MATHEMATICS MIDDLE SCHOOL

The square of the sum of two numbers is 144 and the sum of their square is 180, find the numbers

Answers

Answer 1

Answer:

Answer:

x = 13.35, y = - 1.35

or, x = 1.35, y = - 13.35

or, x = - 13.35, y = 1.35

Step-by-step explanation:

Let us assume that x and y are the two numbers.

So, given that (x + y)² = 144

⇒ x² + 2xy + y² = 144 ........ (1)

⇒ x + y = ± 12 ......... (2)

Again, x² + y² = 180 ........... (3)

Now, from equations (1) and (3) we can write 2xy + 180 = 144

⇒ 2xy = - 36

⇒ xy = - 18 ........ (4)

Now, for x + y = 12

⇒ $x - (18)/(x) = 12$

⇒ x² - 18 = 12x

⇒ x² - 12x - 18 = 0

Using the quadratic formula

$x = \frac{12 \pm \sqrt{(-12)^(2) - 4(1)(-18) } }{2}$

⇒ $x = (12 \pm 14.7)/(2) = 13.35, 1.35$

Now, for x = 13.35, from equation (4) we get, y = - 1.35

And for x = 1.35, from equation (4) we get, y = - 13.35

Now, for x + y = - 12

⇒ x² + 12x - 18 = 0

Using the quadratic formula,

$x = \frac{- 12 \pm \sqrt{12^(2) - 4(1)(-18)}}{2}$

⇒ $x = (- 12 \pm 14.7)/(2) = 1.34, -13.35$

Now, for x = - 13.35, from equation (4) we get, y = 1.35

And for x = 1.35, from equation (4) we get, y = - 13.35

Therefore, x = 13.35, y = - 1.35

or, x = 1.35, y = - 13.35

or, x = - 13.35, y = 1.35 (Answer)

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2355 x 2 = 4710.

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R^2 + 4r = 0 please show work

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${ r }^( 2 )+4r=0\n \n r\left( r+4 \right) =0\n \n \therefore \quad r=0\quad \wedge \quad r=-4$

$r^2 + 4r = 0\nr(r+4)=0\nr=0 \vee r=-4$

29 percent as a fraction in simplest form

Answers

The correct simplest formof 29 percent as a fraction is 29/100, where numerator is 29 and denominator is 100.

What is fractions?

A fractions is a part of whole or a numerical number that isn't a whole number the upper value of line is called numerator and the number below the line is called denominator.

What is percentages?

Percentages are as a fractions where the denominator is 100.

29% = 29 ÷ 100 = 29/100 or 0.29

29/100 here 29 is a numerator and 100 is denomenator.

Therefore, the simplest form for 29 percent is 29/100.

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Answer:

29/100

Step-by-step explanation:

29 = 29/100

Write 10 feet and 6 yards as a fraction in simplest form

Answers

10 feet and 6 yards as a fraction in simplest form is 5/9.

What is the fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, 10 feet and 6 yards.

We know that, 1 yard =3 feet

Then, 6 yards =18 feet

Now, the fraction for 10 feet and 6 yards is

10/18

= 5/9

Therefore, the fraction is 5/9.

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1 yard is 3 feet
4 yards is 12 feet
so 6' to 12' is 6/12
or 1/2

Select all expressions that are equivalent to (2n+6)(n+3)

Answers

Answer:

(2n+6)(n+3)=

(2*n+2*3)(n+3)=

2(n+3)(n+3)=.....(1)

2(n+3)^2=....(2)

2(n^2+2*n*3+3^2) =

2(n^2+6n+9)=....(3)

2n^2+2*6n+2*9=

2n^2+12n+18.... (4)

A bakery bakes 184 loaves of bread in 4 hours. How many loaves does the bakery bake in 1 hour?

Answers

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