Answer:
x = 14
Step-by-step explanation:
Extend line AB so that it intersects ray CE at point G. Then angles BGC and BAD are "alternate interior angles", hence congruent.
The angle at B is exterior to triangle BCG, and is equal to the sum of the interior angles at C and G:
138 = (376 -23x) +(x^2 -8x)
Subtracting 138 and collecting terms we have ...
x^2 -31x +238 = 0
For your calculator, a=1, b=-31, c=238.
__
<em>Additional comment</em>
You will find that the solutions to this are x = {14, 17}. You will also find that angle BCE will have corresponding values of 54° and -15°. That is, the solution x=17 is "extraneous." It is a solution to the equation, but not to the problem.
For x=14, the marked angles are A = 84°, C = 54°.
To solve this, you need to divide 127.5 by 51:
127.5/51 = 2.5
To find the percent, multiply 2.5 by 100:
2.5 x 100% = 250%
So 127.5 is 250% of 51
1. Any number above 13 works. Why? Because 20-7=13, and to be greater than 20, you must add a number larger than 13.
Examples: 14+7 > 20, 30+7 > 20, 100+7 > 20
2. Any number below 25/3 (which is also 8.3 with a repeating 3) works. Why? Because 25/3=8.3 with a repeating 3, and to remain less than 25, you must multiply by a number less than 8.3 with a repeating 3.
Examples: 3(8) < 25, 3(5) < 25, 3(0) < 25
3. 4 buses. 1 bus will hold 60 students, 2 will hold 120, 3 will hold 180, and 4 will hold 240. The question is trying to trick you into putting now 3.3333333333... buses because that's what 200/60 is, but there is no such thing as a third of a bus. So you need at least 4 buses. (There will be an extra 40 spaces for passengers on the 4th bus, but that is okay.)
To find this answer I did 200/60 and got 3.3 with a repeating 3. You must round to the higher whole number. Rounding down to 3 buses leaves you with 20 students without a bus.
4. 19 boxes. 18 boxes will only hold 288 candies. The question is trying to trick you into putting down 18.75 boxes because that's what 300/16 is, but there is no such thing as 75% of a box. So you need at least 19 boxes. (There will be an extra 4 spaces for candies in the 19th box, but that is okay.)
To find this answer I did 300/16 and got 18.75. You must round to the higher whole <span>number. Rounding down to 18 boxes leaves you with 12 candies without a box.</span>
Answer:
Step-by-step explanation:
According to the table, function g(x) reaches the max height of 33, approx.
The equation of motion is f(x) = -16x^2 + 42x + 12. We need to determine the maximum of this function. To do this, find the x-coordinate of the vertex, which is x = -b/(2a), or x = -42/(2*-16), or 1.31 sec.
Evaluating f(x) = -16x^2 + 42x + 12 at x = 1.31 sec, we get f(1.31) = 39.6.
So it appears that f(x) has a higher max than does g(x); the difference is approx. 39.6 - 33, or 6.6
