Express ✓-25 as a complex number

We have to evaluate each expression to find if the equality stands or not.

a)

This expression is equivalent.

b)

The expressions are not equivalent, although they have a solution for x.

(Note: equivalent expression would give infinite solutions for x).

c)

The expressions are not equivalent,.

d)

Answer: the only pair of expressions that are equivalent are 4-6x=2(2-3x).

Given that there are 16 paintings to sell at a PTA auction.

In order to pay for the materials, he needs to sell each of the paintings for $1.75 each. So, the cost of material is

The total cost of the material is $28.

Two of the paintings are damaged during transportation. So he needs to sell only 14 paintings to get $28.

So, he needs to sell each of the paintings at:

Thus, the new minimum price he needs to set for the remaining paintings in order top

The answers are x1 = 14.37 and x2 = -2.37

x1 is the positive and x2 is the negative

There are two solutions x1 = 14.37, x2 = -2.37

Answer: volunteer within each block should live in similar environments to each other when it comes to mosquitos

Step-by-step explanation:

The researchers using a randomized block design should form the blocks by making the;

Volunteers within each block should live in similar environments to each other when it comes to mosquitos.

       A randomized block design is simply a type of experiment where the experimental units are put in groups known as blocks.

Now, we are told that;

- A company is designing an experiment where volunteers will be assigned either the bracelet or bug spray to use at their homes.

- They are doing the experiment because they want to make a bracelet that can repel mosquitoes so people don't have to wear bug spray anymore.

        Now, this implies that the environment they find themselves has a big impact on the outcome of the experiment. This is because different environments could have different exposure conditions to mosquitoes and as a result it will be better for them to be within the same environment for better experimental results.

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The word best describes the degree of overlap between the two data sets

O low

The degree of overlap generally refers to the extent to which two or more sets share common elements.

Specifically the degree of overlap can be defined as the number of elements that are contained in more than one of the sets being considered

In the problem the degree of overlap is low, since the data points shared only points 50 and 55

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The 0.0035 hr⁻¹ first-order degradation rate constant in the 40 °C, 1.0 mg/ml solution, where R = 1.987 cal/mol/degree and 2,000 cal/mol activation energy indicates;

a. The rate constant for first-order degradation of N₂O₂ at room temperature is approximately 4.12595 × 10⁻² hr⁻¹

A first order reaction is one that has a rate that varies linearly with the concentration of one reactant

The given parameters are;

Temperature of the solution = 40°C

T₁ = 40 °C + 273.15 = 313.15 K

The rate constant, K₁ = 0.00351 hr⁻¹

Concentration of the solution = 1.0 mg/ml

Activation energy, Eₐ = 2000 Cal/mol

R = 1.987 cal/mol/degree

The formula by which the rate constant can be found is presented as follows;

\(log\dfrac{k_2}{k_1} =\dfrac{E_a}{2.303\times R} \times \dfrac{T_2-T_1}{T_1\cdot T_2}\)

a. Room temperature = 25 °C

T₂ = 25 °C + 273.15 = 298.15 K

Therefore;

\(log\dfrac{k_2}{0.00351} =\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\)

\(k_2=0.00351 \times 10^{\left(\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\right)} \approx 4.12595\times 10^{-2}\)

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Answer:

a. If the selection is made with replacement, they are NOT independent because they affect each other.

b. The probability of selecting TWO accurate orders is .7157 and the events ARE independent.

Step-by-step explanation:

Add the accurate orders:

315+273+248+125=961

Add the inaccurate orders:

38+56+37+17=148

148/961=0.1540 probability of getting ONE inaccurate order

1.0-0.1540=0.846 probability of selecting ONE accurate order

0.846 * 0.846 = 0.7157 the probability of selecting TWO accurate orders

Therefore, the probability is .7157 and the events ARE independent.

John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.

Total number of bills with John = 15

Total money with John = $145

John has a mix of $5, $10 and $20 bills

Let the number of $5 bills be x, $10 bills are y and $20 bills be z

Formulating the equations:

5x + 10y + 20z = 145-------(1)

x + y + z = 15--------(2)

As per the question, the number of ten dollar bills is one less than twice the number of twenty dollar bills:

y = 2z - 1

Putting y = 2z-1 in equating (1) and (2) we get:

5x + 10(2z-1) + 20z = 145

5x + 20z - 10 + 20z = 145

5x + 40z = 155--------(3)

x + y + z = 15

x + 2z - 1 + z = 15

x + 3z = 16--------(4)

Multiplying equation (4) with 5 and using Gaussian Elimination to equate (3) and (4)

5x + 40z = 155

5x + 15z = 80

25z = 75

z = 3

Putting z=3 in (4) we get

x = 7 and y = 5

So, John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.

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There are 4 cubes of size 1/4 foot would fill the inside of the prism.

We have to given that;

Height of cuboid = 3 feet

Length of cuboid = 3/4 feet

Width of cuboid = 1/2 feet

We know that;

Volume of cuboid = Length x width x height

Hence,

V = 3/4 x 3 x 1/2

V = 9/8

Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,

= (9/8) ÷ (1/4)

= (9/8) x 4

= 9/2

= 4.5

Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

the 20 +2

Step-by-step explanation:

Answer:

  (x, y) = (4, -9)

Step-by-step explanation:

You want to solve this system of equations by elimination:

The coefficients of x are not integer multiples of each other, but the coefficient of y in the first equation is 4 times the coefficient in the second equation. To eliminate y, we can multiply the second equation by -4 and add the result to the first equation:

  (-8x -4y) -4(-5x -y) = (4) -4(-11)

  12x = 48

  x = 4

Using the second equation to find y, we have ...

  -5x +11 = y

  -5(4) +11 = -9 = y

The solution is (x, y) = (4, -9).

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:

The solution (x,y) is (3,19).

Step-by-step explanation:

We are given two equations for y.

y = 5x + 4

y = 3x + 10

They are equal, which means that we can find x. So

5x + 4 = 3x + 10

2x = 6

x = 3

With x, we can find y:

y = 5*3 + 4 = 19

So the solution (x,y) is (3,19).

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Step-by-step explanation:

here,

midpoint of line segment LP

=( X1 +X2÷2 , Y1 + Y2÷ 2)

=(4+0÷2 , 2+2 ÷2)

=(4÷2 ,4÷2)

=(2,2)

Therefore the midpoint of segment LP with L (4,2) and P (0,2) = (2 ,2).

Answer:

No.

Step-by-step explanation:

An integer is defined as a whole number.

The number given, "1.765", is not a whole number, as it includes the decimal .765. 1.765, as implied by decimal point, is a decimal number.

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Answer:

2.4

Step-by-step explanation:

Use formula y2-y1/x2-x1

Points = (-2,-7) and (3,5)

5 - (-7)/3 - (-2)

NB: Negative times negative gives positive.

5 + 7/3 + 2

12/5

2.4

Slope = 2.4.

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Answer:

n<-1.25

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Explanation: The GCF of 56 and 64 is 8 , as 8 goes into 56 exactly 7 times and into 64 exactly 8 times. 8(8)+7(8)=8(7+8).

The total number of hours that Carly studied for 9 days is; 7¹/₂ hours

She wants to study 5/6 of an hour per day for 9 days.

Thus;

Number of hours studied per day = 5/6 * 1 hour = 5/6 hours

Therefore for 9 days, the total number of hours she will study is;

5/6 * 9

= 45/6

= 15/2

= 7¹/₂ hours

That value denotes the total number of hours that she studied for 9 days

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Complete question is;

Carly needed to study for 5/6 of an hour for 9 days. How many hours did she study?

If Kyle and Matt never are at the same distance at the same time, the lines described by the system of equations will never cross each other.

We can use the situation where both have the same speed, and Matt drives 50 miles before Kyle starts travelling.

In this case, they're at the same speed, but separated by 50 miles, thus they never will be at the same distance, at the same time.

The system would be:

Since the two lines never touches, the system has no solutions.

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, \([x = \frac{-b}{2a}, h(\frac{-b}{2a})]\).

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for a and b into the equation to solve for the x-coordinate of the vertex.

\(x = \frac{-b}{2a}\)

\(x = \frac{-8}{2(1)}\)

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the y-coordinate of the vertex:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

The y-intercept is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : \(f(x) = ( 25 - x^{2} )\)

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               \(Area = \int\limits^{maxX}_ {minX} \, f(x)dx\)

               \(Area = \int\limits^5_ {-5} \, (25-x^{2} )dx\)

Hence, Option A correctly calculates the area of the graph given.

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\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Answer:14

Step-by-step explanation:

Akigr sksjb82792?/ =x so that is ansewr

After evaluating the expression, the simplified form is  \(= \dfrac{2}{ 21}\)

Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.

In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.

There are many types οf numbers. It has a cοmprehensive list including whοle numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, οrdinal numbers, etc.

Given to evaluate:

\($\frac{4!\times 5!}{3!\times7!}\)

\(\Rightarrow \dfrac{4 \times 3 \times 2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}{ 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}\)

\(\Rightarrow \dfrac{4}{ 7 \times 6}\)

\(\Rightarrow \dfrac{4}{ 42}\) \(= \dfrac{2}{ 21}\)

Hence, After evaluating the expression, the simplified form is  \(= \dfrac{2}{ 21}\)

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