hectictar

We want to know what each company charges for a 5 mile trip, so we want to know what is the fare price when the number of miles is 5 ?

So look at  5  on the miles axis, then go up until you reach the fare price at  5 miles.

When the fares of the two cab companies are compared, what is the cheaper fare for a 5-mile trip?

Let's find the fare that each company charges for a 5-mile trip.

On the ABC Cabs graph, there is the point  (5, 12) .

(Also notice that the point  (5, 10)  is not on the graph.)

So when the number of miles is 5, the fare is 12 dollars.

ABC Cabs charges 12 dollars for a 5-mile trip.

On the Tary Taxicabs graph, there is the point  (5, 9) .

(Also notice that the point  (5, 8)  is not on the graph.)

So when the number of miles is 5, the fare is 9 dollars.

Tary Taxicabs charges 9 dollars for a 5-mile trip.

9 dollars is the cheaper fare for a 5-mile trip.

We can see that two of the points that the line goes through are  (0, -1)  and  (1, 5)  .

slope of line that goes through   (0, -1)  and  (1, 5)   =  \(\frac{\text{rise}}{\text{run}}\,=\,\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{5--1}{1-0}\,=\,\frac{5+1}{1}\,=\,\frac61\,=\,6\)

Also, you can count how many units up and right a point on the line is from another to find the slope.

The point  (1, 5)   is  6  units up and  1  unit right from the point  (0, -1)  ,

so the slope is  6/1 ,  which is  6 .

Thank you, I finally get it now  

Since  ∠ABC  and  ∠CBE  form a straight line...

m∠ABC   =   180° - m∠CBE   =   180° - 125°   =   55°

The sum of the angles in a triangle is always  180° , and each angle is greater than  0° , so the sum of any two angles has to be less than 180° . So...

55° + (15x - 92x - 25)°   <   180°

55 + 15x - 92x - 25   <   180

30 - 77x   <   180

-77x   <   150

x   >   - \(\frac{150}{77}\)

And...

0°  <  (15x - 92x - 25)°

0   <   -77x - 25

25   <   -77x

-\(\frac{25}{77}\)  >  x

- \(\frac{25}{77}\)   >   x   >   - \(\frac{150}{77}\)

All possible values of  x  are in the interval  (-\(\frac{150}{77}\), -\(\frac{25}{77}\))

Let the amount of oranges that Kim could buy if the price rose to  4x  cents per orange be  n .

the amount of money Kim has   =   40 * 3x

the amount of money Kim has   =   n * 4x

n * 4x   =   40 * 3x

4nx   =   120x

                         Divide both sides of the equation by  x .

4n   =   120

                         Divide both sides of the equation by  4 .

n   =   30

The sum of the angles in every triangle is  180° , so..

∠A + ∠B + ∠C   =   180°

21° + 90° + ∠C   =   180°

∠C   =   180° - 21° - 90°

∠C   =  69°

∠D  corresponds to  ∠A  so...

∠D   =   ∠A   =   21°

∠F  corresponds to  ∠C  so...

∠F  =  ∠C  =  69°

△EDC  is similar to  △ABC ,  so side  DC  corresponds to side  BC .

Let the scale factor from  △EDC  to  △ABC  be  s .

DC * s   =   BC

4 * s   =   6

s   =   6/4

s   =   1.5

So each side of  △ABC  is  1.5  times the corresponding side of  △EDC.

△EDC  is similar to  △ABC ,  so side  EC  corresponds to side  AC .

EC * 1.5   =   AC

And we can see from the picture that   EC  =  x   and   AC  =  12.5 - x  , so....

x * 1.5   =   12.5 - x

1.5x   =   12.5 - x

                                 Add  x  to both sides of the equation.

1.5x + x   =   12.5

2.5x   =   12.5

                                 Divide both sides by  2.5 .

x   =   5

△GHI  is congruent to  △JKL .  So....

GH   =   JK   =   25 in

GI   =   JL   =   14 in

KL   =   HI   =   26 in

∠J  =  78°

∠K  =  31°

∠I  =  71°

The easiest way for me to think of these is to find the scale factor.

Let the scale factor from  △DEF  to  △HJK  be   s  .  So....

5s  =  8.75

s  =  8.75/5

s  =  1.75

So each side of  △HJK  is  1.75  times the corresponding side of  △DEF .

x   =   1.75 * 4   =   7

y   =   1.75 * 8   =   14