Answer:
c. 112 ft
Step-by-step explanation:
the diagonal of a rectangle creates a right-angled triangle with a length and a width of the rectangle (the diagonal is the Hypotenuse or baseline).
and this means we can use Pythagoras :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle).
diagonal² = 100² + 50² = 10000 + 2500 = 12500
diagonal = sqrt(12500) = 111.8033989... ft ≈ 112 ft
Answer:
It's A.
Step-by-step explanation:
Let's look at option A:
From the second equation y = -10 - x. Substituting in the first equation:
-10 - x = x^2 + 3x - 5
x^2 + 4x + 5 = 0
Checking the discriminant b^2 - 4ac we get 16 - 4*1*5 = -4 so there are no real roots. (A negative discriminant means no real roots).
So A has no real solution.
B.
x^2 + 3x - 5 = (20 - 4x)/5 = 4 - 0.8x
x^2 +3.8x - 9 = 0
b^2 - 4ac = (3.8)^2 - 4*1*-9 = 50.44 (positive) so there are real roots.
C.
x^2 + 3x - 5 = -9 - x
x^2 + 4x + 4 = 0
b^2 - 4ac = 4^2 - 4*1*4 = 0 so there are real roots.
Answer:
C. (1, 10) and (6, 5)
Step-by-step explanation:
To find the point with a distance of 5 units.
Let the points be x and y.
x = x1 and x2
y = y1 and y2
x2 - x1 = 5 units
y2 - y1 = 5 units.
A quick look at the options, we can tell that the correct option is C.
From points (1, 10) and (6, 5)
x1 = 1, x2 = 6, y1 = 10 and y2 = 5
Substituting into the equation above, we have;
x2 - x1 = 6 - 1 = 5 units
y2 - y1 = 5 - 10 = -5 units.
Therefore, option C with points (1,10) and (6,5) have a distance of five units between them.
Answer:
x = 1035 = MXXXV
Step-by-step explanation:
<u>Roman Numbers
</u>
It's an ancient number system developed in Rome where numbers are represented by the letters {I,V,X,L,C,D,M}. The value of each are, respectively {1,5,10,50,100,500,1000}. If some letter is repeated, then it's value must be multiplied by the number of times the letter is present. For example, XXVII has two X's and two I's, so the conversion is 10+10+5+1+1=27.
If a less-valued letter appears before a greater one, it subtracts. For example CDI=-100+500+1=401
Our numbers are
MMMMMMMMCDXV=8*1000-100+500+10+5=8415
MDCCCLXIII = 1000+500+300+50+10+3=1863
DLXI = 500+50+10+1=561
XXVII = 20+5+2=27
We now operate in our numerical system
Converting back to roman
