6. Calcule os valores das funções

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Luden [163]

Answer:

x = -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Step-by-step explanation:

Step 1: Define equation

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Step 2: Solve for x

Distribute: 36 - 4.5x + 36 = 102 - 7.5x - 60
Combine like terms: -4.5x + 72 = -7.5x + 42
Add 7.5x on both sides: 3x + 72 = 42
Subtract 72 on both sides: 3x = -30
Divide 3 on both sides: x = -10

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24)
Simplify: 4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24)
Multiply: 4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24)
Add: 4.5(18) + 36 = 102 - 2.5(-6)
Multiply: 81 + 36 = 102 + 15
Add: 117 = 117

Here we see that 117 does indeed equal to 117.

∴ x = -10 is a solution of the equation.

7 0

2 years ago

Find the equation of the line that is perpendicular to the line

ddd [48]

Answer:

$y=-x+16$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)
Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

y=x-9

Rewrite the equation

y=1x-9

Now, we can identify clearly that the slope of the line is 1. The negative reciprocal of 1 is -1, so therefore, the slope of a perpendicular line would be -1. Plug this into $y=mx+b$ :

$y=-1x+b\\y=-x+b$