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Charra [1.4K]
2 years ago
9

Find all the missing values to make the equation true

Mathematics
1 answer:
Georgia [21]2 years ago
4 0

The missing value in the logarithm are as follows:

  • log₃ 7 - log₃ 2 = log₃ (7 / 2)
  • log₉ 7 + log₉ 4 =  log₉ 28
  • log₆ 1 / 81  =  
  • - 4 log₆ 3

<h3>How to solve logarithm?</h3>

Using logarithm rule,

logₐ b - logₐ c = logₐ (b / c)

logₐ b + logₐ c = logₐ (b × c)

Therefore,

log₃ 7 - log₃ 2 = log₃ (7 / 2)

log₉ 7 + log₉ 4 = log₉ (7 × 4) =  log₉ 28

log₆ 1 / 81 = log₆ 81⁻¹ = log₆ 3⁻⁴ =  - 4 log₆ 3

learn more on logarithm here: brainly.com/question/24515212

#SPJ1

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Tiffany collects perfume bottles. She has 99 bottles in her collection. Two thirds of her perfume bottles are made of crystal. H
Lubov Fominskaja [6]
To find the number of perfume bottles that are made of crystal, multiply 99 by 2/3.

An easy way to do this in your head is to divide 99 by 3, and then multiply it by 2.

99/3=33
33*2=66

66 bottles in Tiffany's collection are made of crystal.
7 0
3 years ago
What is the following quotient? sqrt 6 + sqrt 11 / sqrt 5 +sqrt 3
just olya [345]

Answer:

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{30} - \sqrt{18} + \sqrt{55} - \sqrt{33}}{2}

Step-by-step explanation:

Let's translate what you've written in words to an expression with mathematical symbols.

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}}

To solve this, you need to multiply both the numerator and denominator with the conjugate of the denominator.

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{30} - \sqrt{18} + \sqrt{55} - \sqrt{33}}{2}

5 0
3 years ago
Read 2 more answers
A force of 60 N is used to stretch two springs that are initially the same length. Spring A has a spring constant of 4 N/m, and
goblinko [34]

Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

F=-kx

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

<u>In spring A</u>

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x

Here the spring extension is 15 m

<u>In spring B</u>

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x

Here the extension on the spring is 12 m

<u>Compare</u>

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

=15m-12m=3m

5 0
3 years ago
The point (-3, -5) is on the graph of a function. Which equation must be true regarding the function?
Alecsey [184]

Answer:

f(- 3) = - 5

Step-by-step explanation:

Given the point (- 3, - 5)

where x = - 3 is the input and y = - 5 is the output

The function can be represented by

y = f(x), that is

f(- 3) = - 5

3 0
4 years ago
The world famous gambler from Philadelphia, Senor Rick, proposes the following game of chance. You roll a fair die. If you roll
Orlov [11]

Answer:

You lose $0.833 while Rick gains $0.833, and so Rick is not Loco

Step-by-step explanation:

There are six numbers on a dice. Thus, probability of rolling exactly one number = 1/6

Probability of rolling two is 2/6.

Rolling a 1 pays $25, and probability = 1/6

Rolling a 2 pays $5,and probability = 1/6

Rolling a 3 pays $0, and probability = 1/6

Rolling a 4 or 5 pays -$10, and probability = 2/6

Rolling a 6 pays -$15, and probability = 1/6

Thus,lets calculate the expected value;

EV = (25 × 1/6) + (5 × 1/6) + (0 × 1/6) + (-10 × 2/6) + (-15 × 1/6)

EV = - $0.833

This means you lose $0.833 while Rick gains $0.833, and so Rick is not Loco.

7 0
3 years ago
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