What should you do first when solving an equation that has a variable on both sides?

The rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

[tex]Log_b (mn)= log_b m + log_b n[/tex]

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

[tex]Log_b \left(\frac{m}{n}\right)= log_b m - log_b n[/tex]

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

[tex]Log_b (m^n) = n log_b m[/tex]

4. A new fundamental rule:

[tex]Log_b m =\frac{log_a m}{log_a b}[/tex]

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The distance between the points (-6, 7) and (-1, -5) is 13 units.

The complete velocity of an object, regardless of direction, is its distance.

Distance is the amount of space an object has traveled, regardless of where it began or concluded.

Knowing an object's distance from us allows us to calculate its true size.

Typically, the following formula is used to determine the distance between two points:

d=((x2 - x1)2 + (y2 - y1)2)

So, the following is the distance formula:

d=((x2 - x1)2 + (y2 - y1)2)

Points are: (-6, 7) and (-1, -5)

Now, put in the values in the above formula and calculate as follows:

d=((x2 - x1)2 + (y2 - y1)2)

d=((-1+6)2 + (-5-7)2)

d=√25+144

d=√169

d=13 units

Therefore, the distance between the points (-6, 7) and (-1, -5) is 13 units.

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Answer:

C. Functional

Step-by-step explanation:

I hope I helped you,

Alex Martin :)

No, Robert has traveled 1,000 meters (600 + 400), or 0.62 miles, by walking 400 meters to and from the store and 600 meters to and from the library.

Miles are used to measure distance. The distance is 1.609 kilometers equivalent. 1,760 yards make up one mile.

The Roman mille passus, sometimes known as the "thousand paces," was 5,000 Roman feet long and served as the model for the statute mile, which is 5,280 feet. Five Roman feet are equivalent to one Roman pace, which is the distance between the heel of one foot being elevated to the heel being laid down again following a step by the other foot.

Assumed distances from home to four different locations are as follows:

To school = 350 meters

To church = 240 meters

To store = 200 meters

To library = 300 meters

Therefore, for Robert to walk a mile, he needs to cover 1,609 meters.

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1/2 is not a whole number.

We know that the whole numbers are numbers that include natural numbers and zero.

That is the set of whole numbers is denotes by W = N ∪ {0},

here N represents the set of natural numbers.

And we know that the natural numbers are nothing but the numbers which can be counted and start from 1 and ends at infinity.

i.e., the set of natural numbers N = {1, 2, 3, . . ., ∞}

and the set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

A set of whole numbers do not include fractions, decimals, or negative integers.

Here, 1/2 is a fraction (number of the form p/q where q ≠ 0)

So, given number 1/2 is not a whole number.

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Answer:

3, 13

Step-by-step explanation:

(3,13)

Answer: (3,13)

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.

Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have

9x=9, divide both sides by 9 and we end up with x=1.

PS. sorry for the bad handwriting but i attached a photo of how i solved it.

There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.

The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.

Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

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The value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

What is the average cost?

We are aware that it is determined by the cost-to-production ratio. The sum of the fixed cost and the variable cost is referred to as the total cost, which is also known as the unit cost. As a result, Average Cost is calculated as Total Cost/Number of Units or (Fixed Cost + Variable Cost)/Number of Units.

Here, we have

In this case, we use the linear function y = 2x + 25, where x is the time after 1985, measured in years, and y is the average cost of a haircut. The slope of the model is m = 2 USD yr.

It means that the average cost of a haircut increased by 2 every year after 1985.

In 1985, y=0, and the cost is 25

In 1986, y=1, and the cost is 25+2 = 27

In 1987, y=2, and the cost is 25+4 = 29

and so on.

Hence, the value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

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The values of angles are  m∠1 = 39° and m∠2 = 51° from the given kite.

What is triangle ?

triangle can be defined in which it consists of three sides , three angles and sum of the angles is 180 degrees

Given figure is a kite.

The diagram is not drawn to scale.

We have to find the measure of angle 1 and 3 in the kite.

From the figure,

Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.

So, sides AB and AD are equivalent adjacent sides.

m∠1 = 39°

AC and BD are diagonals.

Diagonals of a kite always meet at right angles.

Let the diagonals intersect at point O.

From right triangle AOB,

m∠1 + m∠2 + m∠O = 180°

39° + m∠2 + 90° = 180

m∠2 = 180° - 90° - 39°

m∠2 = 90° - 39°

m∠2 = 51°

Therefore, m∠1 = 39° and m∠2 = 51°.

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Step-by-step explanation:

3√64/343

3√4^3/7^3

3√(4/7)^3

4/7

Answer:

4/7

Step-by-step explanation:

[tex]\sqrt[3]{\frac{64}{343} }[/tex]

[tex]\frac{\sqrt[3]{64}}{ \sqrt[3]{343} }[/tex]

[tex]\sqrt[3]{64}[/tex] = 4

[tex]\sqrt[3]{343}[/tex] = 7

[tex]\frac{4}{7}[/tex]

Purple shows 20 times and 20/100 is 1/5 when we simplify the fraction

Fraction represents a part of a whole or, more generally any number of equal parts. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator.

So we need to find the fraction of many times does purple show up in 20 trays in which every tray has 5 colors.

To find the answer we need to find the overall number of all colors and that is 20 trays * 5 colors and that equals to 100 colors. So purple shows 20 times and 20/100 is 1/5 when we simplify the fraction

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In the word problem , Ashley harvested  [tex]\frac{1}{2}[/tex] acre more than Jill.

What is Word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided expressions are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here according to the question,

Acre harvested by Ashley = [tex]\frac{5}{6}[/tex]

Acre harvested by Jill = [tex]\frac{1}{3}[/tex]

Now to find number of more acre harvested by Ashley than Jill then,

=> Acre harvested by Ashley - Acre harvested by Jill

=> [tex]\frac{5}{6} -\frac{1}{3}[/tex]

=> [tex]\frac{5-2}{6}[/tex]

=> [tex]\frac{3}{6}[/tex]

=> [tex]\frac{1}{2}[/tex]

Hence Ashley harvested  [tex]\frac{1}{2}[/tex] acre more than Jill.

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Vertical lines have NO SLOPE. We can't divide by zero, which is of course why this slope value is "undefined". This relationship is always true: a vertical line will have no slope, and "the slope is undefined" or "the line has no slope" means that the line is vertical.

Now, According to the question:

The slope of a vertical line is infinite or undefined as it has no y-intercept. The slope of a vertical line is undefined. That’s because, in a horizontal line, the change in the x-value will always be 0. You can figure this out by calculating the horizontal difference between the two x-coordinates. Remember the slope formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

With a vertical line, this results in a bottom denominator of 0. However, dividing by 0 is something that doesn’t exist in math! Even though the difference in y-coordinate may change, dividing any number by the change in x-coordinate, 0, will result in an undefined slope.

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Answer:

Step-by-step explanation:

Choose two pairs of data from the data table and calculate the slope (m = Δy/Δx):

(430 - 295) / (6 - 3) = 135/3 = 45

She adds 45 cards to the collection every week.  This is like finding the slope of the line you would graph using this data.  

To find how many cards she starts out with, use the point-intercept form

y - y1 = m(x - x1)    m = 45, use the point (3, 295)

y - 295 = 45(x - 3)

y - 295 = 45x - 135

y = 45x + 160   now the equation is in slope-intercept form y = mx + b

The y-intercept (b) is where x = 0.  So, she had 160 cards to start with.

The phrase "inconsistent pair of linear equations" refers to a set of linear equations that cannot be solved.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answer:B

Step-by-step explanation: To solve this, we first need to find the ratio of concenrate to water for each mixture. A is 2:3.5, B is 5:8, and C is 0.5:2. Now, we can roughly estimate them. C is .25, B is around .6, and A is around .57. This means that B is the most lemony.

Selecting a larger sample size increases the likelihood of selecting a mean height less than 70 inches. The normal distribution also increases the chances of having a mean height less than 70 inches.

The normal  is a bell-shaped curve, which means that most of the data points will be close to the mean. Therefore, when you take a larger sample size, the mean of the sample will be closer to the population mean. Additionally, due to the nature of the normal distribution, you will have a better chance of having a mean height less than 70 inches when you take a sample size of 20 people. Therefore, you are more likely to select a sample of 20 women with a mean height less than 70 inches.

You are more likely to select a sample of 20 women with a mean height less than 70 inches. This is because when you select a sample of 20 people, you are taking a larger sample size and therefore the mean will be closer to the population mean than if you select just one person. Additionally, when you select a sample of 20 people, you will have a better chance of having a mean height less than 70 inches due to the nature of the normal distribution.

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Answer:

the answer is either 47 or 35

Step-by-step explanation:

this is. Because the only factors of five are 5 or 1 so all you can do is 5x3weeks=15 so 32+15=47

Or it can be 32+(1x3weeks)=32+3=35

Answer:

3515.3443 grams

The answer is given below.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

35z>34

=> z>34/35

=> z> 0.97

which is < 1

hence, The answer is given below.

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The median weekly income for someone with a bachelor's degree is 1137.006

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

The median weekly income for someone with a high school diploma was $629.00. If they continued their education and obtained abachelor's degree,

their median weekly income increased about 63.7%.

so we have to Determine the median weekly income for someone with a

bachelor's degree.

That is,

678x0.677=459.006

=459.006+678

=1137.006

Therefore, The median weekly income for someone with a bachelor's degree is 1137.006

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The ratio scale is the measurement is being used when a researcher measures the number of car accidents that participants have been involved in during their lifetime.

A ratio scale is a quantitative scale where there is a true zero and equal intervals between neighboring points. A zero on a ratio scale means there is a total absence of the variable you are measuring.

A ratio Scale is a type of measurement scale that is quantitative in nature, it has an absolute zero and its intervals or differences are used for comparison.

A ratio scale is the most informative because it tends to tell the order and number of objects between scales.

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Answer:

Look at the explanation.

Step-by-step explanation:

A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.

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Andrew collected 3/15 of the stamps in form of fraction.

To find the fraction of stamps collected by Andrew, we need to divide the number of stamps he collected by the total number of stamps collected by all 4 students:

Fraction collected by Andrew = Number of stamps collected by Andrew / Total number of stamps collected

= 15 / (19 + 15 + 23 + 18)

= 15 / 75

= 3/15

So, Andrew collected 3/15 of the stamps.

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The proof that the square root of 2 is irrational can be shown using proof by contradiction.

Assume that the square root of 2 is rational, meaning that it can be expressed as the ratio of two integers (p/q, where p and q are integers and q is not equal to zero).

This means that:

√2 = p/q, where p and q are integers and q is not equal to zero.

Squaring both sides of the equation:

2 = p^2/q^2

multiply both sides by q^2

2q^2 = p^2

Now, since p and q are integers, p^2 and q^2 are also integers.

Therefore, 2q^2 is an even integer.

However, if 2q^2 is an even integer, q^2 is also an even integer, which means that q is even.

Therefore, p and q have a common factor of 2. But, this contradicts the assumption that p and q have no common factors other than 1.

Therefore, our assumption that the square root of 2 is rational must be false.

Hence, we can conclude that the square root of 2 is irrational.

Answer:

To prove that the square root of 2 is irrational, we will use a proof by contradiction. Suppose that the square root of 2 is rational, which means that it can be expressed as a fraction a/b, where a and b are integers with no common factors. Then, we can square both sides of this equation to get:

2 = (a/b)^2 = a^2 / b^2

Multiplying both sides by b^2, we get:

2b^2 = a^2

This means that a^2 is an even number, because it is equal to 2 times b^2. Therefore, a must be an even number, because the square of an odd number is always odd. Let a = 2c, where c is an integer. Substituting this into the previous equation, we get:

2b^2 = (2c)^2 = 4c^2

Dividing both sides by 2, we get:

b^2 = 2c^2

This means that b^2 is an even number, and therefore b must also be an even number. However, this contradicts our original assumption that a and b have no common factors. Therefore, our assumption that the square root of 2 is rational must be false, and the square root of 2 is indeed an irrational number.

Answer:

The one under the 1st I am pretty sure.

Step-by-step explanation:

Answer:

each pencil costs 11 cents

Step-by-step explanation:

1.35 divided by

Answer:

Step-by-step explanation:

Firstly, divide the figure into 2

You will have a rectangle on the bottom and a triangle on top. Let's name your shapes by saying that the rectangle is FIG -1 and your triangle is FIG -2

FIG -1

b x h

8 x 11

88 cm^2

FIG -2

b x h / 2

7 x 11 / 2

77/2

38.5 cm^2

Total = 88 + 38.5

        = 126.5 cm^2  

The measure of ∠F is 57 degree.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. Degree is the unit of measure is used to measure the magnitude of an angle.  A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

cos F = (e² + g² - f²)/2eg

cos F = (2.6² + 8.3²- 7.2²)/2(2.6)(8.3)

  = 0.5516

∠F = arccos 0.5516

∠F = 57° (rounded to the nearest degree)

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