All categories

2 years ago

The sum of two numbers is 7 and the difference of their squares is 105. Find the numbers. If there

Mathematics

1 answer:

ValentinkaMS [17]2 years ago

3 0

Answer:

11 and -4

Step-by-step explanation:

Let the required two numbers be x and y

If the sum of two numbers is 7, then

x + y = 7 .. 1

If the difference of their squares is 105, then;

x² - y² = 105 ...2

From 1;

x = 7 - y... 3

Substitute 3 into 2;

(7-y)² - y² = 105

Expand

49-14y+y² -y² = 105

49-14y = 105

-14y = 105 - 49

-14y = 56

y = -56/14

y = -4

Substitute y = -4 into 3

x = 7 - y... 3

x = 7 - (-4)

x = 7+4

x = 11

Hence the numbers are 11 and -4

You might be interested in

A garden is being created in an area that is shaped like an isosceles trapezoid, as shown. Topsoil is needed to fill the garden,

Alla [95]

Answer: 12

Step-by-step explanation:

6 0

2 years ago

Hello can someone help me simplify 4) and 5)? Thank you and please include steps :)

Leni [432]

Alrighty

remember some rules
$(ab)^c=(a^c)(b^c)$
and
$x^{-m}=\frac{1}{x^m}$
and
$x^0=1$ for all real values of x
and
$(a^b)^c=a^{bc}$
and
$(\frac{a}{b})^c=\frac{a^c}{b^c}$
and
(a/b)/(c/d)=(ad)/(bc)
and
$(a^b)(a^c)=a^{b+c}$
and
$\frac{a^m}{a^n}=a^{m-n}$
and don't forget pemdas
example: $-x^m=-1(x^m)$ but $(-x)^m=(-1)^m(x^m)$

so

4.
$(\frac{c^{-2}}{2})^{-2}=$

$\frac{(c^{-2})^{-2}}{2^{-2}}=$

$\frac{c^4}{\frac{1}{2^2}}=$

$\frac{c^4}{\frac{1}{4}}=$

$4c^4$

5.

$\frac{(-a)^4bc^5}{-a^2b^{-3}c^0}=$

$\frac{(-1)^4(a)^4bc^5}{-1(a^2)(\frac{1}{b^3}(1)}=$

$\frac{(1)a^4bc^5}{\frac{(-1)(a^2)}{b^3}}=$

$\frac{(a^4bc^5)b^3}{(-1)(a^2)}=$

$\frac{-a^4b^4c^5}{a^2}=$

$-a^2b^4c^5$

3 0

3 years ago

The United States congress includes 2 sectors from each state ,plus members of the house of representatives. if r means the numb

astra-53 [7]

Answer:

2+-($)(*(*()($_((*_77392973673993939$9

6 0

3 years ago

HELP PLS!!!<br> Fill in the blank below!<br> __+11=22

andreyandreev [35.5K]

11 is the answer to this question

4 0

3 years ago

At the end of a party, 3/4 cup of dip is left. Jim divides 4/5 of the leftover dip equally between 2 friends. How much dip does

Rudik [331]

First, we need to find the amount of dip that was divided amount the two friends.

We know that it is 4/5 of the left dip
therefore:
amount divided among the two friends = (4/5) x (3/4) = 3/5 of the original amount of dip.

This amount is divided among two friends,
therefore:
amount that each friend gets = (3/5) / (2) = 3/10 = 0.3 of the amount of dip

6 0

3 years ago