Answer:
x = -5/2 , 5/2
Step-by-step explanation:
x^ -2 = 4/25
negative exponents means flip from numerator to denominator ( or vice versa)
(1/x) ^2 = 4/25
take the square root of each side (remember you get a positive and negative result)
sqrt(1/x) = sqrt(4/25)
1/x = + 2/5 1/x = -2/5
multiply each side by x
1 = + 2/5 x 1 = -2/5 x
multiply by 5/2 multiply by -5/2
5/2 = + 2/5 x * 5/2 -5/2 = -2/5 x *- 5/2
5/2 = + x -5/2 = x
x = 5/2 , -5/2
Step-by-step explanation:
the total surface area is the sum of the 5 individual areas in the surface :
2 triangle sides (left and right).
1 back rectangle side
1 rectangle floor
1 inclined rectangle front side
to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras
c² = a² + b²
where c is the Hypotenuse (the side opposite of the 90° angle).
c² = 3² + 4² = 9 + 16 = 25
c = 5
so, now, we have everything we need.
the area of a triangle side (since it is right-angled) :
4×3/2 = 6
2 sides, that makes 12
the area of the back side
6×3 = 18
the area of the floor
6×4 = 24
the area of the inclined front side
6×5 = 30
so, the total surface area is
12+18+24+30 = 84
The general form of the equation of a straight line is ax+by+c=0
slope = -a/b
so the slope in your equation = 3
to get the y-intercept put x = 0
y = -11
the equation is y = 3x -11
you can also get it by isolating the y , it will give you the same equation
<span>Two numbers that multiply to get 72 but add to get -22
4 x 18= 72
4 + 18 = 22
just change the signs depending on the problem</span>
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.