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emmasim [6.3K]
3 years ago
15

Hello i need some help

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

Answer:

y = 2x - 1

Step-by-step explanation:

(3, 5) (5, 9)

slope = (9-5)/(5-3) = 4/2 = 2

y = mx + b

5 = 2(3) + b

-1 = b

y = 2x -1

gizmo_the_mogwai [7]3 years ago
4 0

Answer:

f(x)=2x-1; y=2x-1

Step-by-step explanation:

First we need to find the slope and to do so you use the equation \frac{y_{1} -y_{2}}{x_{1}-x_{2}} .

Plugging in for the values we get (9-5)/(5-3)=4/2=2, which means we have a slope of 2.

Now we just have to find the y-intercept, and to do this we multiply the x-value by the slope (2) and see what we have to add to that to get the y-value.

For example, 5*2=10, 10-1=9, so -1 is our y-intercept.

This means our equation in slope-intercept form is y=2x-1 and in function form is f(x)=2x-1

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Solve. Check for extraneous solutions. √2 x+6 - √x-1 =2
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x = 5 is not an extraneous solution of the equation.

✓(2x + 6) - ✓(x - 1) = 2

✓(2x + 6) = 2 + ✓(x - 1)

Squaring both the sides of equation, we get

(✓(2x + 6))² = (2 + ✓(x - 1))²

2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))

2x + 6 = 4 + x - 1 + 4(✓(x - 1))

x + 3 = 4✓(x - 1)

Squaring again on both the side of the equation, we get

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x² + 3² + 2×3×x = 16(x - 1)

x² + 9 + 6x = 16x - 16

x² - 10x + 25 = 0

By applying middle term splitting on equation (1), we get

x² - 5x - 5x + 25 = 0

x(x - 5) -5(x - 5) = 0

(x - 5) (x - 5) = 0

x = 5 and 5.

Check for extraneous solutions by putting value of x in original equation -

✓(2×5 + 6) - ✓(5 - 1) = 2

✓16 - ✓4 = 2

4 - 2 = 2

2 = 2

LHS = RHS

x = 5 is not an extraneous solution of the equation.

Know more about roots of equation -

brainly.com/question/4098861

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Read 2 more answers
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