Twice the difference of a number and 3 is equal to 2. Translate the sentence into an equation

Answer:  

Segment GE is congruent to segment GE - They are the same segment

Angle HEG is congruent to angle FEG, and angle HGE is congruent to angle FGE  - Definition of angle bisectors

Triangle HGE is congruent to triangle FGE - Angle Side Angle

The hikers are 5.9 miles apart.

Let O represents the base camp,

Suppose after walking 3.5 miles west, the first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, the second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras' theorem,

BD² = BD'² + DD'²

[tex]BD = \sqrt{2^{2} + 5.5^{2} } = \sqrt{4+30.25} =\sqrt{34.25} = 5.9[/tex]

Hence, the hikers are 5.9 miles apart.

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Answer: Y=-2x+1

Step-by-step explanation:

because the slope is x and the 1 is y-intercept

Answer: The slope and y-intercept calculator takes a linear equation and allows you to calculate the slope and y-intercept for the equation. The equation can be in any form as long as its linear and you can find the slope and y-intercept.

Step-by-step explanation:

The plane travels a distance of 11710 feet from point A to point B.

Tangent function of an angle in a right angled triangle is defined as the ratio of the opposite side to the adjacent side.

The figure representing the situation is given below.

From triangle AOC,

tan 19° = AC / OC

tan 19° = 7425 / OC

OC = 7425 / tan 19°

OC = 21563.77 feet

Similarly for triangle BOD,

tan 37° = BD / OD

tan 37° = 7425 / OD

OD = 7425 / tan 37°

      = 9853.31 feet

AB = CD

     = OC - OD

     = 21563.77 feet - 9853.31 feet

     = 11,710.46 feet

     ≈ 11710 feet

Hence the distance plane travelled from point A to point B is 11710 feet.

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The mapping diagram does not show a function, because the input -1 is mapped into two different values.

A function is a relation that maps elements from one set (called the domain) into another set (called the range), such that each input can be mapped into only one value.

In this case, we have a relation that maps elements from set A into set B. And you can see that the element -1 is mapped into two different values ( which are 8 and 9), then the mapping does not repsent a function.

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Answer:

[tex] 1.{x}^{2} - 64[/tex]

[tex]2. {y}^{2} - 100[/tex]

[tex]3. {m}^{2} - 16[/tex]

Answer:

1. (x + 8) (x - 8) = x^2 - 64

2. (y + 10)(Y - 10) = y^2 - 100

3. (m - 4)(m + 4) = m^2 - 16

4. (n - 9)(n + 9) = n^2 - 81

5. (3x + 1)(3x - 1) = 9x^2 - 1

6. (5c + 4)(5c - 4) = 25c^2 - 16

7. (11z - 7)(11z + 7) = 121z^2 - 49

8. (20x + 9)(20x - 9) =  400x^2 - 81

9. (8x + 3y)(8x - 3y) = 64x^2 - 9y^2

Step-by-step explanation:

:)

The solution of the integral operation is [tex]e^{2x - 5y + 7z}[/tex]

The integral is a concept in mathematics that involves finding the total amount of a quantity that changes continuously over a given region.

In this case, we are calculating the triple integral of the function [tex]e^{2x - 5y + 7z}[/tex] over a region defined by the conditions 0 ≤ x ≤ 1, 0 ≤ y ≤ −x + 1, and 1 ≤ z ≤ 2.

In order to start solving the integral, we need to first visualize the region defined by the conditions in 3D space.

This region can be seen as a triangular prism with vertices at (0,0,1), (1,0,1), and (1,1,2).

Next, we need to break down the integral into smaller parts. We will use cylindrical coordinates, where x = rcosθ, y = rsinθ, and z = z, to simplify the calculation of the integral.

The triple integral can then be written as

=> [tex]\int\int\int e^{(2rcos\theta - 5rsin\theta + 7z)} r dr d\theta dz,[/tex]

where the limits of integration for r, θ, and z are defined by the conditions stated above.

The final result will be the total amount of the function is

=> [tex]e^{2x - 5y + 7z}[/tex]

over the region defined by the conditions.

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Answer:

D

Step by step explanation:

[tex]F = \frac{9}{5}C + 32[/tex]

The main objective is to isolate C and to make C the subject of the equation:

[tex]= F - 32= \frac{9}{5} C[/tex]

[tex]= C = \frac{5}{9} (F - 32)[/tex]

Now substitute the given value of F:

[tex]C = \frac{5}{9} (68-32)[/tex]

[tex]=C = \frac{5}{9} (36)[/tex]

[tex]= C = 20^{o} C[/tex]

Answer:

D. C = 5/9 ( F - 32 ) ; conversion: 68° F = 20° C

The number of units of electricity used in one hour is 1.6

An oven uses 8.24 units of electricity in 5 hours

The number of unit used in one hour can be calculated as follows

= 8.24/5

= 1.6

Hence 1.6 units of electricity was used in one hour

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Answer:

3x² + 6x + 16

Step-by-step explanation:

The big-Oh order of the expression f(n) = 24n²nlogn + 280 is O(n²), which means that the time complexity of the algorithm is proportional to n².

The big-Oh order is a way of measuring the growth of a mathematical expression in terms of time complexity. It is used in computer science to analyze algorithms and to predict their performance.

In this case, we are looking at the big-Oh order of the expression f(n) = 24n²nlogn + 280.

To determine the big-Oh order, we need to find the dominant term in the expression, or the term that grows the fastest as the input size (n) increases.

In this expression, the dominant term is 24n²logn, since it grows much faster than the constant term 280.

Now, we can simplify the expression further. The logarithmic term is a much slower growing term compared to the polynomial term, so we can ignore it.

This means that the big-Oh order of the expression is O(n²), which means that the time complexity of the algorithm represented by the expression is proportional to n².

This means that the time taken by the algorithm will increase rapidly as the input size (n) increases.

Complete Question:

What is the Big-Oh order of the following growth expression?

f(n)=24n+2nlg(n)+280

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True, A confidence interval is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies.

Now, According to the question:

A confidence interval (CI) refers to the amount of uncertainty associated with a sample population estimate (the mean or proportion) of a true population. Say you wanted to determine the average age of victims of robberies in Chicago last year. Now, while there is a true answer, say 30 years old, the best you can do is find an interval that the true answer probably lies in, say, 20-40 years old.

The confidence interval is the sample mean or proportion plus or minus the margin of error (ME), which is the value used to calculate the upper limit and lower limit of the sample statistic. In this case, the upper limit is 40, and the lower limit is 20.

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The surface area of a pyramid with a base equilateral triangle is 480 + 100√3 square inches.

The total surface area (S) of a regular pyramid is given by the formula as

1/2 Pl + B         ...... (i)

Here, p represents the perimeter of the base, l is the slant height, and B is the base area of the pyramid.

As per the question, we have

Side of equilateral triangle = 20 inches

The slant height of the pyramid(l) = 16 inches.

First, we have to determine the perimeter and Area of the base pyramid.

The perimeter of an equilateral triangle (p):

= 3 × side                                                        

= 3×(20)

= 60 inches

Area of an equilateral triangle (B):

= (√3/4) × side²                                              

= (√3/4) × (20)²

= 100√3 square inches.

Substitute the above values in equation (i), and we get

The total surface area (S):

= 1/2 x 60 x 16 + 100√3

= 480 + 100√3 square inches

Hence, the surface area of the given pyramid is 480 + 100√3 square inches.

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Answer:

Step-by-step explanation:

We are given that T varies as the square root of the ratio of s and t, and we are trying to find the value of T when s=33 and t=18.

The relationship between T, s and t can be represented by the following equation:

T = k * √(s/t)

Where k is a constant.

We are given that when S=36, t=16, T=18. We can use this information to find the value of k.

We know that T = k * √(s/t)

and, T = 18 when s=36, t=16.

So we can substitute these values in the equation

18 = k * √(36/16)

Solving for k, we get:

k = 18/2 = 9

Now that we know the value of k, we can use it to find the value of T when s=33 and t=18.

T = k * √(s/t) = 9 * √(33/18) = 9 * √(11/6) = 9 * √(11/6)

The value of T when s=33, t=18 is 9 * √(11/6),

It is not possible to give the exact value of T because the value of the square root of (11/6) is not a whole number.

All parts of the problem regarding die rolls have been solved and explained below.

In order to find the probability of getting any one point out of the 6 after rolling the die, we first need to Add up all of the number of points in the die, that is -

= 1+2+3+4+5+6

= 21.

We also know that after any roll of one die, the probability of getting about one particular point is 1/6.

So, the expected number of points after one roll can be calculated is-

= 21/6= 3.5

After two rolls, we can just twice the probability of it happening before-

= (2 x 21)/6 = 7.

Similarly, after 100 rolls =  350, and after N rolls, 3.5(N).

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Answer:

3

negative infinity

negative infinity

Step-by-step explanation:

Real zeros are x values where the graph f(x) crosses the x-axis. Basically what values will you put in to get 0. There are 3 such values where the graph crosses the x axis.

You can see at we move right along the x -axis (x values towards infinity) the graph goes down and keeps going down, so we can say that it is going towards negative infinity in y direction because down is negative and up is positive. Same with the other side, as x values move towards left, graph moves down.

Answer:

Step-by-step explanation:

i wish i knew! i wish i knew you wanted me

Jason wants to know if student grade point average (GPA) is impacted by being involved in a romantic relationship. In Jason's study, GPA is the dependent variable.

The variable that is changed during a scientific experiment is known as an independent variable. In a laboratory experiment, an independent variable is one that can be changed or manipulated. It will stand in for the reason or cause behind an outcome.

The variable being evaluated or analyzed during a laboratory experiment is known as the dependent variable. It is obvious that the dependent variable relies on the independent variable. While a result, we can now see and note changes in the dependent variable as the experimenter modifies the independent variable.

A controlled variable is one that is maintained constant throughout a scientific experiment. As a result, we also understand the controlled variable to be a constant variable or occasionally just a "control."

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The complete question is:

Jason wants to know if student grade point average (GPA) is impacted by being involved in a romantic relationship. In Jason's study, GPA is the:

a. Independent Variable

b. Dependent Variable

c. Control Variable

d. None of the Above

Answer:

i believe it is the second answer choice

Step-by-step explanation:

Answer:

We can solve this by giving the velocities opposite signs.

Step-by-step explanation:

Traveling west at 5 miles per hour can be given a positive sign and traveling east is opposite to west on a straight line, so we can denote that with a negative sign.

Hence, we can distinguish the velocities without using the words "east" and "west" by giving the velocities opposite signs.

ln(8x+1) = (28+14)/6 = 7

8x+1 = e^7

8x = e^7 - 1

x = (e^7 - 1)/8

Answer:x=e^7-1/8

Step-by-step explanation:

6 ln(8x+1)-14=28

               +14  +14

6 ln(8x+1) =42

6 ln(8x+1)/6   42/6

log e (x) = a-->e^a=x

8x+1=e^7

8x/8 =e^7-1/8

x=e^7-1/8

The statement ∃x∀y (xy = 0) the domain of discourse is the set of real numbers is true.

The term called domain in math is defined as the set of values that we are allowed to plug into our function.

Here we have know that the statement ∃x∀y(xy = 0) and the domain of discourse is the set of real numbers

Here we have to check whether the given statement is true or not.

Here we know that the domain of each variable consists of all real numbers ∀x∃y(xy =0 )

Here we also know that for every real value of x function x2 =y exist means there exist value y which also a real number.

Hence the truth value is TRUE.

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Answer:

Numbers on die = 1, 2, 3, 4

Colors on board = Red, Green, Blue, Orange (equal sized sections)

To find:

The number of different possible outcomes are there if she rolls a fair die in the board.

Solution:

According to the given information,

The total possibilities for numbers = 4

Total possibilities for colors = 4

Total possibilities = Possibilities for number × Possibilities for colors

                            = 4x4

                            = 16

So, total 16 possible outcomes are there if she rolls a fair die in the board.

Let Red=R, Green=G, Blue=B, Orange=O, then list of total possible outcomes is:

{1R,1G,1B,1O,2R,2G,2B,2O,3R,3G,3B,3O,4R,4G,4B,4O}

Therefore, the total possible outcomes are 16 and the lies of outcomes is {1R,1G,1B,1O,2R,2G,2B,2O,3R,3G,3B,3O,4R,4G,4B,4O}.

There are 8 different possible outcomes if Rashon rolls a pyramid-shaped die labeled with 4 sides and flips a coin.

It is a branch of mathematics that deals with the occurrence of a random event.

If Rashon rolls a pyramid-shaped die that has four sides labeled 1 to 4, then the number of possible outcomes for the die roll is 4.

Additionally, flipping a coin has 2 possible outcomes, either heads or tails.

To find the total number of possible outcomes for rolling the die and flipping the coin, we need to multiply the number of outcomes for the die roll by the number of outcomes for the coin flip.

So, the total number of possible outcomes for rolling the die and flipping the coin is:

4 (number of die outcomes) x 2 (number of coin outcomes) = 8

Therefore, there are 8 different possible outcomes if Rashon rolls a pyramid-shaped die labeled with 4 sides and flips a coin.

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a) 96 hotdogs purchased from Value Market would cost $96. This is because Value Market sells hotdogs for $1 each. Therefore, 96 hotdogs would cost $96.

Value Market is an investment approach that focuses on buying assets that have the potential to generate returns that exceed the market average over the long term. It involves buying stocks or other assets at a price lower than their intrinsic value, or the stock's true underlying worth. This approach requires investors to do extensive research and analysis to identify undervalued assets and purchase them at prices that are below their true worth.

b) 96 hotdogs purchased from Sammy's Bulk Store would cost $48. This is because Sammy's Bulk Store sells hotdogs in packs of 8 for $4 each. Therefore, 96 hotdogs would cost $48 (96/8 = 12 packs of 8 hotdogs, 12 x $4 = $48).

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If Stephanie need prove that two sides of the parking lot meet in a right angle , then the options that apply are :

(a) Find the slopes of AC and CB. If the product of the slopes is -1, then the sides meet in a right angle.   and

(e) Find AB, BC, and AC. If AB²+ BC² = AC² then the sides meet in a right angle.  

The endpoints of the triangle parking are : A(0,0) , B(50,0) and C(18, 24) .

Option (a) : The slope of AC = (24-0)/(18-0) = 24/18 = 4/3 .

slope of CB = (0-24)/(50-18) = -24/32 = -3/4 .

the product of slope of AC and CB = -1 , hence the triangle is Right Triangle .

Option (e) : The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, the hypotenuse.

In this case, AB and BC would represent the two shorter sides and AC would represent the longest side. If AB² + BC² = AC², then the three sides form a right triangle and the two sides meet in a right angle.

Stephanie is drawing the layout of a parking lot on a coordinate grid and needs to verify that two sides meet in a right angle. In her sketch, one side of the parking lot has endpoints A(0,0) and B(50,0). The second side of the parking lot has endpoints B(50,0) and C(18, 24). How can Stephanie prove that the two sides of the parking lot meet in a right angle? Select all that apply.

(a) Find the slopes of AC and CB. If the product of the slopes is -1, then the sides meet in a right angle.

(b) Find the slopes of AB and AC. If the product of the slopes is -1, then the sides meet in a right angle.

(c) Find the slopes of CB and AB. If the slope of AB is the opposite of the slope of AC, then the sides meet in a right angle.

(d) Find AB, BC, and AC. If AB + BC = AC, then the sides meet in a right angle.

(e) Find AB, BC, and AC. If AB² + BC² = AC² then the sides meet in a right angle.

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