Find the solution to the system of equations represented by this matrix equation using an inverse matrix.

Answer:

D. Miko found an incorrect quotient and checked her work using multiplication incorrectly

Step-by-step explanation:

We are given the equation

[tex]\frac{5}{\frac{5}{3} }[/tex]

This can be rewritten as

[tex]5*\frac{3}{5} =3[/tex]

Miko's work is incorrect as she did not multiply by the reciprocal of denominator's fraction. Instead she just multiplied by that fractions.

Which is the most accurate description of Miko’s work?

After completing the fraction division 5 divided by 5/3, Miko used the multiplication shown to check her work. 3 x 5/3=3/1 x 5/3 = 15/3 or 5

Answer: D) Miko found an incorrect quotient and checked her work using multiplication incorrectly.

I hope this helps you! ☺

I think the answer is 144 minutes

Answer:

A. x= three over two and x = −4

Step-by-step explanation:

2x^2 + 5x = 12

I will use complete the square

Divide each side by 2

2x^2 /2 + 5/2 x = 12/2

x^2 +5/2 x =6

Take 5/2 , divide by 2 and then square it

5/2 ÷2 = 5/2   (5/4) ^2 = 25/16

Add this to both sides

x^2 + 5/2 x + 25/16 = 6 + 25/16

(x+5/4)^2 = 6 *16/16 + 25/16

(x+5/4)^2 = 96/16 +25/16

(x+5/4)^2 = 121/16

Take the square root of each side

sqrt((x+5/4)^2) = sqrt(121/16)

x+5/4 = ±11/4

Subtract 5/4 from each side

x+5/4-5/4 = ±11/4 -5/4

x =  ±11/4 -5/4

x = -11/4 - 5/4      and x = 11/4 - 5/4

x = -16/4 = -4      and x = 6/4 = 3/2

Answer:

the answer will be 125 people

Answer:

Some customers who rate their service as high quality return for additional services.

Step-by-step explanation:

Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services.

This shows than some customers are satisfied overall and return back for additional services.

Answer:

There are 23 $10 notes and 11 $5 notes

Step-by-step explanation:

x= Number of $10 notes  

y= Number of $5 notes  

1 x + 1 y = 34 .............1  

Total value  

10 x + 5 y = 285 .............2  

Eliminate y  

multiply (1)by -5  

Multiply (2) by 1  

-5 x -5 y = -170  

10 x + 5 y = 285  

Add the two equations  

5 x = 115  

/ 5  

x = 23  

plug value of x in (1)  

1 x + 1 y = 34  

23 + y = 34  

y = 34-23  

y = 11  

y = 11  

x= 23 Number of $10 notes  

y= 11 Number of $5 notes

There are 23 notes of $10.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.  

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A wallet contains 34 notes, all of which are either $5 or $10 notes.

let x be Number of $10 notes  

let y be Number of $5 notes  

x + y = 34 .............(1)  

and, 10 x + 5 y = 285 .............(2)

Solving equation (1) and (2), we get

-5 x -5 y = -170  

10 x + 5 y = 285  

_____________

5 x = 115  

x= 11/5/5

x = 23  

and, x+ y= 34

y= 34- 23

y= 11

Hence, there are 23 notes of $10.

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Answer:

180

Step-by-step explanation:

because it doesn't has to be exact you can do: 10 × 18 = 180

Answer:

180

Step-by-step explanation:

This is a good question to keep in mind. When you do use a calculator the answer to this estimate will tell you if your work on the calculator is correct.

round the cost of the pizza to 10

18 * 10 = 180 dollars. So you should get an answer that is under 180 dollars -- about 3 dollars short. (0.17 * 18 which is another guess).

Now pick up your calculator and do the math. It comes to 176.94

If you do any grocery shopping, this is a good skill to have.

Answer:

D is the correct answer

Step-by-step explanation:

Let the age of Holly is x years. Now from the statements of the question we will form the equations.

Sue was born three years before Holly.

Sue = Holly + 3 = x + 3------(1)

Jeremy = Sue + 5

From equation (1)

Jeremy = (x + 3) + 5 = x + 8------(2)

Now statement says the product of Sue's age and Jeremy's age is at most 150.

Sue × Jeremy ≤ 150

(x + 3)(x + 8) ≤ 150

x² + 11x + 24 ≤ 150

Therefore inequality x² + 11x + 24 ≤ 150 can be used to find the age of each sibling.

HAVE AN AMAZING DAY, GLAD TO HELP. ^.^

The matrix

[tex]A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}[/tex]

has eigenvalues [tex]\lambda[/tex] such that

[tex]\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0[/tex]

[tex](\cos\theta-\lambda)^2+\sin^2\theta=0[/tex]

[tex](\cos\theta-\lambda)^2=-\sin^2\theta[/tex]

[tex]\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}[/tex]

[tex]\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}[/tex]

[tex]\sin^2\theta\ge0[/tex] for all values of [tex]\theta[/tex], so we need to have [tex]\sin\theta=0[/tex] in order for [tex]\lambda[/tex] to be real-valued. This happens for

[tex]\sin\theta=0\implies\theta=n\pi[/tex]

where [tex]n[/tex] is any integer, and over the given interval we have [tex]\theta=0[/tex] and [tex]\theta=\pi[/tex].

The matrix a will always have real eigenvalues for any value of θ.

To find the values of the angle θ for which the matrix a has real eigenvalues, we need to determine when the determinant of the matrix is greater than or equal to 0. The matrix a can be written as:

a = cos(θ) -sin(θ)

sin(θ) cos(θ)

To calculate the determinant, we use the formula det(a) = cos(θ) * cos(θ) - (-sin(θ)) * sin(θ) = cos²(θ) + sin²(θ) = 1. Since the determinant is always 1, the matrix a will always have real eigenvalues for any value of θ.

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Answer:

Yes, because as x grows larger so does y, that means to be in a proportional relationship.

Step-by-step explanation:

Answer: For this to be a proportional relationship, the function would have to be y=4x. Since y=mx+b, this is not a proportional relationship because each time the value of x increases, the value for figure 0 is added on.

So, no. This is not proportional.

Hope this helps!

Answer:

0.81

Step-by-step explanation:

P(success) = 0.9

P(failure) = 1 - 0.9 = 0.1

Binomial probability:

P(X=n) = nCr (0.9)^n (0.1)^r

Here, n=2 and r=0:

P(X=2) = ₂C₀ (0.9)² (0.1)⁰

P(X=2) = 0.81

X is the number of free throws made  P(X = 2) is  0.81

Probability is a branch of mathematics that deals with the occurrence of a random event.

calculation:-

⇒P( sucess event ) = 0.9

⇒P(failure event) = 1 - 0.9 = 0.1

Binomial probability:

    P(X=n) = nCr (0.9)ⁿ (0.1)ˣ

      let, n=2 and r=0:

          P(X=2) = ₂C₀ (0.9)² (0.1)⁰

                P(X=2) = 0.81

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The probability of not getting a sum of 4 when rolling two six-sided dice is 33/36 or 92%. The probability of getting a sum greater than 5 when rolling two six-sided dice is 13/18 or approximately 72%.

The subject area for this question is in Mathematics, specifically probability. The question asks to determine the probability of a sum not being 4, and of a sum being greater than 5 when two six-sided dice are rolled.

(a) The possibilities of getting a sum of 4 are (1,3), (2,2), and (3,1). That's 3 possibilities out of a total of 36, therefore the probability of not getting a sum of 4 is 1 - (3/36) = 33/36 (in simplified form) and as a percentage that's approximately 92%.

(b) The possibilities of getting a sum greater than 5 are (2,4),(3,3),(3,4),(4,2),(4,3),(4,4),(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5), and (6,6). That's 26 possibilities out of 36, therefore the probability of getting a sum greater than 5 is 26/36 or 13/18 in simplest form, and as a percentage that's approximately 72%.

In this way, understanding of probability and how to calculate it properly can help in accurately determining outcomes in different scenarios.

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The probability of the sum not being 4 is (36 - 3) / 36, and the probability of the sum being greater than 5 is 21 / 36.

When two six-sided dice are rolled, there are 36 possible outcomes. To find the probability that the sum is not 4, we need to calculate the number of outcomes where the sum is not 4 and divide it by the total number of outcomes.

There are 3 outcomes with a sum of 4, so the probability is (36 - 3) / 36.

To find the probability that the sum is greater than 5, we need to calculate the number of outcomes where the sum is greater than 5 and divide it by the total number of outcomes.

There are 21 outcomes with a sum greater than 5, so the probability is 21 / 36.

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The answer is gonna be (B)

Answer:

the mean absolute deviation of the data set is 2.

Step-by-step explanation:

To calculate the mean absolute deviation of a data set, we need to follow the following steps:

Step 1: Calculate the mean.

Step 2: Calculate how far away each data point is from the mean (always keeping a possitive distance).

Step 3: Calculate the mean of the deviations.

Step 1: The mean of the data set is:

Mean = (12 + 10 + 10 + 8 + 6+ 7 + 7 + 12)/8 = 72/8 = 9

Step 2:

{12 -9, 10-9, 10-9, 9-8, 9-6, 9-7, 9-7, 12-9} = {3, 1, 1, 1, 3, 2, 2, 3}

Step 3: (3 + 1 + 1 + 1 + 3 + 2 + 2 + 3)/8 = 2

In conclusion, the mean absolute deviation of the data set is 2. Which corresponds to the option B.

Answer:

750 yards

Step-by-step explanation:

I entered the area of the field into a Pythagorean Theorem Calculator and it concluded that the diagonal length of the field would be approximately 750 yard.

Answer:

300 yd saved

Step-by-step explanation:

The length of the diagonal of the field is found using the Pythagorean Theorem and is

d = √( 450 yd)² + ( 600 yd)² ) = √562500 yd² = 750 yd is the diagonal distance.  If, on the other hand, the farmer walks the length and width of the perimeter of the field, that would be 450 yd + 600 yd, or 1050 yd.

The farmer could spare himself 1050 - 750, or 300 yd, of walking if he crosses the field along a diagonal.

the answer will be B

Answer:

D.) 10.4 yd

Step-by-step explanation:

In the given figure the alternate angles are equal and hence a right angle triangle with one of its angle as 30 degree is formed .

For angle 30 degrees adjacent side is 18 yard and opposite side is x.

Tan of an angle is equal to [tex]\frac{opposite}{adjacent}[/tex]

[tex]Tan 30=\frac{x}{18}[/tex]

x=Tan 30 (18)

x= 10.39

x= 10.4 yard (rounded  to tenth place)

Option D is the right answer.

Answer:

B

Step-by-step explanation:

x<5

When we multiply by negative number sign of inequality should be  changed also.

x*(-1) > 5*(-1)

-x>-5

For this case we have the following expression:

[tex]x <5[/tex]

By definition we have to:

Let [tex]c <0[/tex]. If [tex]a <b,[/tex] then [tex]ac> bc[/tex]

That is to say:

If we multilate on both sides of the inequality by -1, the sign automatically changes direction.

[tex](-1) (x) <(- 1) (5)\\-x> -5[/tex]

ANswer:

Option B

Answer: 0.88

Step-by-step explanation:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(x = 4) + P(X = 5) + P(X = 6)

             =    0.21    +    0.35   +     0.21   +   0.06   +   0.05

             = 0.88

Answer:

A, C, F

Step-by-step explanation:

Definition: The circumcenter is  the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. If point H is the circumcenter of the triangle DEF, then the circumcircle passes through its vertices D, E and F (option A is true).

Option B is false, the circumcircle doesn't pass through the points L, M and N. This option is true for inscribed circle, not for circumcircle.

Option C is true, because HD and HE are the radii of the circumcircle.

Option D is false. This option is true for inscribed circle, not for circumcircle.

Option E is false. This option is true for inscribed circle, not for circumcircle.

Option F is true, because both these angles are right angles.

Answer:

Step-by-step explanation:a+b

ANSWER

B. y=8x +1200

EXPLANATION

If the family's well pumps on average 8 gallons of water per minute, then the unit rate of change is 8.

This implies that, the slope of the linear equation that models this situation is

[tex]m = 8[/tex]

It was also given that, the well's tank had 1200 gallons of water in the morning.

This implies that the y-intercept of the straight line is

[tex]b = 1200[/tex]

The equation is given by:

[tex]y = mx + b[/tex]

We substitute the values to obtain:

[tex]y = 8x + 1200[/tex]

The amount of water in the tank, y after it has been pumping for x minutes is

[tex]y = 8x + 1200[/tex]

haya, brooke, curra is the order, i believe

To line up alphabetically by name, Brooke comes first followed by Curra, and Haya is last.

The question requires organizing the names of three girls in alphabetical order without speaking and within a time limit. Given the names are Haya, Curra, and Brooke, we can determine the alphabetical order by looking at the first letter of each name.

Brooke

Curra

Haya

To line up alphabetically by name, Brooke would be first because 'B' comes before 'C' and 'H' in the alphabet. Curra would be second since 'C' comes after 'B' but before 'H'. Finally, Haya would be last because 'H' comes after both 'B' and 'C'.

Answer:

(77, 77)

Step-by-step explanation:

Carry out the indicated multiplication:

3(-0.8, 6.3) → (-2.4, 18.9)

Next, combine like terms:

(79.4, 58.1) + (-2.4, 18.9).  In other words, combine the x terms 79.4 and -2.4 separately and then the y terms 58.1 and 18.9 separately:

(79.4, 58.1) + (-2.4, 18.9)  → (77, 77)

The resultant of the following linear combination is:

                      (77,77)

We are asked to find the linear combination of the expression:

             (79.4, 58.1) + 3(-0.8, 6.3)

We multiply each of the term in the second coordinate by 3 .

i.e. this could also be given by:

(79.4, 58.1) + (3×-0.8, 3×6.3)

=  (79.4, 58.1) + (-2.4, 18.9)

Now as there is a addition sign in between the two coordinates i.e. each of the first and the second coordinate will get added

i.e.

= (79.4+(-2.4),58.1+18.9)

= (79.4-2.4,58.1+18.9)

= (77,77)

i.e.

 (79.4, 58.1) + 3(-0.8, 6.3)=(77,77)

Answer:

18 mm

Step-by-step explanation:

To find the side length of the scale drawing, multiply the length of the side by the scale factor

450 * 1/25 =18

The side length in the drawing is 18 mm

Answer:

The correct inequality for the given graph is x + 3y < -3 ⇒ 1st answer

Step-by-step explanation:

* Lets study the graph

- The angle between the positive part of x-axis and the line is obtuse,

 that means the slope of the line is negative value

- The shaded part is under the line, that means the solutions of the

 inequality are under the line , so the sign of the inequality is <

- The y-intercept is < -1 ⇒ (the value of y when x = 0)

* Now lets check the answers to find the correct answer

- At first we will choose the answer with sign <

∴ The answers are x + 3y < -3 OR x - 3y < -1

- At second lets check the y-intercept (put x = 0)

- Substitute x by 0 in the two answer to choose the right one

∵ x = 0

∴ 0 + 3y < -3 ⇒ ÷ 3 both sides

∴ y < -1

* OR

∵ x = 0

∴ 0 - 3y < -1 ⇒ ÷ -3 both sides

∴ y > 1/3 ⇒ because we divide the inequality by negative number

  we must reverse the sign of inequality

∵ the y-intercept is < -1

∴The first equation is right

* To be sure check the slope of each line

∵ y < mx + c, where m is the slope of the line

- Put each inequality in this form

∵ x + 3y < -3 ⇒ subtract x from both sides

∴ 3y < -3 - x ⇒ ÷ 3

∴ y < -1 - x/3

∴ m = -1/3 ⇒ the slope is negative

* OR

∵ x - 3y < -1 ⇒ subtract x from both sides

∴ -3y < -1 - x ⇒ ÷ -3

∴ y > 1/3 + x/3

∴ m = 1/3 ⇒ the slope is positive

∵ The slope of the line is negative

∴ The correct inequality for the given graph is x + 3y < -3

Answer:

28.6%; 313,099

Step-by-step explanation:

Lawyers are either male or female, so if 71.4% are male, then 100% minus that are female.

100% - 71.4% = 28.6%

28.6% of 1,094,751 is:

0.286 × 1094751 = 313098.786

Rounded to the nearest whole number, there are 313,099 female lawyers.

Answer:

70

Step-by-step explanation:

The equation derived from the problem is 7x - 35 = 3x + 53. Solving this equation by combining like terms and isolating the variable x gives us the certain number, which is 22.

We need to find the certain number mentioned in the problem. According to the problem, '35 less than seven times a certain number is fifty-three more than 3 times that number.' We can translate this into an equation:

7x - 35 = 3x + 53

Where 'x' represents the certain number. Now, let's solve the equation step by step:

First, subtract 3x from both sides to move the variable terms to one side of the equation. 7x - 3x - 35 = 3x - 3x + 53 4x - 35 = 53

Next, add 35 to both sides to isolate the variable term. 4x - 35 + 35 = 53 + 35 4x = 88

Finally, divide by 4 to solve for x. 4x / 4 = 88 / 4 x = 22

So, the certain number we are looking for is 22.

Answer:

2pi

Step-by-step explanation:

Answer: an endless cylinder with radius 4 mm and centerline

I believe the answer is 70 degrees. If you divide 360 by 9 (amount of degrees divided by amount of sides) you get 40 and we know that the three angles in a triangle add up to 180 degrees. So if we subtract the 40 we got for the top angle we get 140 degrees. We know the other two angles in the triangle are congruent so we can divide 140 by 2 to get the degree of both angles which is 70. Hope this helps!

Answer:

2

Step-by-step explanation:

The first equation is that of a an ellipse. The second equation is that of a line.

Attached is the graphs of both of these equations.

If you think about it, there can only be 2 possible ways of solutions (intersection points) of an ellipse and a line.

1. The line will not intersect the ellipse at all, so no solution

2. The line will intersect the ellipse at 2 points maximum

So, we can clearly see from the reasoning that the maximum number of possible solutions would be 2. The graph attached confirms this as well.

Answer:

The maximum number of solutions that the system can have are 2

Step-by-step explanation:

We have a system of equations composed of an ellipse of equation [tex]x ^ 2 + 4y ^ 2 = 64[/tex] and a line of equation [tex]x + y = 5.[/tex]

The solution to the system of equations gives information about when the values of both equations coincide. In other words, the solutions of the system of equations give information about the number of times that the line [tex]x + y = 5[/tex]. touch or intercept the graph of the ellipse [tex]x ^ 2 + 4y ^ 2 = 64[/tex]

Graphically you can verify that a line can only touch an ellipse once or can intercept an ellipse a maximum of two times, or never touch it

Therefore, the maximum number of solutions that the system can have are 2.