The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?

Answer:

Function: [tex]x+y=9[/tex]

Not Function: [tex]x^2+y^2=1[/tex]    and     [tex]x=y^2[/tex]

Step-by-step explanation:

Given

[tex]x+y=9[/tex]

[tex]x^2+y^2=1[/tex]

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

Required

Determine if [tex]y[/tex] is a function of [tex]x[/tex]

Solving x+y=9

[tex]x+y=9[/tex]

Make y the subject of formula

[tex]y = 9 - x[/tex]

Hence; y is a function of x

Solving [tex]x^2+y^2=1[/tex]

[tex]x^2+y^2=1[/tex]

Subtract x² from both sides

[tex]y^2=1 - x^2[/tex]

Square root of both sides

[tex]y =\± \sqrt{1 - x^2}[/tex]

This implies that

[tex]y =\sqrt{1 - x^2}[/tex]     or     [tex]y =-\sqrt{1 - x^2}[/tex]

Because [tex]y[/tex] can be any of those two expressions, it is not a function.

Solving [tex]x=y^2[/tex]

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

Reorder

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

Take square roots

[tex]y = \±\sqrt{x}[/tex]

This implies that

[tex]y = \sqrt{x}[/tex]      or        [tex]y = -\sqrt{x}[/tex]

Because [tex]y[/tex] can be any of those two expressions, it is not a function.

Answer:

54 lol not 40 its 20

Step-by-step explanation:

================================================

Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.

A function assigns the values. The only function that represents y as a function of x is D.

A function assigns the value of each element of one set to the other specific element of another set.

For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.

A.) x = y⁴

It represents x in terms of y, therefore, No.

B.) 6x² + y = 4

It represents constant in terms of x and y, therefore, No.

C.) 6x + y² = -1

It represents constant in terms of x and y, therefore, No.

D.) [tex]y = \sqrt{1-x^2}[/tex]

The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.

E.)  -2xy = 1

It represents constant in terms of x and y, therefore, No.

Hence, the only function that represents y as a function of x is D.\

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Answer:

250 meters/min = 15 km/hr

Step-by-step explanation:

The approximate number to divide from is 16.667. Divide the speed value by 16.667

Answer:

1500m

Step-by-step explanation:

If you ride 150 m every one min then you can ride 150 times 10 in 10 min.

150 times 10 = 1500m

Answer:

The total years of sleep = 25.05 years

Step-by-step explanation:

Given total time in minutes = 3.95 x 10^7

Now convert the total time in hours = (3.95 x 10^7) / 60 = 658333.333 hours

Now covert the total hours into the day. Since a day has 24 hours so divide the total hours by 24 = 658333.333 / 24 = 27430.5555 days.

A person sleeps 8 hours a day, so total hours of sleep = 8 × a number of days.

A person sleeps 8 hours a day, so total hours of sleep = 8 × 27430.5555 days.

Thus, total sleeping hours = 219444.444

Now convert it into a number of years.

Convert total hours into the day and then years.

Number of days = 219444.444 / 24 = 9143.5185 days.

Now covert the total days in to years = 9143.5185 / 365 = 25.05 years

The spreadsheet is missing, so i have attached it.

Answer:

Option A - $295

Step-by-step explanation:

From the spreadsheet, net pay = $2300 and interest earned on savings = $20

Therefore, her total income = $2300 + $20 = $2320

Now,from the spreadsheet, total expenses = 800 + 120 + 90 + 45 + 95 + 80 + 275 + 520 = $2025

Now, net cash flow = Total income - Total expenses

Net cash flow = $2320 - $2025

Net cash flow = $295

Answer:

a. 295

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. the slope is -7/2

2. the slope is 2/3

y = mx + b

m is the slope

Slope is the number before the x so

1. -7/2

2. 2/3

Answer:  348 in²

Step-by-step explanation:

Area of a circle is πr².  Area of a sector is the same formula but only for the section so you need to determine what fraction of the circle it is.  You do this by dividing by 360° if degrees are provided or by 2π if radians are given.

[tex]A=\pi r^2 \bigg(\dfrac{\theta}{360^o}\bigg)[/tex]

Given: r = 17

          Ф = 138°

[tex]A=\pi(17)^2\bigg(\dfrac{138^o}{360^o}\bigg)\\\\\\.\quad =289\pi \bigg(\dfrac{23}{60}\bigg)\\\\\\.\quad =\dfrac{6647\pi}{60}\pi\\\\\\.\quad =347.9\ in^2[/tex]

Answer:

-6 5/8 or -6.625

Step-by-step explanation:

31/8 - 84/8 = -53/8

-53/8 = -6 5/8 or -6.625

Answer:

9(x + 19)

Step-by-step explanation:

Product is a multiplication key word where you'll usually always put parenthesis when multiplying, and where the keyword sum comes you'd add x and 12 for your equation :)

Answer:4mph

5mph

Slower

Step-by-step explanation:

The average rate of change for the runner is 0.667 miles per hour².

To calculate the average rate of change, we follow the following formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.

In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.

So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.

Thus, we can calculate the average rate of change a, using the formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².

Therefore, the average rate of change for the runner is 0.667 miles per hour².

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Answer:

C = $5 + $1.5(w)

Step-by-step explanation:

Given the following information :

Total shipping cost :

One time fee + fee based on package weight

Given the table :

Weight in pounds - - - - Total shipping cost($)

___4__________________11

___8__________________17

___12_________________23

___16_________________29

We can deduce from the table

For a package that weighs (w) 4 pounds

Total shipping cost = $11

Let one time fee = f

Fee based on weight = r

f + 4(r) = 11 - - - - - (1)

For a package that weighs (w) 8 pounds

Total shipping cost = $17

One time fee = f

Fee based on weight = r

f + 8r = 17 - - - - - (2)

From (1)

f = 11 - 4r - - - (3)

Substitute f = 11 - 4r in (2)

11 - 4r + 8r = 17

-4r + 8r = 17 - 11

4r = 6

r = 6/4

r = 1.5

Put r = 1.5 in (3)

f = 11 - 4(1.5)

f = 11 - 6

f = 5

Hence one time fee = $5

Charge based on weight = $1.5

Hence, Total shipping cost 'C' for a package weighing 'w' will be :

C = $5 + $1.5(w)

Answer:

In bold below.

Step-by-step explanation:

The slope = coefficient of x = 2.

The y-intercept is when x = 0 and x-intercept is when y = 0.

y = 2(0) + 1 = 1  so the y -intercept is (0, 1).

2x + 1 = 0

x = -0.5 so the x-intercept is (-0.5, 0)

Answer:

3.4

Step-by-step explanation:

Answer:

[tex]a > \frac{22}{21}[/tex]

Step-by-step explanation:

Given the inequality function [tex]\frac{14a}{11}>\frac{4}{3}[/tex], to write the inequality in interval notation, we need to first get the solution to the inequality as shown;

[tex]\frac{14a}{11}>\frac{4}{3}\\cross\ multiply\\14a \times 3 > 11 \times 4\\42a >44\\divide \ both \ sides \ by \ 42\\\frac{42a}{42} > \frac{44}{42}\\ a>\frac{22}{21}[/tex]

Hence the expression in interval notation is [tex]a > \frac{22}{21}[/tex]

Answer:

7-3j

Step-by-step explanation:

Answer:

7 - 3j

Step-by-step explanation:

5(2-j) + (2j-3)

Open the brackets. Take note of the signs.

10-5j + 2j-3

Rearrange.

10 - 3 -5 j + 2j

= 7 - 3j

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Answer:

65 i think

Step-by-step explanation:

Answer:

65 Im preety sure

Step-by-step explanation:

The answer for this question I don’t think could be answered by anyone but yourself. To help you figure this out, just simply think about all of the math courses you’ve had previous to your current course and think about which course you did best in.

Answer:

0.1069062

Step-by-step explanation:

divide the mass value by 32000

hope this helps.

Answer:

B.28

Step-by-step explanation:

Answer:

Try 57/125

Step-by-step explanation:

Step 1: 0.456 = 456⁄1000

Step 2: Simplify 456⁄1000 = 57⁄125

Answer:

Step 1: 0.456 = 456⁄1000

Step 2: Simplify 456⁄1000 = 57⁄125

Hope this helps! （づ￣3￣）づ╭❤～

Answer:

Perpendicular bisector for the given segment AB is shown below.

Step-by-step explanation:

Construction steps for the perpendicular bisector for the given segment AB are:

1. Open your compass more than half of the distance between end points of the given segment, i.e., A and B.

2. Place the compass on point A and mark two arc on each side of line segment AB.

3. Place the compass on point B and mark two arc on each side of line segment AB, which intersect the previous arcs.

4. Arcs meet at two points. Mark them C and D.

5. Draw the line between C and D.

The perpendicular bisector for the given segment AB is shown below.

Answer:

A

Step-by-step explanation:a

Answer:

$21

Step-by-step explanation:

Provided total value = $50

$50 = 5,000 cents.

We are provided,

10 cent coins value = 30%  of total value

= 0.3 [tex]\times[/tex] 5,000 cents = 1,500 cents

Value of 20 cents coin = 28% of total value

= 0.28 [tex]\times[/tex] 5,000 cents = 1,400 cents

Therefore, remaining value of cents = Total value of 50 cents coins

5,000 cents - value of 10-cent coins - value of 20-cent coins = total value of 50 cents coins

5,000 - 1,500 - 1,400 = 2,100 cents = $21

Which means number of 50 cents coin = [tex]\frac{2,100}{50} = 42\ coins[/tex]

Alternatively,

To calculate value of 50 cent coins

Total value = 100%

Value in 10-cent coins + 20-cent coins = 30% + 28% = 58%

Value in 50-cent coins = 100 - 58 = 42%

= $50 [tex]\times[/tex] 42% = $21

Answer:

angle AEF is 60 degrees

Step-by-step explanation:

120 - 90 = 30

90 - 30 = 60

Answer:

C.  [tex]\sqrt{17}[/tex]

Step-by-step explanation:

use pythagorean

= [tex]\sqrt{1^2 + 4^2}[/tex]

= [tex]\sqrt{17}[/tex]

therefore, the answer is C. [tex]\sqrt{17}[/tex]

Answer:

C. √17

Step-by-step explanation:

point P to line m

= √(1² + 4²

= √17

Answer:

36

Step-by-step explanation:

PQ + QR = PR

substituting the values we have:

8 + 7x = 9x

8 + 7x - 7x = 9x - 7x

8 = 2x

8/2 = 2x/2

4 = x

Now, for the value of PR:

9 x 4

36

Answer:

The two numbers are 35 and 73.

Step-by-step explanation:

We can solve this problem by creating two simultaneous equations using the information given.

Let number 1 = x

Let number 2 = y

x = y - 38 -> ( 1 )

x + y = 108 -> ( 2 )

We can solve simultaneous equations using substitution or elimination. For this question, we will use substitution as it is the easier and shorter option.

Substitute ( 1 ) into ( 2 ):

x + y = 108 -> ( 2 )

( y - 38 ) + y = 108

2y - 38 = 108

2y = 146

y = 146 / 2

y = 73 -> ( 3 )

Substitute ( 3 ) into ( 1 ):

x = y - 38 -> ( 1 )

x = ( 73 ) - 38

x = 35

Therefore:

x = 35 , y = 73