Answer:
slope = - 
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (23, - 30) and (x₂, y₂ ) = (- 7, 18)
m = 
= 
= 
= -
Answer:
5/12
Step-by-step explanation:
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
Answer:
each bottle of juice costs $2.34
Step-by-step explanation:
2.74+10x=26.14
10x=26.14-2.74
10x=23.40
x=23.40/10
x=2.34
Answer:
y = -2/3x + 6
Step-by-step explanation:
To find the slope, find how much y changes in proportion to x. Here, when x changes by 1, y changes by -2/3. So, the number before x is -2/3.
To find the y-intercept, we need to find what y will be when x is 0. Since we know that when x is 1, y is 16/3, and when x decreases by 1, y increases by 2/3. So, when x is 0, y is 16/3 + 2/3, which is 18/3, or 6.
