What is the height, x, of the equilateral triangle?

Step-by-step explanation:

f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.

y = 3x - 1

3x = y + 1

x = 1/3(y + 1)

and now we rename x to y and y to x, so that we get a normal function definition :

y = 1/3(x + 1) = (1/3)x + 1/3

now we create the first derivative d/dx of this function :

y' = 1/3

since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function.

so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.

therefore also d/dx f^-1(11) = 1/3.

y = 2×sqrt(x)

sqrt(x) = y/2

x = y²/4

again we rename the variables, so that we get a normal function definition for the inverse function :

y = x²/4

the first derivative is :

y' = 2x/4 = x/2

so, d/dx f^-1(6) = 6/2 = 3

Use the inverse function theorem: if f(x) is continuously differentiable at x = a, and given f(a) = b, then f is invertible around x = a, and

[tex]\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}[/tex]

Both the given functions f(x) meet the conditions above. Note that you don't need to actually compute the inverse function itself.

If f(x) = 3x - 1, then f(x) = 11 when

3x - 1 = 11   ⇒   3x = 12   ⇒   x = 4

Now if f(4) = 11, it follows from the inverse function theorem that

[tex]\left(f^{-1}\right)'(11) = \dfrac1{f'(4)} = \boxed{\dfrac13}[/tex]

since f'(x) = 3.

If f(x) = 2√x, then f(x) = 6 when

2√x = 6   ⇒   √x = 3   ⇒   x = ±9

But note that f(x) is defined only for x ≥ 0, so we must take x = 9. Now if f(9) = 6, the inverse function theorem says

[tex]\left(f^{-1}\right)'(6) = \dfrac1{f'(9)} = \dfrac1{\frac1{\sqrt9}} = \boxed{3}[/tex]

since f'(x) = 1/√x.

Answer:

Step-by-step explanation:

Answer:

-15/4

Step-by-step explanation:

Answer: Its - 15/4 or 05/12 but the person above me is correct

Step-by-step explanation:

Answer:

first one, u can't ride a decimal of a ride

Step-by-step explanation:

y = 7.50 + 2.50x

Answer:

20 ft by 12 ft

Step-by-step explanation:

(10 in x 24) / 12 ft = (240 in / 12 ft) = 20 ft

(6 in x 24) / 12 ft = (144 in / 12 ft) = 12 ft

the answer is (-0.5) (-7.0)= 3.5

Answer:

Probably how much you want this job, if you say 0, than they are prob gonna assume you dont want to do this job, and you wont do your best. If you say 5, then you do want this job and your excited and youll give your all

Step-by-step explanation:

Questions regarding the level of excitement or happiness of one's self are called mental health or happiness test.

Hence, the type of test on this context is Happiness test.

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Answer:

A. y = –x^2 + 4

Step-by-step explanation:

Find the vertex form.

y = − ( x + 0 ) 2 + 4

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

( 0 , 4 )

Focus:  

( 0 , 15 /4 )

Axis of Symmetry:  

x = 0

Directrix:  

y

=

17

4

x

y

−

2

0

−

1

3

0

4

1

3

2

0

Answer:

Your first equation y=1/2(1+0.3)^t is going to be growth

Your second equation y=0.3(0.95)^t is going to be decay

Your third equation y=((1+0.03)^1/2)^2t is going to be growth

your fourth equation y=200(0.73)^t is going to be decay

your last equation y=4(1/4)^t is going to be decay

Step-by-step explanation:

You can find this by graphing each of you equations on desmos

Answer:

Step-by-step explanation:

See attachment

Yes because when I solve he gets 4 x-intercepts. The x-intercept is a point where the y value is zero.

The degree of a polynomial always determines the number of roots such polynomial function will have;

Given the polynomial function studied by Harvey as g(x) = (4x – 3)(x – 3)(x2 +5)

Taking the product of the leading variables

g(x) = (4x – 3)(x – 3)(x2 +5)

g(x) = 4x(x) (x^2)

g(x) = 4x^4

Since the degree of the polynomial is 4, hence the polynomial has four real roots.

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7 1/2.

2 goes into 15 7 times with one left over.

Answer:

I got this from one of my textbook for the previous years

Hope this helps:)

Answer:

None of those answers are right. It should be

[tex] - \frac{23}{24} [/tex]

Step-by-step explanation:

You have to find common denominators first. Multiply -5/6 by 4/4 to get -20/24. Multiply 1/8 by 3/3 to get 3/24.

[tex] - \frac{20}{24} = z + \frac{3}{24} [/tex]

Subtract 3/24 from both sides since it is being added.

[tex] - \frac{20}{24} = z + \frac{3}{24} \\ - \frac{3}{24} \: \: \: \: \: \: \: \: \: \: - \frac{3}{24} [/tex]

Since there are two negatives on the left, add the fractions together and keep the negative sign.

[tex] - \frac{23}{24} = z[/tex]

You cannot reduce this fraction.

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

[tex]\frac{4}{5} ^{3}[/tex]

To solve this you would cube the numerator and then the denominator:

The answer is [tex]\frac{64}{125}[/tex]

Hope this helps!

Answer:

VALUE OF C = SUCK IT BRO

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Answer: 8/175

Step-by-step explanation:

Answer: 8/175

Step-by-step explanation: to multiply fractions, multiply both numerators first then the denominators.

4x2=8

35x5=175

Answer:

a. the ratio of the sides is 6: 8, or 3:4

b. the ratio of the surfaces is [tex]\frac{6\times 6}{8\times8}[/tex] or 9:16, the square of the ratio of the sides.

c. the ratio of the volumes is [tex]\frac{6\times6\times6}{8\times8\times8}[/tex] or 27:64, the cube of the ratio of the sides.

Answer:

The given equation is in point-slope form. The slope is 5 and is seen on the right side before the parentheses. The point is (-3, -1).

Hope this helps! :)

Answer:

Yes

Step-by-step explanation:

The equation y + 1 = 5(x  + 3) is in point slope form. Point slope form is y - y1 = m(x - x1). In the given equation the point would be (-3, -1) with a slope of 5.

Answer:

20 dollars

Step-by-step explanation:

.10 x 4 (each quareter) = .40

.40 x 50 = 20.00

= $20.00

What are the options

Answer: The top right one

Step-by-step explanation: A function means that each input has exactly ONE output, so no x coordinate can have more than one y. The top right is the only one that fits that description. You can check to see if a point is exactly above a given point.

Is this what you needed ?

Based on the question, the volume of the cylinder is approximately 56,520 cubic meters.

The formula for the volume of a cylinder is seen as:

V = πr²h

where

V  = volume

r =  radius of the base

h = height of the cylinder.

Then by Substituting the given values, we will have:

V = π(10m)²(18m)

= π(100m²)(18m)

= 18000π cubic meters

To be able to  find the value to the nearest tenths place, we need to use π ≈ 3.14. hence:

V ≈ 18000 × 3.14

= 56520 cubic meters

Therefore, the volume of the cylinder is about 56,520 cubic meters to the nearest tenths place.

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Answer:

270°

Step-by-step explanation:

∠ PQR = 90° ( angle in a semicircle )

PRST is a cyclic quadrilateral

The opposite angles in a cyclic quadrilateral are supplementary, sum to 180°

Then

∠ PRS + ∠ PTS = 180°

∠ PQR + ∠ PRS + ∠ PTS = 90° + 180° = 270°