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2 years ago

12

Name 5 decimal numbers that are between 4.78 and 4.79. Explain your answer.

2 answers:

Karolina [17]2 years ago

6 0

4.781, 4.782,4.783,4.784,4.785

I can't explain though:(

sweet-ann [11.9K]2 years ago

4 0

So many numbers between 4.78 and 4.79
4.788888
4.780001, 4.780002, 4.780003 and so on. It can go on for infinity

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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

2 years ago

You earned the following scores on four english tests: 96, 88, 74, and 76. The greatest score you can earn on a test is 100. Is

svetlana [45]

Answer:

No

Step-by-step explanation:

96+88+74+76=334/4=83.5

96+88+74+76+100=434/5=86.8

The average can't be higher than a 91%

5 0

2 years ago

These two parallelograms are similar

Nastasia [14]

it equals 12 i believe

8 0

3 years ago

Read 2 more answers

Steven paid 15% down on a car. His down payment was $2,100. How much does he still owe on the car?

My name is Ann [436]

Answer:

315

Step-by-step explanation:

because 15% of 2,100 is 315

3 0

2 years ago

Slope = -2/5, contains the point (10,3)

Daniel [21]

Answer: if this is supposed to be in slope-intercept form

the equation would be: y = -2/5x + 7

Step-by-step explanation:

so the slope is: -2/5 and the point is (10,3) considering that x = 10 and y = 3

so we would plug this information into this equation: y = mx + b (slope-intercept form)

3 = -2/5(10) + b

3 = -4 + b

b = 7

and if we plug this in:

y = -2/5x + 7

5 0

3 years ago