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Alexxandr [17]
3 years ago
5

Which of the following points would fall on the line produced by the point-slope form equation y - 8 = 4/5(x - 1) when graphed​

Mathematics
1 answer:
HACTEHA [7]3 years ago
6 0
This says that x will equal -9

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Miguel biked 14 km in the same amount of time that linda hiked 10 km. Miguel's rate was 4 km/h more than linda's. How fast did e
matrenka [14]

The first thing we must do is define a variable.

We have then:

x: Linda's speed.

Then, by definition, the time traveled is equal to the distance between the velocity.

We have then:

For Linda:

t = \frac{10}{x}

For Miguel:

t = \frac{14}{x + 4}

Then, since time is the same, then:

\frac{10}{x} = \frac{14}{x + 4}

Clearing Linda's speed we have:

10 (x + 4) = 14x

10x + 40 = 14x

40 = 14x-10x

40 = 4x

x = \frac{40}{4}

x = 10

Then, Miguel's speed is:

x + 4 = 10 + 4 = 14

Answer:

Linda's speed is 10 Km/h

Miguel's speed is 14 Km/h

3 0
2 years ago
Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t
Anika [276]

Answer:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c

Step-by-step explanation:

Given

\int\limits {\frac{x}{x^4 + 16}} \, dx

Required

Solve

Let

u = \frac{x^2}{4}

Differentiate

du = 2 * \frac{x^{2-1}}{4}\ dx

du = 2 * \frac{x}{4}\ dx

du = \frac{x}{2}\ dx

Make dx the subject

dx = \frac{2}{x}\ du

The given integral becomes:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du

Recall that: u = \frac{x^2}{4}

Make x^2 the subject

x^2= 4u

Square both sides

x^4= (4u)^2

x^4= 16u^2

Substitute 16u^2 for x^4 in \int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du

Simplify

\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du

In standard integration

\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)

So, the expression becomes:

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)

Recall that: u = \frac{x^2}{4}

\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c

4 0
2 years ago
If correct Brainliest
ElenaW [278]

Answer:

a

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
There is 3 4 of an apple pie left from dinner. Tomorrow, Victor plans to eat 1 4 of the pie that was left. Enter how much of the
lora16 [44]

Answer:

3/16

Step-by-step explanation:

Let the size of the whole apple be T

Given that 3/4 of the apple is left, it means the size left

= 3T/4

Since Victor plans to eat 1/4 of the pie that was left, this amounts to

1/4 * 3T/4

= 3T/16

This means that Victor will eat 3/16 of the whole pie tomorrow

5 0
2 years ago
Santa's Wonderland is an extravagant holiday light display that is open from early November through January each year. The entry
Fofino [41]
Ok,
 f(0.35)= 7f/20

f(-5.2)=-26f/5

f(10)= 10f

f(-0.5)= -f/2

as for the last question I am not quite sure, sorry....hope I helped a little :)

5 0
3 years ago
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