write the equation for a line perpendicular to y = 3x - 2

The logarithmic form of the equation is [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex] .

We have given an equation [tex](\frac{1}{3})^3 =\frac{1}{27}[/tex] .

Taking log on both sides , we get

   [tex]log(\frac{1}{3})^3 =log(\frac{1}{27})[/tex]                    ..(1)

Applying the property of logarithm which is given by [tex]log_ab=bloga[/tex] in equation (1) ,we get

        [tex]3log(\frac{1}{3}) =log(\frac{1}{27})[/tex]

On rearranging the above equation , we get

         [tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})} =3[/tex]                          ..(2)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\

  [tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})}[/tex]   can be written as  [tex]log_{\frac{1}{3} }\frac{1}{27}[/tex] using property

Putting in equation (2) , we get

     [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex]

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Answer:3) Find the domain of each, express answers in interval notation x+1 a) f(x) = 3x +2 b) f(x)=. 5 x² - 4x-12 x+1 for x < -2 ... 1 a) g(x) = f(x+10) b) g(x)

Step-by-step explanation:

Answer:

3/7y= -8/7

Step-by-step explanation:

reduce the greatest common factor on both sides of th equation

Answer:

Cross two lines then put one line above the point of intersection and below the point of intersection. straightforward though

The inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The given parameters are

Your rate, r1 = 6 miles per hour

Your friend's rate, r2 = 6.6 feet per second

Distance apart = 55 feet

Convert your rate to feet per second, we have

Your rate, r1 = 6 * 1.47 feet per second

Evaluate

Your rate, r1 = 8.8 feet per second

To calculate the time that your friend is ahead of you, we use the following expression

r1 * t < distance apart + r2 * t

So, we have

8.8t < 55 + 6.6t

Collect the like terms

So, we have

8.8t - 6.6t < 55

Evaluate the like terms

So, we have

2.2t < 55

Divide both sides by 2.2

So, we have

t < 25

Hence, the inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

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Answer:

12

Step-by-step explanation:

See attachment for step-by-step instructions

According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.

According to the statement

We have to find that the correct statement.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile.

Then

The equation is given as,

y = mx + c

Where m is that the slope of the road and c is that the y-intercept of the line.

Let y be the whole amount and x be the amount of miles.

Samir can rent a moving truck from Company A for $135 plus $0.50 per mile. Then the equation are going to be

y = 0.5x + 135 ....1

Company B for $125 plus $0.70 per mile. then the equation are going to be

y = 0.7x + 125 ....2

For the identical rent, the amount of miles are going to be

0.7x + 125 = 0.5x + 135

0.2x = 100

x = 500 miles

Renting from Company A are going to be cheaper if Samir drives the truck 500 miles. Then the right option is A .

So, According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.

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The area of this rectangular object is equal to 12 × 10⁹ square microns.

Given the following data:

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given parameters into the formula, we have;

Area of a rectangle = 6,000 microns × 2,000,000 microns

Area of a rectangle = 12 × 10⁹ square microns.

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The average change in speed each second is 0.0583 miles per squared second

The given parameters are:

Speed = 3.5 miles per second

Time = 60 seconds

The average change in speed each second is calculated as

Average change = Speed/Time

This gives

Average change = (3.5 miles per second)/60 seconds

Evaluate the quotient

Average change = 0.0583 miles per squared second

Hence, the average change in speed each second is 0.0583 miles per squared second

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The maximum number of people who can go to the amusement park is 7 based on tickets cost of $20.50 per person

What is the total cost function for the amusement park?

The total cost is made up of cost of admission and parking and the tickets cost per person, which means that the total cost can be modeled as shown below based on the fact the number of persons that can attend is x

total cost=6.25+20.50x

total cost=155

155=6.25+20.50x

155-6.25=20.50x

148.75=20.50x

x=148.75/20.50

x=7(rounded to the nearest whole number)

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The unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

We have the fare for 81 minutes to be $56. 70

Then we are to find the amount that would be needed for 31 minutes.

In order to get this value we would have to cross multiply

such that we would have

81 minutes = $56.70

31 minutes = ?

then 56 * 31 = 1736

1736 / 81

= 21.4 dollars.

Hence we would conclude that the unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

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Answer:

2.5£ =25tacos

1£ =?

=1*25/2.5

=10 tacos:

Answer:

-2

Step-by-step explanation:

Integer math!

Answer:

You didn’t add the data chart. But I’ll try my best to help.

Step-by-step explanation:

If it landed on the same time multiple times than you will most likely land the same time again.

Answer:

The coordinates of G' after being translated is (-8,6)

Step-by-step explanation:

Answer:

BC.

Step-by-step explanation:

Answer:

Line segment BC.

Step-by-step explanation:

Parallel lines are always the same distance apart at least. In this instance, FG and BC are parallel.

Answer:

7.9

Step-by-step explanation:

yep

Step-by-step explanation:

When we plug in the values we get

[tex]f(g(x)) = ({x}^{2} - 3x + 1) - 4 \\ = {x}^{2} - 3x - 3 [/tex]

[tex]g(f(x)) = {(x - 4)}^{2} - 3(x - 4) + 1[/tex]

[tex] {x}^{2} - 3x - 3 = {(x - 4)(x - 4)} - 3x + 12 + 1 \\ {x }^{2} - 3x - 3 = {x}^{2} - 8x + 16 - 3x + 13 \\ \\ {x}^{2} - {x}^{2} - 3x + 8x + 3x - 3 - 16 - 13 = 0 \\ 8x - 32 = 0 \\ 8x = 32 \\ \frac{8x}{8} = \frac{32}{8} \\ x = 4[/tex]

Answer: 3.4/8 or 0.425

Step-by-step explanation:

Use this Rule: a/b * c/d = ac/bd

Simplify numerator (top): 1 * 3.4 = 3.4

Than Simplify denominator (bottom): 2 * 4 = 8

Finally: 3.4/8 or 0.425 (decimal)

This is my answer and I know this is correct because of using the Rule which demostrates that you should multiply top and bottom

Answer: 1b. 5x - 30, 1c. -8x - 32, -8x + 12, 1e. -6x + 21, 1f. 3( 3x - 9)

Step-by-step explanation:

You multiply the number outside of the parentheses by the numbers inside, if it's just an "x", you assume there's a 1 beside it, ex: 8(x + 2)... 8 multiplied by x will give you 8x, 8 multiplied by 2 will give you 16.

if the numbers are both negative when you multiply them it becomes a positive, ex: -8(x - 2)... -8 multiplied by x will be -8, and -8 multiplied by -2 will become positive 16.

But if one number is negative and the other is positive then the answer will be negative.

The complete statement is 30.9mm =  1. 21  in

Conversion of units is simply the conversion between different units of measurement for a particular quantity.

Given the statement;

30.9mm = in

It is important to note that;

25. 4 millimeters = 1 inch

Then;

30. 9 millimeters = x inches

Cross multiply

x ×  25. 4 = 30. 9 × 1

To make 'x' the subject

Divide both sides by 25. 4, we have;

x = 30. 9/ 25. 4

x = 1. 21 Inches

Thus, the complete statement is 30.9mm =  1. 21  in

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The amount a customer will save if she buys 5 CDs will be equal to $ 30.25

We are given that:

Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.

If a customer registers for the store member, he get a discount = 15 %.

Now, let the regular priced CD purchased be x and the application for store member be y.

So, the functions will become:

For rebate:

R (x) = 5 x

For discount:

M (y) = 15 % of x

M (y) = 0.15 x

Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x

If x = 5 ( number of CD)

= 6.05 ( 5)

= $ 30.25

Therefore, we get that, the amount a customer will save if she buys 5 CDs will be equal to $ 30.25

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The coupon gives Shanice 40% off the original price, based on the coupon of $20 on an original price of $50

What is the price after having considered the coupon?

The price of the pair of jeans after having considered the coupon is the original price of $50 minus the $20 coupon

price after the coupon=$50-$20

price after the coupon=$30

However, the task at hand is to determine the coupon as a percentage of the original price

coupon as % of original price=$20/$50

coupon as % of original price=40.00%

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The methods used to analyze data produced by scientific studies are called statistics. Option (c) is correct.

What are experiments and how do we analyze them using statistics?

Experiments are procedures or methods carried out under controlled conditions to discover a new fact or to test or  establish a hypothesis  that already exists.

From experiments we generate certain scientific data but to analyze data we need statistics.

Statistics is a process of collecting and analyzing and interpreting data.

Therefore the methods used to analyze data produced by scientific studies will be done by statistics.

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Answer:

Step-by-step explanation: Hello,

the answer

The simplified form of the given expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is option d 49.

Given,

The expression = [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]

We can simplify this expression by using Laws of Indices;

The first rule: [tex]a^{n}[/tex] × [tex]a^{m}[/tex] = [tex]a^{m+n}[/tex]

The second rule: [tex](a^{n}) ^{m}[/tex] = [tex]a^{mn}[/tex]

The third rule: [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]

The fourth rule: [tex]a^{0}[/tex] = 1

The fifth rule: [tex]a^{-1}[/tex] = [tex]\frac{1}{a}[/tex]  ; [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

The sixth rule: [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]  ; [tex]a^{\frac{1}{m} }[/tex] = [tex]\sqrt[m]{a}[/tex]  ; [tex]a^{\frac{n}{m} }[/tex] = [tex](a^{\frac{1}{m} } )^{n}[/tex] = [tex](\sqrt[m]{a} )^{n}[/tex]

Here we can use First, Second, Fifth and Sixth rule:

[tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]

= [tex](7^{5} )^{\frac{1}{6} }[/tex] ×[tex](7^{7} )^{\frac{1}{6} }[/tex]

= [tex]16807^{\frac{1}{6} }[/tex] × [tex]823543^{\frac{1}{6} }[/tex]

= 5.061140185 × 9.68161288

= 49

That is, the simplified form of the expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is 49.

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The number of times that the Great Wall of China is as long as the Panama Canal will be 2 × 10².

It should be noted that the Great Wall of China built in the 7th century BCE, is about 1 x 10⁴ miles long and the Panama Canal, built two thousand years later, is about 5 x 10^1 miles long.

Therefore, the number of times that the Great Wall of China is as long as the Panama Canal will be:

= 1 × 10⁴ / 5 × 10¹

= 2 × 10²

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Applying the linear pair postulate:

y = 30

m<ACB = 160°

According to the linear pair postulate, the sum of two adjacent angles that form a linear pair is equal to 180 degrees.

Given the following:

m<ACB = (4y + 40)°

m<DCE = (y - 10)°

Angles ACB and DCE are a linear pair. Therefore:

m<ACB + m<DCE = 180°

Substitute

(4y + 40) + (y - 10) = 180

Solve for y

4y + 40 + y - 10 = 180

Combine like terms

5y + 30 = 180

Subtract 30 from both sides

5y + 30 - 30 = 180 - 30

5y = 150

Divide both sides by 5

5y/5 = 150/5

y = 30

Find m<ACB:

m<ACB = (4y + 40)°

Plug in the value of y

m<ACB = 4(30) + 40

m<ACB = 120 + 40

m<ACB = 160°

Thus, applying the linear pair postulate:

y = 30

m<ACB = 160°

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Answer: A=(pi)r^2

Step-by-step explanation:

multiply pi (3.14) times the radius to the power of 2.

[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

Another law of indices says that if two terms having same base are multiplied together, then their indices are added.

i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]

According to the given condition,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]

Applying the laws of indices mentioned above,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]

= [tex]5^{3} .( 5 )[/tex]  = [tex]5^{3 + 1}[/tex]

= [tex]5^{4} = 625.[/tex]

Thus,  [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

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