What do u need help with?
3/4 x 144 = 108
108 x 5/9 = 60
B. 60 female students voted for you.
Answer:
Option B) Acute
Step-by-step explanation:
we know that
if a triangle contains an obtuse angle, then the other two angles must be acute.
<em><u>Verify</u></em>
The sum of the interior angles of a triangle must be equal to 180 degrees
in the triangle of the figure
113°+15°+x°=180°
Solve for x
118°+x°=180°
x=180°-118°=62°
62° < 90°
therefore
The angle x is an acute angle
Let x be the amount of Columbian coffee in the mixture and y the amount of Sumatra coffee in the mixture, then
x + y = 1 . . . (1)
9.25x + 14.25y = 12.50 . . . (2)
(1) x 9.25 => 9.25x + 9.25y = 9.25 . . . (3)
(2) - (3) => 5y = 3.25 => y = 3.25/5 = 0.65
From (1), x + 0.65 = 1 => x = 1 - 0.65 = 0.35
1 pound of the mixture contains 0.35 Columbian coffee and 0.65 Sumatra coffee
Therefore, 12 pounds of the mixture will contain 0.35 x 12 = 4.2 pounds of Columbian coffee and 0.65 x 12 = 7.8 pounds of Sumatra coffee
Answer:
there are no real solutions
Step-by-step explanation:
![\log_5(x-1)+\log_5(x+3)-1=0\\\\\log_5(x-1)+\log_5(x+3)=1](https://tex.z-dn.net/?f=%5Clog_5%28x-1%29%2B%5Clog_5%28x%2B3%29-1%3D0%5C%5C%5C%5C%5Clog_5%28x-1%29%2B%5Clog_5%28x%2B3%29%3D1)
there is a rule that says
![\log_b(a)+\log_b(c)=\log_b(ac)](https://tex.z-dn.net/?f=%5Clog_b%28a%29%2B%5Clog_b%28c%29%3D%5Clog_b%28ac%29)
so we have
![\log_5(x-1)+\log_5(x+3)=\log_5((x-1)(x+3))=1](https://tex.z-dn.net/?f=%5Clog_5%28x-1%29%2B%5Clog_5%28x%2B3%29%3D%5Clog_5%28%28x-1%29%28x%2B3%29%29%3D1)
and we have the definition
![\log_a(b)=c\\\\a^{c} =b](https://tex.z-dn.net/?f=%5Clog_a%28b%29%3Dc%5C%5C%5C%5Ca%5E%7Bc%7D%20%3Db)
so we have
![5^{1} = (x-1)(x+3)\\\\5=x^{2} -1x+3x-3\\\\5=x^{2} +2x-3\\\\0=x^{2} +2x-3-5\\\\0=x^{2} +2x-8\\\\](https://tex.z-dn.net/?f=5%5E%7B1%7D%20%3D%20%28x-1%29%28x%2B3%29%5C%5C%5C%5C5%3Dx%5E%7B2%7D%20-1x%2B3x-3%5C%5C%5C%5C5%3Dx%5E%7B2%7D%20%2B2x-3%5C%5C%5C%5C0%3Dx%5E%7B2%7D%20%2B2x-3-5%5C%5C%5C%5C0%3Dx%5E%7B2%7D%20%2B2x-8%5C%5C%5C%5C)
and using the quadratic formula we get that
there are no real solutions