Find the midpoint between
-7 + 4i
and
3 - 2i

Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]

Given principal of Ms. Drake is [tex]\$1000[/tex]

Rate of interest is [tex]8.5 \%[/tex]

Time is [tex]2[/tex] years.

Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]

            [tex]=\frac{17000}{100}\\=170[/tex]

Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.

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If CD is perpendicular on AB then the x intercept of CD is (17,0).

Given that CD is perpendicular on AB and passes through C(5,12) and the coordinates of A and B are  (-10,-3), (7,14).

When two lines are perpendicular on other line then the product of their slopes is equal to -1.

It is given that CD is perpendicular on AB. So we need to first calculate the slope of AB.

Slope=[tex](y_{2} -y_{1} /x_{2} -x_{1} )[/tex]

Slope of AB=(14+3/7+10)

=(17/17)

=1

According to rule product of slopes of AB and CD should be -1.

So the slope of CD will be -1.

Now we have to form equation of CD from slope -1 and point (5,12).

y-12=-1(x-5)

y-12=-x+5

x+y-17=0

We have to find out x intercept.

We know that x intercept is a point where the line touches x axis. So here the value of y =0.

x+y-17=0

put the value of y=0.

x+0-17=0

x=17

Point will be (17,0)

Hence the x intercept of CD will be (17,0).

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Question is incomplete as it should include in its beginning that CD is perpendicular on AB.

The trigonometric values are:

[tex]cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }[/tex]

The given trigonometric identities are:

[tex]cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})[/tex]

Note that:

[tex]\pi=180^o\\\\\frac{3\pi}{4}=135^0[/tex]

Therefore, using the calculator for the given expressions:

[tex]cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }[/tex]

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Answer:

The scale factor from the original triangle to the image is 1/2.  The scale factor from the image to the original is 2.

Step-by-step explanation:

I make a sketch of the information.  Look at the corresponding sides.  Side AC on the big triangle is 8 and A'C' is 4.  It is half of the size of the large triangle.  That is true for each pair of sides.

If I went the other way, the original sides are twice as big as the images sides.

The probability in all given conditions is 1/4.

According to the statement

Number of coin tossed = 3

Total outcomes = 8

Now, we have to find the probabilities on different conditions.

Probability = A head on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

Probability = alternating tale and head / total outcomes

Probability = 2/8

Probability = 1/4.

Probability = A No tails on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

So, The probability in all given conditions is 1/4.

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The pounds of pressure needed to reach a fire 50 feet away is 48 pounds

d = 1/2n + 26

where

If d = 50 feet

d = 1/2n + 26

50 = 1/2n + 26

50 - 26 = 1/2n

24 = 1/2n

n = 24 ÷ 1/2

n = 48 pounds

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W

a system can only be a function if there are no more than one value of y for each value of x. if a value of x is repeated twice or more in a table, it means it is not a function.

The x-coordinate of the point is -2

The points are given as:

J = (-6, -2)

K = (8, -9)

m : n = 2 : 5

The x-coordinates of the point is calculated as:

[tex]jk = \frac{m}{m+n} *(x_2 -x_1) +x_1[/tex]

So, we have:

[tex]jk = \frac{2}{2+5} *(8+6) -6[/tex]

This gives

[tex]jk = \frac{2}{7} *14 -6[/tex]

So, we have:

jk = 4 - 6

Evaluate

jk = -2

Hence, the x-coordinate of the point is -2

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Answer: The lowest common multiple of 12, 18, and 56 would be 504. Why? Well, see below for an explanation!

Step-by-step explanation: What is the lcm? Well, the lcm of two or more numbers is the lowest possible number that each number has in common as a multiple. Because we are dealing with large numbers, we can tell that the lcm will be a multiple of these numbers times at least 5. I multiplied all the numbers by 10, and it was too large and did not work. However, I backed up and tried 9.

56 x 9 = 504.

Why is this acceptable? Well, this is acceptable because I found that 504 can be divided by 12 and 18 both to get a whole number.

504 divided by 18 equals 28.

504 divided by 12 equals 42.

Using this principle, we will find that 504 is the lowest number that 12, 18, and 56 have in common.

Your final answer: 504 is the lowest common denominator. If you need extra help, let me know and I will gladly assist you.

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consist of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 18 \ \ \ 56}\\ \ 6 \ \ \ \ 9 \ \ \ \ 28\\ \ 3 \ \ \ \ 9 \ \ \ \ 14\\ \ 3 \ \ \ \ 9 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 3 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 1 \ \ \ \ \ 7\\ \ 1 \ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                        [tex]\sf{L.c.m.(12,18,56)=2\times2\times2\times3\times3\times7}[/tex]

                                        [tex]\sf{L.c.m.(12,18,56)=2^{3}\times3^{2}\times7 }[/tex]

                                            [tex]\boxed{\boxed{\sf{L.c.m.(12,18,56)=504}}}[/tex]

The lowest common multiple of 12, 18, and 56 is 504.

Patrick has an absolute advantage in playing quarterback.

Given a table containing touchdowns and field goals by Partrik and Field goals as under:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

We are required to find a person who has an absolute advantage in playing quarterback.

Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.

Total of touchdowns and field goals by Patrik=39+13=52

Total of touchdowns and field goals by Jimmy=25+5=30

We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.

Hence Patrick has an absolute advantage in playing quarterback.

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Question is incomplete as it should include the following table:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

-16t^2 represent the position on the graph on the negative side.

According to the statement

we have given equation is h(t)=5+100t-16t^2 -(1)

And we have to find representation of -16t^2

we know that the equation number (1) represent the Quadratic Equation

And in this we have to solve the Quadratic Equation and find the representation of the given terms. then

h(t)=5+100t-16t^2

5+100t-16t^2 = 0

16t^2 -100t-5 = 0

In this equation 16t^2 represent the equation on the graph.

It means that it shows the position on the graph.

Overall, -16t^2 represent the position on the graph on the negative side.

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The measure of BC from the figure shown is 26

A line is the distance between two points. From the given line AC;

AC = AB + BC

Given the following parameters

AC = 8x - 20

AB = 3x - 1

Required
Length BC

Substitute

8x-20 = 3x-1 + BC
BC = 8x-20 -(3x - 1)

BC = 8x - 20 - 3x + 1

BC = 5x - 19

Since  B is the midpoint of AC, then;

AB = BC
3x - 1 = 5x - 19

-2x = -18

x = 9

Determine the length of BC

BC = 5(9) - 19
BC = 45 - 19
BC = 26

Hence the measure of BC from the figure shown is 26

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Answer:

This is your answer.

Step-by-step explanation:

There are different kinds of angles:

Angles below 90= Acute

90= Right

91–179= Obtuse

180= Straight Angle

181–359= Reflex Angle

360= Complete Angle or Circle.

Because 80 degrees is less than 90 degrees, Angle ABC is an acute angle.

Intermediaries who are independent, but agree to cooperate have likely formed a(n) contractual distribution system.

The most commonplace form of Contractual VMS is Franchising. In franchising, the manufacturer authorizes the distributor to promote its product below the producer's call against some annual license rate. For example, McDonald's, Dominos, Pizza Hut, etc. are all styles of a franchise that might be operating on a contractual foundation.

A form of vertical advertising machine in which unbiased firms at unique degrees of distribution are tied together by using contracts to achieve economies of scale and more income impact.

A vertical advertising system refers to a marketing system that aims to draw and attain organizations running inside the same industry. then again, horizontal advertising and marketing device refers to an advertising and marketing system whereby corporations which can be on equal degree join collectively to advantage economies of scale.

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Answer:

the answer is 17y 3y+6y is 9y plus 8y is 17y

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathsf{(3y + 6y + 8y)}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\mathsf{\rightarrow 9y + 8y}[/tex]

[tex]\mathsf{\rightarrow 17y}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The number of feet of wood that is needed is given as 35 feet of wood.

We have to do this through the use of pythagoras theorem

a² = b² + c²

8² + 6²

a = √100

= 10

4² + 6²

= 52

a = √52

Then we would have

10 + 10 + √52 + √52

= 34.42

This is approximately 35 feet

The feet of wood that is needed is given as 35 feet

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Answer:

The number of feet of wood that is needed is given as 35 feet of wood

Step-by-step explanation:

I just did it on E2020 and got it right

The proofing of the triangle is illustrated below.

AB = c

BC = a

AC = b

h² = b² - x²

h² = a² - y²

a² - y² = b² - x²

a² = b² - x² + y²

Note that x = c - (c - x) = c

a² = b² - (-x)² + y²

a² = b² + c² + y²

Cos A = x/b

cos = adjacent/hypothenuse

x = bcosA

a² = b² + c² - 2bx

a² = b2 + c² - 2bccosA

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The area of the shaded circle is given as follows: 84.82 cm².

The area of a circle of radius r is given by pi multiplied by the radius squared, as given by the formula presented next:

[tex]A = \pi r^2[/tex]

In this problem, we have that the important data is given in the bullet-points as follows:

Hence the shaded area in cm² can be found a applying the formula given at the beginning of this problem, as is presented below:

[tex]A = 0.75\pi \times 6^2 = 84.82[/tex]

The multiplication by 0.75 happened because as stated in the bullet point, the shaded area corresponds to only 75% of the entire circle.

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The ratio of all the corresponding sides of the triangle are equal to each other.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be similar if they have the same shape and the same corresponding angles.

Also, the ratio of all the corresponding sides of the triangle are equal to each other.

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The 3 numbers which should be placed between 12 and 60 are; 24, 36 and 48.

It follows from the task content that the first and last numbers are; 12 and 60 respectively.

Hence, since the difference between 12 and 60 is 48 and there are 4 transitions between the two numbers to have 5 total numbers,

It follows that the common difference is; 48/4 = 12 and the three numbers required are; 24,36 and 48.

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The recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

The sequence is given as:

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

The first term of the above sequence is

[tex]b(1) = -0.25[/tex]

Calculate the common ratio using

r = b(2)/b(1)

So, we have:

r = -2/-0.25

Evaluate

r = 8

So, we have:

[tex]b(n) = b(n-1)\cdot 8[/tex]

Hence, the recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

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Complete question

Complete the recursive formula of the geometric sequence

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

[tex]b(1) =[/tex]

[tex]b(n) = b(n-1)\cdot[/tex]

x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.

Given that,  

f(x) = [ x + 3 ] which is an absolute value function.

Therefore,

| x+3 | > 0

By removing the modulus,

x+3 > 0

x > - 3

Hence x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ].

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Consider this absolute value function.

f(x) = [ x + 3 ]

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

Answer:

The Answer is C. X+3, x > -3

for edmentum users

Step-by-step explanation:

Answer:

8 ×10=80

Step-by-step explanation:

because 1 time

8

10 times

add so

90

less

so that's it

80

Answer:

57pi

Step-by-step explanation:

First, let's get the area of the entire circle, including the shaded region:

pi*(8+3)^2 = 121pi

Next, let's get the area of the unshaded circle

pi*8^2 = 64pi

If we subtract the inner circle from the full circle, we get the shaded region:

121pi-64pi =

57pi

Answer: 57π

Step-by-step explanation:

You have to calculate the area of the whole circle created by the sum of the inner circle and the ring, so 8+2=11=r, now use the formua for getting area of a circle, π*r², which is "121π"

After that, subtract the area of the inner circle (its area is π*8²)

So 121π-64π = 57π

Answer:

Undefined

Step-by-step explanation:

No multiplicative inverse exists for 0

Answer:

undefined

Step-by-step explanation:

a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.

The standard error of the estimate of average height in the city is 0.25.

Given average height 64 inches, sample mean and sample standard deviation of 4 inches.

We have to determine the standard error of the estimate of the average height in the city.

Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.

n=256

μ=mean

s = sample standard deviation

Standard error=s/[tex]\sqrt{n}[/tex]

=4/[tex]\sqrt{256}[/tex]

=4/16

=0.25

Hence the standard error of the estimate of the average height is 0.25.

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Answer:

BT = 18, DA = 6

Step-by-step explanation:

- EBT and SDA are similar triangles

- EBT has a perimeter of 63

- SDA has a perimeter of 21

- BT = 6x

- DA = x+3

We know that EBT has side lengths that are three times bigger than the side lengths of SDA since 63 = 21 x 3.

so

6x is equal to 3(x+3).

6x = 3x + 9

3x = 9

x = 3

Now we know that:

BT = 18

and

DA = 6

Answer:

21655

Step-by-step explanation:

minus the values