What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3

The solution to the given complex number expression is; 0 + [1/(-2√6))]i

We are given the expression as;

(√-4)/[(√-8)√-12)]

Now, when it comes to complex numbers, we know that the square root of a negative number for example √-25 would result in 5i.

Similarly, i² = -1

Thus, our expression is now;

2i/(2i√2 * 2i√3)

= 2i/(-4√6)

= i/(-2√6))

= 0 + [1/(-2√6))]i

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Answer:

100,000,000,000cm

Step-by-step explanation:

there are one hundred billion cm in one billion meters.

By using some exponent properties, we can simplify the expression to get:

√(100)² = 100

Here we will be using two exponent properties, these are:

√a = a^(1/2)

And:

(a^n)^m = a^{n*m}

The given expression here is:

√(100)²

Using the first property, we can rewrite this as:

( 100¹/²)²

And using the second property, we can rewrite as:

( 100¹/²)² = 100²*⁽¹/²⁾ = 100¹ = 100

That is the simplified expression.

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The Angle Bisector Theorem states that in a triangle, if a line bisects one angle of a triangle and is also a median to the side opposite of that angle, then the ratio of the length of the median to the length of the side opposite the angle bisected is equal to the ratio of the length of the other two medians.

Therefore, if the angle bisector divides the opposite side into segments 6 cm and 9 cm long, the ratio of the length of the median to the length of the side opposite the angle bisected is 6/9.

Let x be the length of the third side of the triangle.

The Angle Bisector Theorem states: (x/22.5) = (6/9)

Solving for x, we get: x = (22.5 * 6/9) = 15

So the length of the third side of the triangle is 15 cm.

This is the only possible length for the third side of the triangle because the Angle Bisector Theorem only holds if the angle bisector is also a median to the side opposite of that angle.

The exact volume of the waffle ice cream cone is 114.75π square inches

From the question, we are to determine the volume of the waffle ice cream cone

The volume of a cone can be calculated by using the formula,

V = 1/3πr²h

Where V is the volume

r is radius

and h is the height

From the given information,

Diameter = 9 in

∴ Radius, r = 9/2 in = 4.5 in

h = 17 in

Putting the parameters into the formula, we get

V = 1/3 × π × 4.5² × 17

V = 114.75π square inches

Hence, the volume is 114.75π square inches

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Answer: C

Step-by-step explanation:

10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310

3 of mixed cereal and 2 of tropical fruit

Answer:

exponential growth

Step-by-step explanation:

This is a mathematical problem that can be solved using algebra. Let P be the original amount borrowed, and R be the interest rate as a decimal (for example, 5% would be represented as 0.05).

We know that at the end of 25 years, the amount borrowed has trebled, so the total amount is 3P. We also know that the interest is calculated using simple interest, which is calculated as P x R x T, where T is the number of years.

So we can set up the equation:

3P = P + P x R x 25

To find R, we can solve for R by dividing both sides of the equation by P:

3 = 1 + 25R

Then by subtracting one from both sides we have :

2 = 25R

Then by dividing both sides by 25 we can find the rate as :

R = 2/25

Finally, to find the interest rate as a percentage, we multiply R by 100:

rate = 2/25 x 100 = 8%

So the interest rate is 8% per annum

The length of the car in Ivans drawing is given as 8 cm

We are to solve for the length of this car by using the figure we have in the scale drawing. The length of car in Megan's drawing is 6 cm. The scale is 3 : 2

Ivan's drawing is in the relation of 2 : 1 cm

We would have to find the actual length of this car but by the use of Megan's ratio

This is given as

6 * 2 / 3

12 / 3

= 4 cm

Next we have to find Ivans length.

4 * (2/1)

= 8 / 1

= 8 cm

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Answer:

380m

Step-by-step explanation:

1km=100m

0.38km=

0.38×1000/1=

380m

The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

State Alternate angle theorem?

The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. These angles are called alternate interior angles.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

Angles that are on opposite sides of the transversal are called alternate angles. All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

In the above-given figure, you can see, two parallel lines intersected by a transversal AB.

So according to the alternate angle theorem,

m∠3 = m∠6

Now moving on to the students' explanations, both logics are correct.

Hence we can say that according to the alternate angle theorem,

m∠3 = m∠6

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Answer:

x = 5

Step-by-step explanation:

5x - 1 = 24

=5x = 24 + 1

=5x = 25

=5x/5 = 25/5

x = 5

Hence the value for x is 5.

Answer:

Step-by-step explanation: 5x - 1 = 24

                                         => 5x = 24 + 1

                                         =>  x = 25/5

                                         =>  x = 5

Answer: D - 124°

Step-by-step explanation: Since y and a are vertical angles, we can determine that angle a is equal to 34°

90° + 34° = 124°

180° - 124° = 56°

Now we know the last angle in the triangle. Since this angle is on the same line as angle b, subtracting it from 180 would give us angle b

180° - 56° = 124°

Answer: C

Step-by-step explanation:

It's C, as they represent the same ratio.

Answer:

Step-by-step explanation:

Sure, here is an example of how the information provided could be organized in an Excel spreadsheet to calculate Taxable Income and Adjusted Gross Income: see in the attached e1 and e2 screenshots.

It's worth noting that the above example is a simplified version, and the actual calculations for tax purposes would depend on the specific tax laws and regulations in the relevant jurisdiction and year. Also, the numbers provided here are not the final Taxable Income, it's only the calculation of Taxable Income based on the information provided.

The output voltage, in millivolts (mV), for the circuit would be equal to 1,350 millivolts.

An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.

The output voltage of an amplifier= input voltage × gains.

We have been given that input voltage = 45 mV

The gain = 30

Therefore, the output voltage= 45×30

= 1350millivolts.

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The horizontal axis is the real axis and the vertical axis is the imaginary axis. We find the real and complex components in terms of r

and θ

where r

is the length of the vector and θ

is the angle made with the real axis.

From Pythagorean Theorem :

r2=a2+b2

By using the basic trigonometric ratios :

cosθ=ar

and sinθ=br

.

Multiplying each side by r

:

rcosθ=a  and  rsinθ=b

The rectangular form of a complex number is given by

z=a+bi

.

Substitute the values of a

and b

.

z=a+bi    =rcosθ+(rsinθ)i    =r(cosθ+isinθ)

In the case of a complex number, r

represents the absolute value or modulus and the angle θ

is called the argument of the complex number.

This can be summarized as follows:

The polar form of a complex number z=a+bi

is z=r(cosθ+isinθ)

, where r=|z|=a2+b2−−−−−−√

, a=rcosθ  and  b=rsinθ

, and θ=tan−1(ba)

for a>0

and θ=tan−1(ba)+π

or θ=tan−1(ba)+180°

for a<0

.

Example:

Express the complex number in polar form.

5+2i

The polar form of a complex number z=a+bi

is z=r(cosθ+isinθ)

.

So, first find the absolute value of r

.

r=|z|=a2+b2−−−−−−√    =52+22−−−−−−√    =25+4−−−−−√    =29−−√     ≈5.39

Now find the argument θ

.

Since a>0

, use the formula θ=tan−1(ba)

.

θ=tan−1(25)    ≈0.38

Note that here θ

is measured in radians.

Therefore, the polar form of 5+2i

is about 5.39(cos(0.38)+isin(0.38))

.

The domain of the function 5h + 2d = 15 is [0, 3].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function 5h + 2d = 15

Where h is the number of hours and d is the distance remaining after h hours.

Now,

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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Step-by-step explanation:

here it is earning more money to the doctor said the

Answer: x = 1, -13

Step-by-step explanation:

      We will solve this by completing the square, as asked in the instructions. If we do this correctly, we will end up with a perfect square that will allow us to solve more easily.

Given:

      x² + 12x = 13

Set the equation equal to 0 by subtracting both sides of the equation by 13:

      x² + 12x - 13 = 0

Group the first two terms:

      (x² + 12x) - 13 = 0

Add and subtract [tex]\frac{b}{2} ^2[/tex] to the grouped terms:

      (x² + 12x + 36 - 36) - 13 = 0

Regroup the terms, move the negative out and simplify:

      (x² + 12x + 36) - 49 = 0

Factor the grouped terms (6 is our perfect square here):

      (x + 6)(x + 6) - 49 = 0

Add 49 to both sides of the equation and simplify the factors:

      (x + 6)² = 49

Square root both sides of the equation:

      x + 6 = 7           x + 6 = -7

Subtract 6 from both sides of each equation:

    x = 1           x - 13

Therefore , solving the provided vector question we can say that Figure B best describes the voltage and current in parallel LC circuit

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow.

Given :

Vector as given :

Figure A, Figure B , Figure C and Figure D

Voltage and current

parallel LC circuit

=>Iₙ * Eₙ = Iₙ

Size and direction are two independent characteristics of a quantity or phenomena known as a vector.

The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

Here,

From observation we can say that ,

Figure B best describes the voltage and current in parallel LC circuit

Figure B

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Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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The percent of the baked foods that are cakes will be 25.33%

It should be noted that a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %. In this situation, the bakery produces 280 loaves of bread and 95 cakes daily.

The percent of the baked foods that are cakes will be:

= Number of cakes / Number produced daily × 100

= 95 / (280 + 95) × 100

= 95 / 375 × 100

= 25.33%

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Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to find the solutions or roots of a quadratic equation in the form of ax^2 + bx + c = 0. The goal of factoring is to rewrite the equation in the form of (x-r)(x-s) = 0, where r and s are the solutions or roots of the equation. Once the equation is in this form, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Here is an example to illustrate the process:

Example: Solve the equation x^2 + 5x - 14 = 0 using factoring.

Step 1: Rewrite the equation in standard form (ax^2 + bx + c = 0). In this case, a = 1, b = 5, and c = -14.

Step 2: Factor the equation by looking for two numbers that multiply to give c and add to give b. In this case, the two numbers are -7 and 2, since (-7)(2) = -14 and -7 + 2 = -5.

Step 3: Rewrite the equation as (x + 7)(x - 2) = 0.

Step 4: Use the zero product property to set each factor equal to zero and solve for x.

x + 7 = 0 or x - 2 = 0

x = -7 or x = 2

So the solutions or roots of the equation are x = -7 and x = 2.

It's important to note that not all quadratic equations can be factored, and in such cases, other methods like completing the square or using the quadratic formula should be used.

It's also important to understand that when factoring, it's important to make sure that you have correctly factored the equation, if not the solution will be wrong.

Answer:

( - inf, 5) (9, inf )

Step-by-step explanation:

The arrow(s) at the end of the line indicate that the highlighted green line does not stop at a specific number, hence the use of infinity signs (inf). If the arrow is going to the left on a line, then the value would be negative infinity. If it is going to the right, then it would be positive.

As for the space in between the green arrows pointing separate ways, there are two points, one which is positioned at the number 5 and the other at the number 9. Because there are two separate points which are both solid green, the use of parentheses is needed. The final answer is, as mentioned, ( - inf, 5) (9, inf ).

Answer:

Step-by-step explanation:

a(b - c) = de

b - c = de/a

-c = de/a - b

c = b - de/a

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Answer: This is evaluataion, To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Step-by-step explanation: In this situation you are going to divide the numerator and denominator by 2. For example 2/8 makes 1/4. 1/4 is equivalent to 2/8 but not fully simplified.

Another way to solve this is to reduce to lowest terms. For example, 5/15 is reduced by dividing the numerator and denominator by 5 to get 1/3.

Divide the numerator and denominator to get a decimal form of the fraction or divide 5+2 by 3+6

Answer: True

Step-by-step explanation: Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.