What is the solution of z + 5 = 6

Answer:

-3 + 5i

Step-by-step explanation:

We can remove the parentheses

2 + i - 5 + 4i

Collect the like terms and do the math

-3i + 5i

The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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Answer:

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square (\(A\)), in square centimeters, is represented by the following function:

\(A = l^{2}\) (1)

Where \(l\) is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square (\(\frac{dA}{dt}\)), in square centimeters per second:

\(\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}\)

\(\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}\) (2)

Where \(\frac{dl}{dt}\) is the rate of change of the side length, in centimeters per second.

If we know that \(A = 25\,cm^{2}\) and \(\frac{dl}{dt} = 4\,\frac{cm}{s}\), then the rate of change of the area of the square is:

\(\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)\)

\(\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}\)

The area of the square is increasing at a rate of 40 square centimeters per second.

The study of explanatory or independent differences based on the dependent variable is a simple statistical method. The correlation between two variables is researched in which only the explanatory variable of them would be present, and the further discussion can be defined as follows:

For point (i):

For point (ii):

For point (iii):

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Answer:

Slope is: y = 6x-4

Step-by-step explanation:

Divide both sides by 2 and you'll get the answer.

Answer:

6

Step-by-step explanation:

a slope equation. is y = mx + b

first you have to get y by itself by dividing both sides by 2

your new equation is

y= 6x + - 4 or just y = 6x - 4

the slope is the m value and in this case its 6

The least positive number with this property is given as follows:

N = 280.

A number N gives remainder 0 when divided by 8, it gives remainder 0, when divided by 7 and it is an even multiple of 5, hence the number is multiple of these 3 numbers.

Before obtaining the number, we must obtain the least common multiple of 8, 7 and 5, factoring them by prime factors as follows:

8 - 7 - 5|2

4 - 7 - 5|2

2 - 7 - 5|2

1 - 7 - 5|5

1 - 7 - 1|7

1 - 1 - 1.

Hence:

lcm(8,7,5) = 2³ x 5 x 7 = 280.

280 is an even multiple of 5, as it is an even number, hence it is the least positive number N with the property in this problem.

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Answer:

-5a-4

Step-by-step explanation:

7a-8-12a+4

7a-12a-8+4

=-5a-4

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

A graph of the image of the figure after a reflection across the x-axis is shown below.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

By applying a reflection over or across the x-axis to triangle GLQ, we have;

(x, y)                →      (x, -y)

G (3, 4)             →      (3, -(4)) = G' (3, -4)

L (1, 2)                →     (1, -(2)) = L' (1, -2).

Q (4, -1)              →      (4, -(-1)) = Q' (4, 1)

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Answer:

44

Step-by-step explanation:

Answer:

use the pythagorean theorem to solve for the sides and the degree for both triangles so your using cos sin or tan im not sure which one

Step-by-step explanation:

i really hope this helps the question is really vague im sorry if this wasnt a help

sin(θ) = Opposite / Hypotenuse

cos(θ) = Adjacent / Hypotenuse

tan(θ) = Opposite / Adjacent

Answer:

64

Step-by-step explanation:

\(\sqrt[3]{512} = 8\\8x8 = 64\)

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer:

Longer side = 145ft

Shorter side = 135ft

Step-by-step explanation:

Here we have a rectangle.

Let's define L as the longest side (the one that is perpendicular to the wall of the house) and S as the shorter side.

We know that the perimeter of a rectangle is:

P = 2*L + 2*S

So if we wanted to fence this rectangle, we would need fencing equal to the perimeter.

But in this case, one of the shorter sides does not need to be fenced, so we only need:

2*L + S of fencing.

And we know that we will use 425ft of fencing, then:

2*L + S = 425 ft

We also know that The length of the fence opposite the house is 10 ft less than  either of the other two sides, then:

S = L - 10ft

Then we have two equations:

2*L + S = 425 ft

S = L - 10ft

Here we can just replace the second equation into the first one to get:

2*L + (L - 10ft) = 425 ft

Now we can solve this for L

2*L + L - 10ft = 425ft

3*L = 425ft + 10ft

3*L = 435ft

L = 435ft/3 = 145ft

This means that the longer side is 145ft long.

And by the equation:

S = L - 10ft

S = 145ft - 10ft = 135ft

S = 135ft

We know that the shorter side is 135ft long.

Using the inequality concept, the expression models the number of days Samuel can afford to rent while staying within his budget is 11x + 18 ≤  40

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

A rental car company charges $22 per day to rent a car and $0.08 for every mile driven

The maximum amount to spend = $80

Fixed charge per day $22

Charge per mile = $0.08

The inequality which represents the number of days Can be expressed thus :

(Charge per day × number of days) + (charge per mile × number of miles) ≤  80

22x + 0.08× 450 ≤ 80

22x + 36 ≤  80

Divided by 2 both sides of an inequality,

11x + 18 ≤  40

Hence, the required inequality expression is 11x + 18 ≤  40

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Answer:

do you still need help on tge questio ?

Answer: c = 10

Step-by-step explanation:

Pythagorean Theorem states that in a right triangle \(a^2 + b^2 = c^2\), where a and b  are the legs of the triangle and c is the hypotenuse.  Thus, because a=6 and b=8, 36+64=c².  Thus 100=c².  Thus 10=c

Answer:

over one to the right, up six

The reflection of the point (1,6) across the x-axis is (1,-6).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

A figure's mirror image in the axis or plane of reflection is its image by reflection.

Given that the coordinate is (1,6). The reflection of the coordinates across the x-axis will be,

R(x₁ , y₁) ⇒ R(x₁,-y₁)

R(1,6) ⇒ R( 1,-6)

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Answer:

Step-by-step explanation:

Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

c=\(\sqrt{a^2+b^2}\)

c=\(\sqrt{28^2+96^2}\)

c=\(\sqrt{10,000}\)

c=100

Therefore, the length of the hypotenuse is 100.

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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9514 1404 393

Answer:

  a) 98

  b) directly

  c) k = 14 pages per hour

Step-by-step explanation:

a) In order to answer the first question, we must assume that the number of pages varies directly with the amount of time. Further, we must find the constant of variation:

  p = kt

  56 = k(4)

  k = 56/4 = 14 . . . . pages per hour

Then in 7 hours, the student will read ...

  p = 14(7) = 98 . . . pages

__

b) As we said in part (a), the variation is direct.

__

c) As we found in part (a), the constant of variation is 14 pages per hour.

Answer:

ion know

Step-by-step explanation:

i think its -6,-50 and 5,70

Answer:

102.2 miles

Step-by-step explanation:

First, convert the minutes to hours:

101.5/60

= 1.69 hours

Multiply this by 60.4 to find how many miles it covered:

= 102.2 miles

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

40 cm

Step-by-step explanation: