How do you find the square root of -6 by imaginary numbers

Answer:

a)  zero triangles.

b)  one triangle.

Step-by-step explanation:

In triangle ABC:

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 51^{\circ}}{10}=\dfrac{\sin B}{28}\)

\(\implies \sf \sin B=\dfrac{28\sin 51^{\circ}}{10}\)

\(\implies \sf \sin B=2.176008...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, zero triangles are possible.

----------------------------------------------------------------------------------

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle A:

\(\implies \sf \dfrac{\sin A}{24}=\dfrac{\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=\dfrac{24\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=1\)

\(\implies \sf A=\sin^{-1}(1)\)

\(\implies \sf A=90^{\circ}\)

Therefore, one triangle is possible (see attachment).

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

mean= sum of all observations /no.of observation

mean=45+80+15+10+94/5

mean=244/5

mean=48.8

this is how the calculator gets 48.8

Answer:

False

Step-by-step explanation:

Answer:

(19, 28)

Step-by-step explanation:

Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

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Answer:

82.76

Step-by-step explanation:

77 x 7.5%=5.775

5.775 +77

Answer:

PR = 288.75 feet

Step-by-step explanation:

There are two triangles that we need to consider:
ΔPRE and ΔPOC

These triangles are similar since
m∠PRE = m∠POC = 90°
∠PRE ≅ ∠POC

∠RPE ≅  ∠OPC (common angle)

AA Similarity theorem..
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.  

∴ ΔPRE ≅ ΔPOC

If two triangles are similar, the ratios of the corresponding sides must be equal

⇒ \(\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\)    (1)

PO = PR + RO
PR is the width of the river that is to be determined
Let PR = x

Then
PO = x + 165

OC = 330, RE = 210

\(\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow \dfrac{x + 165}{165} = \dfrac{330}{210}\\\\\)

Left side:
\(\dfrac{x+165}{x} = \dfrac{x}{x} + \dfrac{165}{x} = 1 + \dfrac{165}{x}\)

Simplify  \(\dfrac{330}{210}\)   by dividing both numerator and denominator by 30

=>
\(\dfrac{330}{210} = \dfrac{11}{7}\\\\\)

Therefore
\(\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow 1 + \dfrac{165}{x} = \dfrac{11}{7}\\\)

Subtract 1 from both sides:
\(\dfrac{165}{x} = \dfrac{11}{7} - 1\\\\\dfrac{165}{x} = \dfrac{4}{7}\\\\\)

Cross-multiply
\(165 \times 7 = 4x\\\\\Rightarrow 4x = 165 \times 7\\\\\Rightarrow x = \dfrac{165 \times 7 }{4} = 288.75\;feet\)

Answer:

The number of right-handed people = 56

Step-by-step explanation:

80% of 70 players = number of right-handed people

So, 80/100 x 70 = 56 players

Therefore, number of right-handed players = 56

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

\(Initial =1\ million\)

\(6\ years\ later = 500,000\)

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

\(\frac{dA}{dt} = kA\)

Where k represents the constant of proportionality

\(\frac{dA}{dt} = kA\)

Multiply both sides by dt/A

\(\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}\)

\(\frac{dA}{A} = k\ dt\)

Integrate both sides

\(\int\ {\frac{dA}{A} = \int\ {k\ dt}\)

\(ln\ A = kt + lnC\)

Make A, the subject

\(A = Ce^{kt}\)

\(t = 0\ when\ A =1\ million\) i.e. At initial

So, we have:

\(A = Ce^{kt}\)

\(1000000 = Ce^{k*0}\)

\(1000000 = Ce^{0}\)

\(1000000 = C*1\)

\(1000000 = C\)

\(C =1000000\)

Substitute \(C =1000000\) in \(A = Ce^{kt}\)

\(A = 1000000e^{kt}\)

To solve for k;

\(6\ years\ later = 500,000\)

i.e.

\(t = 6\ A = 500000\)

So:

\(500000= 1000000e^{k*6}\)

Divide both sides by 1000000

\(0.5= e^{k*6}\)

Take natural logarithm (ln) of both sides

\(ln(0.5) = ln(e^{k*6})\)

\(ln(0.5) = k*6\)

Solve for k

\(k = \frac{ln(0.5)}{6}\)

\(k = \frac{-0.693}{6}\)

\(k = -0.1155\)

Recall that:

\(\frac{dA}{dt} = kA\)

Where

\(\frac{dA}{dt}\) = Rate

So, when

\(A = 600000\)

The rate is:

\(\frac{dA}{dt} = -0.1155 * 600000\)

\(\frac{dA}{dt} = -69300\)

Hence, the amount of oil was decreasing at 69300 barrels, yearly

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

It's b, a waiter does get paid a paycheck but it isn't much, tips also count as commission. Tip your waiters!

Step-by-step explanation:

Also brainly says the word "b r u h" is inappropriate what terrible moderation on this site.

An example of a continuous random variable is a Normal random variable.

What is a normal random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).

Here, we have

We have to determine the example of a continuous random variable.

We concluded that the example of a continuous random variable is a normal random variable.

Hence, an example of a continuous random variable is a Normal random variable.

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Answer:

he has 8 counters.

Step-by-step explanation:

3+5=8

Answer:

8

Step-by-step explanation:

5+3= 8

The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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Answer:

I believe h do 9 times 6. and u should get 54

a) The probability that the woman selected will not meet the age requirement for the internships is:  

0.175

b) The probability that at least 30% of the women in the sample will not meet the age requirement for the internships is:

0.0003

The probability that a woman selected at random from the women in STEM majors at the university will not meet the age requirement for the internships can be found by adding the probabilities of the ages that do not meet the age requirement. This includes the probabilities for ages 17, 18, and 19, which are 0.063, 0.005, and 0.107, respectively. Adding these probabilities gives us:

P(not meeting age requirement) = 0.063 + 0.005 + 0.107 = 0.175

This can be found using the binomial probability formula:

P(X ≥ 30) = 1 - P(X < 30) = 1 - ∑(n choose x) * p^x * (1-p)^(n-x)

Where n is the sample size (100), x is the number of women not meeting the age requirement (less than 30), and p is the probability of not meeting the age requirement (0.175). Using this formula, we can find the probability that at least 30% of the women in the sample will not meet the age requirement for the internships:

P(X ≥ 30) = 1 - P(X < 30) = 1 - ∑(100 choose x) * 0.175^x * (1-0.175)^(100-x)

P(X ≥ 30) = 1 - (0.825^100 + (100 choose 1) * 0.175 * 0.825^99 + ... + (100 choose 29) * 0.175^29 * 0.825^71)

P(X ≥ 30) = 0.0003

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Answer:

She bought more of the solid ribbon.

Step-by-step explanation:

Let's look for the LCD

The common denominator is 72

So we have 63/72 and 64/72

Thus, 63/72 < 64/72.

Emma bought solid ribbons more as 8/9 is greater than 7.8.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Emma bought 7/8 yards of striped ribbon and 8/9 yards of solid ribbon.

Now, The LCM of the denominators 8 and 9 is 72.

So, (7×9)/(8×9) and (8×8)/(9×8).

63/72 and 64/72.

As the numerator of the solid ribbon is greater the fraction 8/9 is greater.

So, She bought more solid ribbons.

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Answer:

x = 6

Step-by-step explanation:

In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.

The final value of x will be 6.

\( PQ^2 + QO^2 = PO^2 \\

x^2 + 8^2 = (4+x)^2 \\

x^2 + 64 = 16 + 8x + x^2 \\

64 = 16 + 8x \\

64 - 16 = 8x \\

48 = 8x \\

6 = x\\\)

Answer:

Variable

Step-by-step explanation:

Answer:

t = 1.2, -1.2

The distance between the points M(-3, -1) and N(2, 3) will be 3 Units.

We know the formula for calculating a distance between two given points. We call it the Distance formula which can be represented by the equation: \(d = \sqrt{(x_{2} - x_{1}) - (y_{2} - y_{1}) }\)  , where d = Distance between two points. Now, M(-3, -1) = (x₁, y₁), and N(2, 3) = (x₂, y₂). Now, Putting these values in the Distance formula, we get :

 =>  \(d = \sqrt{(x_{2} - x_{1}) - (y_{2} - y_{1}) }\)    =>  \(d = \sqrt{(2 - (-3) + (3 - (-1)}\)

 =>  \(d = \sqrt{(2 + 3) + (3 + 1)}\)      =>  \(d = \sqrt{9}\)

 => d = 3 Units.

We get the distance d = 3 units by using the Distance formula.

Hence, the distance between two points M(-3, -1) and N(2, 3) calculated by the Distance formula will be 3 Units.

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Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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Answer:

A function is a mathematical device that converts one value to another in a known way. ... The set of allowable inputs to a given function is called the domain of the function. The set of possible outputs is called the range of the function.

Step-by-step explanation:

Hopefully this was mindfull

The input set of a function is called the "Domain" of the function.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For any function, the values which we are putting form a set of intervals called domain.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Hence "The input set of a function is called the "Domain" of the function".

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1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.

2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.

In the standard producer theory, a producer minimizes costs for a given level of output.

This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).

The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).

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Answer:

that is wrong

Step-by-step explanation:

28^2+45^2=2809

which is 53^2

Answer:

Wrong

Step-by-step explanation:

the Pythagorean theorem is x^2+y^2=z^2 Not (x+y)^2=z^2 so Nadia is wrong