Which of the following is equidistant from a given directrix and focus?​

Answer:

[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=e^{3x-1}[/tex]

Replace f(x) with y:

[tex]\implies y=e^{3x-1}[/tex]

Take natural logs of both sides:

[tex]\implies \ln y = \ln e^{3x-1}[/tex]

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer: None

Step-by-step explanation:

There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

Answer:

When -3v = -18 is solved, the result is:

21v

The result of this mathematical sentence is v=6

First degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.

*Note: Equal signs, the result will be equated as positive.

-3v = -18

v = -18/-3

v = 6

Therefore, the correct value of this equation is v = 6.

The amount of Rita deposit is $2556.

The interest calculated on the principal amount or the initial investment.

It is given in the question

If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.

P = ?

S.I. =  $63.90

Interest = 6%

T = 150days

S.I. = (P *R*T)/100

63.90 = P * 6 * 150*100 /360

63.90 * 360*100 /( 150 *6) = P

P = $2556

Therefore the amount of Rita deposit is $2556.

To know more about Simple Interest

https://brainly.com/question/22621039

#SPJ1

The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

Answer:

The experimental probability is 4%

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

Learn more about samples on:

https://brainly.com/question/17831271

#SPJ1

Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{5 - x} - 3[/tex]

The radicand must be at least 0.

So, we have:

[tex]\sqrt{5 - x} \ge 0[/tex]

Square both sides

[tex]5 - x \ge 0[/tex]

Rewrite as:

[tex]5 \ge x[/tex]

Solve for x

[tex]x \le 5[/tex]

This means that the domain is [tex]x \le 5[/tex]

For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]

This means that:

[tex]f(x) \ge 0 - 3[/tex]

[tex]f(x) \ge - 3[/tex]

Hence, the range of the function is [tex]f(x) \ge - 3[/tex]

Read more about domain and range at:

https://brainly.com/question/10197594

#SPJ1

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

Read more on price elasticity here: https://brainly.com/question/24384825

#SPJ1

Answer:

a. D. f⁻¹(x) = x - 21, for all x

b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x

Step-by-step explanation:

See attached picture.

The required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:

x = y + 21

Now, let's solve for y:

y = x - 21

Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.

b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.

First, let's calculate f(f(x)):

f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42

Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.

Now, let's calculate f¯¹(f(x)):

f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x

Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.

Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Therefore, the required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Learn more about inverse functions here:

https://brainly.com/question/29141206

#SPJ2

Answer: not a triangle

Step-by-step explanation:

If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.

First, we should determine if it is a triangle.

Answer:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

Answer:

2.66666666667

Step-by-step explanation:

(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.

Answer:

Step-by-step explanation:

First, label it out:

Then, we add up 12 twice (Since the length is on 2 sides):

Now, we write down a 6 in the ?:

Width = 6.

We are not done!

Now, we have to solve for area.

This proof was correctly started by both eric and maggie.

The next step in the proof is to set the right side of the equations equal.

This would be done by the transitive property of equality.

This refers to the use of inference to make an argument to show the logical conclusion to a set of assumptions.

Based on the given diagram that shows Triangle XYZ and the mathematical proof that both Eric and Maggie are trying to prove, they both give the correct proof and the next step was to make the right side of the equations equal.

Read more about the law of sines here:

https://brainly.com/question/2807639

#SPJ1

Answer:

1: both

2: set the right side

3: transitive property

Step-by-step explanation:

got it right on plato :)

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...

The common difference of an arithmetic sequence is determined as: a term - previous term.

For the sequence, 8, 3, -2, -7,.. the common difference is:

-7 - 2 = -2 - 3 = 3 - 8 = -5.

Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...

Learn more about common difference on:

https://brainly.com/question/503167

#SPJ1

The volume of 10 ounces of lemonade in litres is 0.295735 litres.

He needs 10 ounces of lemonade.

To know the volume in litres, we have to convert from ounces to litres.

Therefore,

1 ounces = 0.0295735 litres

10 ounces = ?

cross multiply

volume in litres = 0.0295735 × 10

volume in litres = 0.295735

Therefore, the volume of the lemonade in litres is 0.295735 litres.

learn more on litres here: brainly.com/question/15322533

#SPJ1

Answer:

-10

Step-by-step explanation:

if we put f(n)=3 , Then

f(3)=f(3-2) + f(3-1)

= f(1) + f(2)

= -6+(-4). [since f(1)= -6 and f(2) = -4)

= -6-4

= -10

Using the vertically opposite angles theorem and corresponding angles theorem, we have proven that alternate exterior angles are congruent

From the question, we are to prove that alternate exterior angles are congruent.

In the given diagram, examples of alternate exterior angles are

∠1 and ∠8

∠2 and ∠7

Now, we will prove that ∠1 = ∠8

In the diagram, we can observe that

∠1 = ∠4 (Vertically opposite angles theorem)

and

∠4 = ∠8 (Corresponding angles theorem)

Then,

By the substitution property of equality

∠1 = ∠8

Hence, alternate exterior angles are congruent

Here is the complete and correct question:

Consider parallel lines cut by a transversal. Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Learn more on Angle theorems here: https://brainly.com/question/24839702

#SPJ1

Answer:

Step-by-step explanation:

Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.

Use the diagram to complete the statements.

Angles 1 and 5 are

✔ congruent

because they are

✔ corresponding

angles.

Angles 4 and 6 are

✔ supplementary

because they are

✔ same-side interior

angles.

The rise from the ground by the skateboard is 5.5 inches

The length of the skateboard is given as:

Length (l) = 18 inches

The angle of elevation (x) is

x = 17∘

Represent the height with h.

The value of h is calculated using the following tangent ratio:

tan(x) = h/l

Make h the subject

h = l * tan(x)

Substitute known values

h = 18 * tan(17)

Evaluate

h = 5.5

Hence, the rise from the ground by the skateboard is 5.5 inches

Read more about elevation at:

https://brainly.com/question/19594654

#SPJ1

Answer: 5.3

Step-by-step explanation:

S​OH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite​=18x​sin 17=sin 17=  x1818x​sin 171=1sin 17​=  x1818x​18 sin 17=18 sin 17=  xxx=5.262690...≈5.3x=5.262690...≈5.3

Answer:

24%

Step-by-step explanation:

there are 50 numbers total

number of 4's: 7
number of 7's: 5

it's asking for the odds of a 4 or a 7 meaning that they're fine with either one. that means you can ADD the number of them up!

7 + 5 = 12

to get the odds, we need to divide!

convert that into a percent!

24%

let me know if you're still confused :))

Answer:

Angle1 and Angle2 are supplementary.

Step-by-step explanation:

There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.

Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:

1&2

2&4

3&4

1&3

5&6

6&8

7&8

5&7

Since angles don't have to touch in order to be supplementary there are many more pairs.