Answer:
b. (12, 485)
Step-by-step explanation:
We have been given the number of men receiving degrees (in thousands) is given by the equation
, and for women, the equation is
, where x is the number of years since 1970.
Let us find the coordinates of the point of intersection of both lines by equating our both equations as:
![14.3x+317=3.6x+443](https://tex.z-dn.net/?f=14.3x%2B317%3D3.6x%2B443)
![14.3x-3.6x+317=3.6x-3.6x+443](https://tex.z-dn.net/?f=14.3x-3.6x%2B317%3D3.6x-3.6x%2B443)
![10.7x+317=443](https://tex.z-dn.net/?f=10.7x%2B317%3D443)
![10.7x+317-317=443-317](https://tex.z-dn.net/?f=10.7x%2B317-317%3D443-317)
![10.7x=126](https://tex.z-dn.net/?f=10.7x%3D126)
![\frac{10.7x}{10.7}=\frac{126}{10.7}](https://tex.z-dn.net/?f=%5Cfrac%7B10.7x%7D%7B10.7%7D%3D%5Cfrac%7B126%7D%7B10.7%7D)
![x=11.7757](https://tex.z-dn.net/?f=x%3D11.7757)
Upon substituting x=11.7757 in our equations we will get,
![y=3.6x+443](https://tex.z-dn.net/?f=y%3D3.6x%2B443)
![y=3.6*11.7757+443](https://tex.z-dn.net/?f=y%3D3.6%2A11.7757%2B443)
![y=42.39252+443](https://tex.z-dn.net/?f=y%3D42.39252%2B443)
![y=485.39252](https://tex.z-dn.net/?f=y%3D485.39252)
![y=14.3x+317](https://tex.z-dn.net/?f=y%3D14.3x%2B317)
![y=14.3*11.7757+317](https://tex.z-dn.net/?f=y%3D14.3%2A11.7757%2B317)
![y=168.3925+317](https://tex.z-dn.net/?f=y%3D168.3925%2B317)
![y=485.3925](https://tex.z-dn.net/?f=y%3D485.3925)
Upon rounding our answers to nearest whole number we will get,
![y=485.3925\approx 485](https://tex.z-dn.net/?f=y%3D485.3925%5Capprox%20485)
![x=11.7757\approx 12](https://tex.z-dn.net/?f=x%3D11.7757%5Capprox%2012)
Therefore, the point (12,485) will be the solution of our given equations and option b is the correct choice.
The solution is (x, y) = (2, 3)
<em><u>Solution:</u></em>
<em><u>Given equations are:</u></em>
y = 3x - 3 ------- eqn 1
y = 2x - 1 ---------- eqn 2
We can solve the equations by substitution method
In eqn 1, we have y equals 3x - 3
If we substitute this in place of y in eqn 2, we can get value of "x"
Substitute eqn 1 in eqn 2
3x - 3 = 2x - 1
Move the variables to one side and constants to other side
3x - 2x = -1 + 3
<h3>x = 2</h3>
Substitute x = 2 in eqn 1
y = 3(2) - 3
y = 6 - 3
<h3>y = 3</h3>
Thus the solution is (x, y) = (2, 3)
Answer:
a: 15 in
b:210 cm
c: 21 yds
Step-by-step explanation:
a: to find the area of a triangle multiply the base and the height, then divide the result by two.
b: to find the area of a trapezoid, multiply the median ( the point where the opposite corners cross) and the height.
c: to find the area of a parallelogram, multiply the lenght and the height.
Hope this helps!
Answer:
5. Inequality form: n ≥ 3
Interval notation: [3, ∞)
6. Inequality form: x < 4
Interval notation: (- ∞, 4)
11. Inequality form: x > 50
Interval notation: (50, ∞)
12. Inequality form: y
8
Interval notation: [8, ∞)
15. Inequality form: z < 8
Interval notation: (- ∞, 8)
16. Inequality form: y
4
Interval notation: [4, ∞)
Step-by-step explanation:
I tried to graph them as best as I could, I hope this helps!
Answer:
54000
Step-by-step explanation:
First, round.
75572=76000
22468=22000
Then solve.
76000-22000=54000