For the first, simply plug in the value of x given (x = 2) into the equation: ![\left\frac{3}{4}x^2 + 5\right.|_{x=2} = \frac{3}{4}\left ( 2^2 \right )+5 = 8.](https://tex.z-dn.net/?f=%5Cleft%5Cfrac%7B3%7D%7B4%7Dx%5E2%20%2B%205%5Cright.%7C_%7Bx%3D2%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%5Cleft%20%28%202%5E2%20%5Cright%20%29%2B5%20%3D%208.)
So, 8 would be your answer.
For the second, the sum of x and 2 would be expressed as x + 2. Twice this sum would be written as 2(x+2). Finally, 8 less than twice that sum would be written as 2(x+2) - 8, which would be your expression.
For the last question, the coefficient refers to the number directly in front of the variable, x. So you need only to check what the x would simplify to in each equation and look for the expression where x has no coefficient (i.e., its coefficient is 1). For Hunter, the coefficient would be 15 (5 × 3x = 15x); for Michael, the coefficient would be 11 (6x + 5x = 11x); for Nate, the coefficient would be 1 (x = 1x); and for Spencer, the coefficient would be 2 (2x = 2x). Thus, Nate's expression has a coefficient of 1 when simplified.
Answer: -√6 + 1
<u>Step-by-step explanation:</u>
![\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctan%5Cbigg%28-%5Cdfrac%7B2%5Cpi%7D%7B3%7D%5Cbigg%29%7D%7B%5Csin%5Cbigg%28%5Cdfrac%7B7%5Cpi%7D%7B4%7D%5Cbigg%29%7D-%5Csec%28-%5Cpi%29%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctan%28240%5Eo%29%7D%7B%5Csin%28315%5Eo%29%7D-%5Csec%28180%5Eo%29%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Csqrt3%7D%7B-%5Cdfrac%7B%5Csqrt2%7D%7B2%7D%7D-%28-1%29%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B-2%5Csqrt3%7D%7B%5Csqrt2%7D%5Cbigg%28%5Cdfrac%7B%5Csqrt2%7D%7B%5Csqrt2%7D%5Cbigg%29%2B1%5C%5C%5C%5C%5C%5C%3D%5Clarge%5Cboxed%7B-%5Csqrt6%2B1%7D)
Answer:
x ≥ 48
Step-by-step explanation:
Answer:
(1, 2/3) (-1, -1) are the points. use the slope formula to find the slope y2-y1/x2-x1
(-1 - 2/3) / (-1 -1) (answer both sides of the division side)
-5/3 / -2 (divide)
slope = 5/6 (the slope)
plug in values you know into point-slope form (y -y1) = m(x-x1)
y - (-1) = 5/6 (x - (-1) (i chose the easier point to plug in. two neg. make a pos. )
y +1 = 5/6 (x +1) (use the distributive property)
y +1 = 5/6x+5/6 (subtract 1 from both sides)
y = 5/6x - 1/6 or B (this is the equation)
Step-by-step explanation:
I hope this helped :))
2*9= 18
2*2*9= 2*18= 36sq cm
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2*3=6
6*2*3=6*6= 36 sq cm