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Find the distance between the complex numbers in the complex plane.
−5 + i, −3 + 5i

Answer:

the slope of these points is 8/3

Answer:

Step-by-step explanation:

Work hours Monday till Friday:

Payment for 5 days:

Payment for Saturday:

Total payment:

Answer:

$ 230 is the answer.

Step-by-step explanation:

Answer:

c) m <2 =m <3

Step-by-step explanation:

since the angles 2 and 3 are equal then they should be alternate angles

then c and d are parallel lines

There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

To determine the number of possible outcomes when rolling a number cube and picking a cube from 4 colored cubes,

we need to multiply the number of outcomes for each event.

For rolling a number cube (assuming it has 6 sides), there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

For picking a cube from 4 colored cubes, there are 4 possible outcomes (one for each color).

Now, to calculate the total number of outcomes, multiply the outcomes of each event:

6 (number cube outcomes) x 4 (colored cube outcomes) = 24 possible outcomes.

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

When rolling a number cube, there are six possible outcomes (numbers 1-6). When picking a cube from four colored cubes, there are four possible outcomes. Therefore, the total number of possible outcomes is the product of the number of outcomes from each event: 6 x 4 = 24 possible outcomes.

When rolling a number cube, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6), since a standard number cube has 6 faces, each with a different number.

When picking a cube from 4 colored cubes, there are 4 possible outcomes, one for each color.

To find the total number of outcomes when performing both actions, you can multiply the number of outcomes for each individual action:

Total outcomes = outcomes from rolling a number cube × outcomes from picking a colored cube
Total outcomes = 6 × 4
Total outcomes = 24

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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Answer:

118°

Step-by-step explanation:

Don't think the answer is 62° this time both 118° and angle x are congruent.

What do I mean by that? Both angles measure the exact same thing.

The only difference is their line length (n) and (m).

3x-y=-9

Step-by-step explanation:

Answer: 3x - y = - 9

Step-by-step explanation:

Re-write the equation in the following form:

3x + 9 = y

Take the y to LHS:

3x + 9 - y = 0

Now, take the 9 to the RHS:

3x - y = -9. This is your answer.

Naturally, the task did not require the values of the two variables.Each tree costs $47 and each bush is $23.

Although I don't have subtotals for the bushes and trees, I could try to add the bushes and trees to get 19 bushes and 6 trees, but this wouldn't help me at all.

So I'll choose two variables ("b" for the quantity of bushes and "t" for the quantity of trees) and construct an equational structure:

13b + 4t = 487 is the first order.

second order: 6b plus 2t equals 232.

When I divide the second row by -2, I obtain:

13b + 4t = 487

-12b – 4t = –464

Therefore, b must equal 23.

Using back-solving, I discover that t = 47.

Naturally, the task did not require the values of the two variables.

The answer, when translated back into English, is:

Each tree costs $47 and each bush is $23.

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Answer:

\(PZQ = 63\)

Step-by-step explanation:

Given

\(OZQ = 125\)

\(OZP = 62\)

Required

Determine PZQ

Since P is an interior of OZQ, we have that:

\(OZQ = OZP + PZQ\)

Solve for PZQ

\(PZQ = OZQ - OZP\)

Substitute values for OZQ and OZP

\(PZQ = 125 - 62\)

\(PZQ = 63\)

Answer:

10

Step-by-step explanation:

1/3 of 30 is 10 because 3 times 10 is 30

Answer: i could tell you that it is equaled to 10

Step-by-step explanation:

The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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I'm going to assume the limit is

\(\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3}\)

since problems like this usually involve indeterminate forms, and

√(x + 1) - 2 = x - 3 = 0

when x = 3.

To get around the discontinuity in the limand at x = 3, rationalize the numerator:

\(\dfrac{\sqrt{x+1} - 2}{x - 3} \times \dfrac{\sqrt{x + 1} + 2}{\sqrt{x + 1} + 2} = \dfrac{\left(\sqrt{x+1}\right)^2 - 2^2}{(x-3) \left(\sqrt{x+1}+2\right)} = \dfrac{x-3}{(x-3)\left(\sqrt{x+1}+2\right)}\)

Now as x approaches 3, the factors of x - 3 cancel, the resulting limand is continuous at x = 3, and we have

\(\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \boxed{\frac14}\)

I think the last one, also a similar formula below . . .

Answer:

No solutions

Step-by-step explanation:

4 + 4x - 3 = 4x + 5

4x + 1 = 4x + 5

Add -4x and -1 on both sides.

4x - 4x = 5 - 1

0 = 4

There are no solutions.

Answer:

x+y=18000

Step-by-step explanation:

x= ammount of students

y= number of days or places going to

Answer: #1. yes it's a function #6. the graph is increasing at (-oo , 2) , #7.  the graph is decreasing at (2,oo) ,

Step-by-step explanation:

hope it helps

6. It is increasing from (-infinity, 4) or ]  i am not sure

7. It is decreasing from ( or [4, infinity)

If the arrow kept on going the f(-12) = x for example, f(4)=2

Important things to know f(x)=y and (x,y)

I am sorry that I can not help with the others!!!

The distance between 2 endpoints on a coordinate grid can be calculated using the following formula;

The correct answer therefore is option D;

c^2= 16 + 144

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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The credit card company calculated a finance charge of $7.66 on Ron's bill if the annual percentage rate is 18%.

The finance charge is the product of the average daily balance and the monthly percentage rate.

The annual percentage rate (APR) is 18% or 0.18.

$510.50× 0.18 / 12 =$7.66

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The required exponential expression is 9⁵ for the numerical expression 9⋅9⋅9⋅9⋅9.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

"9⁵," or "nine to the fifth power is respectable because we have multiplied the number "9" by itself "five times."

Hence, the value is equal to:    

⇒ 9⋅9⋅9⋅9⋅9 is equal to:  " 9⁵ " ;  

that is, "nine to the fifth power"  or "nine to the power of "five" ;

Thus, the required exponential expression is 9⁵ for the numerical expression 9⋅9⋅9⋅9⋅9.

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Answer:

60°

Step-by-step explanation:

90°-30°…

according to your question

The measure of the angle DAB for the right angled triangle ABD is found as   45°.

A right-angled triangle has two acute angles that add up to 90°. The smallest angle is the one that is opposite the smallest side, and the greatest angle is the one that is against the largest side.

In a triangle, the two angles that face the two equivalent sides are also equal. There can only be one right angle and one obtuse angle in a triangle.

For the question-

Triangle ABC is right angled at B.

D point makes:  AC = CD

And , AB = BC

Since ∠ABD = 90, given C is mid point.

Then, It is altitude on AD and it bisects the angle ABD into 2 equal halves as: ∠ABC = ∠CBD = 45.

Now, For triangle ABC

∠ABC = 45

∠BCA = 90

Then,

∠BAC + ∠ABC + ∠BCA = 180

∠BAC + 45 + 90 = 180

∠BAC = 180 - 135

∠BAC = 45°

Thus, the measure of the angle DAB for the right angled triangle ABD is found as  45°.

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Kristin bought 4 fancy shirts and 3 plain shirts.

Let's assume Kristin bought "x" fancy shirts and "y" plain shirts.

We know that:

x + y = 7 (the total number of shirts Kristin bought)

28x + 15y = 131 (the total amount of money she spent)

We can use the first equation to solve for one of the variables in terms of the other.

For example: y = 7 - x

Substituting this into the second equation:

28x + 15(7 - x) = 131

28x + 105 - 15x = 131

13x = -74

x = -5.692307692 (approximately)

Since x must be a positive integer (the number of fancy shirts cannot be negative or a fraction), this solution is not valid.

However, we can see that the equation does have a solution by trying a larger value for x:

x = 1

y = 6

This gives us:

28 * 1 + 15 * 6 = 131

28 + 90 = 131

118 = 131

This solution is not valid either, since the total amount spent cannot be less than the cost of the shirts.

By repeating this process, we can find that the solution is x = 4 and y = 3.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:  

w=2 , w=6 are the zeroes of the expression

Explanation:

We have been given the expression

after cross multiplication of the given expression so as to simplify it we will get

Solution to the given equation is w=2,w=6

Therefore these are the solutions of the given expression.

A characteristic of a simple random sample is that all samples of the same population have an equal chance to be selected.

A subset of a statistical population called a simple random sample is one in which each member has the same chance of being picked or selected.

A subset of participants is chosen at random by the researcher using this sampling approach from a population.

To make sure that the sample represents the population, simple random sampling is often performed and this technique helps to sample bigger populations more frequently than smaller subpopulations.

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Answer:

Solve for y by simplifying both sides of the equation, then isolating the variable.

y=−40

please give brainllest

The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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