What are the values of x and y for this equation?
(x+yi)+(8-5i)=4+3i

1) Given

2) Segment addition postulate

3) Substitution property

4) Segment addition postulate

5) Transitive property of equality

An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.

[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]

Hence, The simplified version of the given expression is (3√2-2)√x³.

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The system of equation has an infinitely many solutions

The equations are given as:

2x + y = -3

-2y = 6 + 4x

Express 2x + y = -3 in slope-intercept form

y = - 3 -2x

Divide through by -2 in -2y = 6 + 4x

y = -3 - 2x

So, we have:

y = - 3 -2x  and y = -3 - 2x

Both equations are the same.

This means that the system of equation has an infinitely many solutions

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Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

[tex]y = \frac{1}{2} x[/tex]

Answer:

Option C is equal to 7^1/3

Hey there ! please refer to the attachment .

I hope its help you !

According to the given synthetic division, the statements that are true are; Options A, C and E

In the synthetic calculation we use the coefficient of the dividend

with the factors of the function.

Therefore;

3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4

Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4

Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12

- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.

- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.

- The degree of the quotient is 1 and so the he quotient is 3x - 1.

Thus, options A, C and E are correct

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Answer:

3125

Step-by-step explanation:

And

Even numbers = 2x +2

Consecutive even numbers = 2x+4

then

(2x+2) + (2x+4)= 38

2x + 2 + 2x + 4 = 38

2x + 2x + 2 + 4 = 38

    4x + 6 = 38

                   4x = 38 - 6

                     x = 32 :4

                    x = 8

2x+ 2 = 2(8)+2 = 16 + 2 = 18

2x+4 = 2(8) +4 = 16 + 4 = 20

The smallest number is 18

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

18 is the smaller number

Step-by-step explanation:

Let us take X for the first even number (it will also be the smallest)

x, x+1, x+2, so on..

the consecutive even number of x+2 is the next even number after x.

so you now get this equation...

x+(x+2) = 38

2x + 2 = 38

2x = 36

x=18

Answer:

every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away

Hope This helps!

Answer:

Is the second expression written correctly?  It reduces to y>-2, since no x is in the equation.

Step-by-step explanation:

We can graph the two equations.  See attached image.  If y>2 is the correct expression, all points to the right.

If the equation was meant to read y=-3x+1, then graph the revised expression.

Gene earns 2% interest after depositing $150 into his account , Option D.

A function is a law that relates an independent variable and a dependent variable with each other.

The function given is

f(x) = 0.02 x +150

Option D , Gene earns 2% interest after depositing $150 into his account

So this verbal description matches the function given as it represents , the total account balance of Gene .

Therefore Option D is the correct answer.

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Answer:

15°

Step-by-step explanation:

angle FGH = angle HGI ( since GH bisects angle FGI)

that means

(2x + 1) = (3x - 9)

= -x = -8

x = 8

angle HGI = (3x - 9)

= 3(8) - 9

24 - 9

= 15°

Answer:

21

Step-by-step explanation:

To find the measure of <HGI we first need to find the value of x

GH bisects angle <FI which means it divided the angle into two equal parts:

<FGH = <HGI

2x + 1 = 3x - 9 transfer like terms to the same side of the equation

1 + 9 = 3x - 2x

10 = x now replace x with 10

3*10 - 9 = 21

The expected length of the arc containing the point (1,0) is; π

First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.

The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.

Thus, we have;

L₁ + L₂ + L₃ + L₄ = 2π

Whereas, the expected value of several random variables is additive as;

E[ L₁ + L₂ + L₃ + L₄] =  [EL₁] + [EL₂] + [EL₃] + [EL₄]

By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.

Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,

π/2 + π/2 = π

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The range:
[tex]{x|70\leq x\leq 82[/tex]

The weight of the smallest rectangular block is 1400 pounds.

The density refers to the heaviness of an object. It is the ratio of mass to volume.

Then we have

Density = Mass / Volume

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.

The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.

The composite stone weighs 40 pounds per cubic foot.

To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

Then the weight of the smallest rectangular block will be

Mass = density x volume

The volume will be

V = 5 x 2 x 3.5

V = 35 cubic feet

Then the weight will be

Mass = 40 x 35

Mass = 1400 pounds

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Answer:

The horizontal asymptote is y=1 and

The vertical asymptote is x=5

Answer:

The answer is 105.

Step-by-step explanation:

The value of a₃₂ is 7 , Option A is the correct answer.

Matrix is an array or an arrangement of numbers or expression in rows and column format.

The matrix is given

For a matrix of size mxn , m is the row and n is the column of the matrix.

a₃₂ = This term means 3rd row and 2nd column of the matrix

which is 7

Therefore the value of a₃₂ is 7 , Option A is the correct answer.

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Step-by-step explanation:

Did you mean.

[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]

[tex] \: [/tex]

[tex] = \sin( - \frac{4\pi}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]

[tex] = \sin( - 4 \times 60 \degree) [/tex]

[tex] = \sin( - 240 \degree) [/tex]

[tex] = \sin(0 - 240 \degree) [/tex]

[tex] = \sin(360 \degree - 240 \degree) [/tex]

[tex] = \sin(120 \degree) [/tex]

[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]

Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x    where r is the growth rate (interest rate)

So the equation can be written as

[tex]m= P(1.04)^t[/tex]    where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

[tex]I = P(1.04)^t-P[/tex]  where I represents the interest paid.

plug the values into the equation

[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]

Answer:

15

Step-by-step explanation:

divide the perimeter by two and minus 1

Answer: 15ft

Step-by-step explanation:

Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!

By the Pythagorean theorem,

[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]

Answer:

infinity 2 is the slope for these point .

Step-by-step explanation:

given points are

(-2,-5) and (3,5)

comparison to

(x1,y1) and (x2,y2)

here ,

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

slope= 5-(-5)/3-(-2)

slope =10/5

slope=2

glad to help you this may help you :)

Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

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Answer: 113 inches cubed

Step-by-step explanation:

Volume of a sphere = 4/3 Pi r^3

Radius = 3 inches

Volume = 113 inches cubed

Hope I helped!

Answer:

Step-by-step explanation:

Answer:

128, -256, -1024

Step-by-step explanation:

multiply 32 by 4, multiply 128 by -2, multiply -256 by 4

Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2