What is the pattern in the values as the exponents increase?

Powers of 2
Value
2 Superscript negative 5
StartFraction 1 Over 32 EndFraction
2 Superscript negative 4
StartFraction 1 Over 16 EndFraction
2 Superscript negative 3
StartFraction 1 Over 8 EndFraction
2 Superscript negative 2
One-fourth
2 Superscript negative 1
One-half
2 Superscript 0
1

add StartFraction 1 Over 16 EndFraction to the previous value
subtract StartFraction 1 Over 16 EndFraction from the previous value
divide the previous value by 2
multiply the previous value by 2

The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

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The equation of the line in the graph given is: y = -3x - 1.

Find the slope of the line, which is: m = rise/run.

Rise of the line = 3 units

Run = 1

Slope (m) = -3/1 = -3

Y-intercept (b) = -1 (at this point, x equals zero)

Substitute m = -3 and b = -1 into y = mx + b

y = -3x + (-1)

y = -3x - 1

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answers

6. y = -1/2x + 8

7. y = 15

8. y = -3/4x + 1

9. y = 6x + 3

10. y = 1/3x - 4

steps

equation of the line that is perpendicular means the number next to the x should be a negative reciprocal

number next to the x is the slope

6. y=2x+5

y = mx + b

m = 2

b = -5

negative reciprocal would be

-1/2x

m = -1/2

(2, 7) means x = 2 y = 7

substitute

7 = -1/2(2) + b

7 = -1 + b

b = 8

answer is y = -1/2x + 8

7.

y = 5; (11, 15)

b = 5

m would be 0 because there is no slope

15 = 0*11 + b

b = 15

y = 15

8.

line goes through

(0,-2) and (3,2)

get slope

y2-y1/x2-x1

2-(-2) / 3 - 0

4/3

y = 4/3x

point slope form

y - y1 = m (x-x1)

y - -2 =  4/3 (x - 0)

y+2 =  4/3x

y = 4/3x - 2

negative reciprocal slope would be for perpendicular

-3/4x

(12, 10)

y = mx + b

10 = 3/4(12) + b

10 = 9 + b

1 =  b

b = 1

y = -3/4x + 1

9.

y = -1/6x + 1; (− 2, — 9)

negative reciprocal slope would be for perpendicular

+6x

(− 2, — 9)

y = mx + b

get b

-9 = 6(-2) + b

-9 = -12 + b

b = 3

y = 6x + 3

10.

6x+2y=14; (12, 0)

2y= -6x+14

y= -3x+7

negative reciprocal slope would be for perpendicular

1/3x

y = mx + b

get b

0 = 1/3(12) + b

0 = 4 + b

b = -4

y = 1/3x - 4

Step-by-step explanation:

[tex] \frac{x}{12} = \frac{x + 4}{5 + 12} \\ [/tex]

[tex] \frac{x}{12} = \frac{x + 4}{17} \\ [/tex]

Now cross multiply...

[tex]12(x + 4) = 17x[/tex]

[tex]12x + 48 = 17x[/tex]

[tex]12x - 17x = - 48[/tex]

[tex] - 5x = - 48[/tex]

Now divide both term by same number

[tex] \frac{ - 5x}{ - 5} = \frac{ - 48}{ - 5} \\ [/tex]

[tex]x = 9.6[/tex]

a. Find the graph in the attachment

b. As h increases, e tends to 90°

Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.

The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.

To plot the graph, we see that the function is the tangent function.

The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°

Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞

So, we plot h = 22tane for 0 ≤ e ≤ 90°

Find the graph in the attachment

From the graph, we seet that at high h or as h increases, e tends to 90°

So, as h increases, e tends to 90°

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Answer:

see explanation

Step-by-step explanation:

(a)

x² - 36 = 0 ← is a difference of squares and factors as

(x - 6)(x + 6) = 0

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 6 = 0 ⇒ x = 6

(b)

x² - 5x + 4 = 0

consider the product of the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

(c)

x² - 2x = 3 ( subtract 3 from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the product of the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are + 1 and - 3 , since

1 × - 3 = - 3 and 1 - 3 = - 2 , then

(x + 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

(d)

6x² - 11x - 10 = 0

consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 10 = - 60 and sum = - 11

the factors are + 4 and - 15

use these factors to split the x- term

6x² + 4x - 15x - 10 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 2) - 5(3x + 2) = 0 ← factor out (3x + 2) from each term

(3x + 2)(2x - 5) = 0

equate each factor to zero and solve for x

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

Answer:

z = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the altitude- on- hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 8 × (8 + 1) = 8 × 9 = 72 ( take square root of both sides )

z = [tex]\sqrt{72}[/tex] = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

[tex]z = 6 \sqrt{2} [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

1, 5

Step-by-step explanation:

-16/4=-4

10/5=2

1/2=1/2

-1/-3=1/3

-1/4/1/2=-1/2

The negative ones are your answer.

Answer:

No, the ratio is not the same.

Step-by-step explanation:

75 total (large tank) / 25 total (small tank) = 3

25 angelfish (large tank) / 5 angelfish (small tank) = 5

The ratio of angelfish to total fish is not the same. When we scale up from the small tank to large tank in terms of total fish, we have a factor of 3. However, when we scale up from the small tank to large tank in terms of angelfish, we have a factor of 5. For the ratio to be the same, these factors would need to be identical.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. The volume of rectangular prism A = 64 m³

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So, area of first figure = k² × area of second figure

Similarly, Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/2.

Scale factor =  (Length of rectangular prism B)/(Length of rectangular prism A)

1/2 = (Length of rectangular prism B)/(Length of rectangular prism A)

Now, the volume of the rectangular prism can be written as,

(Scale factor)³ = (Volume of rectangular prism B)/(Volume of rectangular prism A)

(1/2)³ = 8 m³ /(Volume of rectangular prism A)

The volume of rectangular prism A = 64 m³

Hence, The volume of rectangular prism A = 64 m³

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Answer:5

Step-by-step explanation:

Answer:

If the population of the United States on July 4,2010 was almost 310000000 then, the number in scientific notation is [tex]$3.1 \times 10^{8}$[/tex].

Step-by-step explanation:

- Given

Population of the United States on July 4,2010 was almost 310000000 .

- To write the number in scientific notation.

- Firstly, move the decimal point so that the first factor is greater than or equal to 1 but less than 10 .

- Then, count the number of decimal places, n, that the decimal point was moved.

- Then, write the number as a product with a power of 10.

- Finally, check the scientific notation.

Step 1 of 2

Moving the decimal point-

Move the decimal after 3 . so that 3.10000000 is between 1 and 10 .

Now, we know the decimal point was moved 8 places to the left.

Step 2 of 2

Writing the number as a product with a power of 10 -

Since, 310000000 is greater than 1 so the power of 10 will have the exponent 8 .

Therefore, the number becomes-

[tex]$$31000000=3.1 \times 10^{8}$$[/tex]

Now, checking the scientific notation-

[tex]$$\begin{gathered}3.1 \times 10^{8}=3.1 \times 100000000 \\=310000000\end{gathered}$$[/tex]

The equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

An equation that has an infinite number of solutions would be in the form

a = a

This means that both sides of the equation would be the same

Start by simplifying the options

3(x – 1) = x + 2(x + 1) + 1

3x - 3 = x + 3x + 2 + 1

3x - 3 = 4x + 3

Evaluate

x = 6 ----- one solution

x – 4(x + 1) = –3(x + 1) + 1

x - 4x - 4 = -3x - 3 + 1

-3x - 4 = -3x - 2

-4 = -2 ---- no solution

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

2x + 3 = 2x + 1 + 2

2x + 3 = 2x + 3

Subtract 2x

3 = 3 ---- infinite solution

Hence, the equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

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Complete question

Which equation has infinite solutions?

3(x – 1) = x + 2(x + 1) + 1

x – 4(x + 1) = –3(x + 1) + 1

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

[tex]\frac 13(6x - 3) = 3(x + 1) - x - 2[/tex]

The solution of the equations will be the point of intersection of the two lines

A line is the shortest distance between two points. The equation of a line in standard form is given as Ax + By = C

According to the question, we are to pot the following lines.

4y +3x = 0

4y - x = 16

The solution of the equations will be the point of intersection of the two lines as attached.

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(You could do this shorter, but by the time i realized that it was too late.)

First, we need one of the variables (x or y) to have the same coefficient.
Lets use the variable y, since it uses smaller numbers.

Multiply the first equation by the denominator of y, which is 3. Then multiply the second equation by the denominator of y in the second equation, which is 4.

You get:
1st equation: [tex]\frac{3}{2} x+ y = 27[/tex]
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we need to multiply the first equation by 3, so we can have "3y" in both of the equations.
1st equation: 9/2x + 3y = 81
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we can subtract both of the equations.
12/5x + 9/2x = 69 We need to make the common denominator for x.
24/10x + 45/10x = 69
69/10x=69
x=10
Now we substitute x into the first equation (or the second, doesn't matter).
1/2 * 10 + 1/3y=9
5 + 1/3y = 9
1/3 y = 4
y = 12

Answer:

(10, 12 )

Step-by-step explanation:

let's begin by clearing the fractions from both equations

[tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{3}[/tex] y = 9 ( multiply through by 6 ( the LCM of 2 and 3 to clear ) )

3x + 2y = 54 → (1)

[tex]\frac{3}{5}[/tex] x - [tex]\frac{3}{4}[/tex] y = - 3 ( multiply through by 20 ( the LCM of 5 and 4 to clear ) )

12x - 15y = - 60 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x )

- 12x - 8y = - 216 → (3)

add (2) and (3) term by term to eliminate x

0 - 23y = - 276

- 23y = - 276 ( divide both sides by - 23 )

y = 12

substitute y - 12 into either of the 2 equations and solve for x

substituting into (1)

3x + 2(12) = 54

3x + 24 = 54 ( subtract 24 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

solution is (10, 12 )

If the function is vertically compressed, the resulting function will be g(x) = 3/4x^2

Quadratic functions are functions that has a leading degree of 2. Given the parent function f(x) = ax^2

where

2 is the exponent/degree

If the function is vertically compressed, the value of a must be less than 1, hence the possible expression when vertically compressed is g(x) = 3/4x^2

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Answer:0

Step-by-step explanation:

Answer:

[tex]y=\dfrac {60} {x}[/tex]   or   [tex]xy=60[/tex]   (depending on your teacher's format preference)

Step-by-step explanation:

Proportionality is sometimes called "variation".   (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

From these examples, we see that two things:

In our question, y is inversely proportional to x, so the equation we're looking at is the following [tex]y=\dfrac {k} {x}[/tex].

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it:  "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

General Inverse variation equation...

[tex]y=\dfrac {k} {x}[/tex]

Substituting known values...

[tex](12)=\dfrac {k} {(5)}[/tex]

Multiplying both sides by 5...

[tex](12)*5= \left ( \dfrac {k} {5} \right ) *5[/tex]

Simplifying/arithmetic...

[tex]60=k[/tex]

So, for our situation, k=60.  So the inverse proportionality relationship equation for this situation is [tex]y=\dfrac {60} {x}[/tex].

The way your question is phrased, they may prefer the form: [tex]xy=60[/tex]

Answer:

I would say b since this would tell him how many people are wiling to join a health club

Hope This Helps!!!

Answer: x=9.

Step-by-step explanation:

Triangle ABC is similar to triangle FED     ⇒

[tex]\frac{77}{21} =\frac{11x+11}{30} \\\\\frac{7*11}{7*3}=\frac{11*(x+1)}{30} \\\\\frac{11}{3}*30 =11*(x+1)\\\\\frac{11*3*10}{3} =11*(x+1)\\\\11*10=11*(x+1)\\10=x+1\\9=x.[/tex]

Good luck an' have a nice day!

Answer:

16 Liters of the correct answer.

Emil started his lemonade stand with 12 litres of Lemonade.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.

When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.

x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4

x - ( x/2) - (x/8) - ( x/24) = 4

[ 24x -12x -3x - x][24] = 4

8x  =  96

x = 12 liters

Therefore Emil started his lemonade stand with 12 liters of Lemonade.

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Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

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Answer:

b d e

Step-by-step explanation:

Answer:

none of these are correct

Step-by-step explanation:

What would be the effect of this change is: a). both area rate and flow rate would increase.

Assuming a driver shift into third gear in which there was reduction in the engine speed while on the other hand the tractor speed increase.

The effect of the change will result in the increase in area rate as well as the  flow rate.

Therefore the correct option  is A.

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The solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

The inequality is given as:

-4(x + 3) ≤ -21

Divide both sides by -4

x + 3 ≥ 5.25

Subtract 3 from both sides

x ≥ 2.25

This means that the solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

See attachment for the number line

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There are 1,16,280 different recital programs possible.

Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces and is carefully considering which song to play first, second, etc.

It means the repetition of pieces is not allowed.

When repetition is not allowed, then the number of ways to arrange n things where r things taken together is given by:-

[tex]^{n} P_{r} =\frac{n!}{(n-r)!}[/tex]

Now, the number of different recital programs are:-

[tex]^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280[/tex]

Hence, there are 1,16,280 different recital programs possible.

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[tex]f(x )= - 2x[/tex]

[tex]g(x) = \frac{1}{2} x {}^{2} + 5[/tex]

#1

Domain

Range

#2

Domain

Range

#3

Its graphed

Domain=Range=(-oo,oo)

#4

Domain

Range

[-3,-oo) or (-oo,-3]

Answer:

its an odd number

Step-by-step explanation:

See below for the calculations of the slopes of the graphs

The slope of a line is calculated using:

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

Using the above formula, we have:

Line 1: (-2, 0) and (3, 2)

Slope, m= (2 - 0)/(3 + 2)

m= 2/5

Hence, the slope is 2/5

Line 2: (2, -3) and (-2, 4)

Slope, m= (4 + 3)/(-2 - 2)

m= -7/4

Hence, the slope is -7/4

Line 3: (-4, -2) and (1, 3)

Slope, m= (3 + 2)/(1 + 4)

m= 1

Hence, the slope is 1

Line 4: (0, 0) and (-3, -4)

Slope, m= (-4 - 0)/(-3 - 0)

m= 4/3

Hence, the slope is 4/3

Line 5: (0, 0) and (-1, -4)

Slope, m= (-4 - 0)/(-1 - 0)

m= 4

Hence, the slope is 4

Line 6: (-2, 1) and (3, 2)

Slope, m= (2 - 1)/(3 + 2)

m= 1/5

Hence, the slope is 1/5

Line 7: (-2, -1) and (2, -4)

Slope, m= (-4 + 1)/(2 + 2)

m= -3/4

Hence, the slope is -3/4

Line 8: (-2, -3) and (-1, -4)

Slope, m= (-4 + 3)/(-1 + 2)

m= -1

Hence, the slope is -1

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Answer:

h ≤ 70 I'm pretty sure I could be wrong

The correct inequality for the maximum height, h, of a fighter pilot is h ≤ 77.

Given that the height of the fighter pilot (h) must be less than or equal to 77 inches.

The symbol "≤" represents "less than or equal to," and 77 inches is the maximum allowable height for a fighter pilot.

The inequality h ≥ 77 would be incorrect since it states that the height of the fighter pilot should be greater than or equal to 77 inches, which would not be a maximum height requirement.

Similarly, the inequality h ≤ 70 would also be incorrect as it would imply a height limit of 70 inches, which is lower than the actual maximum height allowed.

Lastly, h ≥ 70 would not be suitable as it would permit heights greater than or equal to 70 inches, potentially exceeding the specified maximum height of 77 inches.

In conclusion, the correct inequality to represent the maximum height of a fighter pilot is h ≤ 77, ensuring that their height does not exceed 77 inches.

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