Suppose you have a tray that is 10 inches squared in area. Choose objects to fill the tray (e.g. muffins, cookies, etc.). Then, establish both a quantity of objects AND the overall density of the objects on the tray.

When we work with complex numbers:

 ⇒ we add all the like terms

     ⇒ terms with 'i' add with terms that have an 'i' ⇒ [tex]i -5i=-4i[/tex]

     ⇒ constants add with constants ⇒ [tex]-4+10=6[/tex]

Let's find the sum now:

  [tex](-4+i)+(10-5i)=-4+10 +(i-5i)=6-4i[/tex]

Answer: The sum of (-4+ i) and (10 - 5i) is 6 - 4i

Hope that helps!

Answer:

C on edge

Step-by-step explanation:

Suppose that r (cos(θ) + i sin(θ)) is a third root of 27 (cos(π/5) + i sin(π/5)), i.e.

[r (cos(θ) + i sin(θ))]³ = 27 (cos(π/5) + i sin(π/5))

Expand the left side using de Moivre's theorem:

r³ (cos(3θ) + i sin(3θ)) = 27 (cos(π/5) + i sin(π/5))

Matching up real and imaginary parts, we have

r³ cos(3θ) = 27 cos(π/5)

r³ sin(3θ) = 27 sin(π/5)

Right away we see that r³ = 27 ⇒ r = 3, which eliminates A.

We also have

(r³ sin(3θ)) / (r³ cos(3θ)) = (27 sin(π/5)) / (27 cos(π/5))

tan(3θ) = tan(π/5)

3θ = tan⁻¹(tan(π/5))

3θ = π/5 + nπ

(where n is an integer)

θ = π/15 + nπ/3

Now,

• n = 0   ⇒   θ = π/15   ⇒   D is a third root

• n = 1   ⇒   θ = π/15 + π/3 = 2π/5

• n = 2   ⇒   θ = π/15 + 2π/3 = 11π/15   ⇒   C is a third root

Using the binomial distribution, it is found that she should expect to roll the number cube 46 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

In this problem:

Then:

[tex]E_s(X) = \frac{23}{0.5} = 46[/tex]

She should expect to roll the number cube 46 times.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:

answer is 46.

Step-by-step explanation:

Answer:

35°

64.267 ft

78.455 ft

Step-by-step explanation:

The given situation can be modeled as a right triangle (see attached).

The interior angles of a triangle sum to 180°

⇒ angle at Jamie's position = 180° - 90° - 55° = 35°

To find the other measures (distances), we can use trig ratios.

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

To find the distance from Rachael to Jamie:

[tex]\implies \sf \tan(55^{\circ})=\dfrac{x}{45}[/tex]

[tex]\implies \sf x=45\tan(55^{\circ})[/tex]

[tex]\implies \sf x=64.267\:ft\:(nearest\:thousandth)[/tex]

To find the distance from Lance to Jamie:

[tex]\sf \implies \cos(55^{\circ})=\dfrac{45}{y}[/tex]

[tex]\sf \implies y=\dfrac{45}{\cos(55^{\circ})}[/tex]

[tex]\sf \implies y=78.455\:ft\:(nearest\:thousandth)[/tex]

Answer:5x^4

Step-by-step explanation: Simplify the radical by breaking the radicand up into a product of known factors, assuming real numbers

Answer:

100

Step-by-step explanation:

Given Average After writing a last test=90

let the last test score be x

Now given

[tex] \frac{80 + 85 + 100 + 85 + x}{5} = 90[/tex]

[tex]80 + 85 + 100 + 85 + x = 450[/tex]

[tex]x + 350 = 450[/tex]

[tex]x = 100[/tex]

I hope it helped you

Answer:

My suggestions could be to;

→ Study

→ Ask for help to the teacher

→ Ask for help to your parents

→ Ask for help to your older siblings

→ Ask your parents to get a tutor for you

→ Pray to our lord and savior Jesus Christ to help you succeed algebra 1

Step-by-step explanation:

Hope this helped! :^)

⭐Brainliest will be appreciated!⭐

✉️Message me if you have any more questions!✉️

- ✨7272033Alt✨

Answer:

the third one hope it helps:)

Answer:

Yes

Step-by-step explanation:

Pythagorean theorem is a^2+b^2 = c^2 where each letter is a side of a triangle. If you know 2 sides then there is only 1 unknown and 1 equation so you can easily find the third side by solving the equation.

4.5% annually

Simple interest is the amount of interest added to a singular sum of money at a fixed rate.

Formula

The formula for simple interest is A = P(1+rt). In this formula, A is the total amount of money in the account, P is the original amount deposited, r is the rate of interest as a decimal, and t is the time in years.

Calculations

To find the rate, plug the information we know into the formula above

Divide both sides by 100

Subtract 1 from both sides

Divide both sides by 5

This gives us the rate as a decimal. So, to find the rate as a percent. Do this by moving the decimal 2 places to the right (or just multiply by 100, they do the same thing). This means that the rate of simple interest is 4.5%.

Answer:

16, 104, 1000

Step-by-step explanation:

8*2

8*13

8*125

Answer:

1,120

Step-by-step explanation:

We start off the multiples of 8 with 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104

The smallest positive 2 digit multiple is 16

The smallest 3 digit multiple is 104

We know 8 x 100 = 800, so we are still in 3 digits

Now we try 8 X 110 = 880

Now let's try 8 x 120 = 960

Now, 8 x 125 = 1,000 which is the smallest 4 digit number we can get

16 + 104 + 1000 = 1,120

The difference between the polynomials (8r⁶s³ - 9r⁵s⁴+3r⁴s⁵) - (2r⁴s⁵ -5r³s⁶ - 4r⁵s⁴) is (8r⁶s³ - 5r⁵s⁴ + r⁴s⁵  + 5r³s⁶).

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The difference between the two polynomials can be solved as,

[tex](8r^6s^3 - 9r^5s^4+3r^4s^5) - (2r^4s^5 -5r^3s^6 - 4r^5s^4) \\\\= 8r^6s^3 - 9r^5s^4+3r^4s^5 - 2r^4s^5 +5r^3s^6 + 4r^5s^4\\\\= 8r^6s^3 - 5r^5s^4+r^4s^5 +5r^3s^6[/tex]

Thus, the difference between the polynomials (8r⁶s³ - 9r⁵s⁴+3r⁴s⁵) - (2r⁴s⁵ -5r³s⁶ - 4r⁵s⁴) is (8r⁶s³ - 5r⁵s⁴ + r⁴s⁵  + 5r³s⁶).

Learn more about Polynomial:

https://brainly.com/question/17822016

Answer:

(- 1, - 7 )

Step-by-step explanation:

substitute the x- coordinate into the equation and if the value obtained is equal to the y- coordinate, then it is a solution

(2, 0 ) → y = 2(2) - 5 = 4 - 5 = - 1 ≠ 0 ← not a solution

(- 1, - 7 ) → y = 2(- 1) - 5 = - 2 - 5 = - 7 → solution to equation

(- 9, - 2 ) → y = 2(- 9) - 5 = - 18 - 5 = - 23 ≠ 2 ← not a solution

(1, 3 ) → y = 2(1) - 5 = 2 - 5 = - 3 ≠ 3 ← not a solution

Answer: 5250 milliliters

Step-by-step explanation:

i hope this will be helpful

Answer: 1 in = 3.6 ft

Step-by-step explanation:

The small car is a model of the large car. The small car is 5 inches long while the large car is 18 feet long.

We currently have a ratio of: [tex]\frac{18 ft}{5 in}[/tex]

We need to get either the 18 or the 5 to one single unit.

18 ft : 5 in

Divide both sides by 5 to isolate 1 inch.

[tex]\frac{18}{5}[/tex] ft : [tex]\frac{5}{5}[/tex] in

Simplify.

3.6 ft : 1 in

We found that the ratio of the scale model is 1 inch of the model is equal to 3.6 ft of the real car.

Therefore, 3.6 ft = 1 in, which is equivalent to 1 in = 3.6ft

Answer:

9)  [tex]\\\frac{14}{16}[/tex]

10) [tex]28\frac{5}{8}[/tex]

Step-by-step explanation:

9)

[tex]1\frac{3}{4}[/tex] you change by multiplying 1 * 3 (the numerator) and adding 4 (the denaminator), putting the result (7) to the numerator and keeping the denaminator (4) = [tex]\frac{7}{4}[/tex]

[tex]\frac{7}{4} * \frac{2}{4} = \frac{14}{16}[/tex]

10) 7*4 = 28

so [tex]28\frac{5}{8}[/tex]

Answer:

Step-by-step explanation:

he cafeteria sold 6 more turkey sandwiches than ham sandwiches. They sold 52 sandwiches in all

If the condition f(-x) = -f(x) is satisfy then the function is an odd function. Then the odd function is f(x) = 6x³ + 2x.

Odd Function - A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.

The equation should be stored in an odd function:

f(-x) = -f(x)

Then the functions are given below.

f(x) = 3x² + x

f(x) = 4x³ + 7

f(x) = 5x² + 9

f(x) = 6x³ + 2x

Then replace x with the negative x, then we have

f(x) = 3(-x)² + (-x) = 3x² - x =

f(x) = 4(-x)³ + 7 = -4x³ + 7

f(x) = 5(-x)² + 9 = 5x² + 9

f(x) = 6(-x)³ + 2(-x) = -6x³ - 2x = - (6x³ + 2x)

More about the odd function link is given below.

https://brainly.com/question/14264818

Answer: D

Step-by-step explanation:

Answer:

A. 12

Step-by-step explanation:

Using the Law of Sines,

Here,

Solving :

Finding MN :

The product of  3a + 5 and 2a2 + 4a – 2 is [tex]\rm 6a^3+22a^2+14a-10\\[/tex], the correct option is A.

When two algebraic expressions are multiplied, the result is called the product, and the two expressions making up the product are called factors and multiplicands.

The multiplication of two algebraic equations can be expressed as a × b.

The product of 3a + 5 and 2a2 + 4a – 2 is determined in the following steps given below.

[tex]\rm =(3a + 5) \times( 2a^2 + 4a -2)\\\\= 3a ( 2a^2 + 4a -2) +5( 2a^2 + 4a -2)\\\\ =6a^3+12a^2-6a+10a^2+20a-10\\\\=6a^3+22a^2+14a-10\\[/tex]

Hence, the product of  3a + 5 and 2a2 + 4a – 2 is [tex]\rm 6a^3+22a^2+14a-10\\[/tex].

To know more about multiplication click the link given below.

https://brainly.com/question/14059007

Answer:

A. 6a^3 + 22a^2 + 14a - 10

Step-by-step explanation:

Ed22

Answer:

B

Step-by-step explanation:

It 4 3/8 is 4.375 which would round down

Answer:

not answered this question

Answer:

266.66mL/s

Step-by-step explanation:

You have:

[tex] \frac{16}{1} \frac{liters}{minute} [/tex]

You can use the conversion factors to convert liters to milliliters, and minutes to seconds:

1L = 1000mL

1 min = 60 sec

Therefore:

[tex] \frac{16}{1} \frac{liters}{minute} \times \frac{1000}{1} \frac{mililiters}{liter} \times \frac{1}{60} \frac{minute}{seconds} [/tex]

Liters cancel and minutes cancel. The units of mL per second is all that remains:

[tex] \frac{16 \times 1000}{60} \frac{mililiters}{second} = 266.66 \frac{ml}{s} [/tex]

Answer:

(3, -1)

Step-by-step explanation:

Given

Subbing the value of y

Answer:

Solution: (3, -1)

Given equations:

Step-1: Reorganize the equations with "y" on the L.H.S

[tex]\rightarrow \left \{ {{4x + 5y = 7} \atop {y = 3x - 10}} \right.[/tex]

[tex]\rightarrow \left \{ {{5y = 7 - 4x} \atop {y = 3x - 10}} \right.[/tex]

[tex]\rightarrow \left \{ {{5y = 7 - 4x} \atop y =-10 + 3x}} \right.[/tex]

Step-2: Make the x-variables the same on both equations

[tex]\rightarrow \left \{ {{3(5y = 7 - 4x)} \atop 4(y =-10 + 3x)}} \right.[/tex]

[tex]\rightarrow \left \{ {{15y = 21 - 12x} \atop 4y =-40 + 12x}} \right.[/tex]

Step-3: Add the equations

[tex]\rightarrow (15y + 4y) = (21 - 40) + (-12x + 12x)[/tex]

[tex]\rightarrow 19y = -19[/tex]

Step-4: Divide both sides by 19

[tex]\rightarrow \dfrac{19y}{19} = \dfrac{-19}{19}[/tex]

[tex]\rightarrow y = -1[/tex]

Step-5: Substitute the value of y into any equation

[tex]\rightarrow y = 3x - 10[/tex]

[tex]\rightarrow -1 = 3x - 10[/tex]

Step-6: Simplify the equation

[tex]\rightarrow -1 + 10 = 3x[/tex]

[tex]\rightarrow9= 3x[/tex]

Step-7: Divide 3 both sides

[tex]\rightarrow \dfrac{9}{3} = \dfrac{3x}{3}[/tex]

[tex]\rightarrow x = 3[/tex]

(Optional) Step-8: Convert the solution(s) into (x, y) form

[tex]\rightarrow (x, y) \rightarrow (x = 3; y=-1) \rightarrow (3,-1)[/tex]

Thus, the value of x and y is 3 and -1. The solution is (3, -1).

scalene triangle

hope it helps...

Answer:

down below - hope this helped :)

Step-by-step explanation:

you can make a scalene traingle with these mesurements

since none of the sides are equal :)

Answer:

x = 2

Step-by-step explanation:

5x + (- x) - 1 = 11 - 2x , that is

5x - x - 1 = 11 - 2x

4x - 1 = 11 - 2x ( add 2x to both sides )

6x - 1 = 11 ( add 1 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Answer:

The value of x is 2

Step-by-step explanation:

=> 5x + (-x) - 1 = 11 - 2x

=> 5x -x -1 = 11 - 2x

=> 4x - 1 = 11 - 2x

=> 4x+2x = 11+1

=> 6x = 12

=> x = 12/6

=> x = 2

Answer:

9

Step-by-step explanation:

The given equation is:

[tex]x^{2}[/tex] - 6[tex]x[/tex] = 5

To complete the square you have to add one number to both sides of the equation.

First, divide the coefficient of the term x by 2 and square the result. This number should then be added to both sides of the equation.

For the equation [tex]x^{2}[/tex] - 6[tex]x[/tex] = 5 the coefficient of the term x is -6.

(6 ÷ 2)² = 9
So you'll add 9 to both sides of the equation.

  [tex]x^{2}[/tex] - 6[tex]x[/tex] (+ 9) = 5 (+ 9)
                 ↓
      [tex]x^{2}[/tex] - 6[tex]x[/tex] + 9 = 14

This can also be written as:
         ([tex]x[/tex] - 3)² = 14

Answer:

1. Sine ratio of angle ∠C = 12/13

2. cos ratio for ∠C = 6/10

Step-by-step explanation:

1. sin = perpendicular /hypotuse

=> 12/13

2. cos = base / hypotuse

=> 6/10

The number of weeks when both Michelle and Zuri would both have their hair done again on the same day is 6 weeks.

In order to determine when they would both have their hair done on the same day, the common multiple of 8 and 5 has to be determined.

A multiple of a number is the product of an integer and that number.

Multiple of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Multiple of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Common multiple = 40

Number of weeks = 40 / 7 = 5.71 = 6 weeks

To learn more about multiples, please check: https://brainly.com/question/26030133