expland and simplify (5x+2)(2x-3)

The required answer is w-z = √2[cos(3π/4) + i sin(3π/4)]

A complex number is a number of the form a + bi, where a and b are real numbers.

Given that,

w = √2cos(π/4) +  i sin(π/4) and z = 2[cos(π/2)+i sin(π/2)]

On simplification we get,

w = √2cos(π/4) +  i sin(π/4)

w = √2(1/√2 + i · 1/√2)

w = 1+i

And,

z = 2[cos(π/2)+i sin(π/2)]

z = 2(0+i)

Now, the value of (w - z)

w - z = (1 + i) - (0 + 2i)

w - z = 1 - i

Polar form of the complex number:-

r = √1²+(-1)² = √2

And, θ would b,

θ = tan⁻¹(-1/1)

= tan⁻¹(-1)

θ = 3π/4

Therefore, polar form =  w-z = √2[cos(3π/4) + i sin(3π/4)]

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The estimated value of y when x1=12, x2=1, and x3=-1 is -204. This is calculated by substituting the given values into the equation ˆy=−184−7x1+47x2+20x3.

ˆy=−184−7(12)+47(1)+20(-1)

ˆy=−184-84+47-20

ˆy=−204

In the multiple regression equation

ˆy=−184−7x1+47x2+20x3

the estimated value of y can be determined by substituting the given values of x1, x2, and x3 into the equation. For example, given

x1=12, x2=1, and x3=-1,

the estimated value of y can be calculated as follows: ˆy=−184−7(12)+47(1)+20(-1). This simplifies to

ˆy=−184-84+47-20, or ˆy=-204.

The equation takes the form of a linear equation, with each independent variable x1, x2, and x3 multiplied by a coefficient, and then added together to give the estimated value of y. In this example, the coefficient for x1 is -7, for x2 is 47, and for x3 is 20. This means that if x1 increases by 1 unit, then the estimated value of y will decrease by 7 units; if x2 increases by 1 unit, then the estimated value of y will increase by 47 units; and if x3 increases by 1 unit, then the estimated value of y will increase by 20 units. Using the multiple regression equation, therefore, the estimated value of y can be calculated when the values of the independent variables are known. In this example, given x1=12, x2=1, and x3=-1, the estimated value of y is -204.

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The complete question is

In the following multiple regression equation, what is the value of x2 when x1 = 15.5 and ˆy is estimated to be -412?ˆy=78−20x1−10x2x2=2)Given the following multiple regression equation:ˆy=−184−7x1+47x2+20x3Determine the estimated value of y whenx1=12x2=1x3=−1ˆy=−204

Dilating the given triangle with a magnitude of 3, the number corresponding to the question mark is 18.

Therefore the answer is 18.

Dilating a triangle means to scale it up or down by a certain factor, in this case, by a factor of 3. To dilate a triangle, you need to multiply the each elements of the matric by the dilation factor.

On multiplying a matrix by a scalar number, each element of the matrix is multiplied by that scalar number.

3 × [3 6 3 | -3 3 3] =  [3×3 6×3 3×3 | -3×3 3×3 3×3]

=[ 9 18 9 | -9 9 9]

That is

[tex]3\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right] = \left[\begin{array}{ccc}-3*3&6*3&3*3\\-3*3&3*3&3*3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}9&18&9\\-9&9&9\end{array}\right][/tex]

So the element corresponding to the question mark is 18.

--The question is incomplete, complete question is given below--

"Dilate the given triangle with a magnitude of 3.

[tex]\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}9&?&-\\-9&-&-\end{array}\right][/tex]"

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False. A data set may have one mode, but it is also possible for a data set to have no mode or multiple modes.

A mode of data is defined as an observation with the highest frequency among the values that appear most frequently in the given data.

If no value is repeated, the dataset has no mode. If two or more values appear with the same maximum frequency, then the dataset has multiple modes.

For example, consider the following dataset:

1, 2, 3, 3, 4, 4, 5

In this dataset, both 3 and 4 appear twice, which means that the dataset has multiple modes.

So, in general, it is not always true that a data set will have exactly one mode. It depends on the values in the dataset and their frequencies.

Therefore, the correct answer would be option (B) False.

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Both Teresa and Leon have constructed regular hexagons. Teresa drew a circle and marked a point on it, then used a compass set to the radius to construct a regular hexagon. Leon drew a segment, then used a circle with the segment as the radius and a compass set to the length of the segment to construct a regular hexagon.

It is important to note that a regular hexagon is a polygon with six congruent sides and six congruent angles, and is constructed by using a compass to draw six equidistant points on a circle, connecting the points with straight lines, forming the hexagon. In both cases described above, it appears that Teresa and Leon were using a compass and the appropriate measurements to construct regular hexagons.

Answer:

-3

Step-by-step explanation:

22-25=-3 because if the first number is smaller than the second number, then the answer is a negative number

The conversion of 0.0088 gr/cm³ is 8.8 kg/m³

The full question is in the attachment. To change the unit of a quantity to another unit is to use the rules that apply to each unit. Rules on mass units

Rules on volume units

To convert units from gr/cm³ to kg/m³

1 gr/cm³ = 1 × 1 gr ÷ 1 cm³

1 gr/cm³ = 1 × 0.001 kg ÷ 0.000001 m³

1 gr/cm³ = 1 × 0.001 × 1,000,000 kg/m³

1 gr/cm³ = 1 × 1,000 kg/m³

1 gr/cm³ = 1,000 kg/m³

0.0088 gr/cm³ = 0.0088 × 1,000 kg/m³

0.0088 gr/cm³ = 8.8 kg/m³

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Using substitution method, the solution of the system of equation 9x + y = 65, y = 3x - 19 is x = 7 and y = 2.

The system of equation can be solved using substitution method, elimination method and graphical method. Let's solve the system of equation using substitution method as follows:

9x + y = 65

y = 3x - 19

let's substitute the value of y in the equation(i)

9x + (3x - 19) = 65

9x + 3x - 19 = 65

12x - 19 = 65

add 19 to both sides of the equation

12x - 19 + 19 = 65 + 19

12x = 84

divide both sides by 12

x = 84 / 12

x = 7

Let's find y

y = 3(7) - 19

y = 21 - 19

y = 2

Therefore, the solution are x = 7 and y  =2.

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The solution of the equation is "True for all value of x".

In the given question, two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats.

The equation 4(x + 1) = 4x + 4 models the paths of the boats.

We have to solve for x.

The equation is 4(x + 1) = 4x + 4

Using the Distributive property

4x + 4 = 4x + 4

Subtract 4 on both side, we get

4x = 4x

Subtract 4x on both side, we get

0 = 0

As we can see that the equation is true for all the value of x.

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The two boats are traveling exactly 0 feet apart in the canal.

The equation 4(x + 1) = 4x + 4 can be rearranged to solve for x. First, subtract 4x from both sides of the equation so that the equation becomes 4(x + 1) - 4x = 4x + 4 - 4x. This simplifies to 4 + 4x = 4, and when 4 is subtracted from both sides of the equation, the result is 4x = 0. To solve for x, divide both sides of the equation by 4, so that x = 0.

This means that the two boats are traveling exactly 0 feet apart in the canal.

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Answer: 1450 Largest, 1045 Smallest

Answer:      1,450 is the largest.

                     1,045 is the smallest.

Please mark on it..

The limit of g(x) as x approaches 4 negative is 2 and the limit of g(x) as x approaches 4 plus is negative 4.

To calculate the limit of g(x) as x approaches 4 negative, let us consider the function g(x) = -2x + 8.

We can calculate the limit of g(x) as x approaches 4 negative by plugging in the value 4 into the function.

When x = 4, g(x) = -2(4) + 8 = -8 + 8 = 0.

Therefore, the limit of g(x) as x approaches 4 negative is 0.

To calculate the limit of g(x) as x approaches 4 plus, let us consider the function g(x) = -2x + 8.

We can calculate the limit of g(x) as x approaches 4 plus by plugging in the value 4 into the function.

When x = 4, g(x) = -2(4) + 8 = -8 + 8 = 0.

Therefore, the limit of g(x) as x approaches 4 plus is 0.

In conclusion, the limit of g(x) as x approaches 4 negative is 2 and the limit of g(x) as x approaches 4 plus is negative 4.

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Answer:

The length of CD is

"The Right Triangle Altitude Theorem says that the product of AD times DB must equal the length of [tex]CD^{2}[/tex]. Since 4 * 6 = 24, CD must be [tex]\sqrt{24}[/tex].

[tex]AC^{2} = AD^{2} + CD^{2}[/tex]

[tex]AC^{2} = 40[/tex]

[tex]AC = \sqrt{40} = 2\sqrt{10}[/tex]

The value of x that makes the sentence 1/7 + x = 1/2 true is (d) 5/14

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

A mathematical sentence

The mathematical sentence is given as

1/7 + x = 1/2

Next, we make x the subject of the formula

This is done by subtracting 1/7 from both sides of the equation

Using the above as a guide, we have the following:

1/7- 1/7 + x = 1/2 - 1/7

Evaluate the like terms on the left-hand side

So, we have the following representation

x = 1/2 - 1/7

Take the LCM of the fractions

x = (7 - 2)/14

Evaluate the difference on the right-hand side

So, we have the following representation

x = 5/14

Hence, the solution is (d) 5/14

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Answer:

Step-by-step explanation:

The statement that a speech that was made to persuade people can also inform or entertain the audience, is A. True.

A persuasive speech is one that is given with the intention of convincing the audience to hold a certain belief or behave in a particular way. This includes a wide range of activities like voting, organ donation, recycling, and more.

A powerful persuasive speech convinces the audience to agree with your point of view by establishing your credibility and subject-matter expertise.

Persuasive speaking is particularly listener-centered since the speaker must, in a sense, meet the audience halfway. It is obvious that the speaker cannot totally control the process because persuasion occurs when the listener concurs with what the speaker says. Because of this, effective speaking requires particular attention to audience study.

Therefore, a persuasive speech would also serve to inform or amuse the audience.

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An inequality that represents the possible dimensions for the garden is ab < 80. And the three different sets of allowable dimensions for the garden are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

The maximum area that is available for a rectangular garden is 80 square feet.

Let a and b are the length and width of the rectangular garden.

And A be the area.

(a).

So, A < 80

That means, ab < 80.

(b).

To find the dimension of the rectangle:

We find the numbers whose product is less than 80.

Let the three number sets are,

{5, 10}, {10, 5} and {6, 6}.

(c).

So, the area of the rectangles are:

5 x 10 = 50 square feet,

10 x 5 = 50 square feet,

And 6 x 6 = 36 square feet.

Therefore, the inequality is ab < 80, three number sets are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

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The perimeter of a square is equal to the sum of all of its sides. Since all sides of a square are equal, to find the perimeter you just need to multiply the length of one side by 4. In this case, the perimeter would be 15 inches * 4 = 60 inches.

The circumference of a square is not defined, as it is a two-dimensional shape and does not have a circumference (which is a measure of distance around the edge of a circular shape).

The area of a square is equal to the length of one side squared. To find the area of a square with sides 15 inches long, you would calculate 15 inches * 15 inches = 225 square inches.

Answer:
Yes

If this help please set brainliest.

Step-by-step explanation:

Yes, a line with a slope of 0 is a horizontal line. It will always intersect the y-axis at a single point, which is known as the y-intercept. The y-intercept is the point where the line crosses the y-axis, and it is represented by the equation y = b, where b is the y-intercept.

For example, consider the line y = 2. This line has a slope of 0 and an y-intercept of 2. It is a horizontal line that passes through the point (0, 2) on the coordinate plane.

The value of unknown v from the given equation 8v - 4(v + 8) = 8 is

v = 10.

Simplifying the given algebraic equation :

8v - 4(v + 8) = 8

Rearrange the terms in equation :

8v - 4(8 + v) = 8

8v - (8 * 4 + v * 4) = 8

8v - (32 + 4v) = 8

Expand and rearrange the terms:

-32 + 8v - 4v = 8

Combine like terms: 8v - 4v = 4v ( on left side )

                                  8 + 32 = 40 (on right side )

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

4v = 8 + 32

4v = 40

Divide each side by '4'.

Simplifying

 v = 10.

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1) Remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2) Their difference will be divisible.

The amount that remains after division is known as the Remainder. The result of division is a value if a number (dividend) cannot be divided entirely by another number (divisor).

1. Suppose the a random number is x and 4 consecutives number are x, x+1, x+2, x+3

Given that,

x² + (x+1)²+ (x+2)²+ (x+3)²

x² + (x² +2x+1) + (x² +4x+4)+ (x²+6x+9)

4x² + 12x + 14

is divisible by 4 with remainder 2

[tex]$ \frac{4x^2 + 12\text x + 14}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 +2}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 }{4} $[/tex] [tex]$+\frac{2}{4}[/tex]

Hence proved, remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2. As both 14 and 21 is divisible by seven, their difference is also divisible by 7, i.e. 70-42 = 28, all the numbers are divisible by 7 and hence the squares of the number are also divisible by seven as well as their numbers.

14²⁰ - 21²

(7 × 2)²⁰ - (7 × 3)²

Thus, their difference will be divisible.

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All the possible values of each expression is given as an inequality as;

0 < a - b < -1

We are given the inequalities of the domain and range as;

3 < a < 4

4 < b < 5

Thus, we can say that the maximum value of a - b will be the difference between the maximum value of a and the minimum value of b to give;

(a - b)max = 4 - 4

(a - b)max = 0

Similarly, minimum value of a - b will be the difference between the maximum value of b and the minimum value of a to give;

(a - b)min = 4 - 5

(a - b)min = -1

Thus, all possible values would be expressed as;

0 < a - b < -1

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The measure of side QR = 5cm

A triangle is a polygon with three edges and vertices, and with vertices A, B, and C is denoted △ABC.

A triangle has three sides, three angles, and three vertices.

The sum of all internal angles of a triangle is always equal to 180°.

The sum of the length of any two sides of a triangle is greater than the length of the third side.

The given information is:

As triangles ABC and QRS are similar ;

So, AC is similar to QS

AC=60cm and QS=6cm, which means if we divide the length of AC by 10 we get the measure of length QS

AC=60/10

AC= 6cm

And, AB is similar to QR and AB=50cm, if we divide this by 10 we get the measure of QR

QR=50/10

QR=5 cm

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Independent variable and dependent variable

What occurs as a result of the independent variable is referred to as a dependent variable.

We anticipate that independent variables will have an impact on dependent variables.

Eg. You plan a study to see if variations in the room's temperature have an impact on students' math test results.

The inside temperature of the space is your independent variable. By making the room cooler for half the participants and warmer for the other half, you can change the temperature.

Test results in mathematics are your dependent variable. Using a standardised test, you measure each participant's math prowess to see if there are any temperature-related differences.

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The correct statement is: 'In any experiment, the cause is called the dependent variable, while the effect or result is called the independent variable.'

We know that an independent variable is a variable which is not changed by the other variables you are trying to measure.

An independent variable is also known as input variable.

Or in any experiment, the cause is represented by the independent variable.

Whereas a dependent variable is nothing but the variable that changes as a result of the independent variable. It depends on the independent variable of an experimetent.

It is also called as output variable.

Therefore,   In any experiment, the cause is called the dependent variable, while the effect or result is called the independent variable.

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Answer:

[tex]\dfrac{10}{7}[/tex]

Step-by-step explanation:

To solve this problem, we first have to understand some exponent rules.

1. When an exponent is a fraction, the exponent's numerator is how many instances of the base there are, and its denominator is the root of those instances.

For example,

[tex]5^{2/3} = \sqrt[3]{5^2} = \sqrt[3]{25}[/tex]

2. When an exponent is negative, the resulting value is reciprocated.

For example,

[tex]3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9}[/tex]

Using these rules, we can rewrite the given expression.

[tex]\left(\dfrac{49}{100}\right)^{-1/2} = \dfrac{1}{\sqrt{\dfrac{49}{100}}}[/tex]

Then, we can simplify the denominator by solving for the square root of the  fraction 49/100.

[tex]\dfrac{1}{\sqrt{\dfrac{49}{100}}} = \dfrac{1}{\dfrac{7}{10}}[/tex]

Finally, we can apply the fraction division rule.

[tex]A \div \dfrac{B}{C} = A \times \dfrac{C}{B}[/tex]

[tex]\dfrac{1}{\dfrac{7}{10}} = 1 \cdot \dfrac{10}{7} = \dfrac{10}{7}[/tex]

Answer:

? = 60.

Step-by-step explanation:

Multiply 3/5 by 20. The answer will yield that 3/5 = 60/100

Answer:

Missing number = 60

Step-by-step explanation:

★ Let the missing number be x.

Forming the equation,

[tex] \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} [/tex]

Now the value of x will be,

[tex] \sf \rightarrow \: \frac{3}{5} = \frac{x}{100} [/tex]

[tex] \sf \rightarrow \: x = \frac{3}{5} \times 100 [/tex]

[tex] \sf \rightarrow \: x = \frac{300}{5} [/tex]

[tex] \sf \rightarrow \boxed{ \sf x = 60}[/tex]

Hence, the value of x is 60.

The number of pennies are 80 and number of nickels are 160.

Two or more expressions with an Equal sign is called as Equation.

Given that $8.80 in pennies and nickels.

The total number of coins are 240.

x+y=240

x is pennies and y is nickel.

0.01x+0.05y=8.8

Now from equation 1, x=240-y

Plug in equation 2

0.01(240-y)+0.05y=8.8

2.4-0.01y+0.05y=8.8

2.4+0.04y=8.8

Subtract 2.4 on both sides

0.04y=6.4

y=160

x+160=240

x=80

Hence, the number of pennies are 80 and number of nickels are 160.

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Considering the expression of a line, the equation of the line that passes through the pair of points (35, -30) and (-12, 34) is y=-4/3x +18.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of said line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points in the expression of a line, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (36, -30) and (x₂, y₂)= (-12, 34), the slope m can be calculated as:

m= (34 - (-30))÷ (-12 - 36)

m= (34+30)÷ (-12 - 36)

m= 64÷ (-48)

m= -4/3

Considering point 2 and the slope m, you obtain:

34= -4/3×(-12) + b

34= 16 +b

34 -16= b

18= b

Finally, the equation of the line is y=-4/3x +18.

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We can call a scatter diagram as a scatter plot, Scatter graph, or correlation chart. By including two variables a scatter diagram is drawn where the first variable is independent and the second variable is dependent on the first. Depending on the correlation between them, scatter diagrams can be divided into the following categories :

1) Scatter diagram with no correlation - we can call this diagram the 'Scatter Diagram with Zero Degree of Correlation ' as the variables do not correlate with each other.

2) Scatter diagram with moderate correlation - we can call this diagram as the 'Scatter Diagram with a Low Degree of Correlation' as here the data points are a little closer and a relationship between these variables can be found.

3) Scatter diagram with strong correlation - we can call this diagram as the 'Scatter Diagram with a High Degree of Correlation' as here the data points are closer and a line can be drawn by following their pattern.

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Evaluating the given expressions, A) 10^14 (option a), B) 10^-6 (option b), C) 10^27 (option b) D) 10^-8 (option c).

A) 10^5 x 10^9

Using the product of power rule, when the base is same, the exponents are added together. Hence,

10^5 x 10^9 = 10^(5 + 9) = 10^14

B) 10^4 x 10^-10

Using the product of power rule,

10^4 x 10^-10 = 10^(4 – 10) = 10^-6

C) 10^30 ÷ 10^3

Using the quotient power rule, when the base is the same, the exponents are subtracted.

10^30 ÷ 10^3 = 10^(30 – 3) = 10^27

D) 10^-12 ÷ 10^-4

Using the quotient power rule,

10^-12 ÷ 10^-4 = 10^(-12 –(-4) = 10^(-12 + 4) = 10^-8

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