In the past you paid $800 per month to rent your apartment. You now pay

The square of the sum of two numbers is 144 and the sum of of their square is 180, find the number... Please I really need the a

mr Goodwill [35]

Answer:

The numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

Step-by-step explanation:

Let the two numbers be 'x' and 'y'.

Given:

The squares of the sum of two numbers = 144

The sum of their squares = 180

The sum of the numbers = $x+y$

The square of the sum of numbers = $(x+y)^2$

Square of first number = $x^2$

Square of second number = $y^2$

The sum of their squares = $x^2+y^2$

Now, as per question:

$(x+y)^2=144---(1)\\\\x^2+y^2=180---(2)$

Expanding equation (1) using the formula $(a+b)^2=a^2+b^2+2ab$

This gives,

$(x+y)^2=144\\\\x^2+y^2+2xy=144\\\\\textrm{Plug in the value of }x^2+y^2\textrm{ from equation (2)}\\\\180+2xy=144\\\\2xy=144-180\\\\2xy=-36\\\\xy=-\frac{36}{2}\\\\xy=-18\\\\y=-\frac{18}{x}---(3)$

Plug in the value of 'y' from equation (3) in equation (1). This gives,

$x^2+(-\frac{18}{x})^2=180\\\\x^2+\frac{324}{x^2}=180\\\\x^4+324=180x^2\\\\x^4-180x^2+324=0\\\\\textrm{On solving, we get:}\\\\x^2=178.2\ or\ x^2=1.8\\\\\textrm{Square root both sides, we get:}\\\\x=\pm13.35\ or\ x=\pm1.35$

Therefore,

$y=-\frac{18}{x}=-\frac{18}{\pm13.35} = \pm1.35\ or\\\\y=-\frac{18}{x}=-\frac{18}{\pm1.35}=\pm13.3$

Therefore, the numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

6 0

3 years ago

If the rr is equal to 25%, what is the value of the money multiplier (simple deposit multiplier)? if $35,000 in cash is taken fr

DENIUS [597]

The money supply in the economy is $1025302.6

Bank loans or invests its excess reserves to earn greater hobby. A one-dollar boom inside the financial base reasons the money deliver to boom through more than one dollar. The growth inside the money supply is the cash multiplier.

The money multiplier is the primary can used to calculate what a change in reserves could do to the money supply. The method for the cash multiplier is 1/r where r is the reserve ratio. once one has calculated the money multiplier, they might then multiply that through the exchange in reserves.

The money multiplier is critical in macroeconomics because it determines the cash supply, which affects interest charges. it is also critical in banking because it impacts economic coverage and the steadiness of the banking region.

Learn more about the money multiplier here brainly.com/question/14182201

#SPJ4

5 0

2 years ago

Consider the graph of the line of best fit, y = 0.5x + 1, and the given data points.

Georgia [21]

Which is the residual vaulewhen x=2
The answer would be -1

5 0

3 years ago

Read 2 more answers

Apply the distributive property to factor out the greatest common factor.<br> 44+48=

Elena-2011 [213]

Answer:

(40+4)+(40+48)

=40+(4+8)+4+8(40)

=44+48+12×40

if u add all

=104×40

=4160

Step-by-step explanation:

4 0

2 years ago

Help me please thanks

Brut [27]

Forget about the negative sign. First you have to find a least common denominator. This would be 63. Since we had to multiply 9 by 7 to get 63 we have to multiply the numerator (4) by 7. This gives us a new fraction of 36/63. Since we ha e to multiply 21 by 3 to get 63 we have to multiply 19 by 3. This gives us 57. So now we have 36/63 and 57/63. Then we add the negative sign back in making 57/63 -57/63. Now we add them together. Because one has a negative sign and one is positive the number has to be closer to zero. So the answer is -21/63.

3 0

3 years ago