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3 years ago

Enter numbers into the table so that the paired values are in a proportional relationship.

Mathematics

2 answers:

Alisiya [41]3 years ago

8 0

Answer:

x- 5

y- 6

Step-by-step explanation:

A proportional relationship is a relationship for which a proportional constant y/x exists and for which it passes through (0,0) or the origin.

The proportional constant is 6.

18/3=6

42/7=7

54/9=6

Thus the filled in blanks should be x 1, 3, 5, 7, 9 and y 6, 18, 30, 42, 54.

Fantom [35]3 years ago

6 0

Answer:

<h2>The missing numbers are 5 and 6.</h2>

Step-by-step explanation:

From the given table, if we divide each pair as y/x, we find the ratio is 6.

$\frac{18}{3}=6\\\frac{42}{7}=6\\\frac{54}{9}=6$

Therefore, the missing numbers have to be in the same ratio.

$\frac{x}{1}=6\\x=6$

$\frac{30}{x}=6\\ x=5$

So, the missing numbers are 5 and 6, because they are also in the same ratio of 6.

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Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept fo

Alla [95]

Answer:

$\displaystyle y=-\frac{1}{2}x+4$

Step-by-step explanation:

<u>Equation of a Line</u>

We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.

We are given a line

$y - 12 = 2x -8$

And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y

$y = 2x +4$

The coefficient of the x is the slope

$m=2$

The slope of the perpendicular line is the negative reciprocal of m, thus

$\displaystyle m'=-\frac{1}{2}$

We know the second line passes through (2,3). That is enough information to find the second equation:

$y-y_o=m'(x-x_o)$

$\displaystyle y-3=-\frac{1}{2}(x-2)$

Operating

$\displaystyle y=-\frac{1}{2}(x-2)+3$

Simplifying

$\displaystyle y=-\frac{1}{2}x+4$

That is the equation in slope-intercept form. Intercept: y=4

8 0

2 years ago

Which points on the curve of x^2 - xy - y^2 = 5 have vertical tangent lines?

algol [13]

We need to differentiate this with respect to x to see if we can find an expression for the derivative of y at various points. That will be the slope of the tangent to the curve. Then we want to see where that derivative might be infinite -- i.e., where the tangent is vertical.

It's not written as a function, but it can still be differentiated using the chain rule:

x2 + xy + y2 = 3

(2x) + (x dy/dx + y dx/dx) + (2y dy/dx) = 0

(I used parentheses to show the differentiation of each term in the original equation.)

2x + x dy/dx + y + 2y dy/dx = 0

2x + y = -x dy/dx - 2y dy/dx

2x + y = dy/dx (-x -2y)

-(2x + y)/(x + 2y) = dy/dx

We have the derivative of y, but it's defined partly in terms of y itself. That's OK. Let's go on...

So where would the slope be infinite? That would happen when x + 2y = 0, or y = -x/2

Let's plug that in for y in the original equation to find points where that's the case.

x2 + xy + y2 = 3

x2 + x(-x/2) + (-x/2)2 = 3

x2 - x2/2 + x2/4 = 3

3x2 / 4 = 3

x2 = 4

x = ±2

So we have two x values where the tangent might be vertical. Let's plug them into the equation and see what the y values are. First x = 2...

x2 + xy + y2 = 3

4 + 2y + y2 = 3

y2 + 2y + 1 = 0

(y + 1)2 = 0

y = -1

So at the point (2, -1) the tangent is vertical.

Now try x = -2...

x2 + xy + y2 = 3

4 - 2y + y2 = 3

y2 - 2y + 1 =0

(y - 1)2 = 0

y = 1

So at the point (-2, 1) the tangent is vertical.

8 0

2 years ago

If g(x) = -3(x) - 5 then g(?) = 25<br> 10<br> -20<br> 5<br> -10

kompoz [17]

Answer:

D) -10

Step-by-step explanation:

We will assign g(x) to be equal to 25, and then solve for x:

25 = -3x-5

30 = -3x

10 = -x

-10 = x

So D is correct

7 0

2 years ago

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Laura and Brent paddled a canoe 6 miles upstream in four hours. The return trip took three hours. Find the rate at which Laura a

Lisa [10]

That would be the average of total time paddled upstream & downstream . . . 12 miles / 7 hours = approx 1.71 miles per hr

3 0

2 years ago

Which could be the area of the base of the triangular prism? [Not drawn to scale]6 ft210 ft212 ft220 ft2

Alexus [3.1K]

For this case, the first thing we must observe is that the base of the prism is a triangle.
The area of the triangle is given by:
$A = (1/2) * (b) * (h)
$
Where,
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h: height of the triangle
Substituting values we have:
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Answer:
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3 years ago

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