Answer:
- slope = 3/2
- y-intercept = 3
- x-intercept = -2
Step-by-step explanation:
The slope is the coefficient of x when the equation is of the form ...
y = (something).
Here, we can put the equation in that form by subtracting 12x and dividing by the coefficient of y:
12x -8y = -24 . . . . . given
-8y = -12x -24 . . . . .subtract 12x
y = 3/2x +3 . . . . . . . divide by -8
This is the "slope-intercept" form of the equation. Generically, it is written ...
y = mx + b . . . . . . where m is the slope and b is the y-intercept
So, the above equation answers two of your questions:
slope = 3/2
y-intercept = 3
__
The x-intercept is found fairly easily from the original equation by setting y=0:
12x = -24
x = -24/12 = -2 . . . . . the x-intercept
_____
A graph of the equation can also show you these things. The graph shows a rise of 3 units for a run of 2, so the slope is rise/run = 3/2. The line crosses the axes at x=-2 and y=3, the intercepts.
Answer:
35.1 units
Step-by-step explanation:
Imagine a right-angled triangle with RS as hypotenuse. The base would be 3 units and the height would be 6 units. By Pythagorus:
RS²=3²+6²
RS=
≈6.7 units
Imagine a right-angled triangle with RT as hypotenuse. The base would be 9 units and the height would be 12 units. By Pythagorus:
RT²=9²+12²
RT=
= 15 units
Imagine a right-angled triangle with TS as hypotenuse. The base would be 12 units and the height would be 6 units. By Pythagorus:
TS²=12²+6²
TS=
≈13.4 units
Perimeter=RS+RT+TS
=6.7+15+13.4
=35.1 units
24 miles is 1 gallon so 360 miles is 15 gallons + 24 is 384 miles so they are not equivalent!
Multiply 60 by .75, which gives you 45 Points. The answer is B.
Answer:
27 inches
Step-by-step explanation:
To find the length of the diagonal, we just need to use the cosine relation of the 48° angle.
The adjacent side to the angle is the height of the canvas, and the hypotenuse formed is the diagonal of the canvas. So, we have that:
cos(48) = height / diagonal
0.6691 = 18 / diagonal
diagonal = 18 / 0.6691 = 26.9 inches
Rounding to the nearest inch, the diagonal of the canvas measures 27 inches
