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3 years ago

Complete these ordered pairs for this equation. (0, ), (2, ), ( ,3)3x-2y=6

1 answer:

6 0

3x-2y=6
3(0)-2y=6
0-2y=6
-2y=6
-2y÷-2=6÷-2
y=-3
First one: (0, -3)
3x-2y=6
3(2)-2y=6
6-2y=6
6-6-2y=6-6
-2y=0
-2y÷-2=0÷-2
y=0
Second one: (2,0)
3x-2y=6
3x-2(3)=6
3x-6=6
3x-6+6=6+6
3x=12
3x÷3=12÷3
x=4
Third one: (4,3)

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Complete the definition.

Sati [7]

Answer:

A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function. Functions can be written as ordered pairs, tables, or graphs. The set of input values is called the domain, and the set of output values is called the range.

Step-by-step explanation:

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2 years ago

9. A box of cereal is packaged and sold at a local

emmasim [6.3K]

Answer:

288 Cubic Inches

Step-by-step explanation:

Assuming the cereal takes up 80% of the total volume of the box, you would take 80% of the total volume.

First, do Base x Width x Height for the volume of the box.

10 inches x 3 inches x 1 foot (1 foot is 12 inches)

10 x 3 x 12 = 360

Now, take 80% of 360 cubic inches.

80% is 0.8 times a number

0.8 x 360 = 288

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2 years ago

Is a positive integer raised to a negative power always positive

Evgesh-ka [11]

Answer:

Yes

Step-by-step explanation:

Many students gets confused with these exponential problems, they often get misguided but understand that there is nothing to be confused of.

When you have a negative number, you just take the reciprocal of the whole exponent number.

What is a reciprocal?

Let's take an integer for example, let's take the number 3.

The reciprocal for 3 is (1/3)

Let's take an other number, let's take 2/3

The reciprocal for 2/3 is (3/2)

In conclusion, we just reverse the denominator and the numerator or just switch it.

We take 3 as (3/1) and that is the reason, the reciprocal would be (1/3)

Now, coming to the negative integers. Taking an example:

(2)⁻¹

This would be become (1/2¹) = (1/2)

Hence, the result of a negative integer is positive but would be a fraction.

Hope I helped!

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3 years ago

Expanded form for 67.943

ratelena [41]

67.943

= 60.000 + 7.000 + 0.900 + 0.040 + 0.003

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3 years ago

Can someone please help me on number 16-ABC

melomori [17]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

-2x < 10

-6 < -2x

<u>Part a) Is x = 0 a solution to both inequalities</u>

FOR -2x < 10

substituting x = 0 in -2x < 10

-2x < 10

-3(0) < 10

0 < 10

TRUE!

Thus, x = 0 satisfies the inequality -2x < 10.

∴ x = 0 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 0 in -6 < -2x

-6 < -2x

-6 < -2(0)

-6 < 0

TRUE!

Thus, x = 0 satisfies the inequality -6 < -2x

∴ x = 0 is the solution to the inequality -6 < -2x

Conclusion:

x = 0 is a solution to both inequalites.

<u>Part b) Is x = 4 a solution to both inequalities</u>

FOR -2x < 10

substituting x = 4 in -2x < 10

-2x < 10

-3(4) < 10

-12 < 10

TRUE!

Thus, x = 4 satisfies the inequality -2x < 10.

∴ x = 4 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 4 in -6 < -2x

-6 < -2x

-6 < -2(4)

-6 < -8

FALSE!

Thus, x = 4 does not satisfiy the inequality -6 < -2x

∴ x = 4 is the NOT a solution to the inequality -6 < -2x.

Conclusion:

x = 4 is NOT a solution to both inequalites.

Part c) Find another value of x that is a solution to both inequalities.

<u>solving -2x < 10</u>

$-2x\:$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)>10\left(-1\right)$

Simplify

$2x>-10$

Divide both sides by 2

$\frac{2x}{2}>\frac{-10}{2}$

$x>-5$

$-2x-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}$

<u>solving -6 < -2x</u>

-6 < -2x

switch sides

$-2x>-6$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)$

Simplify

$2x$

Divide both sides by 2

$\frac{2x}{2}$

$x$

$-6$

Thus, the two intervals:

$\left(-\infty \:,\:3\right)$

$\left(-5,\:\infty \:\right)$

The intersection of these two intervals would be the solution to both inequalities.

$\left(-\infty \:,\:3\right)$ and $\left(-5,\:\infty \:\right)$

As x = 1 is included in both intervals.

so x = 1 would be another solution common to both inequalities.

<h3>SUBSTITUTING x = 1</h3>

FOR -2x < 10

substituting x = 1 in -2x < 10

-2x < 10

-3(1) < 10

-3 < 10

TRUE!

Thus, x = 1 satisfies the inequality -2x < 10.

∴ x = 1 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 1 in -6 < -2x

-6 < -2x

-6 < -2(1)

-6 < -2

TRUE!

Thus, x = 1 satisfies the inequality -6 < -2x

∴ x = 1 is the solution to the inequality -6 < -2x.

Conclusion:

x = 1 is a solution common to both inequalites.

7 0

3 years ago