Find g(f(x)).

f(x) = x + 1
g(x) = [tex]\sqrt{x} -3[/tex]

Please show work so I can understand it because my teacher has been out all week and I need to know how to do this for a test tomorrow.

Using quadratic function concepts, it is found that:

1) The equation is [tex]y = -0.08x^2 + 4x[/tex]

2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

A quadratic equation has the following format:

[tex]y = ax^2 + bx + c[/tex]

In this problem:

Item 1:

The vertex is: [tex]V(x_v,y_v)[/tex], in which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, it is (25,50). Thus:

[tex]-\frac{b}{2a} = 25[/tex]

[tex]-b = 50a[/tex]

[tex]b = -50a[/tex]

[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]

[tex]-b^2 = 200a[/tex]

[tex]-(50a)^2 = 200a[/tex]

[tex]-2500a^2 - 200a = 0[/tex]

[tex]200a(-12.5a - 1) = 0[/tex]

Then, as [tex]a \neq 0[/tex]

[tex]a = -\frac{1}{12.5} = -0.08[/tex]

[tex]b = -50a = -50(-0.08) = 4[/tex]

Thus, the equation, in standard form, is:

[tex]y = -0.08x^2 + 4x[/tex]

Item 2:

The distances are the values of x for which:

[tex]y = 10[/tex]

Then

[tex]-0.08x^2 + 4x = 10[/tex]

[tex]-0.08x^2 + 4x - 10 = 0[/tex]

Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:

[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]

[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]

[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]  

The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

A similar problem is given at https://brainly.com/question/24713268

Answer:

Step-by-step explanation:

Cost of 1 kg of Potatoes = $ 2

Cost of 1 kg of Carrots = $ 2.40

Let the cost of 1 kg of Potatoes = x

Let the cost of 1 kg of Carrots = y

ATQ , 8x + 5y = 28 - 1)

2x + 3y = 11.20 - 2)

Multiplying 2) by 4

8x + 12y = 44.80 - 3)

Applying Elimination method in 1) and 3)

8x + 5y = 28.00

8x + 12y = 44.80

0 + -7y = - 16.80

y = 16.8/7

y = 2.4

Putting the value of "y" in 1)

8x + 5(2.4) = 28

8x + 12 = 28

8x = 16

x = 16/8

x = 2

Answer:

option 4 is the right answer

Answer:

The last option is right

Answer:

-13x/2+1.7

Step-by-step explanation:

The difference of the given expression is - 6.5 x + 1.7.

Given that, (−2.6x+4.2)−(3.9x+2.5).

To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

Now, (−2.6x+4.2)−(3.9x+2.5)

= (-2.6x-3.9x)+4.2-2.5

= - 6.5 x + 1.7

Therefore, the difference of the given expression is - 6.5 x + 1.7.

To learn more about the subtraction of expression visit:

brainly.com/question/12959016.

#SPJ2

answer:

-8.3733995^12

Answer:

y = -2/3x - 2

Step-by-step explanation:

Picking two points on the line: (0,-2) & (-3,0)

Using the slope formula:

[tex]\frac{x2-x1}{y2-y1}[/tex]

= (0-(-2))/(-3-0)

= 2/-3

= -2/3

y = -2/3x + c

Subsituting (0,-2) into 'y = -2/3x+c':

-2 = 0 + c

c= -2

Hence,

y = -2/3x -2

Hope this helps, and be sure to have a wonderful time ahead at Brainly! :D

Feel free to mark this as brainliest :D

Answer:

24 Combinations

Step-by-step explanation:

There are 8 people and there is a possibility that each can be either 1st, 2nd, 3rd. You would multiply 8 x 3 to get 24 or add 3 eight times

Answer:

3rd option

Step-by-step explanation:

3(x + 8) - 9x = 6(4 - x) ← distribute parenthesis on both sides

3x + 24 - 9x = 24 - 6x , collect like terms on left side )

24 - 6x = 24 - 6x

Since both sides are the same then any value of x will make the equation true.

That is all real numbers are solutions

Answer: C g(x) is a function because f(x) is one-to-one.

Step-by-step explanation:

Answer:

f(-1) = 1

Step-by-step explanation:

f(-1) just means you plug -1 into the equation:

-3x + 2x

-3(-1) + 2(-1)

3 - 2

1

Hopefully this helps!

Brainliest please?

Answer:Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.

Step-by-step explanation:

y coordinate

m = slope

x = x coordinate

b = y intercept

Answer: acute angle

Step-by-step explanation:

___________

[tex] \: [/tex]

[tex] {4}^{4} ( {4}^{ - 7} )(4) = ...[/tex]

[tex] = {4}^{4 + ( - 7) + 1} [/tex]

[tex] = {4}^{ - 3 + 1} [/tex]

[tex] = \bold{{4}^{ - 2} } \to({ \sf{d.}})[/tex]

Answer:

Step-by-step explanation:

1) Initial water level = 30 feet

2) Rate of change = (30 - 25) / (0 - 1) = 5/(-1) = -5

5ft  per hour

3) y-intercept = 30

Answer:

26 minutes/ t=26

Step-by-step explanation:

F) c=14t

S) 364=14t

E) t=26

No solution. The first two equations would need to equal each other, but they don't, so it is mathematically impossible.

Answer: k=0

Step-by-step explanation:

[tex]kx+z=3\\\\-z -z[/tex]

[tex]kx=3-z[/tex]

[tex]\frac{kx}{k} =\frac{3}{k}-\frac{z}{k}[/tex]

[tex]x=\frac{3-z}{k}[/tex]

Feel free to let me know if it's wrong

Answer:

45

Step-by-step explanation:

That means in every group of 15, there are 5 children

135 / 15 = 9. So Nine groups of 15. 9 x 5 = 45

Answer:19

Step-by-step explanation:

Answer:

there is no question if you provide one in comments I will edit my answer to answer the question

Step-by-step explanation:

Answer:

590 decimal form is 5.9

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is only a division

5/90 =

5 : 90 =

0.05555555555

Answer:

x = 5

Step-by-step explanation:

3x + 1 should equal 16

Answer:

X=5

Step-by-step explanation:

3x+1=16

move the 1 over to the 16 so it is 16 - 1 = 15

3x=15

Move the 3 over to where the 15 is in order to get x by itself

3/3 = x

3/15 = 5

so X should = 5

Answer:

Step-by-step explanation:

Volume = 21^3 cm^3.

Answer:

1/3

Step-by-step explanation:

gradient or slope = m

m = change in y ÷ change in x

= (-4 - -2) ÷ (-3 - 3)

= (-4 + 2) ÷ (-3 - 3)

= -2 ÷ -6

= 1/3

Answer:

[tex]y=\displaystyle-\frac{4}{3}x+22[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Determine the slope (m):

[tex]y=\displaystyle-\frac{4}{3}x -1[/tex]

The slope of the given line is [tex]\displaystyle-\frac{4}{3}[/tex], since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be [tex]\displaystyle-\frac{4}{3}[/tex]. Plug this into y=mx+b:

[tex]y=\displaystyle-\frac{4}{3}x+b[/tex]

Determine the y-intercept (b):

[tex]y=\displaystyle-\frac{4}{3}x+b[/tex]

To find the y-intercept, plug in the given point (6,14) and solve for b:

[tex]14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22[/tex]

Therefore, the y-intercept of the line is 22. Plug this back into [tex]y=\displaystyle-\frac{4}{3}x+b[/tex]:

[tex]y=\displaystyle-\frac{4}{3}x+22[/tex]

I hope this helps!

the correct answer is b :)

Answer:

56 degrees

Step-by-step explanation:

Answer:

X 56 Y 56

Step-by-step explanation:

because 180-124=56

Answer:

I believe it's also 74°

Step-by-step explanation:

Because AGF and CGE are congruent,so the angle measurement should stay the same

Answer:

CGE is 74°

Step-by-step explanation:

AGF = FGD

FGD = CGE

AGF = EGB

AGF = 74°

FGD = 74°

CGE = 74°

EGB = 74°

360° is a circle and CGA = BGD

74 + 74 + 74 + 74 + x + x = 360

296 + 2x = 360

2x = 360 - 296

2x = 64

2x/2 = 64/2

x = 32

CGA and BGD are 32

CGE is 74°

Hope This Helps! •v•

Answer:

Since the two base angles are congruent (same measure), they are each 70°. If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°.

Answer:

degrees

Step-by-step explanation: