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2 years ago

Which is the graph of the linear equality 2x-3y<12

Mathematics

1 answer:

WINSTONCH [101]2 years ago

7 0

Answer:

The graph below shows the answer to

2x - 3y < 12

Also shown as

-3y < -2x + 12

Step-by-step explanation:

You can rearrange the inequality by subtracting 2x from both sides to isolate the y.

You now have -3y < 12 -2x

which can be put into the standard linear equation form of

-3y < -2x + 12

Then you divide both sides by -3 to get singular value of y, which is something like

-3/-3y < -2/-3x + 12/-3

which is

y > 2/3x -4

Note: I switched direction of the inequality because you are dividing both sides by a negative value.

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A perfect square is the square of an integer. Of the integers from 2 through 99, how many have at least one perfect square facto

N76 [4]

Answer:

Six numbers have perfect square factors

Step-by-step explanation:

The numbers with perfect square factors are those numbers that have perfect squares as one of the numbers that can divide them.

They include:

4 = 2 * 2

16 = 4 * 4

36 = 6 * 6

49 = 7 * 7

64 = 8 * 8

81 = 9* 9

These numbers above have perfect square factors because they are formed from integers that multiply themselves.

8 0

2 years ago

EPCIUCNO

cluponka [151]

Answer:

1 ⇒ D

2 ⇒ H

3 ⇒ B

4 ⇒ G

5 ⇒ A

6 ⇒ F

7 ⇒ E

8 ⇒ C

Step-by-step explanation:

* Lets explain how to solve the problem

- The left column has expressions and the right column has the

equivalent expressions

- We must find the equivalent letter for each number

# 7(12)

∵ 12 can be a sum of two numbers

∴ The equivalent expression to 7(12) is 7(8 + 4)

∴ 1 ⇒ D

# 3(15)

∵ 3 can be a sum of two numbers

∴ The equivalent expression to 3(15) is (2 + 1)(15)

∴ 2 ⇒ H

# 3a + 9

∵ 3 and 9 have a common factor 3

∵ 3a + 9 ⇒ divide them by 3

∵ 3a ÷ 3 = a and 9 ÷ 3 = 3

∴ 3a + 9 = 3(a + 3)

∴ The equivalent expression to 3a + 9 is 3(a + 3)

∴ 3 ⇒ B

# 9a + 3

∵ 9 and 3 have a common factor 3

∵ 9a + 3 ⇒ divide them by 3

∵ 9a ÷ 3 = 3a and 3 ÷ 3 = 1

∴ 9a + 3 = 3(3a + 1)

∴ The equivalent expression to 9a + 3 is 3(3a + 1)

∴ 4 ⇒ G

# 5 + 15a

∵ 5 and 15 have a common factor 5

∵ 5 + 15a ⇒ divide them by 5

∵ 5 ÷ 5 = 1 and 15a ÷ 5 = 3a

∴ 5 + 15a = 5(1 + 3a)

∴ The equivalent expression to 5 + 15a is 5(1 + 3a)

∴ 5 ⇒ A

# 10 + 5a

∵ 10 and 5 have a common factor 5

∵ 10 + 5a ⇒ divide them by 5

∵ 10 ÷ 5 = 2 and 5a ÷ 5 = a

∴ 10 + 5a = 5(2 + aa)

∴ The equivalent expression to 10 + 5a is 5(2 + a)

∴ 6 ⇒ F

# 3x + 6y + 9z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 6y ÷ 3 = 2y

∵ 9z ÷ 3 = 3z

∴ 3x + 6y + 9z = 3(x + 2y + 3z)

∴ The equivalent expression to 3x + 6y + 9z is 3(x + 2y + 3z)

∴ 7 ⇒ E

# 3x + 3y + 3z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 3y ÷ 3 = y

∵ 3z ÷ 3 = z

∴ 3x + 3y + 3z = 3(x + y + z)

∴ The equivalent expression to 3x + 3y + 3z is 3(x + y + z)

∴ 8 ⇒ C

4 0

2 years ago

The length of a rectangle is 59 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the

melamori03 [73]

The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width

Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!

5 0

3 years ago

Which of the following is not an example of like terms?

Viktor [21]

Answer:

A. 2 and-6

Step-by-step explanation:

Like terms are terms that contain the same variables raised to the same powers. In other words, they have the same variables with the same exponents.

So in option A, we have the terms 2 and -6. These terms are not like terms because they do not have the same variables.

4 0

1 year ago

Read 2 more answers