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photoshop1234 [79]
3 years ago
9

Eight times a number plus five times another number is -13 the sum of the two numbers is 1 what are these numbers

Mathematics
1 answer:
m_a_m_a [10]3 years ago
4 0

The two numbers are -6 and 7

<em><u>Solution:</u></em>

Given that eight times a number plus five times another number is -13

The sum of two numbers is 1

To find: the two numbers

Let the two numbers be "a" and "b"

From given information,

Eight times a number plus five times another number = -13

eight times a number "a" + five times another number "b" = -13

8a + 5b = -13 ---- eqn 1

Also given that sum of two numbers is 1

sum of two numbers = 1

a + b = 1 ---- eqn 2

<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "b"</u></em>

From eqn 2,

a = 1 - b ----- eqn 3

Substitute eqn 3 in eqn 1

8(1 - b) + 5b = -13

8 - 8b + 5b = -13

8 - 3b = -13

-3b = -13 - 8

-3b = -21

<h3>b = 7</h3>

Substitute b = 7 in eqn 3

a = 1 - 7

<h3>a = -6</h3>

Thus the two numbers are -6 and 7

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Answer:

The length of the diagonal HJ is 10.82 units

Step-by-step explanation:

* Lets revise the rule of the distance between two points

- d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}, where

 (x_{1},y_{1}) and (x_{2},y_{2}) are the two points

* Lets use this rule to find the length of the diagonal HJ

∵ The coordinates of point H are (-4 , 3)

∵ The coordinates of point J are (5 , -3)

∴ x_{1}=-4 and x_{2}=5

∴ y_{1}=3 and y_{2}=-3

- Lets find the length of the diagonal HJ by using the rule above

∴ HJ = \sqrt{(5-(-4))^{2}+(-3-3)^{2}}=\sqrt{(5+4)^{2}+(-6)^{2}}

∴ HJ = \sqrt{(9)^{2}+36}=\sqrt{81+36}=\sqrt{117}=10.81665

∴ HJ = 10.82

* The length of the diagonal HJ is 10.82 units

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