The complete question is;
Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. The length of D E is (3 y + 6) centimeters, the length of E B is (5 y minus 10) centimeters, and the length of E C is (2 y + 4) centimeters. How long is the brace that connects points B and D? 8 cm 16 cm 30 cm 60 cm
Answer:
60 cm. Option D is the correct answer
Step-by-step explanation:
From the image, the diagonals of the parallelogram bisect each other. Thus;
AE = EC and BE = ED
We are given that;
DE = 3y + 6 cm and BE = 5y - 10 cm, thus;
3y + 6 = 5y - 10
Rearranging, we have;
5y - 3y = 6 + 10
2y = 16
y = 16/2
y = 8 cm
The brace that bisects point B and D is BD. So, BD = BE + DE
So, BD = 5y - 10 + 3y + 6
BD = 8y - 4
Putting 8 for y to obtain;
BD = 8(8) - 4
BD = 64 - 4
BD = 60cm
X+y=8 —> y=-x+8
Parallel lines have the same slope so the slope for your line is -1.
Plug in -5 as x and 8 as y into y=mx +b
8=-1(-5)+b
8=5+b
b=3
Your equation is y=-x+3
If you use this equation then you say that the ground is h=0 and solve as a quadratic.
The quadratic formula is (-b±<span>√(b^2-4ac))/2a when an equation is in the form ax^2 + bx + c
So the equation you have been given would be -16t^2-15t-151 = 0
This equation has no real roots which leads me to believe it is incorrect.
This is probably where your difficulty is coming from, it's a mistake.
The equation is formed from S=ut+(1/2)at^2+(So) where (So) is the initial height and S is the height that you want to find.
In this case you want S = 0.
If the initial height is +151 and the initial velocity and acceleration are downwards (negative) and the initial velocity (u) is -15 and the initial acceleration is -32 then you get the equation S=-15t-16t^2+151
Solving this using the quadratic formula gives you t = 2.64 or t = -3.58
Obviously -3.58s can't be the answer so you're left with 2.64 seconds.
Hope this makes sense.
</span><span>
</span>
Multiply 10 cm by 0.4 and mult. 30 cm by 0.4 also:
The height of the smaller triangle is then 4 cm and the length of the base is 12 cm.
Answer: 45.4% of students like both building snowmen and skiing
18.1% of students who do not like building snowmen also do not like skiing
Step-by-step explanation:
__________________________________________________
likes snowmen doesn't like snowmen total
__________________________________________________
likes skiing 50 30 80
__________________________________________________
doesn't like skiing 10 20 30
_________________________________________________
total 60 50 110