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3 years ago

Find [g o f](x)=5x-5,g(x)=3x-2

Mathematics

1 answer:

wariber [46]3 years ago

7 0

Answer:

$→f(x) = 5x - 5 \\→g(x) = 3x - 2 \\ [gof](x) = g(f(x)) = 3(5x - 5) - 2 \\ [gof](x) = 15x - 15 - 2 = 15x - 17 \\ \boxed{[gof](x) = 15x - 17}✓$

<u>[gof](x) = 15x - 17</u> is the right answer.

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Can someone please explain to me how they got 44 degrees??

prisoha [69]

Answer:

Sine rule states that the ratio of a side of a triangle to the angle opposite the side is equivalent for all 3 sides and their respective opposite angles.

$\boxed{ \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c} }$

Thus, the side opposite ∠B is side AC, which is 10 units long. The side opposite ∠A is side BC, which is 8 units long. Substitute these values into the formula. (We are at line 2 of working)

Line 3: multiply both sides by 10 to find sinB

This would give us

$sinB = \frac{10sin34°}{8}$

This is can also be written as: (as seen in line 4)

$sinB = \frac{10}{8}( sin34°)$

To find the measure of angle B:

$m∠B = sin^{ - 1} ( \frac{10sin34°}{8} ) \\ m∠B = 44° \\ (nearest \: degree)$

<em>~ Explanation for line 6 and onwards~</em>

The sine of an angle is positive in quadrants I and II. Since sinB is positive (≈0.69899), we are looking at these 2 quadrants. Since the reference angle is 44° rounded off to the nearest whole degree, in quadrant I, the angle would be 44° too.

In quadrant 2, the angle would be 180° -44°= 136°.

6 0

3 years ago

What is log(z^4/5) written in expanded form?

Ostrovityanka [42]

To get answer:

$\mathrm{Apply\:log\:rule}:\quad \log _c\left(\frac{a}{b}\right)=\log _c\left(a\right)-\log _c\left(b\right)\\\log _{10}\left(\frac{z^4}{5}\right)=\log _{10}\left(z^4\right)-\log _{10}\left(5\right)\\=\log _{10}\left(z^4\right)-\log _{10}\left(5\right)\\\mathrm{Simplify}\:\log _{10}\left(z^4\right)\\\log _{10}\left(z^4\right)\\\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0\\=4\log _{10}\left(z\right)\\$

Answer: $4\log _{10}\left(z\right)-\log _{10}\left(5\right)$

Answer: 4logz−log5

4 0

4 years ago

Suppose you own a home worth $185,325 and your property tax is 1.5%. How much are you liable to pay at the end of the year?

jarptica [38.1K]

Answer:

$ 2779.88

Step-by-step explanation:

185 325 x 1.5 % =

185 325 x .015 = 2779.88

8 0

2 years ago

What's 95/300 in simplest form?

Nonamiya [84]

Answer is 19/60. The gcf of both numbers is 5. So divide both top and bottom by 5
95 divided by 5 is 19
300 divided by 5 is 60
19/60 can't be divided any further so that is the answer

7 0

3 years ago

75 percent of 88 is the same as 60 percent of what number?

tangare [24]

First we need to know 75% of 88.
To find this number we multiply 88 by 0.75.
Hence, 0.75 * 88 = 66

Therefore, 60% of a certain number equals 66.
Then 1% of that certain number equals 66 / 60
Finally, to find our number (which equals 100%) we multiply by 100.
So 66 / 60 * 100 = 110.

Hence, 75 percent of 88 is the same as 60 percent of 110.

5 0

3 years ago