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3 years ago

7

Solve the following equation for x.

1 answer:

Drupady [299]3 years ago

5 0

Answer:

$6 {x}^{2} + 54x + 120 = 0 \\ factors : 4 \: and \: 5 \\ = (6x + 24)(x + 5) \\ = > x = -4 \: and \: - 5$

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Crystal is paying the bill at a restaurant. Ignoring all taxes, the

Leona [35]

Answer: She will pay $64.90 in total.

Step-by-step explanation: The bill at the restaurant comes to $55 and Crystal wants to include an 18% tip.

So you will convert this into decimal form, which will be 0.18.

Now, you will multiply 55 by 0.18, giving you 9.9.

Add that to 55 and you will have your answer.

Have a great day!

8 0

3 years ago

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

Point S is on line segment \overline{RT}

Semenov [28]

Answer:

RT = 20

Step-by-step explanation:

Point S is on line segment

R------------S------------T

RS + ST = RT

Given

ST=3x-8

RT=4x

RS=4x-7,

Step 1

We find x

4x - 7 + 3x - 8 = 4x

4x + 3x -7 - 8 = 4x

7x - 15 = 4x

7x - 4x = 15

3x = 15

x = 15/3

x = 5

Step 2

We find RT

RT = 4x

x = 5

RT = 4 × 5

RT = 20

The numerical length of RT is 20

3 0

3 years ago

Determine the slope for each of the following situations.

s344n2d4d5 [400]

Answer:

A= a slope of 4

B= a slope of 5

C= a slope of 3

Note: All are positive slopes

8 0

3 years ago

Question 3<br>34° Celsius is equal to<br>o<br>Fahrenheit

grigory [225]

False, 34° celcius is NOT equal to 0° Fahrenheit. It is 93.2°F

3 0

3 years ago

Read 2 more answers