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

Mathematics

1 answer:

Luden [163]3 years ago

7 0

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.

You might be interested in

(Hurry fast I don’t have a lot of time pls) Tatiana wrote the steps that are commonly used to solve a system of equations with t

igor_vitrenko [27]

Answer:

1. Multiply the value of the first variable by one of the original equations to solve for the second variable.

2. Solve for one of the variables.

3. Substitute the value of the known variable into one of the original equations to solve for the unknown variable.

Step-by-step explanation:

3 0

3 years ago

Suppose that the useful life of a car battery, measured in months, decays with parameter 0.03 . We are interested in the life of

scZoUnD [109]

Answer:

a) X ~ $e(0.03)$

b) μ = 100/3

c) $\sigma = 100/3$

d) A battery is expected to last 100/3 months (33 months and 10 days approximately).

e) For seven batteries, i would expect them to last 700/3 months (approximately 19 years, 5 months and 10 days).

Step-by-step explanation:

a) The life of a battery is usually modeled with an exponential distribution X ~ $e(0.03)$

b) The mean of X is μ = 1/0.03 = 100/3

c) The standard deviation is $\sigma = 1/0.03 = 100/3$

d) The expected value of the bateery life is equal to its mean, hence it is 100/3 months.

e) The expected value of 7 (independent) batteries is the sum of the expected values of each one, hence it is 7*100/3 = 700/3 months.

4 0

3 years ago

A Ladder that is 32 ft long leans against a building. The angle of elevation of the ladder is 70 degrees. To the nearest tenth o

kolezko [41]

See the picture attached to better understand the problem

we know that
in the right triangle ABC
sin 70°=opposite side angle 70°/hypotenuse

in this problem
opposite side angle 70°=AB
hypotenuse=AC----> 32 ft
sin 70°=AB/32------> AB=32*sin 70°-----> AB=30.07 ----> AB=30.1 ft