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LUCKY_DIMON [66]

3 years ago

10

Graph the system of linear inequalities, please explain the process in solving this problem so I know how to do ones similar to

this!

1 answer:

Ierofanga [76]3 years ago

4 0

Graph the system of linear inequalities

x + y > 5

- x - y < -5

First we graph x + y >5

Step 1: replace > symbol by = sign

x + y =5

step 2 : Solve the equation for y

x + y =5 (subtract x from both sides)

y = 5 - x

step 3: Now we make a table . plug in some number for x and find out y

x -----> y

-1 -----> 6 ( y=5-x => y=5-(-1)= 6)

0 -----> 5 ( y=5-x => y=5-(0)= 5)

1 -----> 4 ( y=5-x => y=5-(1)= 4)

Step 4: we graph the table.

step 5: Shade the region that satisfies our inequality

x + y > 5. Greater than symbol implies that we shade the graph to the right

Graphing second inequality - x - y < -5

All terms have negative sign . so divide all the terms by -1. When we divide an inequality by -1 its sign changes

- x - y < -5 becomes x + y > 5

Follow the same steps to graph this inequality

After dividing the second equation by -1 , we got the same as the first equation.

So we will get the same graph

Both graphs overlaps

The graph of first and second inequality overlaps

The graph is attached below

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miv72 [106K]

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12: 1, 2, 3, 4, 6, 12
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12: 3 * 4
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Sides: 3, 4, and 5

Then multiply to get the volume:

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The graph shows the speed of Sam’s car over time. A graph titled Speed of Car. The horizontal axis shows time (hours) and the ve

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3 0

3 years ago

Read 2 more answers

Can someone help me with these and show the work also?

Snezhnost [94]

QUESTION:

Simplify each expression

ANSWER:

1.) $\green{{- 8n}}$

2.) $\green{{- 2b - 60}}$

3.) $\green{{- 10x - 14}}$

4.) for number 4 study my step-by-step explanation so you can answer that

STEP-BY-STEP EXPLANATION:

1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1

WHY?

Learn why:

Why is it considered that the coefficient is 1?

Remember that any term multiplied by $\blue{{1}}$ remains the same :

$\blue{{1}}$ ${× x = x}$

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of $\blue{{1}}$ and itself:

${x = }$ $\blue{{1}}$ ${× x}$

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

${x = 1x}$

This is why we can write the term without the coefficient as a term with coefficient ${1}$

Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1

${n - 9n}$

$\red{{1}}$ ${n -9n}$

Second, Collect like terms by subtracting their coefficients

$\red{{1n - 9n}}$

$\red{{( 1 - 9)n}}$

Third, Calculate the difference

how?

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger

$\red{{1 - 9}}$

$\red{{- (9 - 1)}}$

Subtract the numbers

- ( $\red{{9 - 1}}$ )n

- $\red{{8}}$ n

$\green{\boxed{- 8n}}$

2.) First, Distribute - 6 through the parentheses

how?

Multiply each term in the parentheses by - 6

$\red{{- 6(b + 10)}}$

$\red{{- 6b - 6 × 10}}$

Multiply the numbers

- ${6b}$ - $\red{{6 × 10}}$

- ${6b}$ - $\red{{60}}$

Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

$\red{{- 6b + 4b}}$

$\red{{(- 6 + 4)b}}$

Calculate the sum

$\red{{(- 6 + 4)}}$ b

$\red{{-2}}$ b

$\green{\boxed{- 2b - 60}}$

3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

$\red{{2(x - 5)}}$

$\red{{2x - 2 × 5}}$

Multiply the numbers

${2x -}$ $\red{{2 × 5}}$

${2x -}$ $\red{{10}}$

Second, Distribute - 4 through the parentheses

how?

Multiply each term in the parentheses by - 4

$\red{{- 4(3x + 1)}}$

$\red{{- 4 × 3x - 4}}$

Calculate the product

- $\red{{4 × 3}}$ x - 4

- $\red{{12}}$ x - 4

Third, Collect like terms

how?

Collect like terms by subtracting their coefficient

$\red{{2x - 12x}}$

$\red{{(2 - 12)x}}$

Calculate the difference

$\red{{(2 - 12)}}$ x

$\red{{- 10}}$ x

Fourth, Calculate the difference

how?

Factor out the negative sign from the expression

$\red{{- 10 - 4}}$

$\red{{- (10 + 4)}}$

Add the numbers

- ( $\red{{10 + 4}}$ )

- $\red{{14}}$

$\green{\boxed{- 10x - 14}}$

That's all I know sorry but I hope it helps :)

6 0

2 years ago

What is the cube root of 27a^l2?<br>-3a4<br>-3a<br> 3a<br> 3a*

GuDViN [60]

Answer:

$3a^4$

Step-by-step explanation:

What is the cube root of $27a^{12}$ ? This is the question.

We can write:

$\sqrt[3]{27a^{12}}$

We will use the below property to simplify:

$\sqrt[n]{a*b}=\sqrt[n]{a} \sqrt[n]{b}$

So, we have:

$\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}$

We will now use below property to further simplify:

$\sqrt[n]{x} =x^{\frac{1}{n}}$

Thus, we have:

$\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}$

We know power to the power rule: $(a^z)^b=a^{zb}$

Now, we have:

$3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4$

This is the correct answer: $3a^4$

4 0

3 years ago