which of the following is a tinomial

Answer:  Choice D

15(cos85° + i sin85°)

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Explanation:

Let's say we had these two general complex numbers, which are in polar form.

[tex]z_1 = r_1*\left(\cos(\theta_1)+i*\sin(\theta_1)\right)\\\\z_2 = r_2*\left(\cos(\theta_2)+i*\sin(\theta_2)\right)\\\\[/tex]

We can abbreviate them into the shorthand form

[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\[/tex]

The notation "cis" stands for "cosine i sine".

Now that we have those complex numbers set up, multiplying them is as simple as saying this:

[tex]z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)[/tex]

We do two basic things:

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With all that in mind, let's tackle the problem your teacher gave you.

The given complex numbers

[tex]z_1 = 5*\left(\cos(15^{\circ})+i*\sin(15^{\circ})\right)\\\\z_2 = 3*\left(\cos(70^{\circ})+i*\sin(70^{\circ})\right)\\\\[/tex]

abbreviate into

[tex]z_1 = 5*\text{cis}(15^{\circ})\\\\z_2 = 3*\text{cis}(70^{\circ})\\\\[/tex]

then those multiply to

[tex]z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)\\\\z_1*z_2 = (5*3)*\text{cis}(15+70)\\\\z_1*z_2 = 15\text{cis}(85^{\circ})\\\\z_1*z_2 = 15\left(\cos(85^{\circ})+i\sin(85^{\circ})\right)\\\\[/tex]

which is why choice D is the final answer.

Answer:

x = 98

Step-by-step explanation:

x and 82 are adjacent angles on a straight line and sum to 180° , then

x + 82 = 180 ( subtract 82 from both sides )

x = 98

Answer:

Step-by-step explanation: Scale [tex]\frac{130}{100} = \frac{13}{10}[/tex]

New dimensions [tex]16 * 1.3 --- 24*1.3 =20.8 cm * 31.2 cm[/tex]

Step-by-step explanation:

Given

x = 3/4

y = -2/5

Now

X + y = 3/4 - 2/5

[tex] \frac{3 \times 5 - 2 \times 4}{20} [/tex]

[tex] = \frac{15 - 8}{20} [/tex]

[tex] = \frac{7}{20} [/tex]

Answer:

7/20

Step-by-step explanation:

x=3/4

y= -2/5

x+y=?

to get the sum, plug in x=3/4 into the x and y= -2/5 into the y

1. x + y = ?

2. 3/4 + (- 2/5) = ?

3. 3/4 - 2/5 =?

4. find the lcm of 4 and 5 to get the common denominator (in this case, the lcm of 4 and 5 is 20)

5. multiply 3/4 by 5 (numerator and denominator) and 2/5 by 4 (numerator and denominator)

6. 15/20 - 8/20 = 7/20

the answer is 7/20

Answer:

Thamkhao

Step-by-step explanation:

Answer:

Wow

Step-by-step explanation:

I love the question pls i also want to know the answer to it

Answer:

[tex]{ \sf{ - 2 {a}^{5} + 4 {a}^{4} + 5 {a}^{3} + \frac{2}{3}a }}[/tex]

Answer:

D

Step-by-step explanation:

A polynomial is in standard equation when the degree of the polynomial are in descending order.

Answer:

x = [tex]\frac{5a-9}{19}[/tex]

Step-by-step explanation:

Given

5(a - 2x) = 9(x + 1) ← distribute parenthesis on both sides

5a - 10x = 9x + 9 ( add 10x to both sides )

5a = 19x + 9 ( subtract 9 from both sides )

5a - 9 = 19x ( divide both sides by 19 )

[tex]\frac{5a-9}{19}[/tex] = x

Answer:

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

To distribute, we must multiple -8x to each term:

-8x(x^2) - 8x(-8x) - 8x(3)

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

[tex] - 8x( {x}^{2} - 8x + 3) \\ = ( - 8x \times {x}^{2}) - ( - 8x \times 8x) + ( - 8x \times 3) \\ = - 8 {x}^{3} + 64 {x}^{2} - 24x[/tex]

distribute -8x to each term in the perenthesis i.e. multiply each term by -8x

Answer:

224 ft

Step-by-step explanation:

The tree makes a 90° angle with the ground, so we have a right triangle.

For the 32° angle, the height of the tree is the opposite leg. The length of the shadow on the ground is the adjacent leg.

The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

Let the length of the shadow of the tree on the ground be x.

tan A = opp/adj

tan 32° = 140 ft/x

x = 140 ft/tan 32°

x = 224 ft

Answer: 224 ft

Answer:

R = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Step-by-step explanation:

P - Q + R = I ( I is the identity matrix )

[tex]\left[\begin{array}{ccc}2&4\\3&5\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-2&2\\4&1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( subtract corresponding elements )

[tex]\left[\begin{array}{ccc}2-(-2)&4-2\\3-4&5-1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Answer: 7/8

Cos2x has 3 formulas, Sinx is given in the question, we should use the formula with sinus. I guess that's the solution.

Answer:

Luis's balance = $25,283.33

Step-by-step explanation:

Given the following data;

To find how much money Luis will have;

First of all, we would have to convert the value of time in months to a year.

Conversion:

12 months = 1 year

8 months = X year

Cross-multiplying, we have;

12 * X = 8

X = 8/12

X = 2/3 years

To find the simple interest, we would use the formula;

[tex] S.I = \frac {PRT}{100} [/tex]

Where;

Substituting the values into the formula, we have;

[tex] S.I = \frac {25,000 * 1.7 * \frac {2}{3}}{100} [/tex]

[tex] S.I = \frac {28333.33}{100} [/tex]

S.I = $283.33

Luis's balance = S.I + Principal

Luis's balance = 283.33 + 25000

Luis's balance = $25,283.33

Answer:

15

Step-by-step explanation:

first find f which is (8-3) × ( 1/4 × 7 + 5)

simplify

5 × (1/4 ×12)

5 × 3

15 is thw answer

Answer:

Step-by-step explanation:

Applying the midpoint formula to the points (a, 0) and (0, a) looks like this:

[tex]M=(\frac{a+0}{2},\frac{0+a}{2})[/tex] which simplifies to

[tex]M=(\frac{a}{2},\frac{a}{2})[/tex]

Answer:

The rea of walk way is 32 ft^2.

Step-by-step explanation:

width, w = 8 feet

length, L = 10 feet

width of walkway, d = 2 feet

length of outer, L' = 10 + 2 + 2 = 14 feet

Area of outer, A' = L' x w = 14 x 8 = 112 ft^2

Area of inner, A = L x w = 10 x 8 = 80 ft^2

The area of walkway = A' - A = 112 - 80 = 32 ft^2

The rea of walk way is 32 ft^2.

Answer:

m∠LMK = 50°

Step-by-step explanation:

This is an isosceles triangle. Isosceles triangles have two sides of equal length and two equal angles. This means ∠K and ∠M will have the same degrees.

The sum of the angles of a triangle is 180°. The following equation can be arranged and solved for the missing angles:

[tex]x+x+80=180\\2x+80=180\\2x=100\\x=50[/tex]

Therefore, m∠LMK = 50°.

Answer:

ERROR

Step-by-step explanation:

Answer:

The answer is 12.

Step-by-step explanation:

Since one of the sides on the smaller polygon is two and on the other one is six that must mean the scale is multiply by 3 because 2x3=6. So 4 times 3 is 12.

So, w = 12

Answer:

The area is 72 cm².

Step-by-step explanation:

Since it is equivalent triangle

h = b

so,

b + b + b (since all sides are equal)= 36 cm

3b = 36 cm

or, b = 36/3

so, b = 12 cm

so

area of triangle = (1/2)×b×h

= (1/2)×12cm×12cm

= 6cm × 12cm

= 72 cm²

Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.

The binary expansion of x is

x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

x = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or

857 = 1×729 + 128 = 1×3⁶ + 128

• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

• How many times does 27 go into 47? Also 1 time,

47 = 1×27 + 20 = 1×3³ + 20

• How many times does 9 go into 20? 2 times,

20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

• How many times does 1 go into 2? Also 2 times,

2 = 2 + 1 = 2×1 + 0 = 2×3⁰

So we found

857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰

which is the ternary expansion of x,

x = 1 011 202₃

Answer:

B) ΔABC and ΔA′B′C′ are congruent.

Step-by-step explanation:

Given

See attachment for [tex]\triangle ABC[/tex] and [tex]\triangle A'B'C'[/tex]

Required

Determine the relationship between both triangles

The single line on all sides of both triangles implies that the sides of the triangles are equal

i.e.

[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- sides

Similarly, the same mark on the three angles of both triangles means that the angles of the both triangles are equal

i.e.

[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- angles

Hence, both triangles are congruent

Answer:

B) ΔABC and ΔA′B′C′ are congruent.

Step-by-step explanation:

Answer:

each costumer owe $35.40

Step-by-step explanation:

so, u get 247.79÷7 (cuz it is 7 people)

u get 35.40.

to check just get 35.40×7 and u will revice their total.

Answer:

-6 and - 65

Step-by-step explanation:

X-12x-29, by completing the square we get (x-6)^2-65

Answer: (a): Good course, (b): Bad course

Step-by-step explanation:

Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.

Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.

Answer:

If its supposed to be simplify it will be -7 . If your finding the derivative it is 0.

Step-by-step explanation:

Answer:

3rd option, $672

Step-by-step explanation:

The area is,

(4×12)+(8×10)

= 128

per square foot it costs $5.25, so the total cost will be,

128×$5.25

= $672

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

use the quadratic formula : [tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], where ax^2+bx+c=0

[tex]y = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(1)(50)}}{2(1)}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{400 - 200}}{2}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{200}}{2}[/tex]

y = 17.07106~ or 2.928932~

Answer:

36 degrees

Step-by-step explanation:

10 corners/sides.

the sum of all exterior angles in a polygon is always 360 degrees.

so, one exterior angle here is 360/10 = 36 degrees

Answer:

6

Step-by-step explanation:

again ?

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6