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2 years ago

Solve the following eqation for x: 6(4x+5)+3=3(x+8)+3. Round to the nearest hundredth

Mathematics

2 answers:

bezimeni [28]2 years ago

8 0

<h2>Steps</h2><h3>Equation: 6(4x + 5) + 3 = 3(x + 8) + 3</h3>

Subtract 3 from both sides

6(4x + 5) + 3 - 3 = 3( x + 8) + 3 - 3

Simplify

6( 4x + 5) = 3(x + 8)

<h3>Apply the distributive law:</h3>

6(4x + 5)

a(b + c) = ab + ac

a = 6, b = 4x, c = 5

= 6 x 4x + 6 x 5

<h3>Simplify</h3>

6 x 4x + 6 x 5

Multiply the numbers: 6 x 4 = 24

= 24x + 6 x 5

Multiply the numbers: 6 x 5 = 30

= 24x + 30

<h3>Apply the distributive law:</h3>

3(x + 8)

a(b + c) = ab + ac

a = 3, b = x, c = 8

= 3x + 3 x 8

Multiply the numbers: 3 x 8 = 24

= 3x + 24

24x + 30 = 3x + 24

Subtract 30 from both sides

24x + 30 - 30 = 3x + 24 -30

Simplify

24x = 3x - 6

Subtract 3x from both sides

24x - 3x = 3x - 6 - 3x

Simplify

21x = -6

Divide both sides by 21

21x/21 = -6/21

Note: Simplify -6/21 to get the value for x.

Answer in fraction: x = -2/7

Answer in decimal rounded to the nearest hundredth: x = -0.29

I know this seems complicated; that's why I did it step by step.

netineya [11]2 years ago

7 0

24x + 33 = 3x + 27

21x + 33 = 27

21x = -6

X = -.29

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Arturiano [62]

The Pythagorean theorem is one that can be used to determine the third unknown side of a given right-angled triangle. Thus the answers required are:

A pair of similar triangles formed are ΔABD and ΔADC
Segment AD is a perpendicular bisector of segment BC, and also bisects angle A in two equal measures
Segment AD = 3

A right-angled triangle is one which has the measure of one of its internal angles equal to $90^{o}$ . Thus to determine the value of one of its unknown sides, the Pythagoras theorem can be used.

Pythagora theorem states that: for a right-angled triangle,

$/Hypotenus/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

Thus from the given question, we have;

Part A: A pair of similar triangles formed are ΔABD and ΔADC.

Part B: In the given triangle, segment AD is a perpendicular bisector of segment BC. Thus segment AD also bisects angle A in two equal measures. So triangle ABC is now divided into two equal pairs i.e ΔABD and ΔADC.

Part C: Given that: If DB = 9 and DC = 4, find the length of segment DA.

Let segment AD be represented by x, so that;

from ΔABC,

$/Hypotenus/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

$/13/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

Thus the appropriate Pythagorean triple for this question is 5, 12, 13.

So that AB = 12, AC = 5 and BC = 13

Let segment AD be represented by x.

Thus from triangle ADC, applying the Pythagoras theorem we have;

$5^{2}$ = $x^{2}$ + $4^{2}$

25 - 16 = $x^{2}$

$x^{2}$ = 9

x = 3

Therefore, segment AD is 3.

For more clarifications on Pythagoras theorem, visit: brainly.com/question/343682

#SPJ1

Kindly contact a 1-on-1 tutor if more explanations are needed.

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