13.Simplify and express the answer in (a + bi) form.
(i) (5 − 6i) + (−7-10i)

The required value of x is  135° in the given polygon. which is the correct answer would be an option (A).

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 8

The required value of x is the equal to measure of one Interior angle in the given polygon.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 8

Sum of Interior angles = (8 - 2) × 180

Sum of Interior angles = (6) × 180

Sum of Interior angles = 1080°

the measure of one Interior angle = 180°/8

the measure of one Interior angle = 135°

Thus, the required value of x is  135°.

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The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

a = - 2, b = 3, c = - 12 and d = - 4

m = - 32, n = 2, p = - 8 and r = 4

Now,

Find the values of the expressions as;

1. bd/a + c

Substitute all the values, we get;

bd/a + c = (3 x - 4)/(-2) + (-12)

             = - 12/- 2 - 12

             = 6 - 12

             = - 6

2. ac/b - (a + d)

Substitute all the values, we get;

⇒ ac/b - (a + d) = - 2 x - 12 /3 - (- 2 - 4)

                    = 8 + 6

                    = 14

3. d³/a² - (c + b)

Substitute all the values, we get;

d³/a² - (c + b) = 3³/(-2)² - (-12 + 3)

                    = 27/4 + 9

                    = 63/4

4. pr/n + m = - 8 x 4 /2 + (-32)

                 = - 16 - 32

                 = - 48

5. p²/m - (np + r) = (-8)²/- 32 - (2 x - 8 + 4)

                         = - 64/32 - (- 16 + 4)

                          = - 2 + 12

                          = 10

6. p³/r² - (m + np) = (-8)³/4² - (- 32 + 2 x - 8)

                           = - 32 - (- 32 - 16)

                           = - 32 + 48

                           = 16

Thus, The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

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Answer:

B and F

Step-by-step explanation:

B: f(x) = 2 lx+1l +3 vertex: (-1,3)

F: f(x) = lx+1l +3 vertex: (-1,3)

Answer:

56 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Area of a rectangle}\\\\$A=w\;l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

The given composite figure is made of two rectangles joined together.

Area of rectangle 1

[tex]\begin{aligned}\implies A&=4 \cdot 8\\&=32\; \sf cm^2\end{aligned}[/tex]

Area of rectangle 2

[tex]\begin{aligned}\implies A&=(8-5)(12-4)\\&=3 \cdot 8\\&=24\; \sf cm^2\end{aligned}[/tex]

Therefore:

[tex]\implies \textsf{Total area}=32+24=56\; \sf cm^2[/tex]

Answer:

56 cm²

Step-by-step explanation:

We are interested in finding the area of the given shape which is made up of two rectangles .

(for figure refer to the attachment)

Step 1 : Find the area of two rectangles

[tex]\longrightarrow Area_{AGHE}= length \times breadth \\[/tex]

[tex]\longrightarrow Area_{AGHE}= 5cm (4cm)\\[/tex]

[tex]\longrightarrow Area_{AGHE}= 20cm^2 [/tex]

Again ,

[tex]\longrightarrow Area_{GBCD}= 3cm(12cm)\\[/tex]

[tex]\longrightarrow Area_{GBCD}=36cm^2[/tex]

Step 2: Add up the areas

[tex]\longrightarrow Area = 20cm^2+36cm^2\\[/tex]

[tex]\longrightarrow \underline{\underline{Area = 56cm^2}}[/tex]

The next numbers in the series will be 0,1,-2,-1,0,-3,-2,-1........

This refers to a pattern of arranging numbers. In the number series problems, we will have to make the rules that result in the formation of a number series.

From the question:

1, 2, 3, 0, 1, 2, -1

First value plus one, second value plus one, Third value minus three. Then the pattern starts afresh again.

1 +1 = 2

2 + 1 = 3

3 -3 =0

0+1  = 1

1 + 1 = 2

2 -3 =-1

-1 + 1 =0

0 + 1 =1

1  - 3 = -2

-2 + 1 = -1

-1 + 1 = 0

0 -3 = -3

-3 + 1 = -2

-2 + 1= -1

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The solution set to the inequality, -1/2m ≥ 7/11, is: m ≤ -14/11 (see attachment for the graph).

Translating the statement given as an inequality, we have:

-1/2m ≥ 7/11

To find the solution, isolate the variable of m to one side of the inequality:

-1/2m ≥ 7/11

Multiply both sides by -2 then change the sign to

-1/2m(-2) ≥ 7/11(-2)

m ≤ -14/11

Therefore, it means the solution is any value of m that is less than or equal to -14/11.

The graph of the solution is shown in the attachment below.

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Answer:

no

Step-by-step explanation:

For a relation to be a function each input must have only one output.

If you look at the points (-4,-1) and (-4,-3) you can see that The input (-4) has more than one output (-1 and -3), so it is not a function.

The equivalent ratio according to the given ratios are 2 : 1 and 1 : 2, 7 : 2 and 7 : 2, 1 : 4 and 1 : 4, 1 : 10 and 2 : 10.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the given question,

The ratios are,

24 : 12 and 6:12 = 2 : 1 and 1 : 2

7 : 2 and 14 : 4 = 7 : 2 and 7 : 2

5 : 20 and 1 : 4 = 1 : 4 and 1 : 4

1 : 10 and 2 : 11 = 1 : 10 and 2 : 10

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Translations do not change the slope of the line, so the original line and the transformed line are always a parallel option (B) is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

As we know, parallel lines never intersect.

Parallel lines result from changing the y-intercept while keeping the slope constant.

The original line and the transformed line are always parallel since translations do not alter the slope of the line.

Thus, translations do not change the slope of the line, so the original line and the transformed line are always a parallel option (B) is correct.

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There are 63 distinct color groupings to make with your paint.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are 6 tubes of paint.

Now,

Number of tubes = 6

So, The number of distinct color groupings to make with 6 paints is;

⇒ 2⁶ - 1

⇒ 64 - 1

⇒ 63

Thus, There are 63 distinct color groupings to make with your paint.

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Answer: The shorter piece is 8 ft and the longer piece is 19 ft.

Step-by-step explanation:

     Let x be the shorter piece. We will write an equation that represents the original problem to help us solve.

           27 ft = x + (2x + 3)

     Now, we will solve this equation.

27 ft = x + (2x + 3)

27 ft = 3x + 3

24 ft = 3x

8 ft = x

     The shorter piece is 8 ft long.

     Then, we will use substitution for the longer piece.

2x + 3

2(8) + 3

19

     The longer piece is 19 ft long.

To do a rough check of our work, 19+8=27 ✓

The interval that represents the middle 95% of his commute times is [45 , 55]

What is standard deviation ?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

68% is the first standard deviation

95% is the second standard deviation about the mean

99.7% is the 3rd standard deviation about the mean.

Therefore. the middle 95% interval is calculated as:

CI = µ + 2 σ

   =  50 ± 2 (2.5)

   = 50 ± 5

  = [45 , 55]

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Answer:

A(1,2) -> A'(3,6)

B(3,1) -> B'(9,3)

Step-by-step explanation:

A(1,2) ×3 -> A'(3,6)

B(3,1) ×3 -> B'(9,3)

Answer:

a)  A = (1, 2),   A' = (3, 6)

b)  B' = (9, 3)

Step-by-step explanation:

From inspection of the given diagram:

   A = (1, 2)

   A' = (3, 6)

As the triangle has been enlarged by a scale factor of 3 and centre (0, 0), to find the coordinates of B' simply mulitply the coordinates of B by the scale factor:

   As B = (3, 1)

   ⇒ B' = (3 × 3, 1 × 3) = (9, 3)

Answer:

Step-by-step explanation:

perimeter of given square = 2 x 4 = 8 units

area of given square = 2^2 = 4 units^2

side of dilated square = 2 x 3 = 6 units

perimeter of dilated square = 6 x 4 = 24 units

area of dilated square = 6^2 = 36 units^2

Small square

The perimeter  is 8

the area is 4

Big Square

the perimeter is 24

the area is 36

The 98% confidence interval estimating the difference in mean shoulder condition score one year after such interventions in the population of patients with persistent shoulder pain is given by:

(-2.5, 5.1).

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error of the distribution of differences is given as follows:

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm ts[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 72 + 65 - 2 = 135 df, is t = 2.35.

Then the bounds of the interval are:

The missing information is given by the image shown at the end of the answer.

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0.2456 = 24.56%  probability of the mean IQ score of people in the sample is less than 99.

What is the Normal Probability Distribution?

The Normal (or Gaussian) distribution is the most common continuous probability distribution. The function calculates the likelihood that an event will occur between any two real number limits as the curve gets closer to zero on either side of the mean. The area beneath the normal curve is always one.

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation, the z-score of a measure X is:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

This is the P value of Z when X = 98.

[tex]z = \frac{x - \mu}{\sigma}[/tex]

z = (99 -100)/15

z = -0.066

z = -0.066 has a P value of 0.2456

Hence, 0.2456 = 24.56%  probability of the mean IQ score of people in the sample is less than 99.

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The linear function is P=-800(t)+1622700 where P and t are population and years respectively.

Domain of P is (1991, 1992, 1993,  ............)

Range of P is (29900, 29100, 298300, .........)

In 2010 there will be 14,700 population

How do you determine a domain's and range's?

How Can I Determine an Equation's Domain and Range? In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

Given that

In 1995 there will be 26700 population and in 2003 there will be 20300 population

So in above statement we can form 2 linear equations

26700=m(1991)+b

20300=m(2003)+b

by this we can solve for m and b

m = -800

b= 1622700

By this now we can find the year for population of 14700

14700 = -800(t)+1622700

t = 2010

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The sales of raincoats next month is 140.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). By examining how the variables vary in relation to one another, correlation evaluates the association or relationship between two variables. Simultaneous changes in two variables are also described by statistical correlation, which is typically illustrated by linear relationships.

Given:

As, from the figure The type of correlation is Positive correlation.

and, when x= 70 the value of y is 140.

So, the sales of raincoats next month is 140.

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The number line that shows the two opposite numbers have a sum of 0 is option B.

What is number line?

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

The number line that shows the two opposite numbers have a sum of 0.

Here,

A) 0+1=1

B) -3+3=0

C) 0+2=2

D) -5+0=-5

Hence, the number line that shows the two opposite numbers have a sum of 0 is option B.

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The exponential function f(x) = 3ˣ has a function table of values calculated below and a graph attached

A function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.

In the function given;

f(x) = 3ˣ

When x = -2

f(-2) = 1/9

When x = -1

f(-1) = 1/3

When x = 0

f(0) = 1

When x = 1

f(1) = 3

when x = 2

f(2) = 2

The function can be represented in a graph below;

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Answer:

26π (This is the answer to the problem as it is posted.)

or

169π (This is the answer to the problem if you meant πr².)

Step-by-step explanation:

π = π; r = 13

πr × 2 = π × 13 × 2 = 26π

If you meant πr², then

πr² = π × 13² = 169π

The percentage of the purchase price is 180%

In this question, the figures are given as

Amount bought = $55

Amount sold = $99

These figures can be represented as

Cost price = 55

Selling price = 99

The sales price as a percentage of the purchase price is then calculated as

Percentage = Selling price/Cost price

Substitute the known values in the above equation, so, we have the following representation

Percentage = 99/55

Evaluate

Percentage = 1.8

Express as percentage

Percentage = 180%

Hence, the percentage is 180%

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The amount that Leo has earned as interest, given the amount that Leo deposited, and the compounding period, is $2, 945.12

First, find the weekly rate on the account:
= Annual rate / Number of weeks in a year

= 2.5 % / 52

= 0.048 %

The number of periods is:

= Number of years x Weeks per year

= 13 x 52

= 676 weeks

The amount  that Leo would have earned after 13 years is:

= Deposit x ( 1 + rate) ^ number of periods

= 7, 671.12 x ( 1 + 0.048%) ⁶⁷⁶

= $10, 616.24

The interest earned is:

= Amount earned - Amount deposited

= 10, 616.24 - 7, 671.12

= $2, 945.12

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Employees are required to achieve short-term performance goals. Employees can better comprehend what is expected of them or their positions when goals are defined for them.

Additionally, it aids in the proper evaluation and direction of workers by employers.

A performance goal is a brief target connected to particular corporate objectives or work duties. Obtaining a new client or reaching a quarterly sales quota are two examples.

Establish a procedure for monitoring progress on important projects, including milestones and decision deadlines, in order to promote concentration on finishing a work. Share by February 10 with the management.

Report on weekly updates. To encourage leadership: "I believe you have a lot of promise as a leader."

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Answer:

This is just comparing fractions:

So, from most to least time spent studying, it would be

Answer:

Wrong

Step-by-step explanation:

Type the math problem correctly please.

The dogs rescued this year were 1738.

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Given that, Last year the animal rescue centre rescued 2520 dogs and cats in the ratio of 3:2. This year, the number of dogs rescued has increased by 15%.

Let the number of dogs and cats be x,

3x+2x = 2520

5x = 2520

x = 504

The number of dogs were = 3*504 = 1512

This year, 1512*115/100 = 1738.8

Hence, The dogs rescued this year were 1738.

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Answer:

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

Steps should be self-explanatory. Happy to explain if anything is not clear.

Answer:

Step-by-step explanation:

1) 4v + 7 = 7, for v?

→ 4v + 7 = 7

→ 4v = 7 - 7

→ v = 0/4

→ [ v = 0 ]

2) 3(u + 4) = 27, for u?

→ 3(u + 4) = 27

→ 3u + 12 = 27

→ 3u = 27 - 12

→ u = 15/3

→ [ u = 5 ]

3) -20 = 10(h + 5), for h?

→ -20 = 10(h + 5)

→ 10h + 50 = -20

→ 10h = -20 - 50

→ h = -70/10

→ [ h = -7 ]

4) -10 = (n - 52)/5, for n?

→ -10 = (n - 52)/5

→ n - 52 = -10 × 5

→ n = -50 + 52

→ [ n = 2 ]

5) (48/x) - 3 = 3, for x?

→ (48/x) - 3 = 3

→ 48/x = 3 + 3

→ 6x = 48

→ x = 48/6

→ [ x = 8 ]

6) 8r = 2r + 42, for r?

→ 8r = 2r + 42

→ 8r - 2r = 42

→ r = 42/6

→ [ r = 7 ]

These are required values.

Alexander is utilizing a scale of 1 inch : 300 feet for his map.

The Alexander's triangle has a height of 4 inches in inches.

When comparing the initial dimensions as used by alexander, the scale of the map may be determined.

The scale is 1 inch: 300 feet since he used 10 inches to symbolize 3000 feet, this is gotten by diving both sides by 10

Using the scale factor 1 inch: 300 feet, the height of 1200 feet would be.

300 feet per inch, then ? inch is 1200 feet

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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