All categories

3 years ago

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

The scale of a map is 1:4 000 000. Hint: 1:4 000 000 means that 1cm on the map = 4 000 000 on the ground. The distance between L

GrogVix [38]

Answer:

325 km

Step-by-step explanation:

Given the scale :

1 : 4 ,000, 000

1cm measure in map = 4000000 on the ground

From the map :

Distance between Leeds and London = 8.125 cm

The actual distance on ground can be calculated thus :

1cm = 4,000,000

8.125cm = x

Cross multiply

x = 32500000 cm

Converting to kilometers :

1 km = 100,000 cm

x = 32500000

Cross multiply

100,000x = 32500000

x = 32500000 / 100000

x = 325

Hence, actual distance between Leeds and London is 325 km

3 0

3 years ago

To complete this component you will need to insert parentheses in Expression 2 to change the order of operations so the expressi

Alika [10]

Given:

The expression is $5+4\times 2+6-2\times 2-1$ .

To find:

The position of parentheses inserted in the expression to get the value 19

Step-by-step explanation:

We have,

$5+4\times 2+6-2\times 2-1$

Now,

$(5+4)\times 2+6-2\times 2-1=9\times 2+6-4-1$

$(5+4)\times 2+6-2\times 2-1=18+6-5$

$(5+4)\times 2+6-2\times 2-1=18+1$

$(5+4)\times 2+6-2\times 2-1=19$

There are more ways to apply the parenthesis, but we do not get 19.

$5+4*\left(2+6\right)-2*2-1=32\neq 19$

$5+4*2+\left(6-2\right)*2-1=20\neq 19$

$5+4*2+6-2*\left(2-1\right)=17\neq 19$

And many more possibilities.

Therefore, the expression after inserting the parentheses is $(5+4)\times 2+6-2\times 2-1$ .

6 0

3 years ago

How to solve (2^3)^4

miv72 [106K]

Answer: 2^12

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the error in the flow chart

sweet-ann [11.9K]

there is no flow chart

7 0

3 years ago

Read 2 more answers

SO CONFUSED PLEASE SOMEONE EXPLAIN! DUE SOON AND NEED HELP!!!!!!!! QUESTION IN PICTURE BELOW

jeka57 [31]

Answer:

=> Apply law of cosine

$c^2=a^2+b^2-2abcos\left(C\right)$

=> input value

$z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)$

=> simplify

$z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}$

=> calulcation

$z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}$

=> apply rule: Distance must be greater than 0

which is about 14.51828

4 0

2 years ago