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3 years ago

List the perfect squares between 100 and 500 that are even numbers.

1 answer:

7 0

The perfect squares between 100 and 500 are:

100 (10²)

121 (11²)

144 (12²)

169 (13²)

196 (14²)

225 (15²)

256 (16²)

289 (17²)

324 (18²)

361 (19²)

400 (20²)

441 (21²)

and

484 (22²) .

The squares of odd numbers are odd.
The squares of even numbers are even.

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Paul left for school at 7:25 AM. He returned home at 3:15 PM. How long was Paul away from home?

Nikitich [7]

7.25 until 8.00 = 35 minutes

8.00 until 3.00 PM = 7 hours

3.00 until 3.15 = 15 minutes

Answer is 7 hours 50 minutes

7 0

3 years ago

Which table shows y as DIRECTLY PROPORTIONAL to x

Furkat [3]

Answer:

Table B

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Verify table B

For $x=1, y=1/2$ -----> $k=y/x=(1/2)/1=1/2$

For $x=2, y=1$ -----> $k=y/x=1/2$

For $x=3, y=3/2$ -----> $k=y/x=(3/2)/3=1/2$

For $x=4, y=2$ -----> $k=y/x=2/4=1/2$

The values of k are the same

therefore

The table B shows y as DIRECTLY PROPORTIONAL to x

Verify table D

For $x=1, y=3$ -----> $k=y/x=3/1=3$

For $x=2, y=5$ -----> $k=y/x=5/2=2.5$

For $x=3, y=7$ -----> $k=y/x=7/3$

For $x=4, y=9$ -----> $k=y/x=9/4$

the values of k are different

therefore

The table D not shows y as DIRECTLY PROPORTIONAL to x

5 0

3 years ago

Linear functions can be used to find the price of a building based on its floor area below are two of these functions,

Alborosie

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) see the explanation

Step-by-step explanation:

The complete question in the attached figure

Part A) Find and compare the slopes

we have

Function 1

$y=40x+15,000$

This is a linear equation in slope intercept form

$y=mx+b$

where

y is the price of the building in thousands

x is the floor area in square foot

m is the slope

b is the y-intercept

we have

$m=\$40\ per\ ft^2$

Function 2

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take two points from the data in the table

(400,32,000) and (700,56,000)

Remember that the price in the table is in thousands

substitute

$m=\frac{56,000-32,000}{700-400}$

$m=\$80\ per\ ft^2$

The slope of the Function 2 is greater than the slope of the Function 1

The slope of the Function 2 is two times the slope of the Function 1

Part B) Find and compare the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

Function 1

$y=40x+15,000$

For x=0

$y=40(0)+15,000=\$15,000$

Function 2

Find the equation in point slope form

$y-y1=m(x-x1)$

we have

$m=80\\point\ (400,32,000)$

substitute

$y-32,000=80(x-400)$

Convert to slope intercept form

isolate the variable y

$y-32,000=80x-32,000\\y=80x$

For x=0

$y=80(0)=0$

The y-intercept of the function 1 is $15,000 and the y-intercept of the function 2 is zero (the line passes through the origin)

Part C) Describe each function as proportional or non proportion

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Function 1

$y=40x+15,000$ -----> is a non proportional linear function (because the line has a y-intercept)

Function 2

$y=80x$ ----> is a proportional linear equation (the line passes through the origin)

7 0

3 years ago

F(x) = 3x2+ 6x - 18 find f (10)

sesenic [268]

Answer:

f(10) = 342

Step-by-step explanation:

f(x) = 3x² + 6x - 18

f(10 = 3(10)² + 6(10) - 18

f(10) = 3(100) + 60 - 18

f(10) = 300 + 60 - 18

f(10) = 360 - 18

f(10) = 342

8 0

3 years ago

12 is 60% of what number?

goldenfox [79]

Answer: 20

Step-by-step explanation:

12 is 60% of what number

12 = 0.60 * n

20 = n

8 0

3 years ago