There are 26 boys and 19 girls,
Take away 7 from 45 to get 2g(# of girls)
45-7=38 38=2g To get to # of girls,find just one g
38/2=19 so 19 girls
45-19=boys 45-19=26 boys
Answer:
-162
Step-by-step explanation:
x²+24x-18=x²+24x+12²-12²-18=(x+12)²-162
(x+12)²≥0
(x+12)²-162≥-162
⇒ the minimum value of the function is -162
Answer:
1 + cosa sina
Step-by-step explanation:
cos³a - sin³a ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
cos³a - sin³a
= (cosa - sina )(cos²a + cosa sina + sin²a)
= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]
Then
= 
← cancel (cosa - sina) on numerator/ denominator
= 1 + cosa sina
A right triangle has two legs and a hypotenuse
a = shorter leg
b = longer leg
c = hypotenuse
We know b-a=4, or b = a+4
The Pythagorean theorem states:
a2 + b2 = c2
a2 + (a+4)2 = c2
a2 + (a+4)2 = 80
a2 + a2 + 8a + 16 = 80
Combine terms
2a2 + 8a - 64 = 0
Divide by 2
a2 + 4a - 32 = 0
Factor
(a+8)(a-4) = 0
a = 4, -8
We throw out the -8 solution because we can't have a negative measure.
So a = 4
b = 8
c = √80 = 4√5
The legs are 4 and 8.
