Answer
Step-by-step explanation:
The number ... n
one quarter of the number ... 1/4 of n = 1/4 * n
one third of the number ... 1/3 of n = 1/3 * n
one quarter of the number is subtracted from one third of the number ... 1/3 * n - 1/4 * n
the result is 7 ... = 7
We can put it together:
1/3 * n - 1/4 * n = 7
4/12 * n - 3/12 * n = 7
1/12 * n = 7 /*12
n = 7 * 12
n = 84
The number you are looking for is 84.
The answer to the first question is D.)
The 6 in front of the parentheses modifies both 'x' and 3
The answer to the second question is D.)
When you plug 4 into the equation, you get 14
3(4) + 2 = 14
12 + 2 = 14
14=14
Hope this helps!
The simple way to do this is to multiply the number of outcomes of one object times the number of outcomes in the other object. In this case a quarter has 2 sides, heads and tails. Since the spinner has 6 sections, there are 6 outcomes.
With this we can do, 2x6=12.
Therefore there are 12 outcomes
Wow this is a doozy! First you have to figure out what is it you are looking for? If you make a dot in the center of the triangle (which is also the center of the circle) and draw a line from the center to one of the vertices of the triangle you have the radius of the triangle and also of the circle. If you draw all 3 radii from the triangle's center to its vertices, you see you have created 3 triangles within that one triangle. The trick here is to figure out what your triangle measures are as far as angles go. If we take the interior measures of those 3 triangles, we get that each one has a measure of 120 (360/3=120). So that's one of your angles, the one across from the side measuring 6. Because of the Isosceles Triangle theorem, we know that the 2 base angles have the same measure because the sides are the same. Subtracting 120 from 180 gives you 60 which, divided in half, makes each of those remaining angles measure 30 degrees. So if we extract that one triangle from the big one, we have a triangle with angles that measure 30-30-120, with the base measuring 6 and each of the other sides measuring 5. If we then split that triangle into 2 right triangles, we have one right triangle with measures 30-60-90. Dropping that altitude to create 2 right triangles not only split the 120 degree angle at the top in half, it also split the base side of 6 in half. So our right triangle has a base of 3 and we are looking for the hypotenuse of that right triangle. WE have to use right triangle trig for that. Since we have the top angle of 60 and the base of 3, we can use sin60=3/x. Solving for x we have x=3/sin60 which gives us an x value of 3.5 inches rounded from 3.464. I'm not sure what you mean by a mixed number unless you mean a decimal, but that's the radius of that circle.
