQ=7√2 in
the answer Part 2d) is
PQ=7√2 in
Part 3) Patrice buys a block of wax in the shape of a right rectangular prism. The dimensions of the block are 20 cm by 9 cm by 8 cm.
<span><span>(a) </span>What is the volume of the block?
volume of the prism=20*9*8-----> 1440 cm³
the answer Part 3 a) is
the volume of the block is 1440 cm³
<span>
Patrice melts the wax and creates a candle in the shape of a circular cylinder that has a diameter of 10 cm and a height of 15 cm.<span>(b) </span>To the nearest centimeter, what is the volume of the candle?
</span></span>volume of a cylinder=pi*r²*h
diameter=10 cm
radius r=10/2----> 5 cm
h=15 cm
volume of a cylinder=pi*5²*15----> 1177.5 cm³-----> 1178 cm³
the answer Part 3b) is
the volume of the candle is 1178 cm³
<span>Patrice decides to use the remaining wax to create a candle in the shape of a cube.<span>(c) </span>To the nearest centimeter, what is the length of the side of the cube?
</span>
the remaining wax=volume of the prism-volume of a cylinder
=1440-1178-----> 262 cm³
volume of a cube=b³
where b is the length side of the cube
262=b³-------b=∛262-----> b=6.40 cm-----> b=6 cm
the answer Part 3c) is
the length of the side of the cube is 6 cm
Answer:
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Step-by-step explanation:
, , , , ,
Order everything, negative to the left side and positive to the right side
<u><em>Negative numbers:</em></u>
, ,
<u><em>Positive numbers:</em></u>
, ,
<em><u>Now order it on a number line:</u></em>
, , , , ,
Answer:
1. The amount of time you keep your porch light on.
2. The temperature you keep your air conditioner at.
Step-by-step explanation:
<u>Porch Light Time Example: </u>
The light does not turn on or off based on the bill, thus its independent, but the bill is effected by the amount of time the light is on thus dependent.
You keep your porch light on for 24 hours a day for 1 month, that month your electricity bill is $50.
Next month you keep your porch light on for 12 hours a day and your electricity bill is $40.
<u>Air Conditioner Temp Example: </u>
The thermostat temperature is not effected by the bill, thus its independent, but the bill is effected by the thermostat, thus dependent.
You set your thermostat to 70 degrees for 1 month, that month your electricity bill is $50.
Next month you set your thermostat to 75 degrees for 1 month, that month your electricity bill is $40.
