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2 years ago

In the plane, Ine kis parallel to the line with equation y = 7x + 5 . Which of the following could be an equation of line k?

Mathematics

2 answers:

matrenka [14]2 years ago

5 0

Answer:

Step-by-step explanation:

Lilit [14]2 years ago

4 0

Answer:

see the explanation

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

In this problem we have

$y=7x+5$

This is the equation of a line in slope intercept form

where

$m=7$ ---> is the slope

$b=5$ ---> is the y-intercept

therefore

Any equation with a slope 7 and y-intercept different of 5 could be the equation of the line k

Note If the slope is 7 and the y-intercept is 5 we have identical lines not parallel lines

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The equation y=−0.0088x2+0.79x+15 models the speed x (in miles per hour) and average gas mileage y (in miles per gallon) for a v

rewona [7]

Answer: 30.72 miles per gallon

To find <span>best approximate for the average gas mileage at a speed of 60 miles per hour you need to replace the variable x with 60. The calculation would be:

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2 years ago

Read 2 more answers

A town has a population of 14,000 and grows 5% every year. What will be the population after 14 years, to the nearest whole numb

hammer [34]

Answer:

23,800 people

Step-by-step explanation:

what is 5 % of 14,000- 700( 0.05 times 14,000)

700 times 14 is 9,800

9800 + 14000 is

0 0

2 years ago

Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate

mars1129 [50]

Answer: In the beginning he was given 27 sweets.

Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.

On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;

8/a = 2/3

By cross multiplication we now have

8 x 3 = 2a

24/2 = a

a = 12

Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;

12/b = 2/3

By cross multiplication we now have

12 x 3 = 2b

36 = 2b

36/2 = b

b = 18

Let the number of sweets he had on day one be called x. If he ate one-third of x and he had 18 left over, then the two-thirds left over is 18, and we now have;

18/x = 2/3

By cross multiplication we now have

18 x 3 = 2x

54 = 2x

x = 27

Therefore Tim was given 27 sweets at the beginning.

3 0

2 years ago

Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$