if A = -3 + 5i, B = 4 - 2i, and C = 1 +6i, where i is the imaginary unit, then A - BC equals

1) 5 - 17i
2) 5 + 27i
3) -19 - 17i
4) -19 + 27i

The answer is:

The coordinates of the midpoint are:

[tex]x-coordinate=2\\y-coordinate=6[/tex]

We can find the midpoint of the segment with the given endpoints using the following formula.

The midpoint of a segment is given by:

[tex]MidPoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

We are given the points:

[tex](12,4)\\[/tex]

and

[tex](-8,8)\\[/tex]

Where,

[tex]x_{1}=12\\y_{1}=4\\x_{2}=-8\\y_{2}=8[/tex]

So, calculating the midpoint, we have:

[tex]MidPoint=(\frac{12+(-8)}{2},\frac{4+8}{2})[/tex]

[tex]MidPoint=(\frac{4}{2},\frac{12}{2})[/tex]

[tex]MidPoint=(2,6)[/tex]

Hence, we have that the coordinates of the midpoint are:

[tex]x-coordinate=2\\y-coordinate=6[/tex]

Have a nice day!

Answer:

The midpoint is (2, 6)

Step-by-step explanation:

Points to remember

The midpoint of a line segment with end points, (x₁, y₁) and (x₂, y₂)

mid point = [ (x₁ + x₂)/2 , (y₁ + y₂)/2]

To find the midpoint of given line

Here (x₁, y₁)  = (12, 4) and (x₂, y₂) = (-8, 8)

Midpoint = [

 = [(12 +-8)/2 , (4 + 8)/2]

 = (4/2 , 12/2)

 = (2, 6)

Therefore midpoint is (2, 6)

Answer: 27, 29

Step-by-step explanation:

Consecutive integers are as follows:

First Integer: x

Second Integer: x + 1

Third Integer: x + 2

Fourth Integer: x + 3

The second and fourth = 58

        x + 1    +      x + 3    = 58

                           2x + 4 = 58

                           2x       = 54

                             x       = 27

First Integer:  x              = 27

Third Integer: x + 2       = 27 + 2      = 29

Answer:

Step-by-step explanation:

n, n + 1, n + 2, n + 3 - four consecutive integers

The equation:

(n + 1) + (n + 3) = 58

n + 1 + n + 3 = 58                combine like terms

(n + n) + (1 + 3) = 58

2n + 4 = 58             subtract 4 from both sides

2n = 54            divide both sides by 2

n = 27 - first

n + 1 = 28 - second

n + 2 = 29 - third

n + 3 = 30 - fourth

Answer:

Step-by-step explanation:

-8

Answer: First  option.

Step-by-step explanation:

We need to remember that:

[tex]\sqrt[n]{a^n}=a[/tex]

[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]

And, according to the Power of a power property we know that:

[tex](a^m)^n=a^{(mn)}[/tex]

Knowing this, we can descompose 32 into its prime factors:

[tex]32=2*2*2*2*2=2^5[/tex]

Then we can rewrite the expression as:

[tex]=\sqrt[5]{(-32)^3}\\\\=\sqrt[5]{(-2^5)^3}[/tex]

Finally, simplifying the expression, we get:

[tex]=\sqrt[5]{(-2)^{15}}\\\\=(-2)^3\\\\=-8[/tex]

This matches with the first option.

Answer: 40

Step-by-step explanation:

the numbers were doubled

Answer:

40

Step-by-step explanation:

Answer:

Option B. [tex]r=\sqrt{\frac{3V}{\pi h}}[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

Solve for the radius r

That means-----> isolate the variable r

Multiply by 3 both sides

[tex]3V=\pi r^{2} h[/tex]

Divide by [tex](\pi h)[/tex] both sides

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

square root both sides

[tex]r=\sqrt{\frac{3V}{\pi h}}[/tex]

If Caroline knows the height and the required volume of a cone-shaped vase, the formula she can use to determine the radius of the vase is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]

Volume of cone (V) = 1/3πr²h

radius = r; height of cone = h

Having the height (h) and volume (V), find r:

1/3πr²h = V

(πr²h)/3 = V

πr²h = 3V

Divide both sides by πh

r² = 3V/πh

Take the square root of both sides

[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]

Therefore, if Caroline knows the height and the required volume of a cone-shaped vase, the formula she can use to determine the radius of the vase is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]

Learn more about the volume of a cone on:

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The number he should add on both sides of the equation to complete the square is 36.

The given equation is [tex]x^{2} - 12x = 16[/tex]

Thus, to make it a complete square, both sides of the equation must be a perfect square.

If we add number 36 on both sides of the equation, then the resulting equation is a perfect square.

⇒ [tex]x^{2} - 12x + 36= 16 + 36[/tex]

⇒ [tex](x-6)^{2} = 52[/tex]

∴  [tex](x-6)^{2} = (2\sqrt{13} )^{2}[/tex]

Thus, the given equation is a complete square from both sides.

Therefore, the number he should add on both sides of the equation to complete the square is 36.

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Final answer:

Add 36 to both sides of the equation x²- 12x = 16 to complete the square, transforming it into a perfect square trinomial.

Explanation:

To complete the square for the equation x² - 12x = 16, you need to take half of the coefficient of x, which is -12, and square it. This process transforms the left-hand side into a perfect square trinomial. Therefore, you calculate (12/2)² which equals 36. This is the value that needs to be added to both sides to complete the square. The equation then becomes x² - 12x + 36 = 16 + 36, which simplifies to (x - 6)²= 52

Answer:

B

Step-by-step explanation:

Since the line segment JK is tangent to the circle C, it creates a 90° angle at the point of intersection.

This means that we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

Plug in the values given.

[tex]24^2+b^2=28^2 \\ \\ 576+b^2=784 \\ \\ b^2=208 \\ \\ b=\sqrt{208} \\ \\ b=14.4[/tex]

The answer would be B I think

Answer:

Journey 1: The travel starts at 30 mph for two hours, after which there is a rest of two hours. The journey then continues slightly faster, at 40 mph for one hour. Then it is time for another rest of one hour. At this point we are 100 miles from home. We return home after two hours of traveling at 50 mph.

Step-by-step explanation:

The slope of the line indicates the speed and can be calculated by dividing the traveled distance by the time it took. This way you can describe all the journeys. Can you do the other two?

The expression that has a value of 36 is A. 9/12 x 48

Which expression has a value of 36?

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

A. 9/12 x 48

B. 6/7 x 21

C. 10/13 x 39

D. 3/7 x 42

Evaluating the expressions, we have

A. 9/12 x 48 = 36

B. 6/7 x 21 = 18

C. 10/13 x 39 = 30

D. 3/7 x 42 = 18

Hence, the expression that has a value of 36 is A. 9/12 x 48

Answer:

the answer is D: 294 sq. cm

Step-by-step explanation:

first you want to split the net into 4 triangles and 1 rectangle

a = 12 cm

b =  6 cm

d = 13 cm

calculate the surface area of the pyramid...

1st find the area of the rectangle base

Rectangle base area

b x a = (6 cm) (12 cm)

= 72 sq. cm

next find the area of the triangle on the left

Left triangle

1/2(b)(d) = 1/2 (6 cm)(13 cm)

= 1/2 (78 sq cm)

= 39 sq. cm

Since all the triangles are congruent (same), you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.

Area of left & right triangles

= 2 (39 sq. cm)

= 78 sq. cm

Find the area of the triangle on the bottom

Bottom triangle area = 1/2 (a)(a)

= 1/2 (12 cm) (12 cm)

= 1/2 (144 sq. cm)

= 72 sq. cm

Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top

Area of top & bottom triangles

2 (72 sq. cm) = 144 sq. cm

Finally...add the area of the 4 triangles to the area of the rectangular base

72 + 78 + 144 = 294 sq. cm

Answer:

D

Step-by-step explanation:

Fun fact: During your life you can produce enough saliva for 2 swimming pools! :O 0.0 :D

First of all, let's convert all the measures to the same unit: 4 feet are 48 inches.

Now, as the wheel turns, there is a proportion between the angle and the distance travelled: for example, when the car moves forward a whole circumference, the angle will be 360°. Conversely, if the wheel turns 180°, then the car will move forward a distance which is half the circumference of the wheel, and so on.

Since the radius is 16 inches, the circumference will be

[tex]C=2\pi r = 32\pi[/tex]

So, we have the following proportion:

[tex]360\div 32\pi = x \div 48[/tex]

that you can read as: "if an angle of 360 corresponds to a distance travelled of [tex]32\pi[/tex], then the unknown angle x corresponds to a distance travelled of 48 inches.

Solving for x, we have

[tex]x = \dfrac{360\cdot 48}{32\pi} = \dfrac{17280}{32\pi} = 171.887338539\ldots \approx 171.9[/tex]

The car wheel with a radius of 16 inches turns through an angle of approximately 171.9° when the car rolls forward 4 feet.

To find the angle through which a car wheel turns when the car rolls forward 4 feet, given that the wheel has a radius of 16 inches, we first convert the distance in feet to inches and then calculate the circumference of the wheel. Finally, we determine the angle using the relationship between the length of arc and the radius.

First, convert the distance from feet to inches:

Next, calculate the circumference of the wheel:

The total distance rolled (48 inches) is less than the circumference of the wheel, so the wheel will not complete a full revolution. To find the angle, we use the formula:

Therefore, the wheel turns through an angle of approximately 171.9° when the car rolls forward 4 feet.

Answer:

A. Volley Ball game: 0.20

B. Rugby 7s game: 90%

Step-by-step explanation:

A. Volley Ball game: 12 ≤ x < 21

To calculate the probability, the first step is to evaluate the number of people meeting the requirement and then the number of the total population.

In this case, let's first sum up the total population, meaning the total audience at the Volley Ball game.  If we sum up all attendance numbers for the Volley Ball game (first column), we get 700 + 1,000 + 3,050 + 250 = 5,000 people.

Now, let's find out how many people we have in that attendance being 12 or older but less than 21.  That's the second line of the table, so 1,000.

That means that the probability the Fan Cam gets one of those 12 ≤ x < 21 fans is 1,000 / 5,000, so 1/5, which is equal to 20% or 0.20

B. Rugby 7s game: x > 12

As before, to calculate the probability, the first step is to evaluate the number of people meeting the requirement and then the number of the total population.

The total population is the total attendance of the game, so 500 + 1,000 + 2,500 + 1,000 = 5,000 people in the stadium.

How many of them are NOT less than 12 years of age?  We have to sum up the last 3 rows of the table: 1,000 + 2,500 + 1,000 = 4,500 people 12 or older.

So, what's the possibility one of those 12 or older will be spotted by the Fans Cam?  4500 out of 5,000 = 9/10, or 90%.

Step-by-step explanation:

displayed price=100%=85

selling price=75% of the displayed price

discount=,25%

Final answer:

To find the amount of sales tax on a $85 jacket with a 7.5% sales tax, convert the percentage to 0.075 and multiply by $85, resulting in a tax of $6.375. Add this to the original price for a total of $91.38.

Explanation:

To calculate the amount of sales tax for an item, you must first convert the percentage to a decimal and then multiply it by the item's displayed price. For the example of a jacket priced at $85 with a 7.5% sales tax, you would use the following equation:

Amount of sales tax = price × rate of sales tax

First, convert 7.5% to a decimal by dividing by 100, which gives us 0.075. Then, multiply $85 by 0.075:

$85 × 0.075 = $6.375

Therefore, the sales tax is $6.375. To find the total cost of the jacket including the sales tax, you simply add the amount of the sales tax to the displayed price:

Total cost = displayed price + sales tax

Total cost = $85 + $6.375 = $91.375

Since the total cost usually needs to be rounded to the nearest cent, the final total cost of the jacket would be $91.38.

Answer:

x < 3

Step-by-step explanation:

2(4+2x)>5x+5

Distribute

8 +4x > 5x+5

Subtract 4x from each side

8 +4x-4x > 5x-4x+5

8 > x+5

Subtract 5 from each side

8-5 > x+5-5

3 > x

X must be less than 3

ANSWER

[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]

EXPLANATION

The given equation is

[tex] {4}^{x - 3} =13.[/tex]

[tex] ln({4}^{x - 3} )= ln(13)[/tex]

We use the power rule of logarithms to get:

[tex](x - 3) ln(4) = ln(13) [/tex]

Expand;

[tex]x ln(4) - 3 ln(4) = ln(13) [/tex]

Solve for x,

[tex]x ln(4)= ln(13) + 3 ln(4) [/tex]

[tex]x ln(4)= ln(13) + ln( {4}^{3} ) [/tex]

[tex]x ln(4)= ln(13) + ln(64) [/tex]

[tex]x ln(4)= ln(13 \times 64) [/tex]

[tex]x ln(4)= ln(832) [/tex]

[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]

Answer:

You are most likely a right triangle.

Step-by-step explanation: A polygon with 5 sides is the pentagon. A square has 4 angles, so with this, I can already tell that it is a triangle if it has 3 angles, (one less than a square). Then it says that it has 1 right angle. This would make the triangle a right. I hope this helps.

Final answer:

The polygon described has 'n - 2' sides, 3 angles with one being a right angle, and the other two totaling 90 degrees.

Explanation:

The polygon described in the question has 2 fewer sides than a regular polygon. Let's call the number of sides of the polygon 'n'. So, the polygon has 'n - 2' sides.

The polygon has 1 less angle than a square, which has 4 angles. So, the polygon has 4 - 1 = 3 angles.

The polygon described in the question has 1 right angle. A right angle measures 90 degrees. Since the polygon has 3 angles, and one of them is a right angle, the other two angles must add up to 180 - 90 = 90 degrees.

Putting it all together, the polygon described in the question has 'n - 2' sides, 3 angles with one of them being a right angle, and the other two angles totaling 90 degrees.

Answer: 20

H(c) = 6.4 + 0.6c

6.4 is the constant.

When the height of the cups is 18.4 the function is:

18.4 = 6.4 + 0.6c

Then, you add 6.4 from both sides

18.4 - 6.4 + 6.4 = 6.4 + 0.6c - 6.4  + 6.4

Simplify

18.4 = 6.4 + 0.6c

Switch sides

6.4 + 0.6c = 18.4

Multiply both sides by 10

6.4 x 10 + 0.6c x 10 = 18.4 x 10

Refine

64 + 6c = 184

Subtract 64 from both sides

64 + 6c - 64 = 184 - 64

Simplify

6c = 120

Divide both sides by 6

6c/6 = 120/6

c = 20

The answer is 180 seconds. The reason for this is that the second carton is 24 times the volume of the first one; so, the time taken to pack the container would be 24 times longer. This means that the answer would be found by the equation 7.5 * 24 which is evaluated to 180 seconds

To find out how long it would take to fill the larger carton, you can use the ratio of the volumes of the two cartons and the time it takes to fill the smaller carton. The formula to calculate the volume of a rectangular prism (like a carton) is:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
First, we calculate the volume of the original carton:
\[ \text{Original Carton Volume} = 3 \text{ ft} \times 2 \text{ ft} \times 1 \text{ ft} = 6 \text{ cubic feet} \]
Next, we calculate the volume of the new larger carton:
\[ \text{New Carton Volume} = 4 \text{ ft} \times 6 \text{ ft} \times 6 \text{ ft} = 144 \text{ cubic feet} \]
Now, you can find out how much bigger the new carton is compared to the original carton by taking the ratio of the volumes:
\[ \text{Volume Ratio} = \frac{\text{New Carton Volume}}{\text{Original Carton Volume}} = \frac{144}{6} = 24 \]
This ratio means the new carton is 24 times larger in volume than the original carton.
Given that it takes 7.5 seconds to fill the original carton, you can now calculate the time it would take to fill the new carton by multiplying the original time by the volume ratio:
\[ \text{Time to fill new carton} = \text{Original Time} \times \text{Volume Ratio} = 7.5 \text{ sec} \times 24 = 180 \text{ sec} \]
Therefore, it would take 180 seconds to fill the carton that measures 4ft by 6ft by 6ft.

Answer:

Both sides are equal, true for all 'b'

Step-by-step explanation:

Add similar elements: b + 0.17b = 1.17b

1.17b = 1.17b

Multiply both sides by 100

1.17b * 100 = 1.17b * 100

Refine

117b = 177b

Subtract 117b from both sides

117b - 117b = 117b - 117b

Refine

0 = 0

Both sides are equal, true for all 'b'

- Mordancy

Answer:

Option B. 4 x 8 x 3

Step-by-step explanation:

we know that

If the resulting cross-section is a rectangular figure with dimensions of 4x8

then

one of the dimensions of the prism must be 4 and another of the dimensions of the prism must be 8

I believe is is B: False

Answer: its true

Step-by-step explanation:

Answer:

The two numbers are 15 and 21

Step-by-step explanation:

Lets x = the larger number.

The smaller number is 6 less than the larger number: x - 6

The sum of two numbers is 36

so the equation:

x + x - 6 = 36

2x - 6 = 36

2x = 42

 x = 21

smaller number: 21 - 6 = 15

The two numbers are 15 and 21

Answer:

3/7x

Step-by-step explanation:

21yz

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

49xyz

We can break this into pieces

21   1        y          z

--- * ---- * ----- *   ----

49    x      y          z

Now we can simplify. canceling the y terms and the z terms

3*7   1         1          1

------ * ---- * ----- *   ----

7*7    x         1          1

Now we can simplify canceling the 7 terms

3         1        

------ * ----

7         x        

We are left with

3/ 7x

Answer:$56 for 4 adults  & 8 students

Step-by-step explanation: so you would do 8*4 then add it to 6*4= 24+32=$56

The expression to represent the cost of 4 adult tickets and 8 student tickets to the museum is 4(6) + 8(4), which totals $56.00.

The question asks for an expression that represents the cost of 4 adult tickets and 8 student tickets to the museum. Given that the price of an adult ticket is $6.00 and the price of a student ticket is $4.00, we can calculate the total cost as follows:
For adult tickets: 4 tickets  imes $6.00 per ticket = $24.00.
For student tickets: 8 tickets  imes $4.00 per ticket = $32.00.
The total cost is the sum of the cost for adult tickets and the cost for student tickets, which can be represented by the expression: 4(6) + 8(4) or $24.00 + $32.00, equaling $56.00 in total.

Answer:

c

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

equals =1.25256565

The right answer is about c

Answer:

x = -2 ±sqrt(7)

Step-by-step explanation:

x^2 +4x =3

We will complete the square

Take the coefficient of the x term, divide by 2 and then square it

4, then divide by 2

4/2

Then square it

2^2 =4

Add 4 to each side

x^2 +4x +4 = 3+4

The left side is equal to (x+ the coefficent /2 )^2

(x+2)^2 = 7

Take the square root of each side

sqrt((x+2)^2) = ±sqrt(7)

x+2 = ±sqrt(7)

Subtract 2 from each side

x+2-2 = -2±sqrt(7)

x = -2 ±sqrt(7)

Answer:

D

Step-by-step explanation:

The data CAN NOT change.

D. How many football games the Texans won in the 2014-2015 season would yield data without variability.

The correct option is D.

The measure of variability is a statistical term that refers to the extent to which data points in a dataset are spread out or dispersed from each other. In other words, it measures how much the individual data points deviate from the central tendency of the dataset.

D. How many football games the Texans won in the 2014-2015 season would yield data without variability.

The number of wins is a fixed value that does not vary, and therefore, the data would not have any variability.

In contrast, the other options involve variables that can vary between individuals or households, and therefore would yield data with variability. For example, different friends may have spent different amounts on downloading music, or different households may watch different amounts of TV.

The height of trees can also vary depending on the species, age, and other factors.

Therefore, option D is correct.

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Answer:

D

Step-by-step explanation:

This is because when making a triangle, the two shortest sides have to add up to be bigger than the biggest side. For example, A would work because if you did 4+6, it would equal 10 which is bigger than the biggest side. B and C add up to something bigger than 6. However, D is different. If you do 2+4, that equals 6. It has to be bigger than six, not equal

For this case we must make a rule of three:

23.47 ----------------> 100%

x -----------------------> 10%

Where the variable "x" represents the tip rate.

[tex]x = \frac {10 * 23.47} {100}\\x = 2,347[/tex]

Thus, the tip should be 2,347 dollars.

Answer:

$ 2,347

Answer: the first answer

.... Please mark branliest!!

Answer:

solution is (4,2)

Step-by-step explanation:

[tex]-3x+5y=-2[/tex]

[tex]3x+7y=26[/tex]

To solve for x  and y , we use elimination method.

we add both equations.

[tex]-3x+5y=-2[/tex]

[tex]3x+7y=26[/tex]

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

[tex]12y=24[/tex]

Divide both sides by 12

y=2

Now we find out x

[tex]-3x+5y=-2[/tex]

[tex]-3x+5(2)=-2[/tex]

[tex]-3x+10=-2[/tex]

Subtract 10 from both sides

[tex]-3x=-12[/tex]

Divide by -3 on both sides

x=4

So, solution is (4,2)