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The logarithmic function is the inverse of the exponential function

The logarithmic equivalent of the exponential function is log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)

The exponential function is given as:

12^3=x^4 y^3 z^6

Take the logarithm of both sides

log(12^3) =log(x^4 y^3 z^6)

Apply the product rule of logarithm

log(12^3) =log(x^4) + log(y^3) + log(z^6)

Apply the power rule of logarithm

3log(12) = 4log(x) + 3log(y) + 6log(z)

Divide through by 3

log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)

Hence, the logarithmic equivalent of the exponential function is log(12) = [tex]\frac 43[/tex]log(x) + log(y) + 2log(z)

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Answer: 1

Step-by-step explanation:

We can start by dividing both sides by 5. This gives us

[tex]6 + s = 7[/tex]

Subtracting 6 from both sides gives us

[tex]s = 7-6=1[/tex]

To check, we can put 1 back in the equation:

[tex]5(6+1) = 35[/tex]

[tex]5(7) = 35[/tex]

Since 5 * 7 is 35, 1 is the answer.

Answer:

28 inches

Step-by-step explanation:

To begin, the area of a rectangle is base · height. Since we are given one of the sides already, you can make an equation to solve for the other value.

5 · x = 45

5x = 45

x = 9

A rectangle has two pairs of parallel sides, or in easier terms, two sets of sides that are the same. So, the perimeter is going to be two lengths plus two widths.

2 · 5 + 9 · 2 = 10 + 14 = 28

Answer:

a) V/2 ; b) V/4

Step-by-step explanation:

a) V = πR²h

If h --> h/2 the new volume V' = πR²h/2 = V / 2

b) πR²h

If D --> D/2 then R --> R/2 and the new volume V" = π(R/2)²h = π(R)²h/4 = V/4

The value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.

A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.

We have a graph of a function:

For [tex]\lim_{x \to -1^{-1}} f(x)[/tex]

As we can see x approaches -1 and it is a left-hand limit.

[tex]\lim_{x \to -1^{-1}} f(x) = 3[/tex]

For [tex]\lim_{x \to -1^{+1}} f(x)[/tex]

The x approaches the +1 and it is the right-hand limit.

[tex]\lim_{x \to -1^{+1}} f(x) = -1[/tex]

For [tex]\lim_{x \to -1} f(x)[/tex]

Since the left hand and right-hand limits are not the same,

[tex]\lim_{x \to -1^{+1}} f(x)[/tex]  = does not exist

From the graph:

f(-1) = 3

Similarly, we can find further values of the limits and functions value:

[tex]\lim_{x \to 2^{-1}} f(x) = 1[/tex]

[tex]\lim_{x \to 2^{+1}} f(x) = 2[/tex]

For [tex]\lim_{x \to 2^{}} f(x)[/tex]

Since the left hand and right-hand limits are not the same,

[tex]\lim_{x \to 2^{}} f(x)[/tex] = does not exist

f(2) = 2

[tex]\lim_{x \to -\infty} f(x) = +\infty[/tex]

[tex]\lim_{x \to +\infty} f(x) = -\infty[/tex]

There are three conditions a graph must follow:

1) function value defined at any given point.

2) left-hand limit and right-hand limit must be equal

3) function value at the point and limit value at the same point must be the same.

In the given function the graph doesn't follow these conditions and its jump continuity.

Thus, the value of limits and function values for a, b, c, d, e, f, g, h, i, and j are 3, -1, does not exist, 3, 1, 2, does not exist, 2 +∞, and -∞ and doesn't follow continuity conditions and its jump continuity.

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Answer:

21.6 m long

Step-by-step explanation:

To do this, we find the scale factor of the fencepost and the shadow.

3/1.8 = 1.66666667

So, we know that when we take the original length and multiply it, we get the new one, so:

1.666666667 * x = 36

x being the original length. Now, we divide both sides by 1.66666667 to get x alone and find the original length.

x = 21.6

To double check, we can take the scale factor and multiply it by the original to get the shadow.

21.6 * 1.666666667 = 36

It is correct

Answer:

C. Monitor and EKG

D. Palpitation and pulse rate

Explanation:

Correct me if I'm wrong:)

Answer:

1 / 0.9

2/ 0.12

3/ 0.2

4/ 0.07

5/ 0.8

6/ 0.72

7/ 0.47

8/ 0.6

9/ 0.02

10/ 0.96

Step-by-step explanation:

Answer:

1. 9/10

2. 12/100 - 3/25  

3. 2/10 - 1/5

4. 7/100

5. 8/10 - 4/5

6. 72/100 - 18/25

7. 47/100

8. 6/10 - 3/5

9. 2/100 - 1/50

10. 96/100 - 24/25

I simplified some of them.

Hope this helped and Brainliest please

Answer:

The dots are used for dot plots, and the given Information Is to help you understand the % or number of people and things etc.

Answer:

75%

Step-by-step explanation:

Answer:

D

it is equivalent to the expression

Answer:

A. 1/49, or 0.02040

Answer:

x³²

Step-by-step explanation:

When raising exponents to another power, multiply the exponents given.

That means that:

(x⁴)⁸ = x⁽⁴⁾⁽⁸⁾ = x³²

Answer:

28 cm

Step-by-step explanation:

Area = 46.75 =  l * (l-3)     shows l = 8.5 cm  (using Quadratic Formula)

    then w = 5.5  

perimeter = 2 * ( 8.5+5.5) = 28 cm

The perimeter of the given card is 28 cm.

Perimeter of an object is given by adding the side lengths of the object.

Given that, the width w of a credit card is 3 cm shorter than the length. The area is 46.75 cm².

We need to find the perimeter of the credit card,

Let the length be l,

Therefore,

Area = length x width

46.75 = l x (l-3)

46.75 = l² - 3l

l² - 3l - 46.75 = 0

Finding l, we get,

l = 8.5, l = -5.5

Since, length cannot be negative so, l = 8.5 cm

So, width = 8.5 - 3 = 5.5 cm

Perimeter = 2(l+w)

= 2(5.5+8.5) = 28 cm

Hence, the perimeter of the given card is 28 cm.

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Answer:

7/8 inch

Step-by-step explanation:

Convert 1 1/4 to improper fraction.

Convert 5/4 to a fraction with a denominator of 8.

Subtract 3/8 from 10/8

Step-by-step explanation:

[tex]c = 2\pi \: r \\ 26.69 = 2\pi \: r \\ r = 26.69 \div 2(3.14) \\ r = 4.25 \: cm[/tex]

Answer:

4.25 cm

Step-by-step explanation:

Circumference of a circle = 2πr  (where r is the radius)

[tex]\implies 26.69=2 \pi r[/tex]

[tex]\implies r=\dfrac{26.69}{2\pi }[/tex]

[tex]\implies r=4.247845431...[/tex]

[tex]\implies r=4.25\:\textsf{cm (nearest hundredth})[/tex]

Using [tex]\pi=3.14[/tex]:

[tex]\implies r=\dfrac{26.69}{2 \cdot 3.14}=4.25\: \sf cm[/tex]

Answer:

16%

Step-by-step explanation:

4 people like rock

and there are 25 ppl all together

4/25=0.16

16%

2/5 on edge

Yw and pls mark me brainiest :D

Answer:

5

Step-by-step explanation:

If it is 18 roses for 90 dollars, what is one rose worth?

90 dollars/18 roses=5 dollar per rose

Answer:

1/5 = 0.2 = 20%

Step-by-step explanation:

Given:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \sf P(yellow) = \dfrac{2}{10}=\dfrac15[/tex]

This can also be written as 0.2 or 20%

Answer:

[tex]Probability=0.2[/tex]

Step-by-step explanation:

Step 1:  List the given information

[tex]Total\ Marbles = 10[/tex]

[tex]Yellow\ Marbles = 2[/tex]

[tex]Blue\ Marbles = 4[/tex]

[tex]Red\ Marbles = 4[/tex]

Step 2:  Determine the probability of choosing yellow

[tex]Probability=\frac{Yellow\ Marbles}{Total\ Marbles}[/tex]

[tex]Probability=\frac{2}{10}[/tex]

[tex]Probability=\frac{1}{5}[/tex]

[tex]Probability=0.2[/tex]

Answer:  [tex]Probability=0.2[/tex]

The graph of the given linear equation, y = 1/2x + 1 (-x+2y=2), is given in the diagram attached below.

The graph of a linear equation is a straight line graph, and it is represented, in slope-intercept form as, y = mx + b, where m is the slope and b is the y-intercept of the graph.

Given the linear equation, -x+2y=2, rewrite in slope-intercept form:

-x+2y=2

2y = x + 2

y = x/2 + 2/2

y = 1/2x + 1

Thus, the graph of the linear equation is drawn as shown in the image attached below.

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Answer:

10

Step-by-step explanation:

boxes= 2.5× 4.5× 6.2= 69.75

tray= 2.5× 9× 31= 697.5

697.5÷69.75= 10

Answer:

y = 3x - 42

Step-by-step explanation:

Answer:

9[tex]\sqrt{2}[/tex]/2

Step-by-step explanation:

Since this is a right triangle designated by the square box in the right side, we know 2 of the angles. 45 and 90. Add these 2 angles and subract them from 180 which turns out to be 45.

We can use the law of sines to solve.

sin90/9 = sin45/x

x = 9sin45 = 6.36 = 9[tex]\sqrt{2}[/tex]/2