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3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics

1 answer:

otez555 [7]3 years ago

8 0

Answer:

$ıf \: {3x}^{3x - 2} = 81$

Step-by-step explanation:

use logarithmic function

$log_{3x}(81) = 3x - 2$

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Use the law of cosines to find the value of cos theta. round your answer to two decimal places

REY [17]

Answer:

The correct answer option is B. 0.21.

Step-by-step explanation:

We are to find the value of $cos \theta$ using the law of cosines.

We know that the formula of the cosine rule is given by:

$c ^ 2 = a ^ 2 + b ^ 2 - 2 a b cos C$

So substituting the given values in the above formula:

$10.9 ^ 2 = 5.8 ^ 2 + 10.5 ^ 2 - 2 (5.8) (10.5) cos C$

$118.81=33.64+110.25-121.8cosC$

$118.81 - (33.64+110.25) = -121.8cosC$

$118.81-143.86=-121.8cosC$

$cosC=\frac{-25.05}{-121.8}$

cos C = 0.21

7 0

3 years ago

Hi, can you please help me answer this direct proportion question?

Oksanka [162]

Answer:

X = 100

Step-by-step explanation:

In proportion questions, they want you to multiply one of the sides by a variable, (i usually represent it with K) and then change the proportion sign to an equal.
This is because proportional means they have a ratio between them, with one side increasing by "k" for each increase in the other side.

Multiply the left by k, so $y = \frac{k}{\sqrt{x} }$
we know that y= 5, for x = 36, so sub this in the equation
$5 = \frac{k}{\sqrt{36} }$
simplify $5 = \frac{k}{6 }$
re-arrange for k, k = 5*6 = 30
now we know k, we can create the real equation, $y = \frac{30}{\sqrt{x} }$
sub in 3 as y
$3 = \frac{30}{\sqrt{x} }$
x = 100

4 0

2 years ago

-2(x+1)+6x<-14 I need help

jeka57 [31]

Answer:

x<-3

Step-by-step explanation:

-2(x+1)+6x<-14

Distribute

-2x-2 + 6x < -14

Combine like terms

4x -2 < -14

Add 2 to each side

4x-2+2 < -14+2

4x < -12

Divide by 4

4x/4 < -12/4

x<-3

3 0

3 years ago

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = 3/ square root of 3x + 4

Elis [28]

Well, your equation y=3/SQRT(3x+4) should be rationalized, but that's not what you want.

If f(x) = 3/SQRT(x+4) and g(x) = 3x

f(g(x)) then = 3/SQRT(3x+4), but rationalizing this = 3SQRT(3x+4)/(3x+4)

3 0

3 years ago

Read 2 more answers

If you are given the following stem and leaf display and asked to construct a frequency distribution chart, what would be the wi

Nuetrik [128]

Answer:

Width of intervals: 8

Step-by-step explanation:

We first look at how data is represented in a stem-leaf diagram.

Any number of the left (before -) is the stem and all numbers on right (after -) are the leaves. Each combination of stem and leaf represents one number. For example: 1 - 332 represents: 13, 13, 12.

Our data is as follows:

13, 13, 12, 24, 25, 31, 31, 35, 37, 42, 43, 41, 52, 51, 51, 52

To calculate the width of the frequency distribution chart, we have the following formula:

$Class\ width = \frac{Range}{Number\ of\ classes}$

The range of any data set = Maximum value in the data set - Minimum value in the data set

Maximum value in this case as seen from the data is 52 and minimum is 12.

Range = 52 - 12 = 40

Since we had only 5 stems in the data, we shall use that as the number of classes required in the frequency distribution chart.

$Class\ width = \frac{40}{5} = 8$

Hence, the class width in this data set will be 8.

To make the intervals, we begin from the minimum value and add 8 to it. The intervals will be:

12 - 20

20 - 28

28 - 36

36 - 44

44 - 52

Observe, that all the values of the stem lie within each interval.

For example, there are 3 values for stem 1: 12, 13, 13 and each lie in the first interval 12 - 20.

Next, the values of stem 2 are 24 and 25. Each of these value lie in the second interval 20 - 28; and henceforth.

8 0

4 years ago