What is the product of ( 4 + 3 i ) and ( 12 − 2 i )

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

≈ 98.7

Step-by-step explanation:

What you want to use is Pythagorean Theorem

96 squared + 23 squared = c squared

≈ 98.7

Answer:

27

Step-by-step explanation:

The triangle shown is a right triangle, indicated by the little square at the bottom right. When trying to find the length of a missing leg of a right triangle we can use the Pythagorean theorem.

Pythagorean theorem : a² + b² = c²

Where a and b = legs and c = hypotenuse ( longest side )

We are given the length of the hypotenuse as well as a leg and we need to find the other leg.

Hypotenuse (c) = 45

Leg (a) = 36

To find the length of the other leg we can plug in the given values of the hypotenuse and the leg into the Pythagorean theorem and solve for b

Recall the Pythagorean theorem : a² + b² = c²

a = 36 and c = 45

(36)² + b² = (45)²

simplify exponents : 36² = 1296 and 45² = 2025

1296 + b² = 2025

subtract 1296 from both sides: 1296 - 1296 cancels out and 2025 - 1296 = 729

b² = 729

take the square root of both sides: √(b)² = b and √729 = 27

We're left with b = 27 meaning that the length of the other leg ( or missing side ) is 27

Answer:

19

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is

difference of 2 sides < x < sum of 2 sides , that is

18 - 2 < x < 18 + 2

16 < x < 20

Then the largest possible length of the third side is 19

Answer:100

Step-by-step explanation:

The question confuses you since there is no extra variable to help you which is you have to create it yourself.

Let's create a variable called 'y' and make it the empty angle inside the triangle and next to x + 30. Since at K it will always equal to 180° because x+30 + y = 180°, we can rearrange to make y alone which would be become:

[tex]y=-x-30+180[/tex] which then becomes [tex]y = -x+150[/tex].

Also since the inside sum of angles in a traingle is equal to 180°, this can be written as

[tex]180 = (x-40) +(x-30)+y[/tex]

if we replace y with the equation we get

[tex]180=(x-40)+(x-30) + (-x+150)[/tex]

which can be simplified to

[tex]180=x+80[/tex] because 2x-x = x and -70+150 = 80

If we rearrange to solve for x, we get:

[tex]x = 180-80[/tex] ⇒ [tex]x=100[/tex]

We can verify this by putting the value of x in both equation:

[tex]y = -100+150 = 50[/tex] angle at k

[tex]100-40=60[/tex] angle at j

[tex]100-30=70[/tex] angle at l

[tex]50+60+70=180[/tex] this match the rules of the sum of interior angle always equal 180°

Answer:

x = 45°, y= 5°

Step-by-step explanation:

x = 9y

90+2x = 180

2x = 90

x = 45

so x = 45

9y = 45

y = 5

Answer:

785/10=78.5

Step-by-step explanation:

You move the decimal point back a slot since your dividing by 10

Answer:

78.5

Step-by-step explanation:

i used a calculator bc im bad at lond division XD

Answer: the answer is C which is .0287

The probability of it raining at most 2 days in a week is approximately 0.0192 or 1.92%. The closest option to this result is:

b) 0.0250

To find the probability of it raining at most 2 days in a week, we need to calculate the probability of it raining 0, 1, or 2 days in a week and then add those probabilities together.

Let's use the binomial probability formula for this calculation:

The probability of getting exactly "k" successes in "n" trials, each with a probability "p" of success, is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

C(n, k) is the binomial coefficient, equal to n! / (k! * (n - k)!)

p is the probability of success (rain in this case)

n is the number of trials (number of days in a week)

In our case, the number of trials (n) is 7 days in a week, and the probability of rain (p) is 0.70.

Now, let's calculate the probabilities for k = 0, 1, and 2:

Probability of raining 0 days in a week:

P(X = 0) = C(7, 0) * 0.70^0 * (1 - 0.70)^(7 - 0)

Probability of raining 1 day in a week:

P(X = 1) = C(7, 1) * 0.70^1 * (1 - 0.70)^(7 - 1)

Probability of raining 2 days in a week:

P(X = 2) = C(7, 2) * 0.70^2 * (1 - 0.70)^(7 - 2)

Now, add these probabilities together to get the probability of it raining at most 2 days in a week:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Calculate the values using the binomial coefficients:

C(7, 0) = 1

C(7, 1) = 7

C(7, 2) = 21

Now, calculate the probabilities:

P(X = 0) = 1 * 1 * 0.3^7 ≈ 0.0002187

P(X = 1) = 7 * 0.7^1 * 0.3^6 ≈ 0.002775

P(X = 2) = 21 * 0.7^2 * 0.3^5 ≈ 0.016215

Finally, add these probabilities together:

P(X ≤ 2) ≈ 0.0002187 + 0.002775 + 0.016215 ≈ 0.0192087

Therefore, the probability of it raining at most 2 days in a week is approximately 0.0192 or 1.92%. The closest option to this result is:

b) 0.0250

So, the correct answer is (b) 0.0250.

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Answer: Perpendicular

Step-by-step explanation: If you graph these points you will get two lines that from at a right angle and cross through each other. This means they are perpindicular.

Answer:

Perpendicular

Step-by-step explanation:

Lines that are parallel have the same slope, and lines that are perpendicular have an negative reciprocal slope.

To clarify, the reciprocal of 2 would be 1/2, and the negative reciprocal of 2 would be -1/2.

Calculate the slope of the lines by dividing the difference in y by the difference in x:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{4-0}{7-1}=\frac{4}{6}=\frac{2}{3}\\\\m_2=\frac{6-0}{3-7}=\frac{6}{-4}=-\frac{3}{2}[/tex]

m₂ is the negative reciprocal of m₁, so these lines are perpendicular.

Showing the graph in the image as an example, though the equations only have the slope and not the y-intercept so the points wont be on the lines.

The point of concurrency in a right triangle is also the midpoint of the hypotenuse is its circumcenter .

A point of concurrency is a place where three or more, but at least three lines, rays, segments or planes intersect in one spot. If they do, then those lines are considered concurrent, or the the rays are considered concurrent.

There are 4 different points of concurrency in the triangle are:

1. Circumcenter

The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.

For an obtuse-angled triangle, the circumcenter lies outside the triangle.

For a right-angled triangle, the circumcenter lies at the hypotenuse.

2. Incenter

The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.

3. Centroid

The point where three medians of the triangle meet is known as the centroid.

4. Orthocenter

The point where three altitudes of the triangle meet is known as the orthocenter.

For an obtuse-angled triangle, the orthocenter lies outside the triangle.

According to the question

The point of concurrency in a right triangle is also the midpoint of the hypotenuse.

According to the Triangle Concurrency Points

For a right-angled triangle, the circumcenter lies at the midpoint of the hypotenuse.

Hence, The point of concurrency in a right triangle is also the midpoint of the hypotenuse is its circumcenter .

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Answer: [tex]f(x) = 200(\frac{1}{2})^{x}[/tex]

Step-by-step explanation:

If you plug in the x value(s) to each equation, you can see that [tex]f(x) = 200(\frac{1}{2})^{x}[/tex] is the correct answer because each y value matches the y value on the table. Therefore, [tex]f(x) = 200(\frac{1}{2})^{x}[/tex] is the correct answer.

The domain is the set of all allowed x values. In this case, we consider the whole numbers between 0 and 10. So we have x = 0, x = 1, x = 2, ... all the way up to x = 10.

To find the y values, you replace each x with the numbers mentioned and simplify.

For instance, if x = 2, then,

f(x) = 3.50x

f(2) = 3.50*2

f(2) = 7

This tells us that x = 2 packages cost y = 7 dollars.

Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

The line has a horizontal length of 2 units and a vertical length of 5 units

The line is then the hypotenuse h of a right triangle.

Using Pythagoras' identity

h² = 2² + 5² = 4 + 25 = 29 ( take square root of both sides )

h = [tex]\sqrt{29}[/tex]

The length of the line given is √29 units.

Hence, the correct option is C.

Given is line on the cartesian plain we need to calculate its length.

Refer to the figure attached.

The figure can be converted into a right triangle with perpendicular = 5 units and the base = 2 units.

The line asked will act as the hypotenuse, so, to find its length we will use the Pythagorean theorem,

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the perpendicular side of the right triangle is given as 5 units, and the base is given as 2 units.

Let's denote the length of the hypotenuse as 'x'.

According to the Pythagorean theorem, we have:

x = 5² + 2²

Simplifying this equation:

x² = 25 + 4

x² = 29

To find the length of the hypotenuse, we take the square root of both sides:

x = √29

So, the length of the hypotenuse, in this case, is approximately √29 units.

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Answer:

yes, it a solution

Step-by-step explanation:

Answer:

24.35775

Step-by-step explanation:

Ty for points xd

Answer:

24.35 miles

Step-by-step explanation:

just divide 39.2 by 1.6

[tex] \: \: \: \: \: \: \: [/tex]

[tex] \frac{3}{10} \\ \\ or \: in \: alternate \: \: form \\ \\ 0.3[/tex]

Answer:

8(2x-1)

Step-by-step explanation:

16x-8=8(2x-1)

Answer:

69 degrees

Step-by-step explanation:

yeah

Answer:

  5π, about 15.708 units

Step-by-step explanation:

A 3-4-5 triangle is a right triangle. When a circle circumscribes a right triangle, the hypotenuse is the diameter of the circle. The circumference of a circle is given by ...

  C = πd

For a diameter of 5 units, the circumference is ...

  C = π(5) = 5π = 15.708 . . . units

_____

Additional comment

The (3, 4, 5) triple is one of the first Pythagorean triples you run across. It is the smallest integer triple, and the only primitive triple with values in an arithmetic sequence. You can show this is a Pythagorean triple by ...

 3² + 4² = 9 +16 = 25 = 5²

That is, these numbers satisfy the Pythagorean theorem relation for sides of a right triangle.

Answer:

x≤30

Step-by-step explanation:

he can spend no more than $30 a week

Answer:

a is 2 b is 5 ď is 3 e is 5 and that is it this is not the correct awns

Answer:

C

ON THE EDGE

Step-by-step explanation:

121/2

Step-by-step explanation:

50/4

it goes 12because of 48.

and then it will remain 2

Answer:

C)

Step-by-step explanation:

Have a great day