<h3>The projected amount the average American spent on health care in 2014 is $ 10075.91</h3>
<em><u>Solution:</u></em>
Given that,
The average American spent $8,508 on health care in 2011
The cost of health care is projected to rise about 5.8% per year for the years 2012-2022
<em><u>The increasing function is given as:</u></em>
![y = a(1+r)^t](https://tex.z-dn.net/?f=y%20%3D%20a%281%2Br%29%5Et)
Where,
y is future value
a is initial value
r is growth rate in decimal
t is number of years
From given,
a = 8508
![r = 5.8 \% = \frac{5.8}{100} = 0.058](https://tex.z-dn.net/?f=r%20%3D%205.8%20%5C%25%20%3D%20%5Cfrac%7B5.8%7D%7B100%7D%20%3D%200.058)
t = 2011 to 2014 = 3 years
<em><u>Substituting the values, we get,</u></em>
![y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91](https://tex.z-dn.net/?f=y%20%3D%208508%281%20%2B%200.058%29%5E3%5C%5C%5C%5Cy%20%3D%208508%281.058%29%5E3%5C%5C%5C%5Cy%20%3D%208508%20%5Ctimes%201.1842%5C%5C%5C%5Cy%20%3D%2010075.914%20%5Capprox%2010075.91)
Thus the projected amount the average American spent on health care in 2014 is $ 10075.91
Answer:
(2, -7)
x = 2
y = -7
Step-by-step explanation:
Let's solve this system of equations by elimination.
Start by multiplying the first equation by 2:
![2(4x)+2(3y)=2(-13)\\8x+6y=-26](https://tex.z-dn.net/?f=2%284x%29%2B2%283y%29%3D2%28-13%29%5C%5C8x%2B6y%3D-26)
Next, multiply the second equation by 3:
![3(-5x)+3(2y)=3(-24)\\-15x+6y=-72](https://tex.z-dn.net/?f=3%28-5x%29%2B3%282y%29%3D3%28-24%29%5C%5C-15x%2B6y%3D-72)
Notice that both equations now have a "6y", meaning we can subtract both equations and thereby eliminating the variable "y" from the equation:
![8x+6y-(-15x+6y)=-26-(-72)\\8x+6y+15x-6y=-26+72\\23x=46](https://tex.z-dn.net/?f=8x%2B6y-%28-15x%2B6y%29%3D-26-%28-72%29%5C%5C8x%2B6y%2B15x-6y%3D-26%2B72%5C%5C23x%3D46)
Divide both sides by 23
![x=2](https://tex.z-dn.net/?f=x%3D2)
Substitute 2 for "x" to solve for "y".
![4x+3y=-13\\4(2)+3y=-13\\8+3y=-13](https://tex.z-dn.net/?f=4x%2B3y%3D-13%5C%5C4%282%29%2B3y%3D-13%5C%5C8%2B3y%3D-13)
Subtract 8 from both sides:
![3y=-21](https://tex.z-dn.net/?f=3y%3D-21)
Divide both sides by 3:
![y=-7](https://tex.z-dn.net/?f=y%3D-7)
Therefore the answer is:
![(x, y)=(2, -7)](https://tex.z-dn.net/?f=%28x%2C%20y%29%3D%282%2C%20-7%29)
Additional Comments:
Note that we can only divide, subtract, multiply, or add both sides of the equation by the same quantity due to the Division, Subtraction, Multiplication, or Addition Property of Equality. These properties state that if you divide/subtract/multiply/add one side of the equation by one quantity, you must do the same to the other side of the equation so that it remains an equation.
Answer:
y=2x+1
Step-by-step explanation:
To find the answer, first graph the equation and find coordinates for atleast 2 points. We can find (0,7) and (1,9). Next we add 3 to the x coordinate of each point. We get (3,7) and (4,9). We know the slope which is 2. So our equation becomes y=2x+b. Next we substitube a coordinate pair, with y and x in the equation. We get 7=2*3+b. Solve and we get 1=b.
Therefore,
y=2x+1.
I hope this helps.
-13 is located the same distance away on the number line from -5 that 3 is.