Solve for x in the triangle. Round your answer to the nearest tenth.

The equation of three lines are given below

kotykmax [81]

Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = $\frac{2}{5}$ x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y = $\frac{5}{2}$ x + $\frac{6}{2}$

I.e y = $\frac{5}{2}$ x + 3

So, slope of this line = $m_1$ = $\frac{5}{2}$

Again , From Line 2

y = $\frac{2}{5}$ x - 1

So, slope of this line = $m_2$ = $\frac{2}{5}$

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - $\frac{6}{4}$ - $\frac{10}{4}$ x

I.e y = - $\frac{5}{2}$ x - $\frac{6}{4}$

So, Slope of this line = $m_3$ = - $\frac{5}{2}$

Now, If the lines are parallel , then the slope of the lines are equal

And If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

$m_2$ × $m_3$ = $\frac{2}{5}$ × ( - $\frac{5}{2}$ )

I.e $m_2$ × $m_3$ = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3 Answer

6 0

3 years ago

Find the product. Write fractions in the simplest form. 5/6(-8/15) *

aliina [53]

Answer:

-75/48

Step-by-step explanation:

multiply 5 by 15

and 6 by 8

5x15 is 75 , put it in numerator

6x8 is 48 , denominator

then the answer should have the negative sign

4 0

3 years ago

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Carter is selling his bike. His research shows that the bike has a current value of $90, which is 45% of the amount Carter paid

GaryK [48]

Carter paid $200 for the bike.

Step-by-step explanation:

Given,

Current value of bike = $90

This represent 45% of the original amount Carter paid for bike.

Let,

x represent the original amount of bike.

45% of x = 90

$\frac{45}{100}x=90\\\\0.45x=90$

Dividing both sides by 0.45

$\frac{0.45x}{0.45}=\frac{90}{0.45}\\x=200$

Carter paid $200 for the bike.

Keywords: percentage, division

Learn more about division at:

#LearnwithBrainly

6 0

3 years ago

What is the slope of the line y = 5x? Just write the number for your answer.

vitfil [10]

Answer:

5

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope
b - y-intercept

Step-by-step explanation:

Step 1: Define

y = 5x

Step 2: Break Function

Identify Parts

Slope m = 5

y-intercept b = 0

5 0

2 years ago

At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other

Juli2301 [7.4K]

Let’s call the speed of the slower car S, then the speed of the other is S+10mph.
At 5pm they have been travelling for 3 hours. The slower car travels a distance 3S and the faster one 3(S+10).
But the two distances must add up to 240 miles so 3S+3(S+10)=240, 3S+3S+30=240, 6S=210, S=35 mph. The faster car’s speed is 45mph. We can see that 3S is the same distance as 3x, so x=S=35 mph, and the distance the faster car travels is 3×45=135 miles.

5 0

2 years ago

Read 2 more answers