If the slope of AB = CD and BC = AD it's a parallelogram:
Slope of AB = 6+1 / -9+5 = -7/4
CD = -2-5 / 3+1 = -74
These are equal.
BC = 5-6 / -1 +9 = -1/8
AD = -2 +1 / 3+5 = -1/8
These are also equal so it is a parallelogram.
Now to find if the diagonals are perpendicular find the slope of the perpensicular points:
AC = 5 +1 / -1 +5 = 6/4 = 3/2
BD = 6+2 / -9 -3 = 8/-12 = -2/3
Because BD is the reciprocal of AC, this means they are perpendicular.
And because AB is not perpendicular to AD ( AB and AD are not reciprocals) it is a rhombus.
Answer:
150 pennies were lost altogether
Step-by-step explanation:
Let the initial number of pennies owned by Dante be x pennies
Let the initial number of pennies owned by Mia be y pennies
Mathematically ;
x + y = 350 •••••••(i)
So after losing half, dante will have x/2 pennies left.
Mia lost 1/3 so she will have 2/3y left
So after all the losses, they both had equal amount of pennies
This means that;
x/2 = 2y/3
Cross multiply;
3x = 4y •••••••(ii)
Let’s solve both equations simultaneously;
From i , x = 350-y
Substitute this into equation ii
3(350-y) = 4y
1050-3y = 4y
7y = 1050
y = 1050/7
y = 150
since x = 350-y
x = 350-150 = 200
Now Dante loss x/2 = 200/2 = 100
Mia lost 1/3y = 1/3 * 150 = 50
Total pennies lost = 100 + 50 = 150
Answer:
12.9
Step-by-step explanation:
Given data
Give the expression
F(t)=8.50(1.15)^3
Let us solve the term in the bracket
F(t)=8.50*1.520875
F(t)=12.9
Hence the final answer is 12.9
:<span> </span><span>You need to know the derivative of the sqrt function. Remember that sqrt(x) = x^(1/2), and that (d x^a)/(dx) = a x^(a-1). So (d sqrt(x))/(dx) = (d x^(1/2))/(dx) = (1/2) x^((1/2)-1) = (1/2) x^(-1/2) = 1/(2 x^(1/2)) = 1/(2 sqrt(x)).
There is a subtle shift in meaning in the use of t. If you say "after t seconds", t is a dimensionless quantity, such as 169. Also in the formula V = 4 sqrt(t) cm3, t is apparently dimensionless. But if you say "t = 169 seconds", t has dimension time, measured in the unit of seconds, and also expressing speed of change of V as (dV)/(dt) presupposes that t has dimension time. But you can't mix formulas in which t is dimensionless with formulas in which t is dimensioned.
Below I treat t as being dimensionless. So where t is supposed to stand for time I write "t seconds" instead of just "t".
Then (dV)/(d(t seconds)) = (d 4 sqrt(t))/(dt) cm3/s = 4 (d sqrt(t))/(dt) cm3/s = 4 / (2 sqrt(t)) cm3/s = 2 / (sqrt(t)) cm3/s.
Plugging in t = 169 gives 2/13 cm3/s.</span>
Step-by-step explanation:
tanA=8/15 and tan B=40/9
tan(A+B)=(tanA+tanB)/1-tanAtanB
(8/15+40/9)/1-(8/15×40/9)
=-672/185
