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2 years ago

Which equation represents the line that passes through and left-parenthesis 4, StartFraction 7 Over 2 right-parenthesis.?

Mathematics

1 answer:

asambeis [7]2 years ago

7 0

Answer:

We want a line that passes through the point (4, 7/2)

and we have no other information of this line, so we can not fully find it, but we can find a general line.

We know that a line can be written as:

y = a*x + b.

Now we want that, when x = 4, we must have y = 7/2.

7/2 = a*4 + b

b = -a*4 + 7/2

Then we can write this line as:

y = a*x - a*4 + 7/2.

Where a can take any value, and it is the slope of our line.

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Question 1(Multiple Choice Worth 1 points)

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Answer:

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2 years ago

April and Sanjay are both using tools to simulate the probability that a family with three children will have exactly one girl.

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The simulations have different theoretical probabilities of a 3-child family having exactly one girl, and the experimental probabilities they generate may differ.

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1 year ago

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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th

Allushta [10]

Answer:

$y>\frac{2}{3}x+3$

Step-by-step explanation:

step 1

Determine the slope of the dashed line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(-3,1) and (0,3)

substitute

$m=\frac{3-1}{0+3}$

$m=\frac{2}{3}$

step 2

Find the equation of the dashed line in slope intercept form

$y=mx+b$

we have

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$b=3$ ---> given problem

substitute

$y=\frac{2}{3}x+3$

step 3

Find the equation of the inequality

we know that

Is a dashed line and everything to the left of the line is shaded

$y>\frac{2}{3}x+3$

see the attached figure to better understand the problem

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Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere.

Advocard [28]

The volume of a sphere is given by:

$V= \frac{4}{3} \pi r^{3}$

So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution) that lies on the same plane. We know from calculus that:

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Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:

 $x^{2}+y^{2}=r^{2}$

Isolationg y:

 $y= \sqrt{r^{2}-x^{2}}$ 

So,

 $f(x)=y=\sqrt{r^{2}-x^{2}}$ 

 $V=\pi \int_{a}^{b}[\sqrt{r^{2}-x^{2}}]^{2}dx$

 $V=\pi \int_{a}^{b}(r^{2}-x^{2})dx$ 

being -r and r the limits of this integral.

 $V=\pi \int_{-r}^{r}(r^{2}-x^{2})dx$

Solving:

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Finally:

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