First we need to get some expressions:
"Four times the number of white marbles" = 4*w
"9 times the number of red marbles" = 9*r
"...exceeded...by 10": So 4*w is 10 more than 9*r or 4*w = 9*r +10
"ratio of blue marbles to red marbles is 3 to 1" : b/r = 3/1
b=3*r
"there is a total of 65 marbles": b+r+w=65
So our system becomes
b = 3*r
65 = b+r+w
4*w = 9*r+10
The first equation allows us to substitute immediately into the second equation so
65 = 4*r+w
however, we can divide the third equation by 4 to get w:
w = (9*r)/4+10/4
This can then be plugged into the second to get:
65 = 4*r+(9*r)/4+10/4 = (16*r)/4 + (9*r)/4+10/4 = (25*r+10)/4
260 = 25*r+10
250 = 25*r
r=10
Now we simply plug this result into the substitutions to get w and b:
w = 90/4+10/4 = 100/4 = 25
b=30
So there are 10 red marbles, 25 white marbles, and 30 blue marbles
Now it sounds like we should be picking some out at random ;)
6.974 rounded to the nearest tenth is 6.97 i think
C. Exactly one unique triangle exists with the given side lengths.
<u>Step-by-step explanation:</u>
A triangle consists of three sides, depending on the measurement of the sides, naming of the triangles can be varied.
If all the three sides are equal in length, it is said to be an equilateral triangle. Only one triangle can be formed using the measures of 7 in, 7 in, 7 in, that is all the three sides are same in measurement of 7 inches.
So, Exactly one unique triangle can be produced with the given side lengths.