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3 years ago

Pls help it due in a hour

Mathematics

1 answer:

Levart [38]3 years ago

6 0

Answer:

The coordinates of the Midpoint of AB will be: (1/2, 5)

Step-by-step explanation:

Given the points

A(-2, 6)

B(3, 4)

Finding the midpoint between (-2, 6) and (3, 4)

$\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)$

$\left(x_1,\:y_1\right)=\left(-2,\:6\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)$

$M.P=\left(\frac{3-2}{2},\:\frac{4+6}{2}\right)$

$=\left(\frac{1}{2},\:5\right)$

Therefore, the coordinates of the Midpoint of AB will be: (1/2, 5)

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2 years ago

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MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

$(1.05)^x=1.885$

In order to solve for x, we have to get it out from its position of an exponent. Do that by taking the natural log of both sides:

$ln(1.05)^x=ln(1.885)$

Applying the power rule for logs lets us now bring down the x in front of the ln:

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For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

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Simplifying gives you

$ln(x^3)=5$

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

$ln(x)=\frac{5}{3}$

Take the inverse ln by raising each side to e:

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$\frac{1}{2}=e^{.1x}$

"Undo" that e by taking the ln of both sides:

$ln(.5)=ln(e^{.1x})$

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$(2^2)^x-6(2)^x=-8$

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When we do that, we can rewrite the polynomial as

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This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor. Now we have to put it back in:

$2^x=4,2^x=2$

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

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Now that the bases are the same, we can say that

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For the second solution, we will raise the 2 on the right to a power of 1 to get:

$2^x=2^1$

Now that the bases are the same, we can say that

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3 years ago