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3 years ago

Solve the system of equations algebraically

Mathematics

1 answer:

EleoNora [17]3 years ago

4 0

Answer:

Step-by-step explanation:

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What is 0.31111... as a fraction

KonstantinChe [14]

Answer: 14/45
explanation:

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3 years ago

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when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3><u>Solution:</u></h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = $a^2$

6 is subtracted from the square of a number = $a^2 - 6$

5 times the number = $5 \times a$

<em><u>So we can frame a equation as:</u></em>

6 is subtracted from the square of a number = 5 times the number

$a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0$

<em><u>Let us solve the above quadratic equation</u></em>

For a quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here in this problem,

$a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6$

Substituting the values in above quadratic formula, we get

$\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}$

We have two solutions for "a"

$\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}$

We have asked negative solution. So a = -1

Thus the negative solution is -1

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3 years ago

Subtract this please

cupoosta [38]

Answer:

B. 3x^2 - 13x + 7

Step-by-step explanation:

6x^2 - 5x + 3 - (3x^2 + 8x - 4)

6x^2 - 5x + 3 - 3x^2 - 8x + 4

3x^2 - 13x + 7

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3 years ago

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If g(x) = 10 - 2x then which of the following is the value of g(7)?

slega [8]

Answer:

g(7)= -4

Step-by-step explanation:

10-2(7)

10-14

=-4

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2 years ago

What is the gradient of the graph shown

Keith_Richards [23]

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Answer:

Step-by-step explanation:

The gradient is the ratio of "rise" to "run". Here, it appears the line crosses the y-axis at y = -1. It appears that it also crosses the grid intersection at (1, 2). This represents a "rise" (change in y) of (2 -(-1)) = 3, for a "run" (change in x) of (1 -0) = 1. Then the gradient is ...

m = rise/run = 3/1 = 3

The gradient of the graph is 3.

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2 years ago