Find the inverse of the function. y = 2^x2 –4

Answer:

The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)

Step-by-step explanation:

4x + 2y = 6 ....… (1)

x − y = 3 …..... (2)

Example, for equation 2 is:

x - y = 3

x = 3 + y

Put in equation 1:

4(y + 3) + 2y = 6

4y + 12 + 2y = 6

6y = -6

y = -6/6

y = -1

We have the value of y, then the value of x will be:

x = 3 + y

= 3 + (-1)

= 3 - 1

= 2

So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)

First, assign variables to the given information:

We're given:

Plug the second equation into the first and solve using substitution:

[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]

Therefore, 325 adult tickets were sold.

325 adult tickets were sold.

Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

The area of field hockey is larger by 3162.85 [tex]m^2[/tex].

The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."

The hockey surface given here is in rectangular shape, so,

Area = length x breadth

Area of the hockey surface at a community centre is,

= 61 m x 30.5 m

=1860.5 [tex]m^2[/tex]

Area of field hockey played at outdoors,

= 91.5 m x 54.9 m

= 5023.35    [tex]m^2[/tex]

Clearly, we can see that area of field hockey is larger.

Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].

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The initial length of the scarf is 50 centimeters.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.

Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:

L + 25h = length of scarf after h hours

Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:

L + 25(3) = 125

L + 75 = 125

L = 50

Therefore, the initial length of the scarf is 50 centimeters.

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Cassandra is knitting a scarf. She increases the length of

the scarf by 25 centimeters each hour she knits. After 3

hours, the scarf is 125 centimeters long what is initial length of scarf.

Answer:

y = 2x - 3

Step-by-step explanation:

Pick two random points for slope

slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]

y intercept form:

y = 2x - 3

It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).

The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.

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Answer:

ST = 12 units

Step-by-step explanation:

Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6 ST = 8(21 - ST)

6 ST = 168 - 8 ST ( add 8 ST to both sides )

14 ST = 168 ( divide both sides by 14 )

ST = 12 units

The number of ways the letters can be permutated in the word SPEECHLESS is 100800.

What is meant by permutation?

An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The  number of letters in SPEECHLESS = 10

The letter E repeats 3 times

The letter S repeats 3 times

The letters P,C,H,L repeats one time.

When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:

[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]

where N = number of arrangements

 n = number of letters

r = total number of times one letter is repeated in the word

For SPEECHLESS,

Therefore the number of ways the letters can be permutated  is:

[tex]N= \frac{10!}{3!3!}[/tex] = 100800

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The expression for the number of paid vacation days for x years is

2 + 3x.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of paid vacation days = 2

Now,

She will receive an additional three days per year of paid vacation for each year she remains with the company.

This means,

For x years,

Number of paid vacation days = 2 + 3x

Now,

The expression for x years.

= 2 + 3x

Thus,

2 + 3x is the expression for the number of paid vacation days for x years.

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The complete question.

A)

Write an expression for the number of paid vacation days for x years.

The measured length of DE will be 4 cm.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.

The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-

AC = DE = 7 / 3.5

DE = AC / 2

DE = 8 / 2

DE = 4 cm

Hence, the value of the side DE will be 4 cm.

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Answer:

49ft

Step-by-step explanation:

Sketching out the problem, we get something like the diagram below. Assuming the canyon makes a roughly 90° angle with the ground, we can see that we have two right-angled triangles formed.

Focusing on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can also find the combined width of the ground and river (let's call this y) using cos:

cos38=230/y

0.7880107536=230/y

y=230/0.7880107536= 291.874189467ft

Focusing now on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can find the width of the ground (let's call this x) using cos:

cos19=230/x

0.94551857559=230/x

x=230/0.94551857559= 243.252756673ft

Therefore, the width of the river must be the difference between the combined width of the ground and river, minus the width of the ground:

291.874189467ft - 243.252756673ft = 48.621432794ft ≈ 49ft

If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.

Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.

The selected members from each group for their sample

The stratified sampling method is defined as the sampling method that divides the total population into the smaller group

Here the total population is divided into three groups according to whether they have brown, blue or green eyes.

Therefore, researcher was using stratified sampling method

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The distance from the town to the North Pole is approximately 2290 miles.

To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.

The length of the meridian arc can be calculated using the formula:

Length = (π/180) x radius of the Earth x angle in degrees

where π is approximately 3.14159, and the radius of the Earth is 3960 miles.

Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.

Plugging in these values into the formula, we get:

Length = (π/180) x 3960 miles x 58°

Length = (3.14159/180) x 3960 miles x 58

Length ≈ 2290 miles

Therefore, the distance from the town to the North Pole is approximately 2290 miles.

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The number of balls that he can make is given as follows:

249 balls.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

Considering the radius of 3 inches, the volume of each ball is given as follows:

V = 4π x 3³/3

V = 113.1 in³.

He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:

28260/113.1 = 249 balls.

(rounding down, as there will not be enough material for the 250th ball).

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Answer:

175m²

Step-by-step explanation:

Total area (of pool):

50 × 21 = 1050

Area of each lane:

1050 ÷ 6 = 175

Answer:

2

Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms

X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.

The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).

The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).

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The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.

An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).

A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."

Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).

In the given question,

The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).

S'(t) = 112

Therefore, when S'(t) = 112, t = 3.5.

This means that the rocket reaches its maximum height at t = 3.5 seconds.

Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.

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The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.

When a coin is flipped the probability of getting a heads and a tail is 50%.

Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.

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The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.

if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.

[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]

[tex](3/4)a^{2} = 144[/tex]

[tex]a^{2} = 192\\a = \sqrt{192}[/tex]

a = 13.85

area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]

= 1.732*192/4

83.136 sq.cm

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Answer:

Step-by-step explanation:

Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8

The correct answer for each of the math expressions is given below:

The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Hence, given that in the graph,

f(x) = 4x + 3

g(x) = [tex]\frac{5}{3} ^x[/tex]

Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.

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Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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The equation of the given information is y(x) = 5x+10

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that cost of renting for different numbers of hours.

The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.

Therefore, the cost (y) of renting a paddle boat for 'x' hours is:

y(x) = 5x+10

here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.

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The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.

Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.

Let's call the height of AB "x". We can use the tangent function to solve for x:

tan(55) = x/20

Multiplying both sides by 20:

x = 20 tan(55)

Using a calculator, we get:

x ≈ 27.8 feet

Therefore,

The height of the portion AB of the lamppost is approximately 27.8 feet.

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Answer: 20 tan 55

Step-by-step explanation:

took test and got it right

See below for the description of the enlarged shapes when dilated

From the question, we have the following parameters that can be used in our computation:

Scale factor = 4

This means that if Mai enlarges the triangular sign by a multiple of 4,

Then the corresponding side in the enlarged sign to side EG is 4 times the length of side EG.

i.e Corresponding side = 4 * Original side

If Mai wanted to turn the sign so that side JK was on the bottom,

Then the corresponding side of the original sign would be the side that was previously opposite to JK.

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