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2 years ago

PLEASE ANSWERR!

Mathematics

2 answers:

VashaNatasha [74]2 years ago

5 0

Answer:

7x+12

Step-by-step explanation:

<h3>1. Multiplying as indicated, we get 6x + 12 - x, which simplifies to 7x+12.</h3>

2. Let their ages be t and j. Then t = j + 2. If Trish is 42, then 42 = j + 2, so that John must be 40.

Zielflug [23.3K]2 years ago

3 0

Answer:

1. is 5x+12 hope it helped !

Step-by-step explanation:

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A particle is moving along the curve y= 4sqrt(5x+11) . As the particle passes through the point (5,24) , its -coordinate increas

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The rate of change of the distance from the particle to the origin at this instant is 3 units per second.

<h3>What is the rate of change?</h3>

The instantaneous rate of change is the rate of change at a particular instant.

A particle is moving along the curve

$y= 4\sqrt{5x+11} .$

The rate of change of y is given as:

dy / dx = 2

by differentiating both sides,

$\dfrac{dy}{dx} = 4\dfrac{1}{2\sqrt{5x+11} } 5\dfrac{dx}{dt} \\\\\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\$

From the question, we have:

(x, y) = (5,24)

Substitute 5 for x and dy / dx = 2

$\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\\\5= \dfrac{10}{\sqrt{5(5)+11} }\dfrac{dx}{dt}\\\\\\\sqrt{5(5)+11} = 2\dfrac{dx}{dt}\\\\\\\dfrac{dx}{dt} = 6/ 2 = 3$

Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.

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2 years ago

What is the equation of the line in point-slope form?

evablogger [386]

Answer:

$y +500 = -\frac{1}{5}(x - 100)$

Step-by-step explanation:

Given

The attached graph

Required

Determine the equation in point slope form

From the graph, we have the following points;

$(x_1,y_1) = (-400,-400)$

$(x_2,y_2) = (100,-500)$

First, we calculate the slope (m):

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

$m = \frac{-500 - (-400)}{100- (-400)}$

$m = \frac{-500 +400}{100+400}$

$m = \frac{-100}{500}$

$m = -\frac{1}{5}$

The equation is then calculated using:

$y - y_2 = m(x - x_2)$

Substitute x and y values

$y - (-500) = -\frac{1}{5}(x - (100))$

$y +500 = -\frac{1}{5}(x - 100)$

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