Why might you need to use the addition or subtraction property of equality more than once after you have used the distributive property and combined like terms?​

Answer:

I have made it in pic hope it helps

Answer:

1 is linear, 2 is linear, 3 is not linear, 4 is not linear

Answer:

Function 1 is linear

Function 2 is linear

Function 3 is not linear

Function 4 is not linear

The rational function with the given characteristics is:

f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

We want to write a rational function with the given characteristics, first we want to have vertical asymptotes at x = -2 and x = 3, then the denominator must be:

(x - 2)*(x + 3)

We also want to have x-intercepts at (-4,0) and (-1,0), this means that the numerator must be:

a*(x + 4)*(x + 1)

Where a is a real number, then the rational function is:

f(x) = a*(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

Now we want to have an y-intercept at (0, 4)

Then we must have:

f(0) = 4 = a*(0 + 4)*(0 + 1)/[(0 - 2)*(0+ 3)]

4 = a*4/-6

(-6/4)*4 = a

-6 = a

The rational function is:

f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]

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Answer:

What is the value of x in the product of powers below?

6 Superscript 9 times 6 Superscript x = 6 squared

Negative 11

negative 7

7

11

Step-by-step explanation:

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: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

The solution to the given expression is x = -20/11

Logarithmic function are inverse of exponential functions. Given the equation below;

log (6 x + 10) = log 1/2 x

In order to determine the solution to the given logarithmic equation, we will first have to cancel the logarithm on both sides to have

6x + 10 = 1/2x

Collect the like terms

6x - 1/2x = 0 - 10

Find the LCD

12x-x/2 = -10
11x/2 = -10

Cross multiply

11x = -2 * 10

11x = -20

Divide both sides by 11

11x/11 = -20/11

x = -20/11

Hence the solution to the given expression is x = -20/11

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Answer:

\(x = 8\)

Step-by-step explanation:

Given

The attached triangle

Required

Determine the value of x

x represents the height of the triangle.

And the area of a triangle is calculated as:

\(Area = \frac{1}{2} * Base * Height\)

Where

\(Base = 4\)

\(Area = 16\)

\(Height = x\)

The expression becomes

\(16 = \frac{1}{2} * 4* x\)

\(16 = 2* x\)

\(16 = 2x\)

Divide through by 2

\(8 = x\)

\(x = 8\)

In conclusion, none of the given statements are correct based on the information provided.

To determine the correct statement, let's analyze the given information and the regression equation:

The regression equation for estimating the number of customers on a given day is y = 1.03x + 229.4, where x represents the day number and y represents the number of customers served.

We are also given that the restaurant has been making a net profit of $5.82, on average per customer:

Now let's evaluate each statement:

A. On day 7, the owner can expect 15 more customers than she has served on day 6.

To determine the number of customers on day 7, we substitute x = 7 into the regression equation:

y = 1.03(7) + 229.4 = 7.21 + 229.4 = 236.61

So, the number of customers on day 7 is approximately 237, which is not 15 more than the number of customers served on day 6.

Therefore, statement A is incorrect.

B. If the number of customers continues to follow the current trend, the restaurant will make a net profit of $1,377 on day 7.

To calculate the net profit on day 7, we need to multiply the average net profit per customer ($5.82) by the number of customers on day 7:

Net profit on day 7 = $5.82 \(\times\) 237 ≈ $1,379.34

So, statement B is incorrect as the net profit on day 7 is not expected to be $1,377.

C. On day 12, the owner can expect a net profit of $1,300.

Since the question only provides information about the number of customers served for the first 6 days, we cannot determine the net profit on day 12.

Therefore, statement C is incorrect.

D. Net profit for days 6 and 7 combined is expected to be less than the earned net profit on day 1.

To calculate the net profit for days 6 and 7 combined, we need to calculate the number of customers on both days using the regression equation and then multiply it by the average net profit per customer.

Let's substitute x = 6 into the regression equation:

y = 1.03(6) + 229.4 = 6.18 + 229.4 ≈ 235.58

Now, let's calculate the net profit for days 6 and 7 combined:

Net profit on days 6 and 7 = ($5.82 \(\times\) 235) + ($5.82 \(\times\) 237) ≈ $2,735.2

Comparing this to the earned net profit on day 1, we cannot determine if it is less or greater without the information provided.

Therefore, statement D is incorrect.

In conclusion, none of the given statements are correct based on the information provided.

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For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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Answer:

A = B + C + D

rearrange the equation

B = A - C - D

Step-by-step explanation:

rearrange the equation so B is on one side of the equal sign

A = B + C + D

A - C - D = B

Answer: B=A-C-D

Step-by-step explanation:

To solve for B, we want to use our algebraic variables to isolate B.

A=B+C+D                       [subtract both sides by C]

A-C=B+D                        [subtract both sides by D]

A-C-D=B

B=A-C-D

The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

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Please help me important question in image

Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

Answer:

it might be both

Step-by-step explanation:

Answer:

t=10.9

Step-by-step explanation:

8t-13t+10(t-2)=34

8t-13t+10t-20=34

5t-20=34

5t=54

t=10.9

Answer:

If Tim actually earned 62 points . Therefore Tim's percent error is 58.1 % .

Step-by-step explanation:

The required answer is the number of drivers between 40 and 50 is 4, the number of drivers between 50 and 60 is 8, the number of drivers between 60 and 70 is 10 and the number of drivers between 70 and 80 is 3.

Given that total number of driver driving the vehicle is 25.

40% of drivers surveyed were driving between 60 and 70 mph.

12% of drivers are between 70 and 80 mph.

The amounts of cars driving between 50 and 60 mph is  double than amounts of cars driving between 40 and 50 mph .

The number of drivers who are driving between 60 and 70 mph is

40% of total numbers of drivers = 40/100 × 25 = 10 drivers.

The number of drivers who are driving between 70 and 80 mph is

12% of total numbers of drivers = 12/100 × 25 = 3 drivers.

The remaining number of drivers is the difference between total number of driver  and sum of number of drivers between 60 and 70 and number of drivers between 70 and 80 is   25 - (10+3) =25 - 13 = 12.

Suppose the number of drivers between 40 and 50 be y then amounts of cars driving between 50 and 60 mph is 2y. The sum of drivers between 40 and 60 is 12.

That implies,  y + 2y = 12.

Thus, 3y = 12.

Therefore, y = 4.

Hence, the number of drivers between 40 and 50 is 4, the number of drivers between 50 and 60 is 8, the number of drivers between 60 and 70 is 10 and the number of drivers between 70 and 80 is 3.

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Answer:

5. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

B(4.4.4.4.4)

Step-by-step explanation:

4^5 = 4*4*4*4*4

Answer:

x = 29.15

Step-by-step explanation:

a^2 + b^2 = c^2

15^2 + 25^2 = 890

square root of 850 is 29.154759....

:)

Answer:

The correct answer is 30.

Step-by-step explanation:

To find this out I found the fraction of 6 and 8 to 10. This is 3/5 and 4/5 to find x on the other triangle all I had to do was multiply 25 times 1 1/5. Sorry for the bad explanation it was kind of confusing to word but I hope this helps!

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

Answer:

6x+5

Step-by-step explanation:

2x+4x =6x

10-5=5

6x+5

Answer:

You would need thirteen and a half( \(13\frac{1}{2}\)) cups of flour.

Step-by-step explanation:

You can find this by taking \(4\frac{1}{2}\) and multiplying it by 3, since 24/8=3. This gives you \(13\frac{1}{2}\) .

Answer:

5th horizontal line on the graph

Step-by-step explanation:

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8