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3 years ago

Determine if the two functions f and g are inverses of each other

Mathematics

1 answer:

Margarita [4]3 years ago

5 0

Answer:

Yes.

Step-by-step explanation:

$f(g(x))$

$f(\frac{x-12}{9})$

( I will have to replace all $x$ 's in $9x+12$ with $(\frac{x-12}{9}$ )

$9(\frac{x-12}{9})+12$

$(x-12)+12$

$x-12+12$

$x+(-12+12)$

$x+0$

$x$

So the answer is yes.

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Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His

sveta [45]

Answer:

d Luis is not eligible for a loan, he should reduce his recurring debt

3 0

2 years ago

Read 2 more answers

Isosceles triangle has an angle that measures 80°. which other angles could be in that isosceles triangle?-

alisha [4.7K]

There are two probabilities of the solution. First if 80° acts as one of the leg angles, second if 80° acts as the vertex angle.

FIRST PROBABILITY
If 80° is one of the leg angles, then the other angle would be 80° too, because iscosceles has two congruent angles on the leg.

Find the vertex angle
the sum of interior angles in a triangle is 180°
vertex angle + angle on the leg + angle on the leg = 180°
vertex angle + 80° + 80° = 180°
vertex angle + 160° = 180°
vertex angle = 180° - 160°
vertex angle = 20°
The interior angles are 80°,80°,20°

SECOND PROBABILITY
If 80° is the vertex angle, we should find the value of the two leg angles. The two legs has congruent angles.

Find the leg angles
the sum of interior angles in a triangle is 180°
leg angle + leg angle + vertex angle = 180°
2 × leg angle + vertex angle = 180°
2 × leg angle + 80° = 180°
2 × leg angle = 180° - 80°
2 × leg angle = 100°
leg angle = 50°
The interior angles are 80°, 50°, 50°

5 0

2 years ago

If Kye can rollerblade 1.5 miles in 8 minutes how many miles does he rollerblade in 1 minute

mixer [17]

Answer:

0.1875 miles

Step-by-step explanation:

3 0

2 years ago

What is the distance between Harry’s home and his office?

Svetach [21]

Answer:

The distance between Harry’s home and his office? is 15 miles.

Step-by-step explanation:

The speed, distance time formula is:

$Speed(s)=\frac{Distance(d)}{Time(t)}$

Given:

Speed (s) = 30 miles/hour

Then the relation between distance and time is:

$s=\frac{d}{t} \\30=\frac{d}{t}\\d=30t...(i)$

If Speed was 60 miles/hour the time taken is $(t-\frac{1}{4})$ hours.

Then the relation between distance and time is:

$s=\frac{d}{t} \\60=\frac{d}{(t-\frac{1}{4}) }\\d=60t-15...(ii)$

Use the value of d = 30t in (ii)

$d=60t-15\\30t=60t-15\\30t=15\\t=\frac{1}{2} hour$

Determine the distance as follows:

$d=30t\\=30\times\frac{1}{2} \\=15\ miles$

Thus, the distance between Harry’s home and his office? is 15 miles.

5 0

3 years ago

Are the two triangles similar? How do you know?

Bess [88]

There are several conditions where triangles can be proved similar:

AA - where two of the angles are same.

SAS - where two sides of a triangle compare to the corresponding sides in the other are in same proportion, and the angle in the middle are equal.

SSS - Where all sides in a triangle and the corresponding sides are in the same proportion.

In the case above, we can only use the method of SAS, as only two sides of the triangles are given.

<HMG = <JMK (vertically opposite angles)

HM/MK = 8/12 = 2/3

GM/MJ = 6/9 = 2/3

As the two sides of a triangle comparing to the corresponding sides in the other are in same proportion, and the angle in the middle are equal, the above triangles are similar, with the prove of SAS.

Therefore, the answer is C.yes by SAS.

Hope it helps!

7 0

2 years ago