The bases of Triangle A and Triangle B are equal. The ratio of the height of
Triangle A to the height of Triangle B is 4 : 5. If the height of Triangle A is
16 cm and its base is 12 cm, what is the area of Triangle B?

Let z = -2 - 2√3 i.

Find the modulus of z :

|z| = √((-2)² + (-2√3)²) = √16 = 4

Find the argument of z (note that z lies in the third quadrant):

arg(z) = arctan(2√3/2) - π = arctan(√3) - π = -2π/3

Then in polar form, we have

[tex]z = -2 - 2\sqrt 3\, i = 4 \exp\left(-i\dfrac{2\pi}3\right)[/tex]

By DeMoivre's theorem, the cube of z is

[tex]z^3 = \left(4 \exp\left(-i\dfrac{2\pi}3\right)\right)^3 = 4^3 \exp(-i 2\pi) = \boxed{64}[/tex]

Answer:

A: He sold 33 copies

B: $4340

Step-by-step explanation:

A: p=80(33) + 2500

   p=2640+ 2500

   p=5140

B: p = 80(23) + 2500

   p=1840+ 2500

   p=4340

Answer:

4°C

Explanation:

Equation: y = -0.36x + 12.6

Simplify

y = -0.36(23)+12.6

y = 4.32°C

y = 4°C       (rounded to nearest degree)

Answer:

please make the image less blurry

Step-by-step explanation:

Answer:

1. a=3

2. a=3

3. a=9

Step-by-step explanation:

1. 9/a+9-4=12-56/8+3

We move all terms to the left:

9/a+9-4-(12-56/8+3)=0

Domain of the equation: a=0

a∈R

We add all the numbers together, and all the variables

9/a+9-4-8=0

We add all the numbers together, and all the variables

9/a-3=0

We multiply all the terms by the denominator

-3*a+9=0

We add all the numbers together, and all the variables

-3a+9=0

We move all terms containing a to the left, all other terms to the right

-3a=-9

a=-9/-3

a=+3

Answer:

7

Step-by-step explanation:

Because it is asking what X value are all the functions equal to just find a point that lies on X that they all come to.

In this case it's 7

Answer:

x = 7

Step-by-step explanation:

The functions are equal to each other where the lines of the functions intersect each other.

The intersection point is (7, 3).

The x-value at this point is 7.

Hence, x = 7.

Answer:

Step-by-step explanation:

Answer:

Check Below

Step-by-step explanation:

given things  : 1. height of cone  = 22* 1/4 feet or  89/4 feet

                       2.  diameter of cylinder = 2* 2/5 times of height

                                                          =  12/5 times of height or 12/5 * 89/4

                                                           = 89*3/5 feet

now formula of volume of cone =  Pi R² * H

                                                       = (3.14) ( D/2)² * H

                                                       = (3.14)*  (89*3/10)² * 89/4

                                                       = (3.14) * (26.7)² * 22.25

                                                       = (3.14) * 712.89 * 22.25

                                                       =  (49806.06)

Hope u find this answer Helpful !

Answer:

: w ≤ - 6

Step-by-step explanation:

The potential energy of the 10-kg object is 294 joules.

Variation is a mathematical term that shows the relationship between two or more parameters or quantities in an equation.

Analysis:

let potential energy be = P

let mass be = m

let height be = h

P ∝ mh

P = kmh

when P = 784, m = 40kg, h = 2 meters

784 = k x 40 x 2

k = 9.8

P = 9.8mh

when m = 10kg, h = 3 meters

P = 9.8 x 10 x 3 = 294 joules.

In conclusion, the potential energy of the object at 3 meter height is 294 joules.

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Step-by-step explanation:

y-x+2 =0 is the right answer so try in that way

Answer:

61.90

Step-by-step explanation:

12.2+14+14+6=46.2

of semi circle

circumference of semi circle = [tex]\pi[/tex]d

[tex]\pi[/tex]x10 = 10[tex]\pi[/tex]

semi circle so divide by 2 = 5[tex]\pi[/tex]

5[tex]\pi[/tex] = 15.7

46.2 + 15.7 = 61.9

Answer:

1/3

Step-by-step explanation:

2 divided by 1/6

2/1 divided by 1/6

2/6 ---> Simplify: 1/3

Answer:

12

Step-by-step explanation:

the answer is 12 because 2 dived by 1/6 is 12 i used a calculator to fund the answer btw

Answer:

P = 12 + 2π cm

Step-by-step explanation:

arc length is calculated as

arc = circumference × fraction of circle

the angle subtended at the centre of the sector = 360° - 300° = 60° , then

arc = 2πr × [tex]\frac{60}{360}[/tex]

      = 2π × 6 × [tex]\frac{1}{6}[/tex]

      = 2π

the perimeter (P) = 6 + 6 + 2π = 12 + 2π

Answer:

fist bubble i am pretty sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. (6)^(4*2) or (6^4)(6^4)(6^4)(6^4)

b. 6^8

Ans57 , 58 , 59

Step-by-step explanation:

The coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

Line segment EF begins at (-1, 5) and ends at (-1, -3). The segment is translated right 4 units and down 2 units to form line segment E'F'. Then the coordinate of E' and F' will be:

E' = (-1 + 4, 5 – 2) = (3, 3)

F' = (-1 + 4, -3 - 2) = (3, -5)

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of the E'F' = √(0 + 64) = 8 units

Thus, the coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.

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Answer:

graph 19 because since it is that means also like the thingy equals that number si then like when the thing is at the highest point it cab maybe actually it will equal that number

Answer:

The question asks, "find the slope".

9) -4/15

10) -1/14

11) -3/4

12) -1/4

13) 11/17

14) -18/13

15) 0

16) -30

17) -5

19) -1/5

21) 1/4

23) -1

25) -2/3

Answer:

See below ~

Step-by-step explanation:

The true statements based on the graph :

The statement(s) that are true is that the measure of the reference angle is 45°.

The conversion of an angle in radian to a degree can be determined by the multiplication of the given angle in radian by 180/π.

From the given information:

[tex]\mathbf{\theta = \dfrac{7 \pi}{4}}[/tex]

To degrees, we have:

[tex]\mathbf{\theta = \dfrac{7 \pi}{4} \times \dfrac{180}{\pi}}[/tex]

[tex]\mathbf{\theta =315^0}[/tex]

A reference angle is an angle that measures the remaining distance (called the terminal distance) to the x-axis.

315° is in the 4th quadrant, i.e.

= 360° - 315°

= 45°

Therefore, the statement(s) that is true is:

Learn more about the conversion of radians to degrees here:

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Answer:

sin(0)=-√2/2

tan(0) = -1

The measure of the reference angle is 45°

Step-by-step explanation:

I took the test

volume = (side length)³

Alternatively we could say that;

Side length = ∛volume

(we have just found the cube root of both sides here, remember we can do what we like to an equation, as long as we do the same to both sides!)

Because we cubed side length to get volume, side length must be the cubic root of the volume, the ∛.

We know that the volume is 1000 cubic feet, so;

Side length = ∛1000

∛1000 = 10

So the length of an edge of the cube is 10 feet.

Answer:

Step-by-step explanation:

Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)

a. 5x + 9y = -45

c. -9x + 5y = 45

b. 9x + 5y = -45

d. 5x - 9y = 45

Answer:

1, 6, 11, and 16 in that order

Step-by-step explanation:

every time the x value increases by 1, the f(x) value increased by 5

Answer:

reflection in the y- axis

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y )

B (5, - 7 ) → B' (- 5, - 7 ) ← is a reflection in the y- axis

Answer:

opens upwards

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

• if a > 0 then parabola opens upwards

• if a < 0 then parabola opens downwards

given

y = 5x² - 17x - 12

with a = 5 > 0

then parabola opens upward