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2 years ago

Find the angle between the lines 2x-3y+5=0 and 2x-3y-7=0

Mathematics

1 answer:

maria [59]2 years ago

7 0

There will be no angle between the lines as the lines are parallel.

We are given the two lines:

2 x - 3 y + 5 = 0 and 2 x - 3 y - 7 = 0

Slope of the line 2 x - 3 y + 5 = 0:

-a₁/b₁ = -2/-3 = 2/3

Slope of the line 2 x - 3 y - 7 = 0

-a₂/b₂ = -2 / -3 = 2/3

Since both the lines have same slopes, they are parallel lines and will not intersect each other.

So, there will be no angle between the lines.

Learn more about parallel lines here:

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In 6 years, Mariya will be as old as Vikram is now. In 2 years, Vikram will be three times older than Mariya. Find their ages no

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Answer:

Mariya is 1 year old

Vikram is 7 years old

Step-by-step explanation:

Here, we want to know the present ages of Mariya and Vikram.

Let the present age of Mariya be M and the present age of Vikram be V

From the question, we are told that in 6 years time, Mariya will be as old as Vikram is now

Thus, mathematically;

M + 6 = V ••••••(i)

Furthermore , in 2 years time Vikram will be 3 time older than Mariya

Mathematically;

( V + 2) = 3( M + 2)

V + 2 = 3M + 6

V = 3M + 6-2

V = 3M + 4 •••••••(ii)

So let’s equate the V

3m + 4 = m + 6

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But V = m + 6

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3 years ago

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Step-by-step explanation:

Interchange x and y: (-6, 8) is the image of (8, -6) after a reflection over y = x.

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

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3 years ago

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Complete the function using the function y=-2x -6<br> -2<br> 0<br> 2<br> 4

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I need more info please!!

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3 years ago

Find the angle between the lines 2x-3y+5=0 and 2x-3y-7=0​

Find the angle between the lines 2x-3y+5=0 and 2x-3y-7=0