Let the base of the ladder be x ft and the extension be y ft.
"when fully extended, a ladder is 28 feet in length."
means: x+y=28
"<span>the extension is 4 feet shorter than the base</span>"
means: y=x-4, that is x-y = 4, (taking y to the side of x, and -4 to the other side of x and y)
thus, we have the system of equations:
1) x+y= 28
2) x-y=4
adding the 2 equations, we have:
(x+y)+(x-y)=28+4
2x=32
x=32/2=16
x+y=28, so 16+y=28, thus y=12
Answer: Base: 16, Extension 12
Answer:
See attached picture.
Step-by-step explanation:
The equation is in point slope form
where m is the slope and
is a point.
For the equation y-2 = 23(x+4), graph the point (-4,2). Then from this point count up 23 and over to the right 1.
This is the graph of the line.
Answer:
y = 1/2 x + -5
Step-by-step explanation:
Slope-intercept form is y = mx + b
where m is the slope and b is the y-intercept
m is equal to change in y/ change in x ( aka horizontal change over vertical change), in the graph the horizontal change is 1 up for every 2 units right, which equals 1/2
b is the y-intercept (when x=0), if you look at the graph x=0 when y=-5
Lastly, you put in m and b into the equation to get y = 1/2 x + -5
Answer:
Yes the information i.e. AT ║ CS and diagonals AS = CT are sufficient to prove that CATS is an isosceles trapezoid.
CATS is an isosceles trapezoid. (Proved)
Step-by-step explanation:
Yes the information i.e. AT ║ CS and diagonals AS = CT are sufficient to prove that CATS is an isosceles trapezoid.
Proof :
Taking Δ CAT and Δ STA,
(i) CT = AS (Given)
(ii) AT is the common side and
(iii) ∠ ACT = ∠ TSA
{Since AT ║ CS and the angles are obtained from the same base AT}
Therefore, by the criteria Side-Side-Angle i.e. SSA, we can say Δ CAT ≅ Δ STA.
Hence, AC = ST {Corresponding sides}
Therefore, CATS is an isosceles trapezoid. (Proved)