Is it possible to calculate the square root of a negative number?

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

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The required measure of the angle m∠B is 121°.

Given that,
Angle A and B are two vertical equal angles.
m∠B = 3x - 17
m∠A = 2x + 29

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
m∠A = m∠B
2x + 29 = 3x - 17
-x = - 46
x = 46

Now,
m∠B = 3  *46 - 17
m∠B =  138 - 17
m∠B = 121°

Thus, the required measure of the angle m∠B is 121°.

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Answer: 48 represents total amount and s represents scarves

Step-by-step explanation:

It tells you when you read the sentence carefully.

Answer:

y = 3

Step-by-step explanation:

Points: (1, y), (-5, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - y)/(-5 - 1) = (-1 - y)/(-6)

slope = 2/3

(-1 - y)/(-6) = 2/3

Multiply both sides by -6.

-1 - y = -6 × 2/3

-1 - y = -12/3

-1 - y = -4

-y = -3

y = 3

Work Shown:

x = some unknown number

2x = twice the number

2x+x = add on the number

2x+x = 87

3x = 87

x = 87/3

x = 29

The equation of the two-step problem is 2x = x + 19

The conditions are given as

Let the variable in the equation be x

So, a possible equation is as follows

2x = x + 19

The solution to the equation is as follows

2x = x + 19

Subtract x from both sides

x = 19

Hence, the equation of the two-step problem is 2x = x + 19

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Answer:

She have to study 4 hours and 42 minutes to get 93 marks.

Step-by-step explanation:

when she studied 4 hours she got 79

when she studied 1 hour she got 4/79

[tex]4 \div 79\times 93[/tex]

is the time when she got 93

= 4.70

It means the time will be 4 hours 42 minutes

Answer:

true

Step-by-step explanation:

its true frfr

Answer:

y=1/5x

y=0

Step-by-step explanation:

The inequality for a child up to and including 26 lb is the third option showing correct number line of inequality.

Given that the inequality is 0<x<=26.

We are required to choose the option which shows the correct number line of inequality.

Inequality is like an equation which shows the relationship between two or more variables but in greater than,less than,greater than or equal to ,less than or equal to signs.

Because we have to include 26 in the inequality so we need to fill the circle on 26. So, the correct option showing the correct inequality is third.

Hence the inequality for a child up to and including 26 lb is the third option showing number line of inequality.

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Answer:

72

Step-by-step explanation:

(6)^2+7(6)-6

36+42-6

72

Answer:

12

Step-by-step explanation:

So: 2x-8=4+x

x-8=4

x=12

No, the picture frame will not fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.

Length of picture frame is given as:

= 7 (6 / 11)

= 7.54 inches

The length of Box is given as = 7.5 inches

From the above, we can see that the length of the box is smaller than the length of the picture frame.

So, the picture frame will not be able to fit in the box.

Therefore, we get that, the picture frame will not be able to fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.

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Your question was incomplete. Please refer the content below:

Rochelle needs to pack a picture frame that measures 7 6/11 (fraction 6 over 11) inches

on each side. Will it fit into a box that measures 7.5 inches on each

side?

all that sides which can be applicable in the given side of triangle are:

F.5

A.7

C.9

Third Side of a Right Angle Triangle Pythagorean Theorem. The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem. You can determine the length of the missing side using algebra and square roots as long as you are only given two lengths.

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

D.3   it is not true since it doesn't satisfies second inequality

F.5   it is true

A.7   it is true

C.9   it is true

E.11   This is clearly false, since it doesn't satisfies inequality third

F.5 This is clearly false, since it doesn't satisfies inequality third

Hence, correct options are:

F.5

A.7

C.9

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He gained $330 of interest in the three months.

Here we will use the Simple interest formula

Simple Interest (SI) = Simple Interest (SI)

initial principal balance = P = 24000

annual interest rate = r = 5.5

time (in years) = t = 3 months out of 1 year

                            = 3/12 = 1/4

Lets substitute the values in the formula

Simple Interest (SI) = (P × R × T)/100

                                = (24000 × 5.5 × 1/4)/100

                                = 330

Simple interest is a quick and straightforward approach to figure out how much interest has accrued on a sum of money. Interest is always applied to the main sum, and there is a constant rate of interest applied during the course of the calculation.

Any bank where we deposit money pays us interest on the amount when we do so. There are other forms of interest charged by banks, but simple interest is one of them. To begin with, let's define a loan before delving further into the idea of simple interest.

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A) The reason why Chris had higher savings by retirement age, is because he saved $5000 annually from ages 25 to 65 while susan did so only from ages 25 to 35 .

B) The reason why Susan had a higher retirement savings than bill is because Susan started investing 10 years earlier than bill and so her investment had a longer period to compound.

A) From the given exponential graph, we see that Chris curve was simialr to that of susan between ages 25 to 35 and suddenly Chris curve began to rise at a faster rate than that of Susan after that until when retired at 65 years of age.

Since we are told that chris continued that amount till retirement at 65, we are told that susan contributed the same amount for only that period between ages 25 and 35. Thus, it means that the reason why Chris had higher savings by retirement age, is because he saved $5000 annually from ages 25 to 65 while susan did so only from ages 25 to 35 .

B) The reason why susan had a higher retirement savings than bill is because susan started investing 10 years earlier than bill and so her investment had a longer period to compound.

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Answer:

  [tex]\textsf{C}\quad f^{-1}(x)=24-6x[/tex]

Step-by-step explanation:

You want the inverse function of f(x) = 24 -x/6.

The function relates x to y by y = f(x). The inverse function gives the reverse relation: x = f(y). Solving this for y gives the inverse function in the form you want.

  x = f(y)

  x = 4 -y/6 . . . . . use definition of f(x)

  6x = 24 -y . . . . multiply by 6

  y = 24 -6x . . . . add y-6x

  f⁻¹(x) = 24 -6x . . . . write using function notation

12 is the population mean or sample mean of given data.

Given that

The collected data

17, 10, 3, 5, 25

To find

The population mean or sample mean

So, according to the question

we have,

The collected data

 17, 10, 3, 5, 25

For calculate the the population mean or sample mean, We have to find out the total of data, and total number of data.

Total of data = 17+ 10 +3 + 5+ 25

Total of data = 60

Total number of data (n) = 5,

So, we know that

Sample mean = [tex]\frac{total\;of\;data}{n\;number\;of\;data}[/tex]

Now, putting the all values,

We will get,

Sample mean =  60/5  

 = 12          

The Sample mean of given data is 12.

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The ordered pairs that solve the system of inequalities is given by:

(3, -2), (1, -1).

To verify if an ordered pair solves a system of inequalities, we have to verify if it respects all conditions.

For this problem, the conditions are given as follows:

For the ordered pair (0,3), we have that:

x - 3y  = -9 < 1, hence it does not respect.

For the ordered pair (-1,1), we have that:

-1 -3 = -4 < 1, hence it does not respect.

For the ordered pair (3,-2), we have that:

For the ordered pair (4,0), we have that:

For the ordered pair (2,3), we have that:

2 - 3(3) = -7 < 1, hence it does not respect.

For the ordered pair (1,-1), we have that:

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Answer:

−19 5/7

None of the options match the answer

Step-by-step explanation:

−9 2/7 −10 3/7

=−65/7 −10 3/7

= −65/7 −10 3/7

= −65/7 − 73/7

= −138/7

= −19 5/7

By using the given graph, we can see that f(-5) = 3.

Here we have an image with the graph of the function y = f(x).

Remember that each point on that grid has the coordinates (x, y), where the values of x are on the horizontal axis, and the values of y are in the vertical axis.

So, if we want to find f(-5), then we want to see what value of y takes f(x) when x = -5.

So, first we need to go to the horizontal axis and find x = -5.

Once we find that value, now we need to move up or down along a vertical line (depending on where is the graph of the function). In this case we would move upwards. Now, count how many units we move up until we hit the graph of the function, that number of units will be the value of y.

In this case, we need to move 3 units upwards to hit the graph, then we have y = 3.

This means that the value of the function when x = -5 is y = 3, so we can write:

f(-5) = 3

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Answer:

0.234

Step-by-step explanation:

The total number of people in the age range from 30-49 is 7282 (3752 + 3530 the totals at the bottom of the column.  The total number of people out of that group that have completed high school is 1704 (787 + 917 the number of people in that column that have finished high school).

[tex]\frac{1704}{7282}[/tex] = .23400164789  Rounded to the nearest thousandths place is .234

The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Given: y = 14.4x + 17,

where: x = number of years after 2004

y = amount spent by businesses

To find: number of years where spending

$89 billion.

Finding:

We are given: y = 89, for which, we have to find the x, i.e., the number of years.

By basic algebra, substituting the value of y and solving for x:

89 = 14.4x + 17

72 = 14.4x

x = 5

Hence, The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

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Answer:

56.25

Step-by-step explanation:

9/4×25

=225/4

=56.25

Answer:

2r+24

Step-by-step explanation:

The number is R · R is added to 12 : R + 12. Double the result: 2 (R + 12). = 2 R + 24. So the answer is ultimatley 2r+24.

Answer: 2R+24

Step-by-step explanation:

(R+12)*2= ==> multiplication comes before addition, so in order to indicate that addition occurs before multiplication, there should be parentheses around

2(R+12)=

2R+2*12=2R+24

Answer:

1. A U C = {a, b, c, d, e}

2. B intersect A = {a, b, d}

3. B' = {c, f, g, h}

4. A - (B intersect C') = {a,c}

Step-by-step explanation:

U is a big set with all the letters a through f in it. Set A, B, and C are subsets of U. They have some of the letters in them. You could pick out the contents of set A, for example, from set U. Same with B and C. There's a little bit of overlap between A and B and C.

So for #1, the U shaped symbol means "Union" and you can remember that because of the U shape symbol. "Union" means throw everything in all together. A U C means all of A and all of C all together. But you don't have to write repeats, just list the letters once.

A is {a,b, c, d} and C is {a, e} so A U C is all of both of them:

{a, b, c, d, e}

The upsidedown Usymbol is "intersect" and that is only what the two sets have in common (whats the same) between the two sets.

BintersectA is what is the same in B{b,e,a,d} and A{a,b,c,d}. They both have a, b and d so that is the answer to BintersectA = {a,b,d}

The "apostrophe" looking mark means "Not this set". So B' means NotB. You list everything that is NOT in B. B is {b,e,a,d} so B' is NotB = {c,f,g,h}

The last one has what looks like a minus sign. Thats like normal "takeaway" along with parenthesis, use that normally like grouping/"do this first" and also intersect and Not. So basically all the work, all in one problem.

C = {a,e} so C' is NotC is {b,c,d,f,g,h}

The BintersectC' is what are the same beween B and NotC:

BintersectC' = {b,d}

A take away {b,d}

would be

{a,b,c,d} - {b,d}

= {a,c}

Answer:

6 is my final answer

Step-by-step explanation:

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The statement that correctly compares the number of songs on Georgia and Scarlet's playlists are is  17 < 36.

Georgia has 17 songs on her playlist while Scarlet has 36 songs on her playlist.

In the number line, the number 36 comes after the number 17. This means that 36 is greater than 17.

The statement that therefore correctly compares the number of songs in the playlist is:

17 < 36

In conclusion, the statement that correctly compares the songs in the two playlists is 17 < 36.

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By adding the number of cups needed for each cake, we conclude that you will need 25 cups of ingredients to make the 4 cakes.

We know that the recipe calls for:

That is for a single cake, so in a single cake you need a total of cups given by the sum of the above quantities, this gives:

(1 + 3/4) + (4 + 1/5) + 3/10 = (1 + 4) + (3/4 + 1/5 + 3/10)

= 5 + (3/4 + 2/10 + 3/10) = 5 + (3/4 + 5/10) = 5 + (3/4 + 1/2) = 5 + 5/4

= 5 + 4/4 + 1/4 = 6 + 1/4

Each cake needs (6 + 1/4) cups of ingredients, so 4 cakes will need:

4* (6 + 1/4) = 24 + 4/4 = 25

You will need 25 cups of ingredients to make the 4 cakes.

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