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2 years ago

Which system of equations has the solution (4,−2)?

Mathematics

1 answer:

Marat540 [252]2 years ago

7 0

Answer:

Step-by-step explanation:

To find the answer we must solve each of the systems separately. Starting with the first one:

x + y = 2

2x - y = 10

We must find what x or y is equal to and then replace it in the second equation. I'll go with y as it seems easier:

x + y = 2

y = 2 - x

Now that we found y we replace it in the second equation this way. Be careful with the signs, the minus with change our signs:

2x - (2 - x) = 10

2x - 2 + x = 10

3x = 12

x = 12/3

x = 4

Now that we have x, we replace the variable with its value in one of the equations. Again, for simplicity I'll go with the one that seems easier.

4 + y = 2

y = 2 - 4

y = - 2

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Function or not a function?

n200080 [17]

Answer:

Not a function.

Step-by-step explanation:

There must only be one output per input but here we see the input 18 has two outputs ; 3 and 15 therefore this is not a function.

8 0

3 years ago

What is the solution to the inequality - 6x + 5 > -1

ExtremeBDS [4]

[ Answer ]

$\boxed{X \ < \ 1}$

[ Explanation ]

Solution To Inequality: - 6x + 5 > -1

-------------------------------------

Subtract 5 From Both Sides

- 6x + 5 - 5 > -1 - 5

Simplify

-6x > -6

Multiply Both Sides By -1 (Reverse Inequality)

(-6x)(-1) < (-6)(-1)

Simplify

6x < 6

Divide Both Sides By 6

$\frac{6x}{6}$ < $\frac{6}{6}$

Simplify

X < 1

$\boxed{[ \ Eclipsed \ ]}$

4 0

3 years ago

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

BaLLatris [955]

Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

$f(x) = x^2 - x +2$

Required

The vertex

We have:

$f(x) = x^2 - x +2$

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

$f(x) = x^2 - x +2$

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

$f(x) = x^2 - x +2$

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

8 0

3 years ago

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Find the circumference of a circle<br> with a diameter of 45.

sleet_krkn [62]

Answer:

141.4 centimeters

Step-by-step explanation:

circumference = diameter * pi c = d * pi c = 45 * 3.1416 c = 141.4 (rounded)

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3 years ago

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Hey can you please help me posted picture of question

enyata [817]

If the total area of a dartboard 30 000 mm² and the area of the target is 700 mm²
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P = 2.3%
Therefore the correct answer is option B.
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3 years ago