Add
(-1 - i) + (-10 + 3i)

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

                     [tex]Area=5000\sqrt{3}units^2[/tex]

                     [tex]Area=14,530m^2[/tex]

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

           [tex]Area=side_1\times side_2\times sin(\alpha)[/tex]

Where, [tex]\alpha[/tex] is the measure of the included angle.

1. Upper triangle:

          [tex]side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2[/tex]

2. Lower triangle:

         [tex]side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2[/tex]

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

            [tex]Area=(1/2)\times base\times height[/tex]

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

                    [tex]sine(\alpha)=opposite\text{ }leg/hypotenuse[/tex]

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

         [tex]sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2[/tex]

3. Lower triangle:

         [tex]sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2[/tex]

Answer:

  $80

Step-by-step explanation:

The formula for p is ...

  p = I/(rt)

Filling in the given values, we get ...

  p = $20/(0.05·5) = $80

The amount that will generate the desired interest is $80.

Answer:

[tex]x = -1[/tex]

Step-by-step explanation:

To do the last question using the quadratic formula, you first need the equation in standard form.

ax² + bx + c = 0.

To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.

2(x - 2)(x + 1) = x² - 4x - 5        Expand brackets first using FOIL

2(x² + x - 2x - 2) = x² - 4x - 5        Collect like terms in brackets (x - 2x = -x)

2(x² - x - 2) = x² - 4x - 5        Distribute, multiply bracket numbers by "2"

2x² - 2x - 4 = x² - 4x - 5        Now make the equation equal 0

2x² - 2x - 4 - x² = x² - 4x - 5 - x²        Subtract x² from both sides

x² - 2x - 4 = -4x - 5        "x²" eliminated from the right side. Simplify left side.

x² - 2x - 4 + 4x = -4x - 5 + 4x        Add 4x to both sides.

x² + 2x - 4 = -5        "4x" eliminated from right side. Simplify left side.

x² + 2x - 4 + 5 = -5 + 5        Add 5 to both sides to eliminate it on the right.

x² + 2x + 1 = 0               Simplified left side.

This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.

a = 1; b = 2; c = 1

Substitute into the quadratic formula

[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex]      (Please ignore the Â, it's a formatting error)

[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex]   Simplify the square root

[tex]x = \frac{-2±\sqrt{0} }{2}[/tex]     The square root of 0 is 0.

[tex]x = \frac{-2}{2}[/tex]      The numerator can only be -2. Simplify the fraction

[tex]x = -1[/tex]         Only one answer for "x".

Whenever the square root equals "0", there will only be one answer for "x".

Answer:

nth term, [tex]T_n=1(2)^n^-^1[/tex]

10th term, [tex]T_1_0=512[/tex]

Step-by-step explanation:

From the question;

We are required to write the formula of getting nth term and find the 10th term of the sequence;

[tex]T_n=a_1r^n^-^1[/tex]

Therefore, in this case;

nth term will be given by;

[tex]T_n=1(2)^n^-^1[/tex], where n is the term in the sequence;

Therefore;

To get the 10th term of the sequence;

[tex]T_1_0=1(2)^1^0^-^1[/tex]

[tex]T_1_0=1(2)^9[/tex]

[tex]T_1_0=512[/tex]

Therefore, the tenth term of the sequence is 512

Answer:

You have to know how to interperet a problem

Step-by-step explanation:

god gave you a brain use it

The diameter of the #12 wire is approximately 0.08081 inches.

Calculating the diameter involves converting the measurement in mils to inches, since an inch is 1000 mils. Once we have the diameter in inches, we can round the answer to five decimal places, as instructed.

So, after performing the necessary calculations, the diameter of the #12 wire with a measurement of 80.81 mils is approximately 0.08081 inches.

A mil is a unit equal to one thousandth of an inch (0.001 inch). To convert mils to inches, we divide the mil measurement by 1000. So, 80.81 mils is equal to

80.81 / 1000 = 0.08081 inches.

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Final answer:

The diameter of the #12 wire in inches is 0.08081 inches, after converting 80.81 mils using the mil to inch conversion factor. The resistance of a wire changes with its gauge; a wire of one gauge number lower would have about 20% less resistance compared to the next higher gauge for the same length.

Explanation:

To convert the diameter of a #12 wire from mils to inches, you need to understand that one mil is equivalent to 0.001 inches. The stated diameter of the #12 wire is 80.81 mils.

By multiplying the value in mils by the conversion factor, we can find the diameter in inches:

80.81 mils × 0.001 inches/mil = 0.08081 inches.

Therefore, the diameter of #12 wire in inches is 0.08081 inches, rounded to five decimal places.

Discussing the resistance and resistivity of copper wire, it's known that resistance is proportional to the length of the wire and inversely proportional to the cross-sectional area.

Gauge sizes have a standardized series of diameters which differ by about 20% from one gauge to the next, which means that a wire with one gauge number lower (higher in diameter) would have approximately 20% less resistance than one of the next higher gauge (smaller in diameter) for the same length of wire.

Answer:

x=2, y=-2. (2, -2).

Step-by-step explanation:

y=x-4

y=4x-10

x-4=4x-10

x-4x-4=-10

-3x-4=-10

-3x=-10+4

-3x=-6

3x=6

x=6/3

x=2

y=2-4=-2

Answer:

4 cm

Step-by-step explanation:

Perimeter of a parallelogram is 2b+2h=30 where b is base and h is height.

if AD is 3cm more than twice AB, then it's 3+2x where x is length of AB.

Input this into the perimeter equation: 2(3+2x)+2(x)=30

Simplify to get 6+6x=30

x=24/6=4

Answer is 4 cm.

Final answer:

The length of AB in the parallelogram is 4 cm after solving the algebraic equation for the given perimeter.

Explanation:

The student is asking us to find the length of AB in a parallelogram ABCD where the perimeter is given as 30 cm, and side AD is 3 cm more than twice the length of AB. We can use algebra to determine the length of AB in a few steps.

Let's denote AB as 'x'. Since opposite sides of a parallelogram are equal, AD and BC will equal '2x + 3' while CD will also equal 'x'. The formula for the perimeter (P) of a parallelogram is P = 2(AB + BC), so substituting our known values and solving for 'x' will give us the length of AB.

Putting it all together:

Therefore, the length of AB is 4 cm.

Answer:

I think it's B. (-1,3)

Step-by-step explanation:

The solution is the point the two lines intersect each other.

The answer is (-1,3)

Answer:

52.5 meters

Step-by-step explanation:

1.5 times 35 would equal 52.5 meters.

Answer:

52.5 meters

Step-by-step explanation:

1.5 * 35

Answer:

6000

Step-by-step explanation:

if you do 200+800=1000 and the if you do 4000+1000=5000+1000=6000

The inequality that represents the amount raised in the second hour of the charity auction is x ≤ 6000.

To represent the amount raised in the second hour of the charity auction, let's use the variable x. According to the information given, the amount raised in the first hour is $4800, which is at most $1200 more than the amount raised in the second hour. This can be represented as the inequality:

x ≤ 4800 + 1200

Simplifying the inequality, we have:

x ≤ 6000

Therefore, the inequality that represents the amount raised in the second hour is x ≤ 6000.

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The perimeter of second plot is 180 feet

Solution:

Given that,

The second parking lot is being designed so that its perimeter is 3/4 of perimeter of the first parking lot

Perimeter = 2(length + width)

From given figure in question,

length = 40 feet

width = 80 feet

Therefore,

Perimeter = 2(40 + 80)

Perimeter = 2(120) = 240

Thus, we got,

Perimeter of first parking plot = 240 feet

Also, given that,

[tex]\text{Perimeter of second plot }= \frac{3}{4} \times \text{Perimeter of first parking plot}\\\\\text{Perimeter of second plot }= \frac{3}{4} \times 240\\\\\text{Perimeter of second plot }= 180[/tex]

Thus perimeter of second plot is 180 feet

To find the perimeter of the second parking lot, you multiply the perimeter of the first parking lot by 3/4. For example, if the first parking lot has a perimeter of 100 meters, the second would be 75 meters.

The problem revolves around the concept of perimeter, specifically of a rectangle. The perimeter of a rectangle is given by the formula 2*(length + width). Now, according to the question, the perimeter of the second parking lot is three-quarters (3/4) that of the first. So, if we denote the perimeter of the first parking lot as 'P', then the perimeter of the second parking lot would be (3/4)*P.

For instance, if the perimeter of the first parking lot is 100 meters, then the perimeter of the second parking lot would be (3/4)*100 = 75 meters. Hence, the second parking lot's perimeter is determined by the first parking lot's perimeter, reduced by a quarter.

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The product of multiplying 7/9 and 6 is 42/9, which can also be expressed as the mixed number 4 and 2/3.

Finding the product of two numbers in mathematics is a fundamental concept which involves multiplying the numbers together.

In the specific case of multiplying a fraction by a whole number, like 7/9 and 6, the process is straightforward.

To calculate 7/9 multiplied by 6, you can think of the whole number 6 as a fraction with a denominator of 1, which would make the problem 7/9 x 6/1.

When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. In this instance, the multiplication would look like (7 x 6) for the numerator and (9 x 1) for the denominator.

That simplifies to 42 over 9, which can be further simplified or left as an improper fraction depending on the context of the problem or the instructor's directions.

In the case of 42/9, which is already simplified, we can conclude that the product of 7/9 and 6 is 42/9, or 4 and 2/3 when written as a mixed number.

Answer:

C

Step-by-step explanation:

0 = 8 is a false statement which means the system has no solutions

The 0 = 8 shows the system has no solutions.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

we have 0= 8.

First whenever we get 0 = 0 in this case the solution will infinite many solution.

and, if we get the quantities on both side are equal then it have unique solution.

Lastly, if we have non equal quantity on both side of equal like 0= 8 then it does not have any solution.

Hence, 0 = 8 shows the system has no solutions.

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Answer:

x>-2

Step-by-step explanation:

13+x>11

x>11-13

x>-2

Answer:

umm give me more examples

Step-by-step explanation:

Answer:

x=8+a

Step-by-step explanation:

sum of a and 8

x=a+8

when they say the sum of you add an equal sign

and when they said of a and 8 it means that whatever the sum is its equal to a+8

since the sum wasn't mentioned the sum will be known as a variable

lets put x as the variable

Answer:

240 miles

Step-by-step explanation:

The actual distance between two towns, which are separated by 6 inches on a map with a scale of 1 inch to 40 miles, is 240 miles.

The subject of this question is Mathematics, specifically focusing on understanding how map scales work. In this case, the map scale is 1 inch equals 40 miles. This means, for every inch on the map, it represents 40 miles in actual distance.

To find out the real distance between two towns that are separated by 6 inches on the map, you multiply the map scale distance (40 miles) by the number of inches (6).

Which is, 6 inches x 40 miles = 240 miles.

So, the actual distance between the two towns is 240 miles.

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Answer:

2n

Step-by-step explanation:

Look at the photo below for the details.

:)

Diameter of circle is known as greatest chord of the circle.

Number of regions created by n unique diameter is 2n.

Diameter of circle is two times of its radius.

By 1 diameter, two region is created in circle

By 2 diameter, 4 region is created in circle.

By 3 diameter , 6 region is created in circle.

Therefore, by n unique diameters, 2n regions is created in circle.

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Answer:

The slope is 5/3

Step-by-step explanation:

In order to find the slope from a graph, you have to use the method called "rise over run". You do this by looking at the point (0,-1). and going up on the y axis and counting until its on the SAME y axis for the next point which is at (3,4). If you count from -1 to 4, you'll get 5, which is the rise number. Next you have to solve the "run" number. Now that we already have our rise number start from (0,4) and count how many ticks/counts it takes to move the x axis to the point (3,4). It takes 3 counts. Since it's called rise/run. You put 5 at the top, and 3 at the bottom.

[tex]\frac{5}{3}[/tex]

Hope this helps :)

Answer:

5

Step-by-step explanation:

The time taken to stuff and seal 63 envelopes by both Tom and Jerry will be 6 minutes.

Given the Parameters :

Combined rate :

Time taken if they work together :

Therefore, the time taken of they both worked together will be 6 minutes

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Answer:

x = 17.

Step-by-step explanation:

We know that the two angles are supplementary (equal 180) as they are found on a straight line. Therefore,

(5x - 18) + (4x + 45) = 180.

9x + 27 = 180.

9x = 153.

x = 17.

Answer:

The Diameter  of the cylinder is  10.29 units

Step-by-step explanation:

Given:

Volume  of the Cylinder =  237 cubic units

Height of the Cylinder =  3 units

To Find :

Diameter = ?

Solution:

The Volume of the cylinder = [tex]\pi r^2 h[/tex]

where

r is the radius

h is the height

On substituting the values

[tex]237 = \pi (r)^2 (3)[/tex]

[tex]\frac{237}{ 3 \pi} = r^2[/tex]

[tex]\frac{79}{\pi} = r^2[/tex]

[tex]25.146 = r^2[/tex]

r = 5.014 units

Noe the diameter is  =  2r = 2( 5.014) =  10.29 units

Answer: The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 fish in the river.

Step-by-step explanation:

The standard deviation of the sampling distribution = [tex]\sqrt{\dfrac{p(1-p)}{n}}[/tex] , where p= population proportion and n = sample size.

Let p be the proportion of  fish in a river are catfish.

As per given , we have

p= 0.47

n= 25

The, the standard deviation of the sampling distribution will be [tex]\sqrt{\dfrac{0.47(1-0.47)}{25}}[/tex]

[tex]=\sqrt{0.009964}\approx0.0998[/tex]

The 10% condition : Sample sizes should be no more than 10% of the population.

But a river can have more than 250 fish [where 10% of 250 =25 (sample size)]

i.e. The 10% condition is met because it is very likely there are more than 250 fish in the river.

So the correct answer is "The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 fish in the river."

Answer:

The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.

Step-by-step explanation:

I got it right on the quiz

Answer:

8 ; 27 ; 125 ; 1000 ; 1331

Step-by-step explanation:

8 = 2³

27 = 3³

125 = 5³

1000 = 10³

1331 = 11³

Answer:

8, 27, 125, 1000, 1331.

Step-by-step explanation:

2^3 = 8

3^3 = 27

5^3 = 125

10^3 = 1000

11^3 = 1331

Answer:

Yes it is. 65 as a decimal is .65, 5/8 is .625, so 65% is greater

Step-by-step explanation:

the answer to your question is yes

Answer:

when ever they say fencing it is perimeter i will send rhe rest later

she did 2×pie (3.14 according to the question )×radius (9)

Answer:

The correct answer is 56.52 feet

Step-by-step explanation:

(I know the question is supposed to be about how skye got the answer but if you wanted to know the real answer im here for you).

Answer:

look at picture shown.