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3 years ago

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Changing Bases to Evaluate Logarithms in Exercise, use the change-of-base formula and a calculator to evaluate the logarithm. Se

e Example 9.
log6 10

1 answer:

Talja [164]3 years ago

5 0

Answer:

1.2850

Step-by-step explanation:

Using the change of base formula,

Log 10 to base 6 = Log 10 ÷ Log 6

Log 10 = 1

Log 6 = 0.7782

Log 10 ÷ Log 6 = 1 ÷ 0.7782 = 1.2850

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What is the value of 2 in 204.75

telo118 [61]

Anything that is behind the decimal point ends with a "ths" or "th"

The '2' is in the "hundreds"
The '0' is in the "tens"
The '4' is in the "ones"
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The '7' is in the "tenths"
the ' 5' is the "hundredths"

So, therefore the value of '2' is in the "hundreds"

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3 years ago

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A car is driving at 70 kilometers per hour. How far, in meters, does it travel in 5 seconds?

notka56 [123]

Answer:

97.2 m

Step-by-step explanation:

$\frac{70 km}{1 h}$ = $\frac{70000 m}{3600 s}$ = 19.4 m/s

Distance = speed x time = 19.4 m/s x 5 s = 97.2 m

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3 years ago

Stella graphs the equation y=1/3x – 2

faltersainse [42]

we have

$y=\frac{1}{3}x-2$

<u>Statements</u>

<u>case A)</u> The graph is a straight line.

The statement is True

Because, this is a linear equation (see the attached figure)

<u>case B)</u> The line passes through the origin.

The statement is False

Because the point $(0,0)$ is not a solution of the equation

Verify

Substitute the value of x and y in the equation

$0=\frac{1}{3}*0-2$

$0=-2$ ------> is not true

the point $(0,0)$ is not a solution

therefore

The line does not pass through the origin

<u>case C)</u> The line passes through the point $(0,-2)$

The statement is True

Because the point $(0,-2)$ is a solution of the equation

Verify

Substitute the value of x and y in the equation

$-2=\frac{1}{3}*0-2$

$-2=-2$ ------> is true

the point $(0,-2)$ is a solution

therefore

The line passes through the point $(0,-2)$

<u>case D) </u>The slope of the line is $3$

The statement is False

Because, the slope of the line is $m=\frac{1}{3}$

<u>case E)</u> The y-intercept of the line is $2$

The statement is False

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For $x=0$

find the value of y

$y=\frac{1}{3}*0-2=-2$

the y-intercept is equal to $-2$

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3 years ago

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Which points on the graph represent values that could be in the table? A B C D

Dafna11 [192]

Answer:

uhhh

Step-by-step explanation:

uh I don't see the graph

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Please help me with this.

zheka24 [161]

The sin A is equal to 12/13 and the tan (A) is equal to 12/5.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: $hypotenuse^2=(leg_1)^2+(leg_2)^2$ . And the main trigonometric ratios are:

$sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\$

The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:

adjacent leg=5

hypotenuse=13

Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.

$hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12$

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

$sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}$

Finally, you can find the tan (A) since:

$tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}$

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

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