Why does the operations subtraction and division Cannot be applied by commutative property and associative property?.

The number of terms in the expansion of {(2x - 3y)² (2x + 3y)²}² are 5

Consider given mathematical expression {(2x - 3y)² (2x + 3y)²}²

We need to find the number of terms in the expansion of {(2x - 3y)² (2x + 3y)²}²

consider, {(2x - 3y)² (2x + 3y)²}²

= {[(2x - 3y) × (2x - 3y)] × [(2x + 3y) × (2x - 3y)]}²

= {[(2x - 3y) × (2x + 3y)] × [(2x - 3y) × (2x - 3y)]}²   ......(commutative property of multiplication)

We know that the expansion of a² - b² = (a + b)(a - b)

Using this identity (2x - 3y) × (2x + 3y) = (2x)² - (3y)²

So given expression becomes,

{(2x - 3y)² (2x + 3y)²}²

=  {[(2x)² - (3y)² ] × [(2x)² - (3y)² ]}²

= {[(2x)² - (3y)² ]²}²

= [(2x)² - (3y)² ]⁴            .........(using properties of exponents)

We know that the number of terms in the binomial expansion of (a + b)^n are (n + 1)

Here, a = (2x)², b = - (3y)² and n = 4

Thus, the number of terms in the expansion of  [(2x)² - (3y)² ]⁴   are 4 + 1 = 5

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The complete question is:

What is the number of terms in the expansion of  {(2x - 3y)² (2x + 3y)²}² ?

The correct pairs pf points and axis of symmetry  are  (-1,-8) & y=-8 respectively.

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph if and the maximum (highest point) of the graph if .

Given here; A parabola with upwards curve.

Now we know, The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward. The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.

Thus we can clearly observe from the graph that (-1,-8) is the vertex of the parabola and we know the parabola is symmetric around its vertex.

Therefore the axis of symmetry of the parabola is y=-8

Hence, The correct pairs pf points and axis of symmetry  are  (-1,-8) & y=-8 respectively.

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Answer:

Step-by-step explanation:

z°=180°-79°=91°

(3x+13)°=79°, so x=22°

Answer:

y = 5.2

Step-by-step explanation:

We can use the laws of sine to solve for this, the laws of sine state that:

[tex]\displaystyle{\dfrac{\sin A}{a}=\dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}[/tex]

In this diagram, we can rewrite the general form of sinA, sinB, sinC as:

[tex]\displaystyle{\dfrac{\sin F}{f}=\dfrac{\sin E}{e} = \dfrac{\sin D}{d} = 2R}[/tex]

We can use the equation of [tex]\diplaystyle{\dfrac{\sin F}{f} = \dfrac{\sin E}{e}}[/tex] to solve for the value of e. In this case, f is 7 since sides are opposite to measurements, and the opposite of measurement F is side length 7 units. The opposite side of measurement E is side length y units. Hence, f = 7 and e = y.

[tex]\diplaystyle{\dfrac{\sin F}{7} = \dfrac{\sin E}{y}}[/tex]

We know that the measurement E is 48°.

[tex]\diplaystyle{\dfrac{\sin F}{7} = \dfrac{\sin 48 \textdegree}{y}}[/tex]

We can find the measurement F by using the euclidean triangle theory that all sides will add up to 180°. This will result in 42° + 48° + F = 180. Solve the equation:

[tex]\displaystyle{90 \textdegree + F = 180 \textdegree}\\\\\displaystyle{F = 180 \textdegree - 90 \textdegree}\\\\\displaystyle{F = 90 \textdegree}[/tex]

Hence, the measurement of F will equal to 90°.  

[tex]\diplaystyle{\dfrac{\sin 90 \textdegree}{7} = \dfrac{\sin 48 \textdegree}{y}}[/tex]

Solve the equation for y by firstly multiplying both sides by 7y to clear off denominators.

[tex]\diplaystyle{\dfrac{\sin F}{7} \cdot 7y = \dfrac{\sin 48 \textdegree}{y} \cdot 7y}\\\\\displaystyle{y\sin 90 \textdegree = 7\sin 48 \textdegree}[/tex]

We know that sin90° = 1 so we will have [tex]\displaystyle{y=7\sin 48 \textdegree}[/tex]. Now input the value in a calculator since we cannot evaluate sin48° with an ordinary method.

When you put 7sin48° in a calculator, you will get 5.20201377... then you round the value to nearest tenth. Hence, y is 5.2 units.

The equation of the line that passes through (6,-3) and is parallel to the line y = -2/3 x + 5  is y = - 2 / 3 x + 1.

The equation of a line can be represented in slope-intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through (6,-3)  and is parallel to y = -2/3 x + 5.

Parallel lines have the same slopes.

Therefore, the slope of the line is - 2 / 3.

Hence, let's find the y-intercept of the line using (6, -3).

Therefore,

y = - 2 / 3 x + b

-3 = - 2 / 3 (6) + b

-3 = -12 / 3 + b

b = -3 + 4

b = 1

Therefore, the equation of the line is y = - 2 / 3 x + 1.

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Answer:

5/8 × 4 = 5/8 × 4/1 = 20/8 = 5/2

Step-by-step explanation:

hope this helps

Answer:

The solution is 5/2

Step-by-step explanation:

[tex] \sf \frac{5}{8} \times 4 \\ = \sf \frac{5}{ \cancel8} \times \cancel4 \\ = \sf \frac{5}{2} [/tex]

Answer:

B = 162

Step-by-step explanation:

B/9 = 18

(9) B/9 = 18(9)

B = 162

Answer:

b = 162

Step-by-step explanation:

Given statement,

→ b divided by 9 = 18

Forming the equation,

→ b/9 = 18

Now the value of b will be,

→ b/9 = 18

→ b = 18 × 9

→ [ b = 162 ]

Hence, value of b is 162.

Answer:

to the left of the zero mark   at the -63.2 mark

Step-by-step explanation:

The rate at which the temperature of the compound rose was 0.75 degrees per hour.

Temperature is a measure of how hot or cold an object or environment is. It is measured in degrees on the Celsius, Fahrenheit, or Kelvin scales. Different objects and environments have different temperatures. For example, the temperature of the human body is usually around 37°C (98.6°F). The temperature of boiling water is 100°C (212°F). The temperature of a winter day can be much colder than the temperature of a summer day.

To solve this problem, divide 1 1/4 degrees by 1 2/3 hours, which equals 0.75 degrees per hour. Therefore, the rate at which the temperature of the compound rose was 0.75 degrees per hour.

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Answer:

123°

Step-by-step explanation:

x + 32 + 25 = 180

x = 123

Answer:

In this example the maximum is the one on the top while the minimum is the one on the curve.

Step-by-step explanation:

Answer:16

Step-by-step explanation:

15+22+13+14=64

64:4=16

the median is 64

please give me the best answer i really need it

We can solve for log bases without a calculator by using  logarithmic formulas and identities.

A logarithm is basically a mathematical operation which is able to determine how many times a particular number, which is known as the base, will be multiplied by itself to reach the other number. We can solve for log bases even without a calculator.

For example, we need to find the value of log 128 to the base 8, which we can write as log₈28.

We know that,

[tex]log_{a} b^{x} = 1/b(log_{a}x)[/tex]

[tex]log_{a} x^{b} = b(log_{a}x)[/tex]

Using this property of logs,

log₈128 = log₂³2⁷

7/3 (log₂2)

Another property is,

[tex]log_{a}a = 1[/tex]

Using this property of logs,

⇒ 7/3(log₂2) = 7/3×1

=7/3

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Answer:

d1=50 and c2 21/25

Step-by-step explanation:

We can calculate limits considering the following rules:

Constant Rule The constant rule of limit calculus is utilized when a function is given in which there is no identical variable available. This rule states that the limit of the constant function remains as it is.

Limu→a k = k

Constant time function rule This rule is utilized when there are stagnant coefficients along with the identical variables of the function. This rule states that the constant coefficient will be written outside the limit notation.

Limu→a kf(u) = k Limu→a f(u)

Sum Rule The sum rule is utilized when there are two or more terms or functions given along with the additional sign among them. This rule states that the denotation of the limit will apply to every function separately.

Limu→a [f(u) + g(u)] = Limu→a [f(u)] + Limu→a [g(u)]

Difference Rule The difference rule is utilized when two or more terms or functions are mentioned along with the minus sign among them. This rule expresses that the notation of the limit will be implied to each function segregation.

Limu→a [f(u) – g(u)] = Limu→a [f(u)] – Limu→a [g(u)]

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Answer:

Step-by-step explanation:

We can calculate limits considering the following rules:

Constant Rule The constant rule of limit calculus is utilized when a function is given in which there is no identical variable available. This rule states that the limit of the constant function remains as it is.

Limu→a k = k

Constant time function rule This rule is utilized when there are stagnant coefficients along with the identical variables of the function. This rule states that the constant coefficient will be written outside the limit notation.

Limu→a kf(u) = k Limu→a f(u)

Sum RuleThe sum rule is utilized when there are two or more terms or functions given along with the additional sign among them. This rule states that the denotation of the limit will apply to every function separately.

Limu→a [f(u) + g(u)] = Limu→a [f(u)] + Limu→a [g(u)]

Difference RuleThe difference rule is utilized when two or more terms or functions are mentioned along with the minus sign among them. This rule expresses that the notation of the limit will be implied to each function segregation.

Limu→a [f(u) – g(u)] = Limu→a [f(u)] – Limu→a [g(u)]

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To find log7 to the base 2 on a calculator, you will need to use the change of base formula that I mentioned earlier: log_b(x) = log_c(x) / log_c(b).

If you want to find log7 to the base 2 on a calculator, you can use the following steps:

Press the log button on your calculator to change to the logarithm mode (usually represented by "log" or "ln").

Enter the number 7

Press the "log" or "ln" button again to switch to the base 2 logarithm mode.

Enter the number you want to find the logarithm of.

Press the division button (/)

Press the log or ln button again and enter the number 7

Press the equals button (=)

The result will be the logarithm of the number with respect to base 2.

Alternatively, you can find the logarithm to base 2 of 7 by dividing the logarithm to base 10 of 7 by logarithm to base 10 of 2 (or natural logarithm of 7 by natural logarithm of 2)

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Answer: $11.25

Hope this helps :)

Step-by-step explanation:

45 * .25 = 11.25

25 out of 100

When using percentages, remember that they are only a number out of 100. This makes it easy to find its decimal. When finding the discount price of a number, multiply it by the percentage as a decimal.

Class range of 9 can be calculated, this can be shown through below illustrations :Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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Answer:

Step-by-step explanation:

Class range of 9 can be calculated, this can be shown through below illustrations:Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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The standard form equation of the  circle which has an area  A=36π and a center of (-4,0),  (x+4)² + y² = 36. So Option A is correct

In mathematics, the circle is a two dimensional rounded figure which has no corner edges.

Area = [tex]\pi r^{2}[/tex]

Perimeter = [tex]2\pi r^{}[/tex]

Standard form = (x - a)² + (y - b)² = r²

Given that,

A circle has an area of A=36π

And a center of (-4,0)

The area of a circle for radius r is,

Area =  [tex]\pi r^{2}[/tex]

[tex]\pi r^{2}[/tex]   = 36π

[tex]r^{2}[/tex]     = 36

r   = 6

here,

a  = -4

b  = 0

Now,

Standard equation,

(x -(-4))² + (y - 0)² = 6²

(x+4)² + y² = 36

Hence, The standard form is  (x+4)² + y² = 36

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The graph of a linear equation is always a straight line.

Linear equations in two variables, for example, are known when they have two variables in them. A, B, and C are constants in the generic linear equation in two variables, which is written as axe + by + c = 0.

Simply assume a set of values for x and compute the corresponding set of values for y to discover the graph of axe + by + c = 0. We now possess a set of coordinates (x, y). Now connect the spots on the graph. A straight line will be generated on the graph.

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When the preceding equation can be factored as (a+b)(ab) (a + b) (a b), it can be written as a^2 - b^2.

Example: Think about (y^2-100) (y^2+100). Each term in this sentence can be rendered as a square. Here, (y+10) and (y10) serve as the factors. Let's try to answer this now. A) Since any integer cannot be divided by 0 without the result being an undefined number, 0 cannot be a factor of any number other than 0.

B) One is the factor of every number because when one divides a number exactly, leaving no residue, the quotient is equal to the original number.

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The two data sets for which a linear regression model is reasonable include the following: a) Aaliyah’s and Julio’s data sets.

In Mathematics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. This ultimately implies that, when one variable increases, the other increases, as well.

In order to determine if a data set has a good linear relationship, we would have to interpret the correlation coefficient (r), which typically ranges between -1 to 1 as depicted by both Aaliyah’s and Julio’s data sets.

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Complete Question:

Aaliyah, Julio, Dan, and Miriam are each studying sets of data. Aaliyah is working with 14 data pairs with a correlation coefficient of 0.9. Julio is working with 13 data pairs with a correlation coefficient of –0.8. Dan is working with 10 data pairs with a correlation coefficient of 0.1. Miriam is working with 15 data pairs with a correlation coefficient of –0.2. For which two data sets is a linear regression model reasonable?

a)Aaliyah’s and Julio’s data sets

b)Julio’s and Miriam’s data sets

c)Dan’s and Miriam’s data sets

d)Miriam’s and Aaliyah’s data sets

The expression to represent each ATM transaction for the month is

10 + 2x.

Where x is the number of ATM transactions.

The total cost for 5 ATM transactions is $20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Monthly account fee = $10

Fee for ATM transaction = $2

The cost of x ATM transaction for a month.

= 10 + 2x

The total cost of 5 ATM transactions for a month.

= 10 + 2 x 5

= 10 + 10

= $20

Thus,

The expression is 10 + 2x.

The total cost is $20.

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Answer:

I'm unable to plot graph, but I can give you the steps to graph the equation y = -²- 10x - 16 on the given set of axes.

Plot the vertex of the parabola: The vertex of the parabola is the point where the parabola changes direction. To find the vertex, you can use the formula (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the equation y = ax² + bx + c. In this case, a = -1, b = -10, and c = -16, so the vertex is (-10/2(-1), -(-10/2(-1))² - 10(-10/2(-1)) - 16) = (5,16).

Plot the roots: The roots of the equation are the values of x that make y = 0. To find the roots, you can set y = 0 and solve for x. In this case, y = 0 = -x² - 10x - 16. This equation can be solved by factoring or by using the quadratic formula. The roots are x = 4 and x = -2.

Plot five points on the parabola, including the vertex and the roots. To do this, you can substitute different values of x into the equation y = -x² - 10x - 16 and find the corresponding y-values. For example, you could plot the point (4,0), which is one of the roots, and (5,16), which is the vertex.

Connect the points to form a parabola.

Keep

Step-by-step explanation:

There are two solutions to the given equation 3x + 4y = 12.

Finding two solutions for the equation 3x + 4y = 12

Putting the value of x = 0 in equation 3x + 4y = 12

⇒3(0) + 4y = 12

⇒ 4y = 12

⇒y = 3

Thus, (0, 3) is a solution to the equation 3x + 4y = 12

Putting the value of y = 0 in the equation 3x + 4y = 12

Thus,

⇒3x + 4(0) = 12

⇒3x = 12

⇒x = 4

Thus, (4, 0) is a solution to equation 3x + 4y = 12

Therefore, (0, 3) and (4, 0) are two solutions to the equation 3x + 4y = 12.

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A limit in mathematics is a point at which a function approaches the output for the specified input values.

The idea of the limit of a geometric net expands the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals.

Limit is said to be exits when f(x) = [tex]\lim_{h \to 0\0} f(h-x) = \lim_{h \to0 \0} f(h+x)[/tex]

It means that when f(x) = L.H.L = R.H.L

LHL means left hand limit and RHL means right hand limit.

Some Property of limits are as follows

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solved, for  x^2+2x=35,   x=5 or x= -7

x^2+2x=35

Subtract 35 from both sides, and we get

x^2 +2x−35=0

To solve the equation, factor

x^2 +2x−35 using the formula  

x^2 +(a+b)x+ab=(x+a)(x+b).

To find a and b, set up a system to be solved.

a+b= 2

ab=−35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. List all such integer pairs that give product −35.

−1, 35

−5, 7

Calculate the sum for each pair.

−1+35=34

−5+7=2

The solution is the pair that gives sum 2, which are

a=−5

b=7

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x−5)(x+7)

To find equation solutions, solve x−5=0 and x+7=0.

x=5

x= −7

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The intensity of earthquakes is measured on the Richter scale. It is a device which compares earthquakes.

Earthquake strength is measured using instruments such as the Richter scale. The Richter scale was invented in the 1930s to help us understand the magnitude and intensity of earthquakes measured by seismographs. Ground surveillance equipment. Standard scale. This is a logarithmic scale measuring a factor of 10. It is measured using information collected by seismographs. It has a base 10 logarithmic scale.

Mathematically, If M is magnitude and I is intensity of earthquake then formula,

M = log(I/Iₛ)

where, Iₛ --> standard intensity

The strength of an earthquake is measured or estimated by two things: amplitude and energy..

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Complete question:

How is the intensity of an earthquake measured ?

Answer: C. 145 degrees

Step-by-step explanation:

Using the information given above, we are now supposed to figure out the measure of angle C. Considering the two angles are supplementary, or two angles with the sum of 180°, we can finally assume that the answer is C.

Angle B + Angle C = 180°

Angle B = 35°

180° - 35° = 145°

Answer: C. 145 degrees

An inequality in one variable that models this scenario is 2(3.00) + 1.90x + 2.50(x + 2) ≤ 27.

The maximum number of whole pounds of grapes he can buy is equal to 4.

In order to write an inequality that represents or models this scenario, we would assign a variable to the number of pounds of grapes, and then translate the word problem into algebraic equation as follows:

From the information provided above, we have the following parameters:

The rate of grapes per pound = $1.90.

The rate of pineapples per pound = $3.00.

The rate of strawberries per pound =  $2.50.

Pounds of strawberries = g + 2.

Therefore, an inequality that represents or models this scenario is given by;

p + x + s ≤ 27

2(3.00) + 1.90x + 2.50(x + 2) ≤ 27

Next, we would solve the above inequality algebraically as follows;

6 + 1.90x + 2.50x + 5 ≤ 27

4.4x ≤ 27 - 11

4.4x ≤ 16

x ≤ 16/4.4

x ≤ 3.64 ≈ 4

x ≤ 4.

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