Simplify the following expression using rational exponents. Assume all variables are positive.

a3/5⋅a3/4

The linear equation can be written as:

y = (3/2)*x - 21/5

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

First, we know that our line has the same slope than:

3x - 2y = 12

Rewriting that we will get:

3x - 2y = 12

3x - 12 = 2y

(3/2)x - 12/2 = y

So the slope of this line is (3/2).

And our lie has the same y-intercept as 5y + 21 = 4x

We can rewrite that to get:

5y = 4x - 21

y = (4/5)x - 21/5

The y-intercept is -21/5

Then the linear equation is:

y = (3/2)*x - 21/5

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The value of machine after 2 years is $346.4.3

Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.

Given:

C = $707 (the original cost),

r = 0.3 (the rate of depreciation),

and t = 2 (years that have gone by)

Using the Formula

V = C [tex](1-r)^t[/tex]

V = (707)(1 - 0.3)²

V = (707)(0.7)²

V = (707)(0.49)

V = 346.43

Thus, the value of machine is $346.43

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Hi there, here's your answer:

Given:

The quotient of twice the difference of five less than a number and six.

Let the number be x.

By this, it is understood that the algebraic equation is in a fractional form, with the numerator being

Twice the difference of five less than a number, i.e.

2(x - 5)

And the denominator is 6.

Therefore, we get the algebraic equation to be:

[tex]\frac{2(x-5)}{6}[/tex]

Hope it helps! Please mark as brainliest!

Answer: Let's say there are a total of 100 students at the middle school. Then, 5 parts out of 7 are playing basketball and 2 parts out of 7 are playing soccer. The percent of students playing soccer can be calculated as follows:

(2/7) * 100 = 28.57% (rounded to the nearest percent)

So, approximately 28.57% of the students at the middle school play soccer.

Step-by-step explanation:

The statements about the number -27 that are true are given as follows:

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

Integer numbers are numbers that have no decimal part, hence -27 is an example of an integer number, which are also rational numbers.

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The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.

A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.

The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".

By combining these, we can rewrite the statement as follows:

If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.

The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.

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Answer : 61.60

Step-by-step explanation:

Answer:61.60

Step-by-step explanation:

i just typed it in

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]

113.097 is the area (i used 3.14) pls comment for explanation :)

Answer:

C

Step-by-step explanation:

An irrational number cannot be shown as a simple fraction. If the number has decimals that are non-repeating (so not 7.85555555... or. 9.121212121...), cannot be shown as fractions (not 1.50000000... as it can be written as 3/2), and does not terminate (aka end).  C is the answer you're looking for, as it cannot be shown as a fraction, the numbers after the decimal go on indefinitely,  and the number's don't follow a noticeable repeatable pattern.

Answer:

Step-by-step explanation:

In the image of the trapezoid the value of angle C is 82 degrees

A trapezoid is a quadrilateral with one pair of parallel sides.

Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.

In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.

When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.

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Answer:

[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]

Step-by-step explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]

Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]  

Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]

Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]

Eq (3) - Eq (2):

[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]

Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex]  from equation (1) into equation (4) we get

[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]

Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get

[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)

If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]

The first equation is:

(5 1/5)^5 = 25x

To solve for x, we need to simplify the left side of the equation first.

(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776

So,

7776 = 25x

Therefore,

x = 7776/25 = 311.04

For the second equation:

If (8 1/3)^2 = 4x, then x =

We need to simplify the left side of the equation first.

(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81

So,

81 = 4x

Therefore,

x = 81/4 = 20.25

So the values of x that make each sentence true are 311.04 and 20.25, respectively.

The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:

Choose the data you want to examine.

gather the data

Clean up the data before analysis.

Study the information

Interpret the analysis' findings

It is common knowledge that data analysts focus on the sample size in order to

To prevent a few outlier responses from distorting the results

ensuring that the data reflects a variety of viewpoints

to prevent making erroneous conclusions due to a tiny sample size

An analyst of data is who?

An individual involved in the handling of data is referred to by this phrase.

Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.

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There is 3/4 of a gallon of bubble solution in the big bottle.

What is an equation?

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equal sign (=). An equation contains one or more variables, which are symbols that represent unknown values, and may also contain constants, coefficients, and arithmetic operations such as addition, subtraction, multiplication, and division.

Let's use "x" to represent the amount of bubble solution in the big bottle, in gallons.

According to the problem, the big bottle was divided equally among 6 small bottles, and each small bottle holds 1/8 of a gallon of bubble solution. Therefore, the total amount of bubble solution in the big bottle is equal to the sum of the amounts in the 6 small bottles:

x = 6 * (1/8)

Simplifying the right-hand side of the equation, we get:

x = 3/4

Therefore, there is 3/4 of a gallon of bubble solution in the big bottle.

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Answer:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Answer:

26.it is all about thinking

Answer:

LCD → 468

Step-by-step explanation:

[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]

[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]

[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]

Hence, the least common denominator for these three fractions would be 468.

To solve the problem we would use tangent as a trigonometric function and find the unknown value.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

From the given triangle we observe that the given values are:

Angle B, side a and side b.

To find any of the unknows in the three we use the trigonometric function tangent.

Tan α = opposite side / adjacent side

For the given figure:

Tan B = b / a

Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.

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Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

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Answer:

Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.

Step-by-step explanation:

The measure of the angles m∠BOX = 77.5° and  m∠AOX = 77.5°.

What is the angle bisector of an angle?

The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.

By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.

As m∠AOB = 155°

m∠BOX = 1/2 * m∠AOB

m∠BOX = 1/2 * 155

m∠BOX = 77.5°

also m∠AOX = 77.5°

Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.

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Answer:

The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.

So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).

Therefore, the values that are solutions to the inequality x < -2 are:

• all real numbers less than -2, such as -3, -4, -5, etc.

Note that -2 itself is not part of the solution set, since it is not less than -2.

Answer:

To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.

Discount = $365 × 0.20 = $73

So, the discount on a $365 purchase is $73.

The price after the discount would be $365 - $73 = $292.

To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:

1. Calculate the discount amount:

Discount = 20% x $365 = $73

2. Subtract the discount from the original price:

Final price = $365 - $73 = $292

Therefore, the final price of the $365 purchase with a 20% discount is $292.

=break your pencil lead while writing, and = feel overly stressed.

=put together a swing set correctly, and =read the directions.

These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).

=make an error on your income tax return, and =file Form 1040 long.

These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.

=have a salad with dinner, and =work on a home project.

These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.

Answer: 10.7 or 10.8

Step-by-step explanation:

so, first  [tex]a^{2} +b^{2} =c^{2}[/tex]

while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]

so, it will be written as,

[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]

[tex]14.0625+100=c^2[/tex]

[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:

[tex]10.7=c[/tex]

That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...

while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.

which will equal to...

[tex]4^2+10^2=c^2[/tex]

[tex]16+100=c^2[/tex]

[tex]116=c^2[/tex] then square root both sides to have an answer of:

[tex]10.77=c[/tex]

[tex]10.8[/tex] ≈ [tex]c[/tex]

hope you've understanded.!

The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (6, 12).

Points on y-axis = (3, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (6 - 3)/(12 - 6)

Slope, m = 3/6

Slope, m = 1/2.

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Answer:

Step-by-step explanation:

6

Answer:

sampling distribution

Step-by-step explanation:

:)

Answer:

61

Step-by-step explanation:

using the rule to find the fifth term from the fourth term 29

5th term = 2 × 29 + 3 = 58 + 3 = 61