-2 (4t-3)+6t=5t-2 solve

consider the line y= 2/3x-0. Find the equation of the line that is parallel to this line and passes through the point (8, 4).

tresset_1 [31]

Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)

slope intercept form :
y=m+b

m=slope

If the line is parallel to y=2/3 x-0, the line will have the same slope, therefore the slope will be: 2/3.

Data:
(8,4)
m=2/3

y-y₀=m(x-x₀)
y-4=2/3(x-8)
y-4=2/3 x-16/3
y=2/3 x-16/3+4
y=2/3 x-4/3 (slope intercept form)

Answer: The equation of the line would be: y=2/3 x-4/3.

if we have the next slope "m",then the perendicular slope will be:
m´=-1/m

We have this equation: y=2/3 x+0; the slope is: m=2/3.

The perpendicular slope will be: m`=-1/(2/3)=-3/2

And the equation of the perpendicular line to : y=2/3 x+0, given the point (8,4) will be:

y-y₀=m(x-x₀)
y-4=-3/2 (x-8)
y-4=-3/2 x+12
y=-3/2x + 12+4
y=-3/2x+16

answer: the perpendicular line to y=2/3 x+0 , given the point (8,4) will be:
y=-3/2 x+16

3 0

3 years ago

Angle P is an acute angle.

TEA [102]

A acute angle is always less than 90 degrees. So the answer is A.

6 0

3 years ago

Imaginen que un maratonista corre toda una carrera a una velocidad constante. Después de dos horas lleva recorridos 22 km

saw5 [17]

For this case we have:

If after 2 hours the marathon runner has traveled 22 kilometers we have:

2h -----------> 22km

Applying a rule of three, we can know the time it takes to run 42km. So, we have:

2h -----------> 22km

x -------------> 42km

Where "x" is the time it takes to travel 42km. Resolving we have:

$x = \frac {(42 * 2)} {22}$

$x = \frac {84} {22}$

$x = \frac {42} {11}$

$x = 3.82 hours$

Thus, after 3.82 hours the marathon runner will travel 42km.

Answer:

3.82 hours

6 0

3 years ago

Can someone please help me with number 2?I don't know what I did wrong.

Dmitry [639]

Part A

Let's say point P is the starting point and point Q is the endpoint

x = one-way distance from P to Q, and vice versa

The goal is to find x, then compute 2x to find the round trip distance traveled.

We'll use this idea

distance = rate*time

which solves to

time = distance/rate

So when going from P to Q, the driver is going 70 mph and travels x miles

So the driver does this for distance/time = x/70 hours.

When going back, the driver slows down to 55 mph so the time taken here is x/55 hours.

The total time values add to x/70 + x/55 hours

Set this equal to the total driving time of 7 hours and solve for x

x/70 + x/55 = 7

70*55*(x/70 + x/55) = 70*55*7

70*55*(x/70) + 70*55*(x/55) = 26,950

55x + 70x = 26,950

125x = 26,950

x = (26,950)/125

x = 215.6 which is the one-way distance in miles

which then means,

2x = 2*215.6 = 431.2

Therefore, the total distance traveled is 431.2 miles

<h3>Answer: 431.2 miles</h3>

=========================================================

Part B

To find the duration of each trip, we simply need to evaluate x/70 and x/55. Those are the durations when going 70 mph and 55 mph respectively. These durations are measured in hours.

x/70 = (215.6)/70 = 3.08

x/55 = (215.6)/55 = 3.92

Note how 3.08+3.92 = 7 to help verify the answers.

<h3>Answers:</h3>

When going 70 mph, it takes about 3.08 hours
When going 55 mph, it takes about 3.92 hours

6 0

3 years ago

Two ninths of 540 students at east side middle school are in chorus. 3/4 of chorus members are girls. 2/5 of the girls in chorus

lisov135 [29]

2/9 • 3/4 • 2/5 = 1/15
1/15 of of the students are girl sopranos in chorus.

5 0

3 years ago