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3 years ago

15

For a class of 25 students, 5 pizzas are needed for

1 answer:

Darina [25.2K]3 years ago

5 0

Answer:

80

Step-by-step explanation:

25:5=400:x

×=(400×5):25

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I need help with questions #7 and #8 plz

katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

$c^2 = a^2 + b^2 - 2ab \cos C$

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

$18^2 = 12^2 + 16^2 - 2(12)(16) \cos C$

$324 = 144 + 256 - 384 \cos C$

$-384 \cos C = -76$

$\cos C = 0.2$

$C = \cos^{-1} 0.2$

$C = 78.6^\circ$

Now we use the law of sines to find angle A.

Law of Sines

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

We know c and C. We can solve for a.

$\dfrac{a}{\sin A} = \dfrac{c}{\sin C}$

$\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}$

Cross multiply.

$18 \sin A = 12 \sin 78.6^\circ$

$\sin A = \dfrac{12 \sin 78.6^\circ}{18}$

$\sin A = 0.6535$

$A = \sin^{-1} 0.6535$

$A = 40.8^\circ$

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

$a^2 = b^2 + c^2 - 2bc \cos A$

$b^2 = a^2 + c^2 - 2ac \cos B$

$c^2 = a^2 + b^2 - 2ab \cos C$

Find angle A:

$a^2 = b^2 + c^2 - 2bc \cos A$

$8^2 = 18^2 + 12^2 - 2(18)(12) \cos A$

$64 = 468 - 432 \cos A$

$\cos A = 0.9352$

$A = 20.7^\circ$

Find angle B:

$b^2 = a^2 + c^2 - 2ac \cos B$

$18^2 = 8^2 + 12^2 - 2(8)(12) \cos B$

$324 = 208 - 192 \cos A$

$\cos B = -0.6042$

$B = 127.2^\circ$

Find angle C:

$c^2 = a^2 + b^2 - 2ab \cos C$

$12^2 = 8^2 + 18^2 - 2(8)(18) \cos B$

$144 = 388 - 288 \cos A$

$\cos C = 0.8472$

$C = 32.1^\circ$

8 0

3 years ago

I’ve tried to work this out but I can’t get it figured out. Can someone help me

Bas_tet [7]

G(2) = -4(2) = -8
f(g(2)) = (-8)^2 = 64

answer
64

5 0

3 years ago

Please I need help is the answer is C

NemiM [27]

It’s d because 2x4x8 = 64

8 0

3 years ago

A girl ran from her home to a store at the rate of 6 mph, and she walked back home at the rate of 4 mph. if it took 15 minutes f

viva [34]

Home is 0.6 miles away from the store

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Given:-

Total time taken by girl to complete the trip = 15 minutes = $\frac{1}{4}$ hours

Speed while riding going = 6 miles per hour

Speed while coming back = 4 miles per hour

Total time taken by girl =

Time taken while going + Time taken while coming back - (1)

Let x be distance from home to store

$\frac{x}{6}$ = Time taken while going

$\frac{x}{4}$ = Time taken while coming back

Substituting in (1) we get

$\frac{1}{4} = \frac{x}{6} + \frac{x}{4}$

$\frac{1}{4} = \frac{2x + 3x}{12}$

$\frac{1}{4} = \frac{5x}{12}$

$x= \frac{12}{20}$

x = 0.6 miles

Thus home is 0.6 miles away from the store

Learn more about time related here :

brainly.com/question/12759408

#SPJ4

6 0

2 years ago

Fill in the blank to this mathematics question

lorasvet [3.4K]

Answer:

x = 24 makes the original equation true

Step-by-step explanation:

2 < x ≤ 24

2 < x signifies x cannot be equal to 2

x≤24 signifies x can be equal to 24.

3 0

3 years ago