2 Points A rational expression is undefined whenever its numerator is zero.

A is the point with coordinates (5,9) B is the point with coordinates (d,17) The line AB has gradient 4 Work out the value of d

yarga [219]

Answer:

d=9

Step-by-step explanation:

The gradient of straight line is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

Plug in our knows

$4=\frac{17-9}{d-5} \text{ Solve for d} \\\\4(d-5)=8\\\\d-5=4\\d=9$

3 0

2 years ago

What is (f - g)(x)?

andrew11 [14]

x^3-6x^2+18x-2 is right snswer

7 0

3 years ago

The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0

2 years ago

Yvonne is interested in testing the effectiveness of a new flea medication on dogs, so she divided some dogs with fleas into two

meriva

Actually, the real answer is "NO, BECAUSE GROUP B SHOULD BE THE CONTROL GROUP". Since Yvonne gave the flea medication to the group A, and we need a control group. If you don't know what it's the control group, it's the group that they don't put the experiment on, just to see if the group(s) being experimented, had any positive or negative changes. In a short summary they need group B to stay like they are to compare it to the experimented group (group A)

Good Luck!

7 0

3 years ago

Read 2 more answers

This figure represents a step in a compass-and-straightedge construction. Identify the construction.

aleksley [76]

a congruent line segment

4 0

3 years ago

Read 2 more answers