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Varvara68 [4.7K]
3 years ago
6

How do I confirm that f and g are inverses?

Mathematics
1 answer:
Anestetic [448]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

To show f and g are inverses we require to show that

f(g(x)) = x and g(f(x)) = x

f(g(x))

= f(6x - 4)

= \frac{6x-4+4}{6} = \frac{6x}{6} = x

-----------------------------------------------------------------------------

g(f(x))

= g(\frac{x+4}{6} )

= ( 6 × \frac{x+4}{6}) - 4

= x + 4 - 4 = x

-------------------------------------------------

Hence f and g are inverses

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3) Round answer to the nearest hundredth. *
DochEvi [55]

Answer:

80 mm

Step-by-step explanation:

Pythagorean theorm can be applied here to solve for the length of the last leg, a^{2} + b^{2} = c^{2}, where (a) and (b) are the legs of the triangle and (c) is the hypotenuse. We can rearrange the pythagorean theorm for our purposes like the following:

b = √c^2 - √a^2

  = √(82)^2 - √(18)^2

  = √6724 - √324

  = √6400

  = 80 mm

5 0
2 years ago
WILL GIVE BRAINLIEST!!! ONLY IF YOU ANSWER ALL!!! :)
Neporo4naja [7]
Wrapping paper design with the elements numbered bisected angle
4 0
3 years ago
If the relationship between the number of tickets sold and the number of hours proportional ? If so, how many tickets were sold
harkovskaia [24]

Answer:

t = 640

Step-by-step explanation:

tickets are directly proportional to number of hours.

t =kh

we find K.

240 = 3k

we divide by 3 in both sides.

k = 80

we substitute K to find how many tickets.

t =80 × 8

t = 640

it doesn't matter if you chose any two, e.g., you would get the same answer even if you used 5 and 400, or 9 and 720

6 0
2 years ago
Read 2 more answers
Find the equation of the line that satisfies the given conditions.
Lemur [1.5K]

Answer:

y = -12/11 is the equation

Step-by-step explanation:

The equation of a line in the slope-intercept form is;

y = mx + b

if slope is 0

y = b

So what we have to do here is to substitute the value of y;

b = -12/11

Thus, the equation is;

y = -12/11

4 0
3 years ago
Calculate the missing angle and give a reason for your answer
larisa86 [58]
Here’s the proof:

The triangle is an Isosceles Triangle. An Isosceles Triangle is a type of triangle that has 2 congruent sides. There is a Theorem called The Isosceles Triangle Theorem, in which states that if a triangle has 2 congruent sides, then it is an Isosceles Triangle, and the angles oppositely the congruent sides will be congruent. Therefore, we know that the triangle is Isosceles because it has 2 congruent sides, so the angles opposite those sides are congruent. We first need to find the angle measures.

1.) Finding the angle measures using the Triangle Sum Theorem. The Triangle Sum Theorem states that all 3 angles in a triangle must sum up to 180°. So, we can create an Algebraic equation to solve and figure out what the angle measures are of the two angles at the bottom of the triangle because they are opposite to the congruent sides.
Equation:
26+2x=180. We know that one angle measure is 26°, and we know the other 2 are angles are congruent, so we will call them X, and there are two of them, so we call them 2x.
26-26+2x=180-26
2x=154
2x/2=154/2
x=77.
Therefore, the angles measure 77°. To check that we can just plug them back into our equation:
26+2(77)=180.
180=180.
The angle measures are correct.

2.) Since we know the angle measures of the triangle, we can use the Alternate Exterior Angles Theorem, which states: if a transversal is intersected by two parallel lines, then the alternating exterior angles are congruent. We can see in the picture that the lane with the triangle on top and trapezoid at the bottom is a transversal (transversal=line intersected by two parallel lines). We can also see that the two lines with arrows are parallel because they are marked parallel with arrows. Therefore, we have a transversal intersected by two parallel lines, so the angles outside the parallel lines and and opposite each other are congruent.

We know that the two angles at the base of the triangle are 77°. The left base angle in the triangle is outside the parallel lines, so angle n or n° must also be 77° because they are both outside the parallel lines (exterior) and alternating from each other.

Therefore, n°=77°
8 0
2 years ago
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