B = bees, w = wasps, x = hornets
b + w + x = 184
b = 3x - 9
w = x + 28
(3x - 9) + (x + 28) + x = 184...combine like terms
5x + 19 = 184
5x = 184 - 19
5x = 165
x = 165/5
x = 33 <== points scored by Hornets
If tan theta is -1, we know immediately that theta is in either Quadrant II or Q IV. We need to focus on Q IV due to the restrictions on theta.
Because tan theta is -1, the ray representing theta makes a 45 degree angle with the horiz axis, and a 45 degree angle with the negative vert. axis. Thus the hypotenuse, by the Pythagorean Theorem, tells us that the hyp is sqrt(2).
Thus, the cosine of theta is adj / hyp, or +1 / sqrt(2), or [sqrt(2)]/2
The secant of theta is the reciprocal of that, and thus is
2 sqrt(2)
---------- * ------------ = sqrt(2) (answer)
sqrt(2) sqrt(2)
Answer:
25x² − 20x + 4
Explanation:
(5x − 2)²
= (5x + −2)(5x + −2)
= (5x)(5x) + (5x)(−2) + (−2)(5x) + (−2)(−2)
= 25x² − 10x − 10x + 4
= 25x² − 20x + 4
Answer:
In order from least to greatest: 0.25, 3 ⅜, 3 <span>⅖</span>;
Or, write as: 0.25 < 3 ⅜ < 3 ⅖ .
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Explanation:
0.25 = ¼ l (less than "1"); the lowest of the three given values.
The remaining two values have the same whole number of 3, and a fraction:
3 <span>⅖ ;</span> and 3 ⅜.
The least common multiples among the denominators of the fraction values is 40. ⅖ = ?/40 ; 5*? =40? 5* 8 = 40, so 2*8 = 16;
Thus, ⅖ = 16/40, and 3 ⅖ = 3 16/40. 3/8 = ?/40? 8*5 =40; so 3*5 = 15 ; thus ⅜ = 15/40; and
and 3 ⅜ = 3 15/40.
3 15/40 is less than than 3 16/40;
as such; 3 ⅜ is less than 3 ⅖.
So, in order from least to greatest: 0.25, 3 ⅜, 3 ⅖;
Or, write as: 0.25 < 3 ⅜ < 3 ⅖ .
