(36-3i) - (12+24i)simplify the expression and then classify the result as a real number or imaginary number. If the result is an imaginary number, specify if it is a pure imaginary number.

Answer:

x= -3

Step-by-step explanation:

Given: 5(x+5) = 10

Find: x

Set the equation up.

5(x+5) = 10

Simplify.

5x + 25 = 10

Subtract 25 from both sides.

5x = -15

Divide to isolate the variable.

x = -3.

Answer:

x = -3

Step-by-step explanation:

Lets start simplifying:

Method 1:

5(x+5) = 10      Multiply parenthesis by 5

5x+25 = 10     Subtract 25 from both sides

5x = -15           Divide by 3 on both sides

x = -3

Method 2:

5(x+5) = 10     Divide by 5 on both sides

x+5 = 2           Subtract 5 from both sides  

x = -3

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The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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Answer:

x = 30

Step-by-step explanation:

15 = 1/2x

multiply both sides of equation by 2

30 = x

Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

We can write 177 as the product of 2 factors:

We can find the other factor by dividing 177 by 3:

The result is 59, that is a prime number.

So the 2 factors of 177 are 3 and 59.

The division is done by:

The given function is represented as the sum of a power series :

n=0 to ∞∑(-1)ⁿ.xⁿ + 1/4 (n=0 to ∞ ∑(-1)ⁿ xⁿ/4ⁿ, I x/4 I < 1, IxI<1

The interval of convergence is I = (-1,1).

Given:

the function is f(x) = 2x+5/x²+5x+4

Let x² + 5x + 4 = x² + 4x + x + 4

This implies

x²+5x+4 = x(x+4)+ 1(x+4)

= (x+4)(x+1)

write it into partial functions:

2x+5/(x+4)(x+1) = A/x+1 + B/x+4

                        = A(x+4)+B(x+1)/(x+1)(x+4)

2x+5 = A(x+4)+B(x+1)

2x+5 = Ax+4A+Bx+B

2x+5 = (A+B)x + (4A+B)

on comparing,

A+B = 2

4A+B=5

subtract both equations.

4A+B-A-B = 5-2

           3A = 3

              A = 1

Substitute A = 1 in the equation A+B = 2

1+B = 2

B = 2-1

B+1

This implies:

2x+5/x²+5x+4 = 1/x+1 + 1/x+4

Now express it as sum of power series:

2x+5/x²+5x+4 = 1/x+1 + 1/x+4

                        = 1/x+1 + 1/4(1+x/4)

                        = n=0 to ∞∑(-1)ⁿ.xⁿ + 1/4 (n=0 to ∞ ∑(-1)ⁿ xⁿ/4ⁿ, I x/4 I < 1, IxI<1

(b) To find the interval of convergence:

n=0 to ∞∑(-1)ⁿ.xⁿ + 1/4 (n=0 to ∞ ∑(-1)ⁿ xⁿ/4ⁿ, I x/4 I < 1, IxI<1 = ∑(-1)ⁿ(1+1/4ⁿ⁺¹)xⁿ

Therefore the interval of convergence is I = (-1,1)

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Answer:

Step-by-step explanation:

Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

Answer:

<

Step-by-step explanation:

The bars on either side of 81.48 are the absolute value symbol.

The absolute value of a number is its positive numerical value.

\(\implies |81.48| = 81.48\)

\(\boxed{\begin{minipage}{5.3cm}\underline{Inequality symbols}\\\\$ < $ means "less than"\\$ > $ means "more than"\\$\leq $ means "less than or equal to"\\$\geq $ means "more than or equal to"\end{minipage}}\)

A negative number is always less than a positive number.

\(\implies -88.48 < |81.48|\)

Therefore, the sign that makes the statement true is "<".

Answer:

-88.48 < ∣81.48∣

Step-by-step explanation:

The given equation is,

→ -88.48 ? ∣81.48∣

The sign which we use will be,

→ -88.48 ? ∣81.48∣

→ -88.48 < 81.48

Hence, the sign we use is (<).

Answer:

3

Step-by-step explanation:

The amount of fewer euros he would receive as a result of the delay is 20 E.

The percentage loss that was caused by the delay is -4%.

Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.

Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday

Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E

Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E

Difference = 500 E - 480 E = 20 E

Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1

Percentage loss = (480 / 500) - 1 = -0.04 = -4%

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Answer:

The appropriate form for this problem is:

(Amount of Type A per bag) + (Amount of Type B per bag) = Total weight per bag

Using the given information, we can fill in the blanks:

(3 kg) + (___ kg) = (36 kg) ÷ (4 bags)

Simplifying the right side:

(36 kg) ÷ (4 bags) = 9 kg/bag

Substituting back into the equation:

3 kg + (___ kg) = 9 kg/bag

Solving for the blank:

___ kg = 9 kg/bag - 3 kg

___ kg = 6 kg/bag

Therefore, there are 6 kilograms of type B in one bag of the blend.

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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The mass of the rider 1 is equal to 4 grams.

In accordance with the statement, we know the mass of the entire system formed by three riders, of which the mass of two riders are known. The mass of the third rider can be calculated from the previous information:

m = m₁ + m₂ + m₃  

Where:

m₁ = m - m₂ - m₃

m₁ = 694 g - 600 g - 90 g

m₁ = 4 g

The mass of the rider 1 is equal to 4 grams.

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Answer:

1.9 gallons ( approx to 1 d.f)

Step-by-step explanation:

Question:

A scooter can go 60 miles using 1 gallon of gas approximately how many gallons of gas will be used to go 180 kilometers

Solution:

First, we need to convert 60 miles to kilometers:

60 miles = 96.56 kilometers

Now, we can set up a proportion:

1 gallon : 96.56 kilometers = x gallons : 180 kilometers

Cross-multiplying, we get:

96.56x = 180

Solving for x, we get:

x = 1.865 gallons

Therefore, approximately 1.865 gallons of gas will be used to go 180 kilometers.

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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The domain and the range of each relation shown in the mapping and in the table of values given can be written as:

Mapping - Domain: {-2, -1, 0, 1}; Range: {-4, -2, 2}

Table - Domain: {-4, -2, 1, 4}; Range: {-2, 1, 4}

(See image attached below).

Recall:

From the mapping shown in the image given, the domain values are:

-2, -1, 0, 1

The range values are:

-4, -2, 2

From the table of values shown in the image given, the domain values are:

-4, -2, 1, 4

The range values are:

-2, 1, 4

Therefore, the domain and the range of each relation shown in the mapping and in the table of values given can be written as:

Mapping - Domain: {-2, -1, 0, 1}; Range: {-4, -2, 2}

Table - Domain: {-4, -2, 1, 4}; Range: {-2, 1, 4}

(See image attached below).

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Answer:

Step-by-step explanation:

75-52.5=x

Answer:

d. 90 cm, 1.2 cm

Step-by-step explanation:

Given that:

The sample size n = 36

For the  length of the link:

The mean \(\overline x\) = 2.5

The standard deviation s = 0.2 cm

In a chosen 36 links, The mean and standard deviation for the length chain is as follows:

Mean = n\(\overline x\)

Mean = 36×2.5

Mean = 90 cm

The Standard deviation = s×√n

The Standard deviation = 0.2×√36

The Standard deviation = 0.2×6

The Standard deviation = 1.2 cm

Answer:

1.97

Step-by-step explanation:

Answer: it is $1.97

Step-by-step explanation: it is $1.97 per gallon because 1.74 euros in usd is $1.97.

"Supplementary" angles add up to 180°.

Opposite angles are supplementary, so . . .

(12x - 4) + (19x - 2)  =  180°

Clear the parentheses:  12x - 4 + 19x - 2 = 180°

Add up all the x's on the left side:  31x - 4 - 2  =  180°

Add up the plain old numbers on the left side:  31x - 6  =  180°

Add  6  to each side:  31x  =  186°

Divide each side by  31 :  x  =  6°

Well !  Now that you know that  x = 6° . . .

Angle  EPC  is  (12x - 4)°

That's  (12·6  -  4)°

Which is  (72 - 4)°

Which is  68°

Answer:

The answer is 3/1 or 3

Step-by-step explanation:

30/10 = 3/1 = 3

Thus, The answer is 3/1 or 3

-TheUnknownScientist 72

Answer:

3/1 and 6/2 is the answer I got hope it helps

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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Answer:

a. Numerical (discrete).

b. Categorical.

c. Numerical (continuous).

d. Numerical (continuous).

e. Categorical.

Step-by-step explanation:

In Mathematics, a categorical data can be defined as a statistical data type that is used to group informations having the same attributes or characteristics. Some examples of a categorical data are age, gender, race, religion etc.

A numerical data can be defined as a data set that is expressed in numbers only or a data set consisting of numbers rather than words. A numerical data is also known as a quantitative data.

Basically, numerical data are classified into two (2) main categories and these are;

1. Discrete data: a discrete data is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

2. Continuous data: a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous data.

a. Number of students in a class of 35 who turn in a term paper before the due date: this is a numerical data and it is discrete in nature because the number of possible values are finite or countable.

b. Gender of the next baby born at a particular hospital: this is a categorical data because it contains a nominal variable (gender).

c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.  

d. Thickness of the gelatin coating of a vitamin E capsule: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.

e. Birth order classification (only child, firstborn, middle child, lastborn) of a math major: this is a categorical data because it is used to categorize an information (birth order).

The coordinates of point F are 4 and negative 2.5. Option C is correct.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

The location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

'c' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x.

The coordinates of point F are 4 and negative 2.5.

Hence, the Option C is correct.

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Answer:

1 5/6, 2 1/3, 2 3/5

Step-by-step explanation:D

Answer:

1 5/6, 2 3/5, 2 1/3

or

1 5/6, 2 1/3, 2 3/5

because 2 1/3 and 2 3/5 are equivalent.