Let,
the numbers be "x" and "y"
According to the question,
x = 4y ......................................................equation (1)
![\frac{1}{x} + \frac{1}{y}= \frac{45}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7By%7D%3D%20%5Cfrac%7B45%7D%7B4%7D%20%20)
...................................equation (2)
Taking equation (2)
![\frac{1}{x} + \frac{1}{y}= \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7By%7D%3D%20%5Cfrac%7B45%7D%7B4%7D)
Substituting the value of "x" from equation (1), we get,
![\frac{1}{(4y)} + \frac{1}{y}= \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%284y%29%7D%20%2B%20%5Cfrac%7B1%7D%7By%7D%3D%20%5Cfrac%7B45%7D%7B4%7D)
![\frac{1}{4y} + \frac{1}{y}* \frac{4}{4} = \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4y%7D%20%2B%20%5Cfrac%7B1%7D%7By%7D%2A%20%5Cfrac%7B4%7D%7B4%7D%20%3D%20%5Cfrac%7B45%7D%7B4%7D)
![\frac{1}{4y} + \frac{4}{4y}= \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4y%7D%20%2B%20%5Cfrac%7B4%7D%7B4y%7D%3D%20%5Cfrac%7B45%7D%7B4%7D)
![\frac{1+4}{4y} = \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B4%7D%7B4y%7D%20%3D%20%5Cfrac%7B45%7D%7B4%7D)
![\frac{5}{4y} = \frac{45}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4y%7D%20%3D%20%5Cfrac%7B45%7D%7B4%7D)
Cross multiplying, we get,
![5*4 = 45*4y](https://tex.z-dn.net/?f=5%2A4%20%3D%2045%2A4y)
![20 = 180y](https://tex.z-dn.net/?f=20%20%3D%20180y)
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![\frac{20}{180} = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B20%7D%7B180%7D%20%20%3D%20y)
![\frac{1}{9} = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B9%7D%20%20%3D%20y)
![y = \frac{1}{9}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B9%7D)
Now,
Taking equation (1)
x = 4y
Substituting the value of "y", we get
![x = 4( \frac{1}{9} )](https://tex.z-dn.net/?f=x%20%3D%204%28%20%5Cfrac%7B1%7D%7B9%7D%20%29)
So, the numbers are
and
Answer:
16
Step-by-step explanation:
Solve 5 to the power of x minus 3 to the power of x when x=2.
So, you do 5 to the power of 2 minus 3 to the power of 2, which is 25-9=16
Answer:
Greater than 4.256
Step-by-step explanation:
Because 24 is a whole number and so is the 4 in 4.256. So Because 24 is larger than 4 it is automatically greater than 4
Answer:
Those areas are: A 1 = 12, A 2 = 19
Step-by-step explanation:
The area of shape 1 : it consists of 1 square + 4 right triangles
Area of the square: A = a², area of the triangle: A = 1/2 · a · h
A 1 = 2² + 4 · 1/2 · 2 · 2 = 4 + 8 = 12
The area of shape 2 : it consists of 2 isosceles triangles
A 2 = 1/2 · 2 · 4 + 1/2 · 6 · 5 = 4 + 15 = 19
Write x-4 instead of y.
x²+(x-4)²=40
x²+x²-8x+16=40
2x²-8x-24=0
x²-4x-12=0
(x-6)(x+2)=0
x=6 or x=-2
for x=6, y=6-4 = 2
for x=-2, y=-2-4 = -6