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Feliz [49]
4 years ago
13

1.) Mathman wants to join a book club. Books-for-less costs $40 to join and $10 per book. Book-Buddy cost $15 per

Mathematics
1 answer:
diamong [38]4 years ago
8 0
Hey can you send me a dollar or...
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Solve using law of sines or law of cosines!
malfutka [58]

Answer:

Part 5) The length of the ski lift is 1.15\ miles

Part 6) The height of the tree is 18.12 m

Step-by-step explanation:

Part 5)

Let

A -----> Beginning of the ski lift

B -----> Top of the mountain

C -----> Base of mountain

we have

b=0.75\ miles

A=20\°

C=180\°-50\°=130\° ----> by supplementary angles

Find the measure of angle B

Remember that the sum of the interior angles must be equal to 180 degrees

B=180\°-A-C

substitute

B=180\°-20\°-130\°=30\°

Applying the law of sines

\frac{b}{sin(B)}=\frac{c}{sin(C)}

substitute

\frac{0.75}{sin(30\°)}=\frac{c}{sin(130\°)}

c=\frac{0.75}{sin(30\°)}(sin(130\°))

c=1.15\ miles

Par 6)

see the attached figure with letters to better understand the problem

<u><em>Applying the law of sines in the right triangle BDC</em></u>

In the right  triangle BDC 20 degrees is the complement of 70 degrees

\frac{BC}{sin(70\°)}=\frac{x}{sin(20\°)}

BC=(sin(70\°))\frac{x}{sin(20\°)} -----> equation A

<u><em>Applying the law of sines in the right triangle ABC</em></u>

In the right  triangle ABC 50 degrees is the complement of 40 degrees

\frac{BC}{sin(40\°)}=\frac{x+15}{sin(50\°)}

BC=(sin(40\°))\frac{x+15}{sin(50\°)} -----> equation B

Equate equation A and equation B and solve for x

(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m

<u><em>Find the value of BC</em></u>

BC=(sin(70\°))\frac{6.6}{sin(20\°)}

BC=18.12\ m

therefore

The height of the tree is 18.12 m

5 0
4 years ago
Joseph tweets 13 times aa day. Define each variable and write an algebraic expression to describe the number of posts after any
Ivahew [28]

Let's say that x is the number of days he tweets. Now, if he tweets any number of days, we can represent all of that with just x. So out expression will look like:

13x

Hope this helps!

5 0
3 years ago
PLS HELP BRO MY GRADE IS LITERALLY A D- IN MATH!
Olenka [21]
Y=mx+b
y=-2/12x-8
Simplify:
y=-1/6x-8
Slope intercept is really easy. m is the slope. All you have to do is find 2 points and use rise/run. Rise is how many up or downs (numerator). Run is left or right (denominator). We are given 2 points in the graph. So I counted, 2 down, 12 left. So 2/12. Now remember if the line is going down from left to right, it’s a negative slope. So -2/12. To find the y intercept, just find where the line meets at the y intercept, here it’s -8. So y=-2/12x-8. y=-1/6x-8
7 0
3 years ago
Triangles and rectangle
torisob [31]

Step-by-step explanation:

Area of triangle (A1)

= 1/2 * b *h

= 1/2 * 1 * 1

= 1/2 ft

Area of rectangle (A2)

= L * b

= 3 *1

= 3 ft

Total area

= A1 + A2

= 1/2 + 3

= (1 + 6 ) / 2

= 7/2 ft²

= 3.5 ft²

Hope it will help :)

7 0
3 years ago
Danielles hoop earring has a diameter of 4 centimeters. What is the radius?
Tanya [424]

Answer:

2 or 8

Step-by-step explanation:

If the radius of the circle is 4 cm, the diameter of the circle is 4 cm x 2, or 8 cm. If you have the circumference of the circle, divide it by pi or π to get the diameter.

8 0
3 years ago
Read 2 more answers
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