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Angelina_Jolie [31]
3 years ago
15

The sum of two numbers is 20, and the difference is 40

Mathematics
2 answers:
Kipish [7]3 years ago
6 0

Answer:

The numbers are 30 and -10.

Step-by-step explanation:

The sum of two numbers is 20 (addition)

x + y = 20

The difference is 40 (subtraction)

x - y = 40

To solve an equation, you can only have one variable. Solve one of these for a variable (it doesn't matter which one).

x - y = 40   Add y to both sides

x = 40 + y

Now you have a new value for x (40 + y), so you can plug it into your other equation.

x + y = 20   Plug in (40 + y) for x

40 + y + y = 20   Combine like terms (y + y)

40 + 2y = 20   Subtract 40 from both sides

2y = -20   Divide both sides by 2

y = -10

Now, plug your y into either equation.

x + y = 20   Plug in -10 for y

x + (-10) = 20   Simplify

x - 10 = 20   Add 10 to both sides

x = 30

Check your work by plugging these numbers into both equations.

x + y = 20   Plug in

30 + (-10) = 20   Simplify

30 - 10 = 20   Simplify

20 = 20

and

x - y = 40   Plug in

30 - (-10) = 40   Simplify

30 + 10 = 40

40 = 40

Feliz [49]3 years ago
3 0

x+y=20\\\underline{x-y=40}\\2x=60\\x=30\\\\30+y=20\\y=-10

<u>-10 and 30</u>

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Percent decrease from 20 to 11
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Step-by-step explanation:

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9 divided by 20= 0.45

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Leona answered all the questions on a test. She had 90% of them correct. There were 40 questions in all. How many did she have c
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Answer:

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Step-by-step explanation:

Let the number be <em>x</em>

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HOPE THIS HELPS

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3 years ago
En la ciudad la temperatura en la noche fue de 2 grados sobre cero y en la madrugada llegó a 12 grados bajo cero. ¿Qué diferenci
alexgriva [62]

Responder:

La temperatura bajó 12 °

Explicación paso a paso:

Dado que:

Temperatura en la noche = + 2 ° (2

Temperatura de la mañana = - 12 (12 ° bajo cero).

La diferencia de temperatura entre la noche y la madrugada:

Temperatura nocturna - temperatura por la mañana temprano

2 - (-12)

2 + 12 = 14

Hay una diferencia de temperatura de 12 °. La temperatura bajó 12 ° entre la noche y la madrugada.

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Describe the graph that would be used to solve the equation –x2 + 4 = x + 2 using a system of equations. How will you use the gr
gayaneshka [121]

Answer:

The solutions are (-2 , 0) and (1 , 3)

Step-by-step explanation:

∵ -x² + 4 = x + 2

* y = -x² + 4 ⇒ is quadratic represented by parabola

 The parabola open downward because coefficient of x² is negative

 The x-coordinate of its vertex = -b/2a, where b is the

  coefficient of x and a is the coefficient of x²

∴ x = 0/2(-1) = 0

∴ The y-coordinate of the vertex = (0)² + 4 = 4

∴ The maximum point of the parabola is (0 , 4)

∵ -x² + 4 intersects x-axis at y = 0

∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4

∵ x² = 4

∴ x = ±√4 = ± 2

∴ the parabola intersects x-axis at -2 , 2

∵ y = x + 2 represented by a line its slope = 1

  It intersects y-axis at 2

∵ x + 2 intersects x-axis at y = 0

∴ x + 2 = 0

∴ x = -2

∴ The parabola and the line intersect each other at

  x = -2 and y = 0

To find all the point of intersection between the 2 equations we will solve them as a system of equations

∵ y= -x² + 4  and y = x + 2

∴ -x² + 4 = x + 2

∴ -x² + 4 - x - 2 = 0

∴ -x² - x + 2 = 0 ⇒ × -1

∴ x² + x - 2 = 0 ⇒ factorize

∴ (x + 2)(x - 1) = 0

∴ x + 2 = 0 ⇒ x = -2

∴ x - 1 = 0 ⇒ x = 1

* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)

* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)

The solution graphically

3 0
2 years ago
Read 2 more answers
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