Answer:
24,19
Step-by-step explanation:
24+19=43
24-19=5
Answer:
10 boys
Step-by-step explanation:
6:2 simplfies to 3:1 30 / 3 = 10
30:10 simplfies down to 6:2
Answer:
(25,18) is the required solution.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of trips to the airport and y represent the number of trips from the airport.
Total number of fares to and from the airport = 43
Thus, we can write the equation:
![x+y = 43](https://tex.z-dn.net/?f=x%2By%20%3D%2043)
Price for a ride to the airport = $12
Price for a ride from the airport = $10
Total amount collected by the driver = $480
Thus, we can write the equation:
![12x+10y=480](https://tex.z-dn.net/?f=12x%2B10y%3D480)
Solving the two equations, we get,
![12x+12y-(12x+10y)=516-480\\\Rightarrow 2y =36\\\Rightarrow y = 18\\\Rightarrow x = 43-18=25](https://tex.z-dn.net/?f=12x%2B12y-%2812x%2B10y%29%3D516-480%5C%5C%5CRightarrow%202y%20%3D36%5C%5C%5CRightarrow%20y%20%3D%2018%5C%5C%5CRightarrow%20x%20%3D%2043-18%3D25)
Thus, the driver made 25 trips to the airport and 18 trips from the airport.
The solution can be represented as (25,18)
Answer:
<em><u>see</u></em><em><u> </u></em><em><u>below</u></em><em><u>:</u></em><em><u>-</u></em>
Step-by-step explanation:
![\displaystyle{8 \frac{3}{4} \div 2 \frac{7}{8} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B8%20%5Cfrac%7B3%7D%7B4%7D%20%5Cdiv%202%20%5Cfrac%7B7%7D%7B8%7D%20%20%7D)
- Convert the mixed fractions into improper fractions.
![\displaystyle{ \frac{8 \times 4 + 3}{4} \div \frac{8 \times 2 + 7}{8} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7B8%20%5Ctimes%204%20%2B%203%7D%7B4%7D%20%5Cdiv%20%20%5Cfrac%7B8%20%5Ctimes%202%20%2B%207%7D%7B8%7D%20%20%7D)
![\displaystyle{ \frac{32 + 3}{4} \div \frac{16 + 7}{8} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7B32%20%2B%203%7D%7B4%7D%20%20%5Cdiv%20%20%5Cfrac%7B16%20%2B%207%7D%7B8%7D%20%7D)
![\displaystyle{ \frac{35}{4} \div \frac{23}{8} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7B35%7D%7B4%7D%20%5Cdiv%20%20%5Cfrac%7B23%7D%7B8%7D%20%20%7D)
![\displaystyle{ \frac{35}{4} \times \frac{8}{23} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7B35%7D%7B4%7D%20%20%5Ctimes%20%20%5Cfrac%7B8%7D%7B23%7D%20%7D)
![\displaystyle{ \frac{35}{ \cancel4} \times \frac{ \cancel8 {}^{2} }{23} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Cfrac%7B35%7D%7B%20%5Ccancel4%7D%20%20%5Ctimes%20%20%5Cfrac%7B%20%5Ccancel8%20%7B%7D%5E%7B2%7D%20%7D%7B23%7D%20%7D)
![\displaystyle{ \frac{35 \times 2}{23} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B%20%5Cfrac%7B35%20%20%5Ctimes%202%7D%7B23%7D%20%7D)
![\displaystyle{ \frac{70}{23} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B%20%5Cfrac%7B70%7D%7B23%7D%20%7D)
![\displaystyle{3 \frac{1}{23} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B3%20%5Cfrac%7B1%7D%7B23%7D%20%7D)
Answer:
y-intercept: 10
concavity: function opens up
min/max: min
Step-by-step explanation:
1.) The definition of a y-intercept is what the resulting value of a function is when x is equal to 0.
Therefore, if the function's equation is given, to find y-intercept simply plug in 0 for the x-values:
![y = 2x^2+7x+10 = 2(0)^2 + 7(0)+10 = 2(0) + 0 + 10 = 0 + 10 = 10](https://tex.z-dn.net/?f=y%20%3D%202x%5E2%2B7x%2B10%20%3D%202%280%29%5E2%20%2B%207%280%29%2B10%20%3D%202%280%29%20%2B%200%20%2B%2010%20%3D%200%20%2B%2010%20%3D%2010)
y intercept ( f(0) )= 10
2.) In order to find concavity (whether a function opens up or down) of a quadratic function, you can simply find the sign associated with the x^2 value. Since 2x^2 is positive, the concavity is positive. This is basically possible, since it is identifying any reflections affecting the y-values / horizontal reflections.
3.) In order to find whether a quadratic function has a maximum or minimum, you can use the concavity of the function. The idea is that if the function opens downwards, the vertex would be at the very top, resulting in a maximum. If a function was open upwards, the vertex would be at the very bottom, meaning there is a minimum. Like the concavity, if the value associated with x^2 is positive, there is a minimum. If it is negative, there is a maximum. Since 2x^2 is positive, the function has a minimum.