MATHEMATICS HIGH SCHOOL

Z=1+4iFind the angle 0(theta) in degrees that z makes in the complex plane.
Round your answer, if necessary, to the nearest tenth. Express 0(theta) between -180 and 180 degrees.

Answers

Answer 1

Answer:

Answer:

76.0 degrees

Step-by-step explanation:

Just got it right on the Khan Academy quiz.

Answer 2

Answer:

Final answer:

The angle θ that z makes in the complex plane is approximately 75.96°.

Explanation:

The complex plane is a mathematical concept used in complex numbers. It's a two-dimensional Cartesian coordinate system where the horizontal axis represents the real part of a complex number, and the vertical axis represents the imaginary part. Complex numbers are plotted as points in this plane, facilitating operations like addition, subtraction, multiplication, and division of complex numbers.

To find the angle θ that z makes in the complex plane, we can use the formula: θ = arctan(y/x), where x and y are the real and imaginary parts of z respectively. In this case, x = 1 and y = 4 as given. Plugging these values into the formula, we get: θ = arctan(4/1). Using a calculator, we find that θ ≈ 75.96°.

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Factor the trinomial below 12x^2-11x-36

Answers

The factors of the trinomial are $(4x-9)(3x+4)$ .

What is a trinomial?

A trinomial is an algebraic expression that has three non-zero terms. If three monomials are separated by addition or subtraction, then it is a trinomial.

For the given situation,

The trinomial is 12x^2-11x-36.

The given trinomial is a quadratic equation.

The quadratic equation can be factored as

⇒ $12x^2-11x-36$

⇒ $12x^2-27x+16x-36$

⇒ $3x(4x-9)+4(4x-9)$

⇒ $(4x-9)(3x+4)$

Hence we can conclude that the factors of the trinomial are $(4x-9)(3x+4)$ .

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Step-by-step explanation:

12x2 - 11x - 36

12x2 - 27x + 16x - 36

3x (4x - 9) + 4(4x - 9)

(4x - 9) and (3x + 4) are the factors

What is the area of a rectangle with vertices at (4, 3), (11, 3), (11, 9), and (4, 9)?

Answers

Answer:

The area of a rectangle is 42 units ².

Step-by-step explanation:

As the diagram is given below.

Distance Formula

$Distance\ formula = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}$

As the rectangle with vertices at A (4, 3), B(11, 3),C (11, 9), and D (4, 9).

Take A (4, 3) to B(11, 3)

$AB = \sqrt{(11-4)^(2)+(3-3)^(2)}$

$AB = \sqrt{(7)^(2)+(0)^(2)}$

$AB = √(49)$

$√(49) =7$

AB = 7 units

As take B(11, 3) to C (11, 9).

$BC = \sqrt{(11-11)^(2)+(9-3)^(2)}$

$BC = \sqrt{(0)^(2)+(6)^(2)}$

$BC = √(36)$

$√(36) =6$

BC = 6 units

As take C (11, 9) toD (4, 9).

$CD = \sqrt{(4-11)^(2)+(9- 9)^(2)}$

$CD = \sqrt{(7)^(2)+(0)^(2)}$

$CD = √(49)$

$√(49) =7$

CD = 7 units

As take D (4, 9) to A (4, 3)

$DA = \sqrt{(4-4)^(2)+(3-9)^(2)}$

$DA = \sqrt{(0)^(2)+(-6)^(2)}$

$DA = √(36)$

$√(36) =6$

DA = 6 units

Thus

AB = DC= 7 units

AD = BC = 6 units

Formula

Area of rectangle = Length × Breadth

Length = 7 units

Breadth = 6 units

Put value in the above

Area of rectangle = 7 × 6

= 42 units ²

Therefore the area of a rectangle is 42 units ².

This is rectangle ABCD, where coordinates of the vertices are: A ( ( 4, 3 ); B ( 11, 3 ); C ( 11, 9 ) and D ( 4, 9 ). The area of the rectangle is: A = L x W ( L - length and W - width ). Length = AB = 11 - 4 = 7. Width = BC = 9 - 3 = 6. Finally: A = 7 * 6 = 42. Answer: The area of a rectangle is 42. Hope this helps. Let me know if you need additional help!

Please help asap! file attached below!

Answers

I got B but you may want to check with some other people's answer choices before you put in my answer hope this helps in the meantime though I'm pretty confident in my answer

Meg started her trip with 11 1/2 gallons of gas in her car's tank. She bought an additional 6 4/5 gallons on her trip and arrived back home with 3 3/10 gallons left. How much gas did she use on the trip?

Answers

Answer:

Hence, the amount of gas she used on the trip is:

15 gallons.

Step-by-step explanation:

Meg started her trip with 11 1/2 gallons of gas in her car's tank.

i.e. we can represent the mixed fraction 11 1/2 in fraction as:

$11(1)/(2)=(23)/(2)gallons$

She bought an additional 6 4/5 gallons on her trip.

i.e. we can represent the mixed fraction 6 4/5 in fraction as:

$6(4)/(5)=(34)/(5)gallons$

Hence, the amount of gas filled in tank:

$=(23)/(2)+(34)/(5)\n\n=(23* 5+34* 2)/(10)\n\n=(115+68)/(10)\n\n=(183)/(10)gallons$

now after coming back home the amount of gas left in the car tank is:

3 3/10 gallons ; which could be represented in fraction as:

$3(3)/(10)=(33)/(10)$

Amount of gas used in the trip is:

=Amount of gas filled-gas remaining

$=(183)/(10)-(33)/(10)\n\n=(183-33)/(10)\n\n=(150)/(10)\n\n=15gallons$

Hence, the amount of gas she used on the trip is:

15 gallons.

Meg used 15 gallons. First you find the lowest common denominator to add 11 1/2 and 6 4/5, which is 10. What you do to the bottom you have to do to the top. You multiply 2 and 5, which gives you 10. 1 times 5 is 5... 11 5/10. 2 times 5 is 10, 4 times 2 is 8... 6 8/10. Add 11 5/10 and 6 8/10 and it gives you 18 3/10. To find out how much she used subtract the total amount she bought and how much she returned home with. The fractions cancel out since 3/10 minus 3/10 equals 0. You're just left with 18 minus 3, which is 15.

What conversion factor can be used to convert the number of blocks to the weight of the blocks, in pounds?

Answers

The correct answer is:

The conversion factor would be the number of blocks multiplied by the weight of 1 block.

Explanation:

Consider the following example:

Suppose 1 block weighs 3 pounds. If there are 15 blocks, to find the total weight of the blocks, we multiply 3 by 15: 3(15) = 45. This means the total weight would be 45 pounds.

For any given number of blocks and any given weight of 1 block, to find the total weight of the blocks we would multiply the number of blocks by the weight of 1 block.

let n represent number of blocks

let m represent weight of 1 block but in pounds because we want to express our total weight in pounds.

if n is number of blocks and m mass of one block, mass of n blocks would be
n*m

that means that conversion factor is m ---> weight of 1 block in pounds

A 9-kg of mangoes for 12$_____per kg