The statement x + 2 = 2 + x is an example of the commutative property of addition.
True
False

The expressions are simplified to;

1. 5x + 11

2. x - 11

3. x - 11y

4. 4x + 20

5. 5x² - y²

6. 5x² - 5y² - 5y

7. -12y²

8. 4x + 20

9. 4x - 20

10. 8x² - 20xy

To simply the algebraic expression, we have to expand the bracket, collect the like terms and then add or subtract them.

From the information given, we have that;

1. 3x + 5 + 2x + 6

collect and add like terms

5x + 11

2. 3x - 5 - 2x - 6

collect and add the like terms

x - 11

3. 3x - 5y - 2x - 6y

collect and add the like terms

x - 11y

4. 6x + 12 - 2x + 8

collect and add the like terms

4x + 20

5. 3x² + 5y² + 2x² - 6y²

collect and add the like terms

5x² - y²

6. 3x² - 5y² + 2x² - 6y

collect and add the like terms

5x² - 5y² - 5y

7. 6x³ - 10y³ + 4x³ - 12y²

collect and add the like terms

-12y²

8. 6(x + 2) - 2(x - 4)

expand the bracket

6x + 12 - 2x + 8

4x + 20

9. 6(x - 2) - 2(x + 4)

expand the bracket

6x - 12 - 2x - 8

4x - 20

10. 6x(x - 2y) + 2x(x - 4y)

expand the bracket

6x² - 12xy + 2x² - 8xy

8x² - 20xy

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Answer:

Gail spent $4 and Jackie spent $7

Step-by-step explanation:

Let j = Jackie

Let g - Gail

j = 2g -1                  j + g = 11

substitute 2g - 1 for j in the second equation

j + g = 11

2g - 1 +g =11  Combine the g's

3g -1 = 11   Add 1 to both sides of the equation

3g = 12  Divide both sides by 3

g = 4

Plug 4 in for g to find j

j = 2g -1

j = 2(4) -1

j = 8 -1

j = 7

Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

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Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Answer:

b. Use an AD/AS diagram to show how a decrease in the inflation target can keep inflation and short-run output from starting to rise in 2021. Explain your diagram and what it reveals about monetary policy.

Answer:

938583

Step-by-step explanation:

Answer:

I think is c 2 hope that works

Step-by-step explanation:

please give brainliest :D

Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

c=\(\sqrt{a^2+b^2}\)

c=\(\sqrt{28^2+96^2}\)

c=\(\sqrt{10,000}\)

c=100

Therefore, the length of the hypotenuse is 100.

Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle

in one hour is c 4

The line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.

If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.

The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.

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Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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Given :

A line 2x + 1 =0 .

To Find :

The slope of the given line .

Solution :

We know , slope of line is given by the tangent of the angle between the x-axis and the line .

Now, for line 2x + 1 =0 i.e \(x=\dfrac{-1}{2}\) .

The line is perpendicular to x-axis and cuts the x-axis at \(\dfrac{-1}{2}\) .

Therefore , the angle between the line and x-axis is \(90^o\) .

So , slope \(m=\tan\ 90^o\) i.e undefined .

Therefore , the slope of given line is not defined .

Hence , this is the required solution .

If the ratio of a basketball players completed free throws to attempted free throws is 9 to 12. If she attempted 20 free throws, the number of  free throws she completed is 27 free throws.

Given data:

Attempted free throws = 9 to 12

Free throws = 20

Formulate

9/12= 20/x

Cross-multiply

9x = 20× 12

9x = 240

Divide both side by 9x

x = 240/9

x = 26.6

x = 27 free throws (Approximately)

Therefore the free throws is 27.

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Area of a rectangular prism:

TA: Total area

BA: Base area

LA: lateral area

side = 13

hight= 16

BA is multiplied times two because there are two bases:

Volume (V):

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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the line shown ISN'T the line of best fit. The slope should INCREASE and the y-intercept should REGRESS.

The line shown is not the line of best fit. The slope should increase and the y-intercept should regress.

We have given the graph of the regression line.

Regression lines can be used as a way of visually depicting the relationship between the independent (x) and dependent (y) variables in the graph.

A straight line depicts a linear trend in the data

Therefore, from the graph, we can conclude that,

The line shown is not the line of best fit.

The slope should increase and the y-intercept should regress.

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Answer:

either 160 or 128

Step-by-step explanation:

the equation is length x width x height so 2x4x20 or 2x4x16

hope this helps!

Answer: Therefore, the value of x is 4√5 meters.

Step-by-step explanation:

To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can see that side a is the hypotenuse, so we have:

a^2 = b^2 + c^2

Substituting the given values, we get:

(6m)^2 = (3m)^2 + (2m)^2

Simplifying:

36m^2 = 9m^2 + 4m^2

36m^2 = 13m^2

Dividing both sides by 13m^2:

36/13 = (4√5)^2/x^2

Simplifying:

x^2 = (4√5)^2 / (36/13)

x^2 = (16513) / 36

x^2 = 260/9

Taking the square root of both sides (and simplifying the surd):

x = 4√(65/9) = 4√5 X m

Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Given:

p = 47% = 0.47

n = 6

Required:

The probability that at least 4 are using their smartphones in meetings or classes.

Solution:

The binomial probability is defind as :

We will use this definition to solve for P at X = 4, X = 5 and X = 6 (since the probability of at least 4 users is asked)

Answer:

35

Step-by-step explanation:

LxWxH

2.5 x 14 x 1

=35

Answer:

Volume = 35\(cm^{3}\)

Step-by-step explanation:

Volume = length x width x height

Volume = 14 cm x 2.5 cm x 1

Volume = 35\(cm^{3}\)

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Answer:

\(P(\bar X>3.4) = 0.385\)

Step-by-step explanation:

Relevant Data provided according to the question is as follows

\(\mu\) = 3.2

\(\sigma\) = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

\(z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }\)

\(P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)\)

\(= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }\)

Now, we will solve the formula to reach the probability that is

\(= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }\)

\(= 1 - P (Z \leq \frac{0.2}{0.4})\)

\(= 1 - P (Z \leq 0.5})\)

\(= 1 - \phi (0.5)\)

= 1 - 0.6915

= 0.385

Therefore the correct answer is

\(P(\bar X>3.4) = 0.385\)

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

y=0.3x+ 18.6, option (b) has the same slope and y-intercept as our equation, so it is the correct answer.

In an equation, the expression on the left side of the equal sign is typically referred to as the "left-hand side" (LHS) and the expression on the right side is referred to as the "right-hand side" (RHS). The equal sign indicates that the two expressions have the same value, and the solution to the equation is the value(s) of the variable(s) that make(s) the equation true.

To determine the linear equation that fits the data for Tree 1, we need to find the slope (m) and y-intercept (b) of the equation y = mx + b.

We can use the given data points (1, 18.6), (3, 19.2), (5, 19.8), (7, 20.0), (9, 21.0), (11, 21.6), and (13, 22.2) to calculate the slope and y-intercept.

First, we can find the slope using the formula:

m = (y2 - y1) / (x2 - x1)

We can choose any two points to calculate the slope. Let's use (1, 18.6) and (13, 22.2):

m = (22.2 - 18.6) / (13 - 1)

m = 3.6 / 12

m = 0.3

Next, we can find the y-intercept by substituting one of the data points and the slope into the equation y = mx + b, and solving for b. Let's use the point (1, 18.6):

18.6 = 0.3(1) + b

b = 18.6 - 0.3

b = 18.3

Therefore, the linear equation that fits the data for Tree 1 is:

y = 0.3x + 18.3

Option (a) and (d) have the same slope as the equation we found, but a different y-intercept. Option (b) has the same slope and y-intercept as our equation, so it is the correct answer. Option (c) has a different slope and y-intercept, so it is not the correct answer.

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The complete question is:

The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Select the linear equation that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches.

TREE 1                                                        TREE 2

YEAR                   TRUNK                           YEAR              TRUNK                                                                      

                          DIAMETER(INCHES)                               DIAMETER

1                         18.6                                     1                              11.4

3                          19.2                                   3                              12.0

5                          19.8                                   5                              12.6

7                           20.0                                 7                              13.2

9                           21.0                                  9                              13.8

11                         21.6                                    11                             14.4

13                         22.2                                  13                             15.0

(a) y=0.3x+ 18.3

(b) y=0.3x+ 18.6

(c) y=0.6x+18.0

(d) y= 0.6x+ 18.3

Please explain and show how you got to this answer.

After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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2x=-25

Explanation

let´s solve the equatoin

Step 1

given

Step 2

finally, to isolate the term where x is, we need subtract 10 in both sides, so

therefore, the answer is

2x=-25

I hope this helps you

Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Answer:                        1. X = 24

                                      2. X = 20

Step-by-step explanation:

3

x

​

−2=6

Multiply both sides of the equation by 3.

x−6=18

Add 6 to both sides.

x=18+6

Add 18 and 6 to get 24.

x=24

_______________________________________________________

5

x

​

+1=5

Multiply both sides of the equation by 5.

x+5=25

Subtract 5 from both sides.

x=25−5

Subtract 5 from 25 to get 20.

x=20