Solve for x. Round to the nearest tenth, if necessary.
56
Z
43°
x
M

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:

yo can maybe try converting those to every possible answer and you can find the answer that way.

Step-by-step explanation:

Applying the tangent ratio, the angle of elevation of the sun, to the nearest degree, is: 36°.

In a right triangle, tan ∅ = opposite length / adjacent length is the tangent ratio.

Given the following:

Apply the tangent ratio:

tan ∅ = 125/172

tan ∅ = 125/172

∅ = tan^(-1)(125/172)

∅ ≈ 36°

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Answer:

Step-by-step explanation:

-4x + 2 = x - 3

-5x + 2 = -3

-5x = -5

x = 1

y = 1 - 3

y = -2

(1, -2)

Answer:

I believe it's true. Good Luck! :)

Step-by-step explanation:

Answer:

the fourth option is correct

Step-by-step explanation:

the first equation represents that the cost of 6 bananas is the same as the cost of nine apples. therefore, y is the cost of a single banana and x is the cost of a single apple. the second equation represents the situation of you buying 4 bananas and 2 apples for $8. If x and y represent the cost of each fruit, then the point (x,y) = (1,1.5) means that x, the cost of an apple, is $1.00 and that y, the cost of a banana, is $1.50.

Answer:

Step-by-step explanation:

The attached image represents the completed Venn diagrams

Diagram 1

We have:

Multiples of 3 and Multiples of 10

When the sets are populated, we have:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 10 = 10, 20, 30

Both = 30

Next, we complete the circles using the above data values

See attachment 1

Diagram 2

We have:

Multiples of 2, Multiples of 3 and Multiples of 5

When the sets are populated, we have:

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 5 = 5, 10, 15, 20, 25, 30

Multiples of 2 and 3 = 6, 12, 18, 24 and 30

Multiples of 2 and 5 = 10, 20 and 30

Multiples of 3 and 5 = 15 and 30

All = 30

Next, we complete the circles using the above data values

See attachment 2

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By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the Theorem of Intersecting Secants.

The Theorem of Intersecting Secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the Theorem of Intersecting Secant, angle P will be given by this formula:

m<P = ½ × (m<RS - m<WT)

Substituting the given parameters into the formula, we have;

35 = ½ × (121 - m<WT)

70 = 121 - m<WT

m<WT = 121 - 70

m<WT = 51°.

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Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

Answer:

AC ≈ 17.3 , BC ≈ 5.3

Step-by-step explanation:

using the tangent ratio in right triangle ACD

tan51° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AD}[/tex] = [tex]\frac{AC}{14}[/tex] ( multiply both sides by 14 )

14 × tan51° = AC , then

AC ≈ 17.3 ( to the nearest tenth )

using the cosine ratio in right triangle ABC

cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{17.3}[/tex] ( multiply both sides by 17.3 )

17.3 × cos72° = BC , then

BC ≈ 5.3 ( to the nearest tenth )

Using the together rate, it is found that it will take them 18 minutes to prepare the cards working together.

The together rate is the sum of each separate rate.

In this problem:

Hence, the time it will take for them to make the cards is given by:

[tex]\frac{1}{x} = \frac{1}{45} + \frac{1}{30}[/tex]

[tex]\frac{1}{x} = \frac{5}{90}[/tex]

5x = 90

x = 18 minutes.

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Answer:

2×2 mark me brainlist

The value of her investment after 8 years is  $8,293.81.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving.

Given:

P= $5600

r= 5.4%

t= 8 years

Then solve the equation for A

A = P(1 + r/n)^nt

A = 5,400.00[tex](1 + 0.054/4)^{4/8}[/tex]

A = 5,400.00[tex](1 + 0.0135)^{32}[/tex]

A = $8,293.81

Hence, the value will be $8,293.81.

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Answer:

x = - 6 , x = 1

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

x² + 5x - 6 = 0

consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)

the factors are + 6 and - 1 , since

6 × - 1 = - 6 and 6 - 1 = + 5 , then

(x + 6)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 1 = 0 ⇒ x = 1

Based on the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.

The ratio of net income to investment is known as return on investment (ROI). A high return on investment (ROI) indicates that the investment's benefits outweigh its cost.

ROI is a performance indicator that is used to assess an investment's effectiveness or to compare the efficiencies of several distinct investments.

First, find the amount earned per year:

= 850 x 12

= $10,200

The yearly expenses would be:

= (390 x 12) + (70 x 12) + (380 x 2) + 500 + (125 x 12)

= 4,680 + 840+ 760+ 500 + 1500

= $8280

The annual ROI is:

ROI= (10,200 - 8280) / 10,200 x 100%

ROI = 18.82%

Therefore the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.

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Answer:

1 + 3 + 5 + A+9 divide by 5​

Step-by-step explanation:

Answer:

[tex]b = \frac{1}{9}[/tex]

Step-by-step explanation:

-9b + b = 2b - (b + 1)

Let's simplify by taking out the parenthesis.

-9b + b = 2b - b - 1

Now, we add like terms.

-8b = b - 1

Now, let's subtract b from both sides of the equal sign in order to isolate b.

-8b - b = b - 1 - b

Simplify!  

-9b = -1

Divide both sides by -9.

-9b ÷ b = -1 ÷ -9

Simplify.

[tex]b = \frac{1}{9}[/tex]

Answer:

[tex]b = \frac{1}{9} [/tex]

Step-by-step explanation:

[tex] - 9b + b = 2b - (b + 1) [/tex]

Solve the brackets.

[tex] - 9b + b = 2b - b - 1[/tex]

Combine like terms.

[tex] - 8b = b - 1[/tex]

Take b to the left side.

[tex] - 8b - b = - 1[/tex]

Combine like terms.

[tex] - 9b = - 1[/tex]

Divide both sides by -9.

[tex] \frac{ - 9b}{ - 9} = \frac{ - 1}{ - 9} \\ b = \frac{1}{9} [/tex]

Answer:

[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]

distance = 16.2788

Step-by-step explanation:

This question is asking you to correctly apply the distance formula. This formula determines the straight line distance between two points by applying Pythagorean's Theorem ([tex]h = \sqrt{x^{2}+y^{2} }[/tex]). The distance formula can be thought of as [tex]distance=\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2})^{2}}[/tex]. It doesn't matter which order you put your coordinates into the equation as long as it's the square root of the change in x-coordinates squared + change in y-coordinates squared.

Step 1: change in x-coordinates

x1 = -2

x2 = -5

x1 - x2 = -2 - (-5) = 3

Step 2: change in y-coordinates

y1 = 6

y2 = -10

y1 - y2 = 6 - (-10) = 16

Step 3: plug into distance formula

[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]

[tex]distance=\sqrt{(3)^{2} +(16)^{2}}[/tex]

[tex]distance=\sqrt{9 +256}[/tex]

[tex]distance=\sqrt{265}[/tex]

distance = 16.2788

Answer:

the answer is 45

Step-by-step explanation:

the answer is 384

Step-by-step explanation:

a1 = 2, a2 = 3, a3 = 4,

an = ?

n = 44

d = a2 - a1 = 3 - 2 = 1

d = a3 - a2 = 4 - 3 = 1

Here, the common difference is the same everywhere

So,

[tex] a_{n} = a + (n - 1) \times d[/tex]

[tex]a_{44} = 2 + (44 - 1) \times 1[/tex]

[tex]a_{44} = 2 + 43[/tex]

[tex]a_{44} = 45[/tex]

The statements that are true about the dollhouses is: 1,4,5.

The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).

Space inside dollhouse 1:

V = 6 (6) (5) + 1/2 (6) (6) (4)

V=180+72

V=252 inches

The space inside dollhouse 2 can be found using the equation

V = 6 (6) (5) + 1/3 (6) (6) (4)

V=180+48

V=228

The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

V1=252

V2=228

Hence:

252-228=24 inches cubed

V1 ≥V2

Therefore the statements that are true about the dollhouses is: 1,4,5.

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The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)

From the diagram attached, we can say that;

Period = 2π/k

where;

k = 2π/2.25

k = 8π/9

Thus;

h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)

h(t) = -24cos (8π/9)t + 24.5

Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;

41 = -24cos (8π/9)t + 24.5

41 - 24.5 = -24cos (8π/9)t

16.5 = -24cos (8π/9)t

-0.6875 = cos (8π/9)t

cos⁻¹0.6875 = (8π/9)t

t = 0.834 min

Thus, time interval is between;

0.834 < t < (2.25 - 0.834)

⇒ 0.834 < t < 1.416 and

(2.25 + 0.834) < t < (2.25 + 1.416)

⇒ (3.084, 3.666)

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The probability to that the student chosen plays football or cricket or both is;

To evaluate the required probability, one must determine the total number of students in the class as follows;

Total number of students = 4 + 8 + (14-8) + (20-8) = 30.

Hence, the required probability is; (30-4)/30 = 26/30 = 13/15.

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Answer:

3^5

Step-by-step explanation:

exponents:

1 - ( - 4 ) = 5

Therefore,

3^5

Answer:

2.559 × 10 to the 1st power

Step-by-step explanation:

using a SNC

Answer:

2.559 * 10^1

Step-by-step explanation:

Rules of scientific notation (that I always remember)

    - the number must be between 1 and 9

    - if number gets smaller, exponent gets bigger; if number gets bigger, exponents gets smaller

25.59 is bigger than 9 so we move the decimal one place value to the left

and the number gets smaller meaning the exponent increases

Answer:

Discount of 25%

Step-by-step explanation:

To find the percent discount, subtract the big number minus small number then divide by the original number.

[tex]\frac{32-24}{32}[/tex]

[tex]\frac{8}{32} \\[/tex]

Reduce

[tex]\frac{1}{4}[/tex]

Change to a decimal by dividing

1/4 = 0.25

Change to a percent by moving the decimal two places right.

0.25 -----> 25%

Answer:

-15876

Step-by-step explanation:

|correct me if I'm not correct|

(Hope it's Help)

[keep safe]

The number is 15876

Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity. These numbers are used as digits and the most common ones are 0 and 1, that are used to represent binary numbers. Digits from 0 to 9 are used to represent other types of number systems.

Given number:

10584

So, the number multiplied by the third of itself

x* 2/3 = 10584

x= 10584* 3/2

x= 15876

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Answer:

he width of the ravin is 47

Answer:

97

Step-by-step explanation:

Number of adult tickets = a.

Number of student tickets = s.

"A total of 388 tickets were sold"

a + s = 388

"the number of student tickets sold was three times the number of adult tickets sold"

s = 3a

a + s = 388

s = 3a

Substitute s in the first equation with 3a.

a + 3a = 388

4a = 388

a = 97

Answer: 97 tickets