Answer:
The given function is
![g(x)=(5-x)(2x+3)](https://tex.z-dn.net/?f=g%28x%29%3D%285-x%29%282x%2B3%29)
The x-intercepts of the graph are at ![g(x)=0](https://tex.z-dn.net/?f=g%28x%29%3D0)
![(5-x)(2x+3)=0](https://tex.z-dn.net/?f=%285-x%29%282x%2B3%29%3D0)
![5-x=0 \implies x=5\\2x+3=0 \implies 2x=-3 \implies x=-\frac{3}{2}](https://tex.z-dn.net/?f=5-x%3D0%20%5Cimplies%20x%3D5%5C%5C2x%2B3%3D0%20%5Cimplies%202x%3D-3%20%5Cimplies%20x%3D-%5Cfrac%7B3%7D%7B2%7D)
Therefore, the x-intercepts are
and
.
The midpoint can be found with the formula
![P_{M}=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )](https://tex.z-dn.net/?f=P_%7BM%7D%3D%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%20%20%7D%7B2%7D%20%2C%5Cfrac%7By_%7B1%7D%20%2By_%7B2%7D%20%7D%7B2%7D%20%29)
![P_{M}=(\frac{5-\frac{3}{2} }{2},0)\\P_{M}= (\frac{\frac{10-3}{2} }{2} ,0)\\P_{M}= (\frac{\frac{7}{2} }{2} ,0)\\ P_{M}= (\frac{7}{4} ,0)](https://tex.z-dn.net/?f=P_%7BM%7D%3D%28%5Cfrac%7B5-%5Cfrac%7B3%7D%7B2%7D%20%7D%7B2%7D%2C0%29%5C%5CP_%7BM%7D%3D%20%28%5Cfrac%7B%5Cfrac%7B10-3%7D%7B2%7D%20%7D%7B2%7D%20%2C0%29%5C%5CP_%7BM%7D%3D%20%28%5Cfrac%7B%5Cfrac%7B7%7D%7B2%7D%20%7D%7B2%7D%20%2C0%29%5C%5C%20P_%7BM%7D%3D%20%28%5Cfrac%7B7%7D%7B4%7D%20%2C0%29)
The minimum value about a parabola is at its vertex. In this case, the parabola has maxium vale only.
The vertex has coordinates of
, where
and
.
Solving the product of the given expression
![g(x)=(5-x)(2x+3)=10x+15-2x^{2} +-3x=-2x^{2} +7x+15](https://tex.z-dn.net/?f=g%28x%29%3D%285-x%29%282x%2B3%29%3D10x%2B15-2x%5E%7B2%7D%20%2B-3x%3D-2x%5E%7B2%7D%20%2B7x%2B15)
Where
,
and
.
![h=-\frac{b}{2a}=-\frac{7}{2(-2)}=\frac{7}{4}](https://tex.z-dn.net/?f=h%3D-%5Cfrac%7Bb%7D%7B2a%7D%3D-%5Cfrac%7B7%7D%7B2%28-2%29%7D%3D%5Cfrac%7B7%7D%7B4%7D)
![k=f(\frac{7}{4})=-2(\frac{7}{4} )^{2} +7(\frac{7}{4})+15 =-2(\frac{49}{16} )+\frac{49}{4}+15\\ k=-\frac{49}{8}+\frac{49}{4} +15=\frac{-49+98+120}{8} =\frac{169}{8}\\ k=\frac{169}{8}](https://tex.z-dn.net/?f=k%3Df%28%5Cfrac%7B7%7D%7B4%7D%29%3D-2%28%5Cfrac%7B7%7D%7B4%7D%20%29%5E%7B2%7D%20%20%2B7%28%5Cfrac%7B7%7D%7B4%7D%29%2B15%20%3D-2%28%5Cfrac%7B49%7D%7B16%7D%20%29%2B%5Cfrac%7B49%7D%7B4%7D%2B15%5C%5C%20k%3D-%5Cfrac%7B49%7D%7B8%7D%2B%5Cfrac%7B49%7D%7B4%7D%20%2B15%3D%5Cfrac%7B-49%2B98%2B120%7D%7B8%7D%20%3D%5Cfrac%7B169%7D%7B8%7D%5C%5C%20k%3D%5Cfrac%7B169%7D%7B8%7D)
The question asks us to convert the given value into units of miles per hour. So, we convert from meters to miles and from s to hours. We do as follows:
<span>3.00×10^8 m/s ( 1 mile / 1610 m ) ( 3600 s / 1 hr ) = 670807453.42 miles per hr
Hope this answers the question. Have a nice day.</span>
Answer:
B. Interquartile range
E.
Range
Step-by-step explanation:
When the variability is to be used for comparing the two data sets so the measures that should be considered is range & interquartile range as it shows the difference also it compared the two different data sets
Therefore option B and E is correct
And, the rest of the options are wrong
Given that 15 food booths were rented out for ‘d’ days at $100 plus $5 per day. On the food booths only, the company will earn 15($100+$5d) = $1500 + $75d Given that 20 game booths were rented out for ‘d’ days at $50 plus $7 per day. On the game booths only, the company will earn 20($50 + $7d) = $1000 + $140d
The total amount that the company is paid is therefore, $1500 + $75d + $1000 + $140d = $2500 + $215d
The answer to this equation is 10 = x