Evaluate log4 7 using the change of base formula. Round your answer to the nearest thousandth. Show all work.

Mathematics

1 answer:

uranmaximum [27]1 year ago

3 0

$\log _47\text{ = }$

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Help please. it would really help if someone explained

Alenkinab [10]

Answer:

0/8

Explanation:

There is no number greater than 10 on the spinner, so there is a 0/8 chance that the spinner will land on a number greater than 10.

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3 years ago

Can a pair of lines be both parallel and perpendicular? explain

alina1380 [7]

No, the 2 lines can never ever be both parallel and perpendicular if I'm not mistaken. This is because a set of parallel lines will never touch each other at all. However perpendicular lines are two lines that meet up to get an angle of 90. You cannot have two lines that never touch and touch at the same time.

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3 years ago

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A geometric sequence has first term 1/9 and common ratio 3. Which is the first term of the sequence which exceeds 1000?

Svetach [21]

$a_{n}= \frac{1}{9} (3)^{n-1}$
(We know this from a=1/9 and r=3)
Simplifying this, we get:
$\frac{1}{9} (3)^{-1} (3)^n$

Since we're finding the first term that exceeds 1000, let's set it equal to 1000.

$\frac{1}{27}(3)^n=1000$
Multiplying both sides by 27
$3^n=27000$

$log_{3}27000=n$

n≈9.2

We have to round n up, since if n=9, the value would be <1000.
Therefore n=10. Substituting n=10,
$\frac{1}{27}3^{10}$
=2187

Therefore the first term that exceeds 1000 is 2187, and it is the 10th term

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3 years ago

Find the perimeter of a triangle with vertices A(3, 1), B(2, -1), and C(-3, 2). Leave

natulia [17]

The perimeter of triangle is: 14.15 units

Step-by-step explanation:

First of all we have to find the lengths of sides of triangles

Given

A(3, 1), B(2, -1), and C(-3, 2)

The distance formula will be used to find the lengths of sides

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\$

So,

$AB = \sqrt{(2-3)^2+(-1-1)^2}\\=\sqrt{(-1)^2+(2)^2}\\=\sqrt{1+4}\\=\sqrt{5}\\=2.24\ unitsBC = \sqrt{(-3-2)^2+(2+1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\= 5.83\ units\\AC = \sqrt{(-3-3)^2+(2-1)^2}\\=\sqrt{(-6)^2+(1)^2}\\=\sqrt{36+1}\\=\sqrt{37}\\=6.08\ units$