The whole number 4 is equivalent to what percent?

Y=8x-2, find the equation of the line that is perpendicular to this line and passes through the point (-5, -6)

Eddi Din [679]

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be negative reciprocals of each other (flip the sign +/- and the fraction/switch the numerator and the denominator)

For example:

Slope = -2 or $-\frac{2}{1}$

Perpendicular line's slope: $\frac{1}{2}$ (flip the sign from - to +, and flip the fraction)

Slope = $\frac{1}{3}$

Perpendicular line's slope = $-\frac{3}{1}$ or -3 (flip the sign from + to -, flip fraction)

y = 8x - 2 The slope is 8, so the perpendicular line's slope is $-\frac{1}{8}$ .

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

$y=-\frac{1}{8} x+b$ To find b, plug in the point (-5, -6) into the equation, then isolate/get the variable "b" by itself

$-6=-\frac{1}{8} (-5)+b$ (Two negative signs cancel each other out and become positive)

$-6=\frac{5}{8} +b$ Subtract 5/8 on both sides to get "b" by itself

$-6-\frac{5}{8} =b$ (To combine fractions, they need to have the same denominator, so multiply -6 by 8/8 so that they will have the same denominator)

$(\frac{8}{8}) (-6)-\frac{5}{8} =b$

$-\frac{48}{8} -\frac{5}{8}$ = b Now combine the fractions

$-\frac{53}{8} =b$

$y=-\frac{1}{8} x-\frac{53}{8}$

3 0

4 years ago

If a is a rational number and B is an irrational number can the product of a and b be rational

MAXImum [283]

Answer:

yes

Step-by-step explanation:

5 0

4 years ago

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

3 years ago

Nayeli light a 4m² space with 12 candles. Citlali lights a 10m² space with 30 of the same type of candles. Whos space is lit bri

Norma-Jean [14]

Answer:

Both spaces have the same amount of brightness per square meter.

Step-by-step explanation:

Nayeli: 12 candles / 4 square meters is the same as 3 candles per square meter.

Citlali: 30 candles / 10 square meters is the same as 3 candles per square meter.

So both Nayeli's and Citlali's spaces have the same amount of brightness per square meter.

5 0

2 years ago

Read 2 more answers

Which pair of angles add up to 180 degrees?

lutik1710 [3]

a and g i think, hope this helps

4 0

3 years ago

Read 2 more answers