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2 years ago

What is an expression for the distance between the origin and a point P(x,y)

Mathematics

1 answer:

kirza4 [7]2 years ago

5 0

Answer:

$d = \sqrt{ {x}^{2} + {y}^{2} }$

Step-by-step explanation:

Distance between origin (0, 0) and point (x, y) is given as:

$d = \sqrt{ {(x - 0)}^{2} + {(y - 0)}^{2} } \\ \\ \red{ \bold{ d = \sqrt{ {x}^{2} + {y}^{2} } }}$

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2 years ago

Estimate √97.5 / 1.96

evablogger [386]

Answer: 5

Step-by-step explanation:

1. You have the following expression given in the problem above:

$\frac{\sqrt{97.5}}{1.96}$

2. You can estimate the result by rounding the numerator and the denominator.

3. As you can see, you can round up 97.5 to 100.

4. Then, you can round up 1.96 to 2.

5. Therefore, you have:

$\frac{\sqrt{100}}{2}$

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6. Therefore, the result is 5.

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2 years ago

Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rat

PilotLPTM [1.2K]

Answer:

Time required by Machine B to create a widget = 4 hours

Step-by-step explanation:

Time taken by Machine A ( $T_{A}$ ) = 3 hours

Time taken by Machine B ( $T_{B}$ )= x hours

Time taken by both machines by working together = 12 hours

The time required to both machines by working together to finish a task is given by the formula = $\frac{T_{A} {T_{B} } }{T_{A} + T_{B} }$

Put the values in above formula we get

⇒ T = $\frac{3 x}{3 + x}$

⇒ 12 = $\frac{3 x}{3 + x}$

⇒ 36 + 12 x = 3 x

⇒ x = - 4 hours

This is the time required by Machine B to create a widget.

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3 years ago

A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

Nastasia [14]

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

$y =\frac{1}{10} x +60$

This is the equation of the line

using a graph tool

see the attached figure

Statements

case a) The slope of the function is $1.00

The statement is False

The slope of the function is equal to $\frac{1}{10} \frac{\$}{tokens}$

case b) The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

for $x=0$

$y =\frac{1}{10}*0 +60$

$y =\$60$

case c) The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to $y =\frac{1}{10} x +60$

case d) The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

case e) The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure

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3 years ago

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