Identify whether the relations given in the options are functions or not.

Answer:

length = 26.6

width = 11.3

Step-by-step explanation:

1. Set up the equation

(2x + 4)(x) = 300

2. Simplify

2x² + 4x = 300

3. Solve by completing the square

Divide by 2 to make "a" equal to 1

x² + 2x = 150

Find term to complete the square by squaring half of "b"

(2/2)² = 1

x² + 2x + 1 = 150 + 1

Factor perfect square trinomial

√x² + 2x + √1 = 151

(x+1)² = 151

Square root each side

x + 1 = ±12.3

Set up two possibilities and solve

x + 1 = 12.3

x = 11.3

x + 1 = -12.3

x = -13.3

The measurement cannot be negative so width is equal to 11.3

4. Use the width to solve for the length

11.3(2) + 4 = 26.6

The length and width is 26.6 and 11.3.

Since The length of the fence is four more than two times the width.

So here the equation should be

(2x + 4)(x) = 300

[tex]2x^2 + 4x = 300[/tex]

Now

Here we divided by 2

So,

[tex]x^2 + 2x = 150[/tex]

Now we determine the term

[tex](2/2)^2 = 1\\\\x^2 + 2x + 1 = 150 + 1[/tex]

Now applied the Factor perfect square trinomial

[tex]\sqrt x^2 + 2x + \sqrt1 = 151\\\(x+1)^2 = 151[/tex]

Now do the Square root each side

x + 1 = ±12.3

Here we required to set up two possibilities and solve

x + 1 = 12.3

x = 11.3

And,

x + 1 = -12.3

x = -13.3

The measurement should not be negative so the width is equal to 11.3

Now the width is

= 11.3(2) + 4

= 26.6

Therefore, The length and width is 26.6 and 11.3.

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Answer:

51°

Step-by-step explanation:

A circle has a total of 360 degrees. So,

360 = 62 + 66 + x + 73 + x + 57

Next, combine like terms:

360 = 2x + 258

Next, isolate your variable by subtracting 258 from both sides:

102 = 2x

Finally, divide both sides by 2 to get x:

x = 51

Answer:

x = 51

Step-by-step explanation:

x + 73 + x + 57 + 62 + 66 = 360

2x + 258 = 360

2x = 360 - 258

2x = 102

[tex]\frac{x}{2} =\frac{102}{2}[/tex]

x = 51

Answer:

Distance between two ships = 73 units

Step-by-step explanation:

Note:

tangent = opposite / hypotenuse

Referring to diagram,

Distance of ship A from tower = 100 tan(90-45) = 100 units

Distance of ship B from tower = 100 tan(90-75) = 100 tan (27) = 27 units

Distance between two ships = 100-27 = 73 units

Answer:

a cone with a base radius of 17 units

Step-by-step explanation:

The computation of three-dimensional shape is shown below:-

Data provided

Perimeter of Triangle = 58 units

One non equal side = 24 units

We will assume two equal side = x units

x + x + 24 = 58

2 x = 58 - 24

2 x = 34

[tex]x = \frac{34}{2}[/tex]

x = 17

As we can see that the triangle is rotated about line k

This will give in a cone as it is a dimensional shape of three

So, the shape which is new will be of cone having radius 17 units

slant height 24

height k units

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

First of all we will take any real number x different from 0, -2, +2 as dividing by 0 is not allowed and then we can write

[tex]\dfrac{( - x - 2)}{x(x^2 - 4)}=-\dfrac{x+2}{x(x-2)(x+2)}=\large \boxed{ -\dfrac{1}{x(x-2)}}[/tex]

because we know that

[tex]x^2-4=x^2-2^2=(x-2)(x+2)[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Correct option: first one

Step-by-step explanation:

The equation f(x) = 5x + 1 is a function, because each value of x gives only one  value of y.

Now let's find the inverse by switching f(x) by x and x by f'(x), then isolating f'(x):

[tex]x = 5f'(x) + 1[/tex]

[tex]5f'(x) = x - 1[/tex]

[tex]f'(x) = \frac{x - 1}{5}[/tex]

The inverse f'(x) is also a function, because each value of x gives only one value of x.

So we have that both the equation and its inverse are function, therefore the correct answer is the first option.

Answer:

5

Step-by-step explanation:

If Lisa has x quarters and Brenda has 3x quarters, we can write:

80% * 3x = 4 + (20% * 3x + x) -- We write 4 because 1 dollar =  4 quarters

0.8 * 3x = 4 + (0.2 * 3x + x)

2.4x = 4 + 1.6x

0.8x = 4

x = 5

Answer:

D. Exponential growth will always exceed linear growth.

Step-by-step explanation:

An "exponential growth function" would always exceed the "linear growth function" in the end because the "x-values" tends to get larger in continuation, so the change rate associated with the "exponential function" also increases in continuation whereas the "linear functions' change rate is considered as constant.

In the question above, option D is correct.

Answer:

4.25%

Step-by-step explanation:

Commision =  441.30 - 375 = 66.30

Commision is based on  = 6560-5000 = 1560

Rate of Commision = (in decimal) 66.30/1560 = 0.0425  

Rate of Commision = 0.0425  * 100 =   4.25 %

Answer:

Step-by-step explanation:

Given

Step one:

Company's initial asset value = $11,283,500

Company's final asset value =   $21,794,600

Step two

we can calculate the company's asset appreciation after 10 years as

$21,794,600- $11,283,500= $10,511,100

Step three

Hence, the growth rate of the company's asset value per  year can be expressed as =  $10,511,100/10= $1,051,110

Answer:

42

Step-by-step explanation:

You can get this right from the table. 42 females had a positive opinion about the campus.

Answer:

42

Step-by-step explanation:

Let's look at the intersection of the "positive opinion" column and "female" row, the number we see at the intersection is 42.

Answer:

0.75

Step-by-step explanation:

The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).

Mathematically:

Average = (Sum of lengths) / frequency

The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.

The average is therefore:

Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8

Average = 0.75

Answer:

Both the equation and its inverse are functions.

Step-by-step explanation:

In order to solve this problem lets first find the inverse of this function. This is done below:

[tex]y = x^2 + 8\\[/tex]

We first swap x and y.

[tex]x = y^2 + 8[/tex]

We now isolate y.

[tex]y^2 = x - 8\\y = \sqrt{x - 8}\\f^{-1}(x) = \sqrt{x - 8}[/tex]

Functions are relations between two groups of numbers, in such a way that one number on the input group must generate a singular answer from the output group. This holds true for both f(x) and its inverse, therefore both are functions.

Answer:

y = 2x+4

Step-by-step explanation:

The y intercept ( where it crosses the y axis ) is 4

The slope is positive because the line goes up from the bottom left to top right

We pick two point ( -2,0) and ( 0,4)

The slope is found by

m= (y2-y1)/(x2-x1)

 = ( 4-0)/(0- -2)

  = 4/ (0+2)

  = 4/2

   = 2

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2x+4

Answer:

The equation to this line is y=-4x+4

Step-by-step explanation:

If you look at the graph you can see that the y intercept is 4.

To find the slope take two points on the graph and plug it into be y2-y1/x2-x1

I chose (0,-2) and (-1,2) So  2+2=4  and -1-0= -1 so  4/-1= -4

Answer:

provide a valid passport

Step-by-step explanation:

Answer:

be a us citizen

Step-by-step explanation:

Answer:

Here we have a triangle rectangle, where the length of one of the cathetus is: 15 (the one at the top)

And the length of the other cathetus is 8 units (i think, i can not see well the image)

Now, if we want to find the angle D.

In this case, the adjacent cathetus is the one of 15 units, and the opposite cathetus is the one of 8 units.

Then we can use the relation:

Tg(A) = (opposite cathetus)/(adjacent cathetus)

So:

Tg(D) = 8/15

D = ATg(8/15) = 28.1°

Now, for the angle F, the adjacent cathetus is the one of 8 units, and the opposite cathetus is the one of 15 units:

F = ATg(15/8) = 61.9°

Answer:

x= 17

Next, find the trigonometry ratios of ∠D.

sin∠D= 8/17

cos∠D= 15/17

tan∠D= 8/15

Finally, find the trigonometry ratios of ∠F.

sin∠F=15/17

cos∠F= 8/17

tan∠F=15/8

Answer:

neither on of those. I can't see the the other answers so your best bet is to look on m-a-t-h-w-a-y. (had to spell out with hyphens but remove them and go to that)

Step-by-step explanation:

Answer:

A. v = 19√3.

B. u = 38.

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 60°

Adjacent = 19

Opposite = v

Hypothenus = u

A. Determination of the value of 'v'

The value of v can be obtained by using Tan ratio as shown below:

Angle θ = 60°

Adjacent = 19

Opposite = v

Tan θ = Opposite /Adjacent

Tan 60 = v/19

Cross multiply

v = 19 × Tan 60

Tan 60 = √3

v = 19 × √3

v = 19√3

Therefore, the value of v is 19√3

B. Determination of the value of 'u'

The value of u can be obtained by using cosine ratio as shown below:

Angle θ = 60°

Adjacent = 19

Hypothenus = u

Cos θ = Adjacent /Hypothenus

Cos 60 = 19/u

Cos 60 = 1/2

1/2 = 19/u

Cross multiply

u = 2 × 19

u = 38

Therefore, the value of u is 38.

Answer:

1/12 and 1/3

Step-by-step explanation:

There are 2 choices for flipping a coin (heads or tails) and 6 choices for rolling the die (1 - 6) so the total possible outcomes are 2 * 6 = 12. Of these, there's only one possibility where we get a tail and a 5 so the answer to b is 1/12. For c, there's only one head but there are 4 numbers less than 5 (1 - 4) so the total number of outcomes that satisfy our condition is 1 * 4 = 4 which makes the probability 4/12 = 1/3.

Answer:

Step-by-step explanation:

The probable results are:

Head + 1/2/3/4/5/6

Tail + 1/2/3/4/5/6.

B. This gives 12 results and tail + 5 is one of them, so the probability of getting that is 1/12.

C. A result with a head and a number less than 5 is available 4 times, making the fraction 4/12 or 3/4

Hope this helps

Answer:

1-9, 1929

Step-by-step explanation:

You do the arithmetic and then study the us government postal codes and then you do kid behavior with my names. So, you get 1929 basically, in a nutshell, forever incessantly. thank yopu  

Answer:

17

Step-by-step explanation:

3m-(m + 5)

Distribute the minus sign

3m -m -5

Combine like terms

2m -5

Let m =11

2*11 -5

22-5

17

Answer:

[tex]17[/tex]

Step-by-step explanation:

[tex]3m-(m + 5)[/tex]

[tex]m= 11[/tex]

Plug m as 11 in the expression.

[tex]3(11)-(11+5)[/tex]

Evaluate.

[tex]33-16[/tex]

[tex]=17[/tex]

Answer:b

Step-by-step explanation:

2 3/8 ÷ 1 1/4

Steps

19/8 x 4/5

= 19/10

= 1 9/10

So the answer to this is B.

Answer:

40 2/5Ibs or [tex]40\frac{2}{5}[/tex] lbs

Step-by-step explanation:

Let weight of object on the moon be represented = Wm

weight of object on the Earth = We

In the above question, we are told:

The weight of an object on the moon is

5 of its weight on Earth.

Hence, mathematically, this is represented as:

 5Wm = We

If a moon rock weighs 202 lbs on Earth

5Wm = 202lbs

Wm = 202lbs/5

Wm = [tex]40\frac{2}{5}[/tex]Ibs

Therefore, the moon rock weighs [tex]40\frac{2}{5}[/tex]Ibs on the moon.

Answer:

[tex] y= cx^2 +dx +e[/tex]

We see that:

[tex] c = a, d= 2a , e= 3[/tex]

The axis of symmetry is defined by this formula:

[tex] X= - \frac{d}{2c}[/tex]

And replacing we got:

[tex] X= -\frac{2a}{2a}= -1[/tex]

Thn the axis of symmetry would be X=-1

Step-by-step explanation:

For this case we have the following function:

[tex] y = ax^2 +2ax +3[/tex]

If we compare this function with the general expression of a quadratic formula given by:

[tex] y= cx^2 +dx +e[/tex]

We see that:

[tex] c = a, d= 2a , e= 3[/tex]

The axis of symmetry is defined by this formula:

[tex] X= - \frac{d}{2c}[/tex]

And replacing we got:

[tex] X= -\frac{2a}{2a}= -1[/tex]

Thn the axis of symmetry would be X=-1

Answer:

The answer is below

Step-by-step explanation:

AD = X + 8 ∠D = 2y +13 ∠C = 16 - x CB = 5y+4

In a parallelogram, consecutive angles are supplementary and opposite sides are equal.

Therefore for parallelogram ABCD, AB = CD, CB = AD

Since AD = CB (opposite sides of a parallelogram are equal):

x + 8 = 5y + 4

5y - x = 8 - 4

5y - x = 4             (1)

∠C + ∠D= 180° (consecutive angles of a parallelogram are supplementary). Therefore:

16 - x + 2y + 13 = 180

2y - x + 29 = 180

2y - x = 180 -29

2y - x = 151             (2)

To find x and y, subtract equation 1 from equation 2:

3y = -147

y = -49

Put y = -49 in equation 2

2(-49) - x = 151

x = -98 - 151

x = -249

Answer:

Step-by-step explanation:

0.6 = 6/10 = 3/5

is the answer

This is because you have to substitute.

Given:

x = 3

y = -1

Unknown:

Final Answer

(x*y^2)/5

((3)(-1*-1)/5

= (3*1)/5

Hope this helped,

Kavitha

Complete Question:

Identify the type of sampling used​ (random, systematic,​ convenience, stratified, or cluster​ sampling) in the situation described below;

A researcher selects every 890th social security number and surveys the corresponding person. Which type of sampling did the researcher ​use?

Answer:

Systematic sampling.

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Random sampling.

2. Convenience sampling.

3. Stratified sampling.

4. Cluster sampling.

5. Systematic sampling.

A systematic sampling is a type of probability sampling method which involves the researcher selecting or collecting data from a larger population.

Under systematic sampling method, samples are selected from an ordered (fixed) sample population at periodic interval. Therefore, numbers are assigned to every member of the population and then, the "nth" member are selected by the researcher after choosing a fixed starting point.

In this scenario, the researcher selects every 890th social security number and surveys the corresponding person.

Hence, the type of sampling used by the researcher ​is systematic sampling.

Answer:

[tex]\huge\boxed{x=\dfrac{52}{7}=7\dfrac{3}{7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x}{4}+\dfrac{3}{5}=\dfrac{3x}{5}-2\qquad\text{multiply both sides by}\ LCD=20\\\\20\cdot\dfrac{x}{4}+20\cdot\dfrac{3}{5}=20\cdot\dfrac{3x}{5}-20\cdot2\\\\5\cdot x+4\cdot3=4\cdot3x-40\\\\5x+12=12x-40\qquad\text{subtract 12 from both sides}\\\\5x+12-12=12x-40-12\\\\5x=12x-52\qquad\text{subtract}\ 12x\ \text{from both sides}\\\\5x-12x=12x-12x-52\\\\-7x=-52\qquad\text{divide botgh sides by (-7)}\\\\\dfrac{-7x}{-7}=\dfrac{-52}{-7}\\\\x=\dfrac{52}{7}[/tex]

Reasoning:

g(x) = 4*ln(x)

g(x) = 2*2ln(x)

g(x) = 2*f(x)

Whatever the output f(x) is, it is doubled to get g(x). Recall that y = f(x), so we're really doubling the y values to visually stretch it vertically by a factor of 2. In short, g(x) is twice as tall compared to f(x).

Answer:

C. g(x) stretches f(x) vertically by a factor of 2.

Step-by-step explanation:

a p e x

Answer:

work is shown and pictured

C, infinitely many solutions.

B, one solution.

C, infinitely many solution.

A system of linear equations is a collection of one or more linear equations involving the same variables.

A system of linear equation has

According to the given questions

the given system of equations

(1). 2x+2y=3 and 4x+4y=6

if we see the graph of the above system of linear equations, the graphs are the" exact at same line".

Hence, they have infinitely many solution.

(2). 7x+5y=8 and 7x+7y =8

if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.

Hence, there is only one solution.

(3). -2x+3y=7 and 2x-3y=-7

if we see the graph of the above system of linear equations, the graphs are exact at same line.

Hence, there is infinitely many solutions.

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