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2 years ago

Question 6 Find the slope of the line passing through the points (11,-5) and (11,6)

Mathematics

1 answer:

zimovet [89]2 years ago

3 0

There are two ways to approach this.

Option #1:

Use the slope formula $m = \dfrac{y_2-y_1}{x_2-x_1}$ .

$m= \dfrac{6-(-5)}{11-11} = \dfrac{11}{0}$

That value is undefined, so the slope is undefined.

Option #2:

Because the two points have the same x-value, they will be vertically above/below one another. This means your line is a vertical line and the slope of a vertical line is undefined.

Either way, your slope is undefined.

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What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

7 0

2 years ago

Find the measure of < B

Vinvika [58]

The measure of angle b is 25°.

Solution:

Given data:

The "L" shape angle is a right angle.

Right angle is splitted by another line and two angles are formed.

One angle is 65° and the other angle is b.

Let us find the other angle b.

65° + m∠b = 90°

Subtract 65° from both sides of the equation.

m∠b = 90° – 65°

m∠b = 25°

Hence the measure of angle b is 25°.

6 0

3 years ago

I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Zina [86]

Answer:

Yes, x and y have a proportional relationship.

Step-by-step explanation:

A proportional relationship means that, when comparing two quanities, that they are both changing at a constant (same) amount. When looking at a table to compare quantities, you can see that the pounds of tomatoes 'x' is increasing by one (1) each time. If you look at the amount spent in dollars 'y', you can see that for each pound (x), the cost is increasing by $4. So, since for every pound of tomatoes that is purchased increases by $4, then their relationship is proportional.

8 0

2 years ago

Write the equation of the line in point-slope form.

HACTEHA [7]

Y-4=2/-3(x-6) I believe that’s the answer hope this helped

4 0

2 years ago

9. Alan invests £425 in a savings account paying 4.14% compound interest.

Artyom0805 [142]

The answer is a cause Alan

6 0

2 years ago