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Trava [24]
2 years ago
13

Bethany needs to solve the equation -x^2 + 4x = x - 4.

Mathematics
1 answer:
notsponge [240]2 years ago
5 0

Answer:

The system of equations she could write is:

   y = -x² + 4x

   y = x - 4

The solutions are (-1 , -5) and (4 , 0)

Step-by-step explanation:

-x² + 4x = x - 4

That means two equations one quadratic which is in the left hand side and the other is linear which is in the right hand side.

They represented graphically by a parabola and a line, the solution of it will be the points of intersection of the two graphs

To find the system of equations take each side and equate it by y

∵ y = -x² + 4x

∵ y = x - 4

∴ The system of equations is:

   y = -x² + 4x

   y = x - 4

Let us solve this system using -x² + 4x = x - 4

∵ -x² + 4x = x - 4

- Subtract x from both sides

∴ -x² + 3x = -4

- Add 4 to both sides

∴ -x² + 3x + 4 = 0

- Multiply both sides by -1

∴ x² - 3x - 4 = 0

Let us use the factorization to solve it

∵ x² = (x)(x)

∵ -4 = (1)(-4)

∵ (x)(1) = x

∵ (x)(-4) = -4x

∵ x + -4x = - 3x ⇒ middle term

∴ The factors of x² - 3x - 4 are (x + 1)(x - 4)

- Substitute x² - 3x - 4 by its factors

∴ (x + 1)(x - 4) = 0

Equate each factor by 0 to find the values of x

∵ x + 1 = 0

- Subtract 1 from both sides

∴ x = -1

∵ x - 4 = 0

- Add 4 to both sides

∴ x = 4

Substitute the values of x in the equation y = x - 4 to find y

∵ y = -1 - 4

∴ y = -5

∵ y = 4 - 4

∴ y = 0

The solutions are (-1 , -5) and (4 , 0)

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Which Venn diagram shows the correct relationship among different set of numbers and correct numbers placement of -648
MA_775_DIABLO [31]

Answer:

A

Explanation:

The whole numbers are the numbers that we use to count like 1, 2, 3, ...

Then, integer numbers are the set that contains the whole numbers and the negative numbers, so the integer number are like ... -3, -2, -1, 0, 1, 2, 3, ...

Therefore, -648 is an integer number.

Finally, the rational numbers are numbers that can be written as a/b, where a and b are integers.

So, the answer is A because rational numbers contain integer numbers, integer numbers contain whole numbers and -648 is a integer number.

5 0
1 year ago
What does it mean to solve an equation?
Vadim26 [7]

Answer:

The variable in the equation is represented by

✔ y

.

To solve the equation, you must find the

✔ value of y

that makes the equation true.

1 is a solution of the equation because

✔ 5 = 5

is a true statement

Step-by-step explanation:

7 0
2 years ago
Determine whether the random variable is discrete or continuous. In each​ case, state the possible values of the random variable
Annette [7]

Answer:

A=discrete; B=continuous

Step-by-step explanation:

(a) The number of free dash throw attempts before the first shot is = discrete

​(b) The time it takes for a light bulb to burn out.=continuous

Discrete variables are countable in a finite amount of time such as the case of free dash throw attempts

Continuous Variables are more difficult to count. In statistics, time is a Continuous Variable

3 0
2 years ago
A developer claims that the percent of city residents who favor building a new football stadium is likely between 52.3% and 61.7
Dmitry [639]

Answer: 453

Step-by-step explanation:

To solve the question, we have to calculate the margin of error which will be:

= (61.7% - 52.3%) / 2

= 9.4% / 2

= 4.7%

4.7% = 1 / ✓n

0.047 = 1 / ✓n

✓n = 1 / 0.047

✓n = 21.28

Square both sides to.gwt the value of n

n = 21.28²

n = 452.69

n = 453

453 residents were surveyed

8 0
3 years ago
What is the explicit formula for this sequence? 7, 2, -3, -8
inn [45]

Answer:

Common difference (d) = -5

Step-by-step explanation:

formula=>

an = a + (n-1)d

=> -8 = 7 + (4-1)d

=> -15 = 3d

=> 3d = -15

=> d = -15/3

=> d = -5

8 0
3 years ago
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