If functions f and g are inverses of each other, then what is their composition, f(g(x))? (only have 2 hours to answer!) a. f(x) b. 0 c. 1 d. x

Answer:

value of

a = 1

b = 2

c =1

and equation is

y = x² + 2x + 1

Step-by-step explanation:

Given quadratic equation  y = ax² + bx + c

It has  y-intercept of (0, 1)

thus, point (0,1) will satisfy equation  y = ax² + bx + c.

putting 1 in place of y and 0 in place of x in equation  y = ax² + bx + c we have

1 = a*0² + b*0 + c

c = 1

Thus, equation until now is y = ax² + bx + 1

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The parabola also goes through the points (2, 9) and (-5, 16)

point (2, 9) will satisfy equation  y = ax² + bx + 1.

putting 9 in place of y and 0 in place of 2 in equation  y = ax² + bx + 1 we have

9 = a*2² + b*2 + 1

9 = 4a+2b+1

=>4a+2b = 9-1 = 8

dividing both side by 2 we have

4a/2+2b/2  = 8/2

=> 2a + b = 4

b = 4-2a

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The parabola also goes through the points (2, 9) and (-5, 16)

point (-5, 16) will satisfy equation  y = ax² + bx + 1.

putting 9 in place of y and 0 in place of 2 in equation  y = ax² + bx + 1 we have

16 = a*(-5)² + b*(-5) + 1

16 = 25a-5b+1

=>25a-5b = 16-1 = 15

dividing both side by 5 we have

25a/5-5b/5 = 15/5

=> 5a - b = 3

second equation is 5a - b = 3

substituting value of b as 4-2a from first equation we have

5a - (4-2a) = 3

=> 5a - 4+2a = 3

=> 7a = 3+4 = 7

=> a = 7/7 = 1

value of b is 4-2a

substituting value of a as 1 in 4 - 2a we have

b = 4 - 2*1 = 4-2 = 2

Thus,

value of

a = 1

b = 2

c =1

and equation is

y = x² + 2x + 1

Answer:

(3 7/8, 2 3/4)

Step-by-step explanation:

To find the midpoint, the formula is (x1-x2)/2 and (y1-y2)/2. So, in this case, our x1 is 4 1/2 and our x2 is -3 1/4. Subtract x2 from x1 and you will get 7 3/4. Then, divide by 2 to get 3 7/8. This is our x-coordinate.

Our y1 is 3 3/4 and our y2 is -1 3/4. Subtract y2 from y1 to get 5 1/2. Then divide by two to get 2 3/4. This is our y-coordinate.

Now we have our x and y coordinates.

(3 7/8, 2 3/4)

Answer:

B

Step-by-step explanation:

The equation of the circle is (x + 1)² + (y + 3)² = 6². When we plug in (-6, -6) we get (-6 + 1)² + (-6 + 3)² = 6², which is a true statement so that means that the point is on the circle.

Answer: Answer choice 1, 3, 5

Step-by-step explanation:

This is more of analyzing a graph rather than a word problem.

We are told that 4 pm is at 16 hrs after midnight. You can see that the graph increases up to 4 pm. We can say 1 is correct.

After 6 pm at 18 hrs, we can see that the graph decreases. We can say 3 is correct.

Looking at the slope of the graph, 12 to 16 has a steeper slope than 8 to 12. We can say the temperature increases faster at 12 to 16 than 8 to 12.

Answer:

False

Step-by-step explanation:

Cost is not a complete ways to compare different modes.  We also need to look at the time of each mode of transportation.  Walking is very cheap  (the cost of shoes and water)  but would take a very long time.  We would also have to look at the convenience factor.  The bus may be cheap but it may not run when and where you need it.

It is, that would be true

Answer:

-385

Step-by-step explanation:

If -5 = x, then f(x) = -15-365-5 which is -385.

Answer:

11. 7x+28

Step-by-step explanation:

Answer:

Step-by-step explanation:

10) 4x+12

11) 7x+28

12)2x+16

13)9x+54

14)3x+33

15) 5x+35

16) 6x+24

17)8x+72

18) 4x+20

Answer:

5^-2 ^2

and 5^2 * 5^-6

Step-by-step explanation:

There are 4 (1/5)'s multiplied together so

(1/5) ^4 = 1^4 / 5^4 = 5^-4

and

we know that 5^-2 ^2 = 5^(2*-2) = 5^-4

and 5^2 * 5^-6 = 5^(2-6) = 5^4

Answer:

A and D

Step-by-step explanation:

[tex](5^{-2})^{2}=5^{-2*2}=5^{-4}=1/{5^{4}}\\\\5^2*5^{-6}=5^{-6+2}=5^{-4}=1/{5^{4}}[/tex]

Answer:

QS ≈ 4.71 units

Step-by-step explanation:

The arc QS is calculated as

QS = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{90}{360}[/tex] ( r is the radius )

     = 2π × 3 × [tex]\frac{1}{4}[/tex]

     = 6π × 0.25 ≈ 4.71 units ( to the nearest hundredth )

Answer:

40%

Step-by-step explanation:

Step 1: 175-125-50

Step 2: 50/125=0.4=40%

Answer:

40% profit

Step by step explanation:

There is a profit of $50.

If you were to find the percentage, you would divide 50 by 125. This would give you 0.4

Answer: a=3, b=3

Step-by-step explanation:

Let's rewrite this expression on the left side so that it matched the form on the right side.

[tex]\frac{(2xy)^4}{4xy}=\frac{16x^4y^4}{4xy}=4x^3y^3[/tex]

Now, you can see the left side matches the same form as the right side.

4x³y³=4xᵃyᵇ

Since they're the same equation, a=3 and b=3.

Answer: 5 branches and 16 birds.

Step-by-step explanation:

If the number of birds is B, and the number of branches is N.

First we have the equation:

B = 3*N + 1

(3 birds per branch + 1 that was flying around)

for the second equation we have:

B = 4*(N - 1)

(4 birds per branch, but one branch had no birds on it, so there are N -1 branches used)

now we can write:

3*N + 1 = 4*(N - 1)

3*N + 1 = 4*N - 4

4 + 1 = 4*N - 3*N

5 = N

So we had 5 branches, now we can replace it in one of the equations and find the number of birds.

B = 3*N + 1 = 3*5 + 1 = 16

Answer:

deposition

Step-by-step explanation:

Answer:

The answer is C

Answer:

Step-by-step explanation:

9x^2 + 24x + 16 = 0

(3x + 4)(3x+4)=0

3x + 4 = 0

3x = -4

x = -4/3

3x + 4 = 0

3x = -4

x = -4/3

Answer:

on    e d g e n u i t y 2020, the answer is Set B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: 1250

Step-by-step explanation:

Let x be the cost before vat

13/100x = 162.50

x = 162.50 x 100/13

x = 162.50 / 2.13

x = 1250

Answer:

(A)a translation 5 units down and 2 units to the right followed by a reflection across the y-axis

Step-by-step explanation:

If a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.

Triangle LMN has points (2, 1), (1, 1), (1, 3).

Triangle L'M'N' has points (-4,-4), (-3,-4), (-3,-2).

From the given options:

Option A: A translation 5 units down and 2 units to the right followed by a reflection across the y-axis

Given the points: (2, 1), (1, 1), (1, 3) of Triangle LMN

Therefore, the sequence of transformation in Option A produces Triangle L'M'N'.

Answer:Which sequence of transformations produces

TriangleL'M'N' from TriangleLMN?

a reflection across the y-axis followed by a translation 5 units down and 2 units right

a translation 5 units down and 2 units to the left followed by a reflection across the y-axis

no sequence of transformations

the answer is ''A'' a translation 5 units down and 2 units to the right followed by a reflection across the y-axis.

Step-by-step explanation:

i took the quiz today.

Answer:

D, a 25 percent discount means the item is at 75 % of what it used to be.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is D. D is showing the actual discount, not the total price with the discount.

Hope this helps! (Please consider giving brainliest)

Answer:

(x+6) (x+6)

Step-by-step explanation:

x^2 + 12x+36

What 2 numbers multiply to 36 and add to 12

6*6 = 36

6+6 =12

(x+6) (x+6)

Answer:

[tex](x + 6)(x + 6)[/tex]

Step-by-step explanation:

[tex]36 + 12x + {x}^{2} \\ {x}^{2} + 12x + 36 \\ {x}^{2} + 6x + 6x + 36 \\ x(x + 6) + 6(x + 6) \\ = (x + 6)(x + 6)[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Hey there! :)

Answer:

m∠8 = 30°.

Step-by-step explanation:

Since AB || CD, m∠4 = m∠8 because they are corresponding angles. Therefore:

If m∠4 = 30°, m∠8 = 30°.

Answer:

30 = <8

Step-by-step explanation:

<4 and <8 are corresponding angles and corresponding angles are equal when the lines are parallel

<4 = <8

30 = <8

Answer:

[tex]263.755[/tex]

Step-by-step explanation:

[tex]48.7 \times 61.2 \div 11.3 \\ 2,980.44 \div 11.3 \\ = 263.755752 [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is 263.755

Look at the attached picture

Hope it will help you

Good luck on your assignment..

Answer:

5

Step-by-step explanation:

3 - (-2)

Subtracting a negative is like adding

3+2

5

Answer:

The series converges to -1.5.

Step-by-step explanation:

This is a geometric series, so it converges if the number in parenthesis is between -1 and 1.

-1 < -3/5 < 1, so the series converges by the geometric series test.

Now we can plug this into the calculator (on TI-84, it's Math->0 summation) to find that the sum is -1.5. You can use 100 or another big number as a placeholder for infinity.

Answer:

108!

Step-by-step explanation:

The area of a trapezoid is

1/2 x h x (b1 + b2)

plug it in!

24 x 1/2 x 9

12 x 9

108

Answer: a) length of the wires are 8.1m and 13.4m

b) length of pole is 8.8m

Step-by-step explanation:

The diagram representing the scenario is shown in the attached photo. Triangle ABC is formed. Since the sum of the angles in a triangle is 180°, it means that angle B would be

180 - (41 + 55) = 84°

a) AC and BC are the lengths of each wire.

CD is the height of the pole

To determine AC, we would apply sine rule which is expressed as

a/SinA = b/SinB = c/SinC

Therefore,

11/Sin55 = BC/Sin 41 = AC/Sin84

1) 11//Sin 55 = BC/Sin 41

Cross multiplying, it becomes

11Sin41 = BCSin55

11 × 0.6561 = BC × 0.8192

BC = 7.2171/0.8192 = 8.8m

2) 11/Sin55 = BC/Sin 41 = AC/Sin84

1) 11//Sin 55 = AC/Sin 84

Cross multiplying, it becomes

11Sin84 = ACSin55

11 × 0.9945 = AC × 0.8192

AC = 10.9395/0.8192

AC = 13.4m

b) triangles ACD and BCD are right angle triangles. To determine CD, we would apply the sine trigonometric ratio.

Sin # = opposite side/adjacent side

Considering triangle ACD,

Sin 41 = CD/13.4

CD = 13.4Sin41 = 13.35 × 0.6561

CD = 8.8m

Answer:

point and line

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

Im not going to go into detail about how to compute sin30 and cos 30, but know that sine and cosine are just the ratios between the sides of a 30-60-90 triangle with a hypothenuse of 1.

With that being said:

sin^2 30 - cos^2 30

=  (1/2)^2 - ((sqrt3)/2)^2

= 1/4 - 3/4

= -1/2

Answer:

-1/2

Step-by-step explanation:

Answer:

1,200

Steps down below

Step-by-step explanation:

Steps

1:  48=4% loaded on truck and they have 96% left to load

2: so set up a proportion and it should look like this

3: 48 over x = 4 over 100

4: 48/x=4/100

6: do cross multiplication 100×48= 4,800÷ 4 = 1,200 total on truck

Answer: 1,200 total on truck

Hope this helps.