Determine the inverse of y= 2x-3

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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Answer: The correct solution using the quadratic formula is:

x = (-(-5) ± sqrt((-5)^2 - 4(1)(-2))) / (2(1))

Simplifying:

x = (5 ± sqrt(33)) / 2

Therefore, the exact solutions of x^2 - 5x - 2 = 0 are:

x = (5 + sqrt(33)) / 2 or x = (5 - sqrt(33)) / 2

So the final answers are:

x = 2.79 or x = 2.21 (rounded to two decimal places)

Your welcome (:

Answer:

C

Step-by-step explanation:

It was right for me

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Answer:

C.  x = 1/2

Step-by-step explanation:

To find x, simply take the cube root of the cube's given volume.  with a volume of 1/8 cubic centimetres, (this is an assumption, as the question expresses the volume in square centimetres, which is not a valid unite of volume; presumably that's a typo), the side length will be:

√(1/8)

= √1 / √8

= 1 / 2

So x is equal to 1/2 of a centimetre.

Answer:

x= 1/2

Step-by-step explanation:

The formula to find the volume of a cube is \(a^3\), we can work backwards with the volume to find the edges:

\(1/8=x^3\\\sqrt[3]{1/8} =x\\1/2=x\)

Answer:

the equivalent expression is 1.1(1.3)^4 ×(1.3)^x

Answer:

d

Step-by-step explanation:

i took the test

Answer:

→ 1 hour : 16/21 dresses

Step-by-step explanation:

you can simplify if you want!

Answer:

the answer to your eqauation is 531,441

Step-by-step explanation:

3^5 x 3^7

243 x 2,187

=531,441

Hope this helped!! :)

The decimal representation of the given sequence is 4,063.21.

The given sequence can be interpreted as follows: "63 ones, 21 hundredths, 4 thousand." To convert this sequence into decimal form, we need to understand the place value of each digit.

Starting from the left, we have "63 ones." This means we have 63 units, which can be represented as 63.

Next, we have "21 hundredths." Since there are two digits after the decimal point, the number becomes 0.21.

Finally, we have "4 thousand." Considering the place value, 4 thousand would be written as 4,000.

Putting it all together, we have 63 + 0.21 + 4,000, which equals 4,063.21. Therefore, the decimal representation of the given sequence is 4,063.21.

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Answer:

The left table's answers are  5, 30, and 60.

The right table's answers are 20, 36, and 22.5

And the bottom table's answers are 32, 12, and 40

Hope that helps!

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______________________________

 \(\bold{Solution~Steps:}\)

\(1.)~Multiply~the~parenthesis:\)

\(2.)~Subtract~the~parenthesis:\)

\(3.)~Subtract~on~the~side~without~an~equal:\)

______________________________

 \(\bold{Answer:}\)

______________________________

 \(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~-TotallyNotTrillex}\)

Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

Answer:

1. The mean is 162 divided 6 = 27 which is like 27 x 6 = 162

2. So since 17 and 19 are in the middle of course you will have to add that together 17 + 19 = 36 but then you MUST ALWAYS divide by 2 which 36 divided by 2 = 18

3. Yes there is a outlier. and i believe it's 82

4. i believe the mean will be 80 but then divided by 5 will be 16

hope this helped :D

Step-by-step explanation:

A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer:

Step-by-step explanation:

x = 2, y = -5

√(2²+(-5)²) = √29

cosθ = 2/√29 = (2√29)/29

sinθ = -5/√29

cscθ = 1/sinθ = -√29/5

tanθ = sinθ/cosθ = -5/2

The values of cos theta is 2/\(\sqrt{29}\) , cosec theta is \(\sqrt{29} /5\) and tan theta is 5/2 if the point on the terminal side of theta is (2,-5).

It says that in a right angled triangle the square of the hypotenuse is equal to the sum of the square of base and square of height.

We have been given a point (2,-5) on the terminal side. Let us plot the point on the graph and join it with origin from both ends.

By pythagoras theorem we can easily find AC=\(\sqrt{5^{2}+2^{2} }\)

AC=\(\sqrt{29}\)

With the help of the sides of the triangle we can find the value of

cos theta=2/\(\sqrt{29}\)

cosec theta=\(\sqrt{29}\)/5

tan theta=5/2

Hence the values of cos theta, cosec theta, tan theta are 2/\(\sqrt{29}\),\(\sqrt{29}\)/5,5/2 respectively.

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The average rate of change of the function over the interval is 1

From the question, we have the following parameters that can be used in our computation:

f(x) = x

The interval is given as

From x = 4 to x = 9

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(4) = 4

f(9) = 9

Next, we have

Rate = (9 - 4)/(9 - 4)

Evaluate

Rate = 1

Hence, the rate is 12

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Answer:

40

Step-by-step explanation:

215% = 2.15

86 / 2.15 = 40

Answer:

\(40\)

I uncertainty

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

c = 5

Step-by-step explanation:

3c - 8c + 7 = -18

-5c + 7 = -18

-5c = -25

c = 5

Answer:

Mochi is growing quicker.

Step-by-step explanation:

At 3 weeks Mochi was 13 pounds but Kappa was only at 11. Hope this helps! I'd really appreciate brainliest.

Answer:

Mochi

Step-by-step explanation:

by 2 weeks Mochi was at weight 9 while Kappa was at 8 in weight the same time.

Here, given successive discounts of 10% and 5%.

So, the net price after discount can be obtained using the formula

now, substitute the values in the given formula to get the answer.

Therefore, the net price is 1795.5 pesos.

Answer:

Step-by-step explanation:

ASQASSA

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

The second term is 3

Step-by-step explanation:

C(n)=-6(-1/3) n-1

The first term of the sequence

C(1) = -6(-1/3)1-1

C(1) = (2)-1

C(1) = 1

C(n)=-6(-1/3) n-1

The second term of the sequence

C(2) = -6(-1/3)2-1

C(2) = -6(-2/3)-1

C(2) = 4-1

C(2) = 3

Answer:

2

Step-by-step explanation:

C(2)= -6(-1/3)^2-1

=2

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

The expanded form of (16x-8) is 16x - 8.

Step-by-step explanation:

In mathematics, the expanded form of a mathematical expression is a way of writing out the terms of the expression using their full definitions.

For example, the expression (16x - 8) can be written in expanded form as 16x - 8. This is because the expression consists of two terms: 16x and -8. The term 16x represents the product of 16 and x, while the term -8 represents the negative of 8.

In general, the expanded form of a mathematical expression is obtained by writing out each term in the expression using its full definition, rather than using abbreviations or symbols. This can be helpful for understanding the structure of an expression and how it is derived.