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3 years ago

(2x+1)/2=(x+2)/5if possible can you show me step by step how to get the answer

Mathematics

1 answer:

katrin2010 [14]3 years ago

8 0

Answer:

$\boxed{\bold{Decimal \ Form: \ x \ = \ -0.125}}$

$\boxed{\bold{Fraction \ Form:x=-\frac{1}{8}}}$

Step By Step Explanation:

Apply Fraction Cross Multiply: If $\bold{\frac{a}{b}=\frac{c}{d}:then\ a\cdot \:d=b\cdot \:c}$

$\bold{\left(2x+1\right)\cdot \:5=2\left(x+2\right)}$

$\bold{\left(2x+1\right)\cdot \:5: \ 10x+5}$

$\bold{2\left(x+2\right): \ 2x+4}$

$\bold{10x+5=2x+4}$

Subtract 4 From Both Sides

$\bold{10x+5-5=2x+4-5}$

Simplify

$\bold{10x=2x-1}$

Subtract 2x From Both Sides

$\bold{10x-2x=2x-1-2x}$

Simplify

$\bold{8x=-1}$

Divide Both Sides By 8

$\bold{\frac{8x}{8}=\frac{-1}{8}}$

Simplify

$\bold{x=-\frac{1}{8}}$

Turn Fraction Into Decimal

$\bold{-1 \ \div \ 8 \ = \ -0.125}$

$\bold{-0.125}$

Regards,

Mordancy

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PLEASE WILL GIVE 50 POINTS PLEASE ANSWER

leva [86]

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Given:

$\sf \tan(A)=\dfrac{60}{45}$

Therefore:

side opposite angle A = BC = 60
side adjacent angle A = AC = 45

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

$a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

$\implies\sf \tan(A)=\dfrac{60}{45}$

$\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)$

$\implies\sf A=53^{\circ}\:(nearest\:degree)$

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

4 0

2 years ago

The length of one side of a square is 3n+2. The perimeter of the square is 4(3n+2). Which expression is equivalent to the perime

deff fn [24]

Answer:

4(3n + 2)

Step-by-step explanation:

as we know perimeter of a square is 4 x side

one side is 3n + 2

4 sides = 4(3n +2)

8 0

3 years ago

The length of a rectangle is 6 in longer than its width.if the perimeter of the rectangle is 68in find the length and width ?

wel

The length and the width of the rectangle are 20 and 14 inches respectively

<h3>How to find the length and width?</h3>

The given parameters are:

Length = 6 + Width

Perimeter = 68 inches

The perimeter of a rectangle is calculated as:

Perimeter = 2 * (Length + Width)

So, we have:

2 * (Length + Width) = 68

Divide both sides by 2

Length + Width = 34

Substitute Length = 6 + Width in Length + Width = 34

6 + Width + Width = 34

Evaluate the like terms

2 * Width = 28

Divide both sides by 2

Width = 14

Substitute Width = 14 in Length = 6 + Width

Length = 6 + 14

Evaluate

Length = 20

Hence, the length and the width of the rectangle are 20 and 14 inches respectively

(2x+1)/2=(x+2)/5if possible can you show me step by step how to get the answer ​

(2x+1)/2=(x+2)/5if possible can you show me step by step how to get the answer