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Naddik [55]
3 years ago
14

Which inequality represents all values of X for which the product below is defined?

Mathematics
1 answer:
goblinko [34]3 years ago
5 0

Answer:

x ≥6

Step-by-step explanation:

Given the product:

√(x-6)*√(x+3)

The function has to be defined if x ≥0

Hence;

√(x-6)*√(x+3)≥0

Find the product

√(x-6)(x+3)≥0

Square both sides

(x-6)(x+3)≥0

x-6≥0 and x+3≥0

x≥0+6 and x ≥0 - 3

x ≥6 and x ≥-3

Hence the required inequality is x ≥6

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Answer:

Step-by-step explanation:

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7 0
2 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
Evaluate ( f/g)(x) if f(x) = 2x and g(x) = 3x – 2 when x = 2.
Evgen [1.6K]

Answer:

1

Step-by-step explanation:

(f/g)(x)

= \frac{f(x)}{g(x)}

= \frac{2x}{3x-2} ← substitute x = 2 into the expression

= \frac{2(2)}{3(2)-2}

= \frac{4}{6-2}

= \frac{4}{4}

= 1

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mote1985 [20]

Answer:

if no discount is allowed

MP = SP = 1500

sp with vat = sp = vat amount

vat amount = vat% of sp

                    = 10% 0f 1500

                    = 150

sp with vat = sp = vat amount

                   = 1500 + 150

                  =   1650

8 0
3 years ago
if a minute hand on a clock turns 1 degree every minute, how many minutes have passed when it's 1/8 of the way around the clock?
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There's 60 min, so 1/8 of 60

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