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2 years ago

You graph a triangle on a grid paper. The slopes of the sides are 0, -3, and undefined. What kind of triangle did you draw?

Mathematics

1 answer:

barxatty [35]2 years ago

5 0

You drew a right triangle. The lines with zero and undefined slopes are perpendicular.

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Coordinates, gradient and tangent work (see image).

Ivenika [448]

Answer:

a) $P(x,2x^2-5),\ Q(x+h,2(x+h)^2-5)$

b) $4x+2h$

c) $4x$

Step-by-step explanation:

Given the curve

$y=2x^2-5$

a) If the x-coordinate of P is $x$ , then the y-coordinate is $2x^2-5,$ so point P has coordinates $(x,2x^2-5)$

If the x-coordinate of Q is $x+h$ , then the y-coordinate is $2(x+h)^2-5$ so point Q has coordinates $(x+h,2(x+h)^2-5)$

b) The gradient of the secant RQ is

$\dfrac{y_Q-y_P}{x_Q-x_P}\\ \\=\dfrac{(2(x+h)^2-5)-(2x^2-5)}{(x+h)-x}\\ \\=\dfrac{2(x+h)^2-5-x^2+5}{x+h-x}\\ \\=\dfrac{2(x+h)^2-2x^2}{h}\\ \\=\dfrac{2x^2+4xh+2h^2-2x^2}{h}\\ \\=\dfrac{4xh+2h^2}{h}\\ \\=4x+2h$

c) If $h\rightarrow 0,$ then the gradient $4x+2h\rightarrow 4x$

5 0

2 years ago

Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x

Marta_Voda [28]

Answer:

A. f(x) = 6x + 9

Step-by-step explanation:

The given equation is:

y - 6x - 9 = 0

We have to write this equation in function notation with x as the independent variable. This means that y will be replaced by f(x) and all other terms will be carried to the other side of the equation to get the desired function notation.

y - 6x - 9 = 0

y = 6x + 9

f(x) = 6x + 9

Therefore, option A gives the correct answer.

5 0

2 years ago

Read 2 more answers

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p

Naya [18.7K]

The IQR is 2 because 120-118=2

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2 years ago

For the function f(t) = Pe^rt, if P= 6 and r = 0.06, then what is the value of f(6) to the nearest tenth? A. 219.6 B. 8.6 C. 0.1

Ann [662]

<span>B. 8.6 Let's substitute the given values into the function and calculate the result. So: f(t) = Pe^rt f(t) = 6e^0.06t f(6) = 6e^(0.06*6) f(6) = 6e^(0.36) f(6) = 6*1.433329415 f(6) = 8.599976487 Rounding to the nearest tenth, gives: 8.6 So the answer is "B. 8.6"</span>

7 0

2 years ago

Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

irakobra [83]

Answer:

24.5 points

8 points

Step-by-step explanation:

khan academy

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2 years ago