IXL question
I don't understand this one and I need more than 0 points :/

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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I think the answer is 144 minutes

Answer:

the answer is A

Step-by-step explanation:

the formula is 2π rh +2πr^2

you put the values in

2π (6*15) +2π(6)^2

then you solve

180π+ 72π= 252π

For this case we have that by definition, the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

A: It's the radio

h: It is the height of the cylinder

We have to:

[tex]r = 6 \ units\\h = 15 \ units[/tex]

Substituting:

[tex]SA = 2 \pi * 6 * 15 + 2 \pi * (6) ^ 2\\SA = 2 \pi * 6 * 15 + 2 \pi * (6) ^ 2\\SA = 180 \pi + 72 \pi\\SA = 252 \pi \ units ^ 2[/tex]

Answer:

Option A

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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Final answer:

To calculate the original loan amount for Scott, who paid $750 in interest at a 3% rate, we use the formula for simple interest and determine that the original loan amount was $25,000.

Explanation:

If Scott pays $750 in interest at a rate of 3%, to find out the original amount of the loan, we can use the formula I = PRT, where I stands for interest, P is the principal amount (the original loan amount), R is the rate of interest, and T is the time in years. Since Scott already knows the interest and the rate, we can rearrange this formula to solve for P:  P = I / (RT).

In this case, we assume the time T to be 1 year, since no specific time was given. The calculation would be:

P = $750 / (0.03 * 1)

P = $750 / 0.03

P = $25,000

So, the original loan amount Scott must have taken out is $25,000.

Answer:

the answer would be like finding the point and then doing the math

after the math u will find you answer on the am going to say either C or D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If g(x) is a transformation of f(x), then we can consider function f(x) as parent function.

So, to get the graph of the function g(x), we have to translate the graph of the function f(x) 8 units up.

This translation will give us the function

[tex]g(x)=f(x)+9\\ \\g(x)=\dfrac{1}{4}\cdot 3^x-6+8\\ \\g(x)=\dfrac{1}{4}\cdot 3^x+2[/tex]

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)

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:

I believe it would be 42.25?  or 42 and 1/4

Step-by-step explanation:

The value of [p] at equilibrium is equivalent to 43.12.

At equilibrium, the demand is equal to supply. Mathematically, we can write -

D{x} = S(x)

Given is are the demand and supply equations.

We have the demand and supply equations as -

D{p} = (-5/8)p + 35

S{p} = (6/5)p - 44

Now, at equilibrium, we can write -

D{p} = S{p}

(-5/8)p + 35 = (6/5)p - 44

(6/5)p + (5/8)p = 35 + 44

p{(48 + 25)/40} = 79

p(73/40) = 79

p = (79 x 40)/73

p = 43.12

Therefore, the value of [p] at equilibrium is equivalent to 43.12.

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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. ^.^

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:

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.

Answer: an endless cylinder with radius 4 mm and centerline

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:

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:

[tex]f(x)=(x-2)^{\frac{1}{3}}-2[/tex] ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = x^1/3

- f(x) shifted 2 units to the right

∴ f(x) = (x - 2)^1/3

- f(x) shifted 2 units down

∴ f(x) = (x - 2)^1/3 - 2

* [tex]f(x)=(x - 2)^{\frac{1}{3}}-2[/tex]

Answer:

Let's suppose the distance between gold town and silver town is 9 kilometers.

The first trip takes 9 km / 6 km / hour = 1.5 hours

The return trip takes 9 / 9 km / hour = 1 hour

TOTAL TRIP = 18 kilometers in 2.5 hours

= 18 / 2.5 = 7.2 hours

Answer is c

Step-by-step explanation:

Divide 50 by 2 so 25 then divide that by 2 so 12.5 =x

The equation 2x² = 50 has two solutions, x = 5 and x = -5.

The equation 2x² = 50 can be solved algebraically by dividing both sides by 2 and then taking the square root of both sides. This gives us two solutions, x = 5 and x = -5.

Another way to solve this equation is to factor the left side. We can see that 2x² = 2(x²). We can also factor x² as (x)(x). This gives us the following equation:

2(x)(x) = 50

Dividing both sides by 2, we get:

(x)(x) = 25

Taking the square root of both sides, we get:

x = ±5

Therefore, the two solutions to the equation 2x² = 50 are x = 5 and x = -5.

We can check our answer by substituting x = 5 and x = -5 back into the original equation.

2(5)² = 50

2(25) = 50

50 = 50

This is true.

2(-5)² = 50

2(25) = 50

50 = 50

This is also true.

Therefore, our solutions are correct.

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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:

the answer will be 125 people

Answer: [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]

Step-by-step explanation:

Let the length of Nina Pinta be ''ln'

According to question, we have given that

the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta.

and 10 ft shorter than that of Nina Pinta is expressed as [tex]ln-10[/tex]

So, the length of Santa Monica be 'ln'-10'

Restriction on ln is that ln>10.

As Length of Santa Monica cannot be negative or equal to zero.

so, [tex]ln>10[/tex]

Hence, [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]

The speed of the Santa Monica, given the hull length of Nina Pinta as 'ln' and that Santa Monica is 10 ft lesser in hull length, can be represented by 1.34 * sqrt(ln - 10). The restriction on this is that ln must be greater than 10 ft.

The hull length of the Santa Monica is defined as ln - 10, where ln is the hull length of the Nina Pinta. The hull speed of the Santa Monica, according to the hull speed formula, is calculated as 1.34 times the square root of the hull length. Therefore, the hull speed of the Santa Monica in terms of the hull length of the Nina Pinta, ln, can be represented by the expression 1.34 * sqrt(ln - 10) where sqrt stands for 'square root'.

The restriction on the domain is that ln must be greater than 10 as the hull length cannot be negative.

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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:

37.8

Step-by-step explanation:

Length = radius * Θ

L=7*5.4

L=37.8

If wrong don't report, just notify me so I can edit.

Have a great day!

The length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

The arc subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm.

As we know, the relationship between radius of the circle, central angle, and arc length is:

s = rθ

r = 7 cm

θ = 5.4 radians.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

s = 7×5.4

s = 37.8 cm

Thus, the length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

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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! ☺

Answer:

10,995.6 ft^3.

2300.3 gallons.

(both to the nearest tenth).

Step-by-step explanation:

Area of the surface of the river =  area of the  outer circle - area of the inner circle.

Radius of the outer circle  = 30 *3 = 90 feet.

So the surface area of the river = π(90)^2 - π(85)^2

= 875π ft^2

Also the volume of the river = surface area * depth = 875π*4 = 3500π ft^3

= 10,995.6 ft^3.

Number of gallons of water it will hold = 10,995.6 /  4.78

= 2300.3 gallons.

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:

2pi

Step-by-step explanation:

The answer is gonna be (B)