Answer:
The function for the outside temperature is represented by ![T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%2085%5C%C2%BA%20%2B%2015%5C%C2%BA%20%5Ccdot%20%5Csin%20%5Cleft%5B%5Cfrac%7Bt-6%5C%2Ch%7D%7B24%5C%2Ch%7D%20%5Cright%5D)
, where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
Mean temperature
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
![T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%20%5Cbar%20T%20%2B%20A%20%5Ccdot%20%5Csin%20%5Cleft%5B2%5Cpi%5Ccdot%5Cfrac%7Bt-6%5C%2Ch%7D%7B%5Ctau%7D%20%5Cright%5D)
Where:
- Mean temperature, measured in degrees.
- Amplitude, measured in degrees.
- Daily period, measured in hours.
- Time, measured in hours. (where t = 0 corresponds with 5 AM).
If , and 
, the resulting function for the outside temperature is:
8/11 of what = 16
8/11x = 16
x = 16 * 11/8
x = 176/8
x = 22......so there are a total of 22 fish in the tank
Answer:
No, No, Yes, Yes.
Step-by-step explanation: 2 times -3 = -6. -6 times -4 = 24.
So, with that said, the first one multiples out to -24.
The second multiplies out to again -24.
12 times 2 = 24.
A negative and a negative multiply to become a positive, so -4 times -6 = 24.
1. commutative property states that : a + b = b + a
<span>2. 3x - 5 = 5x - 17 -- add 5 to both sides </span>
<span>3x = 5x - 17 + 5 -- subtract 5x from both sides </span>
<span>3x - 5x = -17 + 5 -- combine like terms </span>
<span>-2x = -12 -- divide both sides by -2 </span>
<span>x = 6 </span>
<span>3. slope formula : slope = (y2 - y1) / (x2 - x1) </span>
<span>(3,-1) x1 = 3 and y1 = -1 </span>
<span>(-2,-5) x2 = -2 and y2 = -5 </span>
<span>now we sub </span>
<span>slope = ((-5 - (-1)) / (-2 -3) </span>
<span>slope = (-5 + 1) / -5 </span>
<span>slope = -4/-5 </span>
<span>slope = 4/5 </span>
<span>4. x = first integer </span>
<span>x + 2 = 2nd integer </span>
<span>x + x + 2 = 80 -- combine like terms </span>
<span>2x + 2 = 80 -- subtract 2 from both sides </span>
<span>2x = 80 - 2 </span>
<span>2x = 78 -- divide both sides by 2 </span>
<span>x = 39 <== this is the smallest number </span>
<span>x + 2 = 41 </span>
<span>5. p = 1/2g - 3 </span>
<span>6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10) </span>
<span>7. 2x + 3y <= 6 -- put in y = mx + b form </span>
<span>3y <= -2x + 6 </span>
<span>y <= -2/3x + 2 </span>
<span>In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2) </span>
<span>To find the x intercept, sub in 0 for y (change inequality sign to equal sign) </span>
<span>2x + 3y = 6 </span>
<span>2x + 3(0) = 6 </span>
<span>2x = 6 </span>
<span>x = 3 </span>
<span>x intercept is (3,0) </span>
<span>So plot your points (3,0) and (0,2) </span>
<span>Connect the points with a solid line because there is an equal sign in there. </span>
<span>Shade below the line because it is less then. </span>
<span>8. 3x + 6y = 8 </span>
<span>6y = -3x + 8 </span>
<span>y = -1/2x + 4/3 </span>
<span>y = 2x - 8 </span>
<span>Perpendicular lines have negative reciprocal slope. All that means is " flip " the slope and change the sign. The slope in these equations are -1/2 and 2. These are negative reciprocals of each other. </span>
<span>9. 7x + 3y - 2 + 6x + 1 + y^2 </span>
<span>y^2 + 3y + 13x - 1 </span>
<span>10. (0,6) x1 = 0 and y1 = 6 </span>
<span>(3,0) x2 = 3 and y2 = 0 </span>
<span>slope(m) = (y2 - y1) / (x2 - x1) </span>
<span>slope(m) = (0 - 6) / (3 - 0) </span>
<span>slope(m) = -6/3 </span>
<span>slope(m) = -2 </span>
<span>y = mx + b </span>
<span>(0,6) x = 0 and y = 6 </span>
<span>6 = 0(-2) + b </span>
<span>6 = b </span>
<span>your equation is : y = -2x + 6 (slope intercept form) </span>
<span>2x + y = 6 (standard form) </span>
<span>11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope </span>
<span>y = -x + 5 (-x is the same as -1x) so your slope is -1 </span>
<span>12. 4y = 8x - 3 -- put in y = mx + b form, and the b stands for the y intercept </span>
<span>y = 8/4x - 3/4 </span>
<span>y = 2x - 3/4 (the y intercept is -3/4 </span>
<span>13. |a| + b --- (a = -1.4 and b = -2.7) </span>
<span>absolute values, whether they have a negative or not, they are always positive </span>
<span>|a| + b </span>
<span>|-1.4 | + (-2.7) </span>
<span>1.4 - 2.7 = -1.3 <== your answer </span>
<span>14. I cannot see the problem </span>
<span>15. -4 < 2t <= 2 --- divide everything by 2 </span>
<span>-2 < t <= 1 </span>
<span>open circle on -2, closed circle on 1, shading in between </span>
<span>16. x + 2y = -9 ---> x = -2y - 9 </span>
<span>now sub -2y - 9 in for x in the other equation </span>
<span>4x - 2y = 14 </span>
<span>4(-2y - 9) - 2y = 14 -- distribute through the parenthesis </span>
<span>-8y - 36 - 2y = 14 -- add 36 to both sides </span>
<span>-8y - 2y = 14 + 36 combine like terms </span>
<span>-10y = 50 -- divide by -10 </span>
<span>y = -5 </span>
<span>now sub -5 in for y in either of the original equations </span>
<span>x + 2y = -9 </span>
<span>x + 2(-5) = -9 </span>
<span>x - 10 = -9 </span>
<span>x = -9 + 10 </span>
<span>x = 1 </span>
<span>answer : x = 1 and y = -5 or (1,-5) </span>
<span>I was really bored so I thought I would just help out :)</span>
None of them are like terms you have 5a 5b and 4
