Solve the inequality and graph the solution a b c or d

10. Damarion is finding measurements from the triangular prism shown.

Rzqust [24]

Answer:

The answer is "32 and 48"

Step-by-step explanation:

Please find the graph file in the attached file.

The perimeter is= sum of sides

$= 10+10+12 \\\\ =32 \ units\\\\$

Calculating the Area of base $= \frac{1}{2} \times base \times height$

$= \frac{1}{2} \times 12 \times 8\\\\= \frac{1}{2} \times 96\\\\=48 \ units^2$

3 0

3 years ago

Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work. 20 Points!!

alexira [117]

|4x + 3| = 9 + 2x

Since the variable is on both sides of the equation, you would, at the end, check for extraneous solutions.

Extraneous solutions are solutions that do not work with the equation, therefore they are "extra" solutions and un-included in your final answer.

Start the problem by splitting the equation into two equations, a positive case and a negative case. Your two equations would look like:

4x + 3 = 9 + 2x {positive case}
4x + 3 = -(9 + 2x) {negative case}

<h2><u>---Solving the equations---</u></h2><h3>[POSITIVE CASE]</h3>

Let's solve for the positive case first. Start by subtracting 3 from both sides of the equation.

4x + 3 = 9 + 2x becomes 4x = 6 + 2x

Now subtract 2x from both sides of the equation.

4x = 6 + 2x becomes 2x = 6

Finish off the problem by dividing both sides by 2 to isolate the variable x.

2x = 6 becomes x = 3.

<h2>---</h2><h3>[NEGATIVE CASE]</h3>

Now let's solve for x in the negative case. Start by distributing the negative sign (-) inside the parentheses.

4x + 3 = -(9 + 2x) becomes 4x + 3 = -9 - 2x

Subtract 3 from both sides just like the positive case.

4x + 3 = -9 - 2x becomes 4x = -12 - 2x

Now add 2x to both sides of the equation.

4x = -12 - 2x becomes 6x = -12

Finish off the problem by dividing both sides by 6 to isolate the variable x.

6x = -12 becomes x = -2.

<h2><u>---Checking for extraneous solutions---</u></h2><h3>[CHECKING X = 3]</h3>

To check for extraneous solutions, or solutions that do not work, substitute what you got for x back into the original absolute value equation: |4x + 3| = 9 + 2x. Substitute 3 and -2 into the equation. Let's start by substituting 3 for x.

|4x + 3| = 9 + 2x becomes |4(3) + 3| = 9 + 2(3)

Start by multiplying 4 and 3 together inside the absolute value symbols.

|4(3) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + 2(3)

Now multiply 2 and 3 together.

|(12) + 3| = 9 + 2(3) becomes |(12) + 3| = 9 + (6)

Add 12 and 3 together inside the absolute value symbols; also add 9 and 6 together.

|(12) + 3| = 9 + (6) becomes |(15)| = (15), which is the same as 15 = 15.

15 = 15 is a true statement so this means that 3 is a solution to the absolute value equation, so it is not an extraneous solution.

<h2>---</h2><h3>[CHECKING X = -2]</h3>

Let's see if -2 is a solution or not - substitute -2 for x into the equation: |4x + 3| = 9 + 2x.

|4x + 3| = 9 + 2x becomes |4(-2) + 3| = 9 + 2(-2)

Multiply 4 and -2 inside the absolute value symbols.

|4(-2) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + 2(-2)

Multiply 2 and -2.

|(-8) + 3| = 9 + 2(-2) becomes |(-8) + 3| = 9 + (-4)

Add -8 and 3 inside the absolute value symbols; also add 9 and -4.

|(-8) + 3| = 9 + (-4) becomes |(-5)| = (5), which is the same as 5 = 5.

5 = 5 is a true statement so that means it is not an extraneous solution. After checking for extraneous solutions, we have come to the conclusion that the two answers for the equation --> I4x + 3I = 9 + 2x <-- are <u>x = 3 or x = 2</u>.

8 0

4 years ago

Write an equation:Three sisters went shopping for Mother’s Day. Each sister bought a gift for their mom. Maggie spent 3 times as

masya89 [10]

Answer:

Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution

When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions

Step-by-step explanation:

* Lets read the problem and solve it

- There are three sisters ⇒ Maggie , Karen , Jasmine

- Each sister bought a gift for their mom

- Maggie spent 3 times as much as Karen

- Karen spent half as much as Jasmine

- Altogether, they spent $60

- Let Jasmine spent x

∵ Karen spent half as much as Jasmine

∴ Karen spent 1/2 x

∵ Maggie spent 3 times as much as Karen

∴ Maggie spent 3 × 1/2 x = 3/2 x

∵ Altogether, they spent $60

∴ x + 1/2 x + 3/2 x = 60

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

* Lets find the share of each one

∵ Jasmine spent x

∴ Jasmine spent $20

∵ Karen spent 1/2 x

∴ Karen spent 1/2 × 20 = $10

∵ Maggie spent 3/2 x

∴ Maggie spent 3/2 x 20 = $30

* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

* Lets describe what happens when an equation has no solution

- "No solution" means that there are no values of x satisfy the equation

- When x disappears from the equation and the two sides of the

equation not equal each other , then the equation has no solution

- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x

∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms

∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides

∴ 4 = 5 ⇒ the two sides not equal

∴ There is no value of x satisfy this equation

∴ There is no solution

* Lets describe what happens when an equation has infinite solutions

- "Infinite solutions" means all numbers are solutions.

- When x disappears from the equation and the two sides of the

equation equal each other , then the equation has infinite solutions

- Ex: solve the equation 2x + 3 = x + x + 3

∵ 2x + 3 = x + x + 3 ⇒ add the like terms

∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides

∴ 3 = 3 ⇒ the two sides are equal

∴ All values of x satisfy the equation

∴ There are infinite solutions

3 0

4 years ago

An object falls d meters in t seconds. what is the independent variable

mylen [45]

The independent variable would be “d meters” because the amount of time depends “dependent variable” on the height of the fall

3 0

4 years ago

Find the center!! PLEASE HELP

BartSMP [9]

D i think it’s right

7 0

3 years ago