Lesson Check (4.NBT.B.6
1. To divide 572 = 4, Stanley estimated to place
the first digit of the whole-number quotient.
In which place is the first digit of the whole-
number quotient?

Answer:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

Step-by-step explanation:

You would need the intial fee in dollars/cents

Expression:

c=initial fee

x=amount of miles

[tex]1.80x+c=12[/tex]

Let y = cos⁻¹(x), so that cos(y) = x.

For some angle y between 0 and π, cos(y) takes on some value between -1 and 1.

For the y in this range, we have cos(y) = -1/2 exactly when y = 2π/3.

Then

tan(cos⁻¹(-1/2)) = tan(2π/3) = sin(2π/3)/cos(2π/3) = (√3/2)/(-1/2) = -√3

2x = x - 4

2x - x = - 4

x = - 4

________

Hope it helps ⚜

Answer:

x=-4

Step-by-step explanation:

2x=x-4

2x-x=-4

x=-4

Proof

2*(-4)=-4-4

-8=-8

Answer: First do 145 - 25, which is 120. Then do 120 ÷ 15 = 8. Therefore the slope intercept is y ÷ 15 = x. Their voyage will last 8 days.

Explanation: Brainliest please

Answer:

21417500

Step-by-step explanation:

Calculate 50% of the given amount then 13% of result

50% of 329500000

= [tex]\frac{50}{100}[/tex] × 329500000

= 0.5 × 329500000

= 164750000

Then

13% of 164750000

= [tex]\frac{13}{100}[/tex] × 164750000

= 0.13 × 164750000

= 21417500

If the two of you can wash 1 car in 6 minutes:

It will take you 10 minutes to wash the car alone

take your friend 15 minutes to wash the car alone

Let the duration you can work be represented by y

Let the duration your friend can work be represented by x

You can wash a car 1.5 times as fast as your friend

That is, y = 1.5x

Working together, the two of you can wash 1 car in 6 minutes

This can be represented by the equation

[tex]\frac{1}{x}+\frac{1}{y} = \frac{1}{6}[/tex]

Substitute x = 1.5y into the equation above

[tex]\frac{1}{1.5y}+\frac{1}{y} = \frac{1}{6}\\\\\frac{1+1.5}{1.5y} = \frac{1}{6}\\\\\frac{2.5}{1.5y} = \frac{1}{6}\\\\1.5y=2.5(6)\\\\1.5y=15\\\\y=\frac{15}{1.5} \\\\y=10[/tex]

It will take you 10 minutes to wash the car alone

Substitute y = 10 into x = 1.5y

x  =  1.5(10)

x  =  15 minutes

It will take your friend 15 minutes to wash the car alone

Learn more here: https://brainly.com/question/25547756

Answer:

12 cups

Step-by-step explanation:

There are 48 hours in two days.

48 · 2 = 96 ( 2 being fluid ounces per hour )

96 ÷ 8 = 12 ( 8 being fl oz in each cup )

I hope that this helped!!!

Answer:

I have attached the answer below.

Step-by-step explanation:

The diagram which has red ink cannot take a perfect feeding path.

Hopefully this helps.

Answer:

40

Step-by-step explanation:

Answer:

40.20 luv:)

Step-by-step explanation:

Answer: should be 86°, not sure.

Step-by-step explanation:

Answer: What do you mean? if you till me i can help you

Step-by-step explanation:

Answer:

x = 38/6

Step-by-step explanation:

x/5 - 2/3 = 3/2

3x - 2x5/3x2 = 3/2

3x-10/6 = 3/2

2(3x-10) = 3x6

6x-20 = 18

6x = 18+20

6x =38

x =38/6 or x = 6.33

Answer:

Step-by-step explanation:

This is a geometric series.

First term = - 2

Ratio = second term ÷ first term = 8 ÷ (-2) = -4

Next three terms are:

-32 *(-4) = 128

128*(-4) = - 512

-512*(-4) = 2048

Answer:

The next 3 terms would be 128, -512, 2048

Step-by-step explanation:

Since we are dealing with a Geometric Sequence we use this formula [tex]a_{n}=a_{1} *r^{n-1}[/tex]

Since the first term([tex]a_{1}[/tex]) is -2 and for us to find R we have to divide 8 by -2 = -4

So we would rewrite the equations to find the next three terms as

[tex]a_{4}=-2*-4^{4-1}=-2*-4^3=128[/tex]

[tex]a_{5}=-2*-4^{5-1}=-2*-4^4=-512[/tex]

[tex]a_{6}=-2*-4^{6-1}=-2*-4^5=2048[/tex]

Answer:

y=1/2x

Step-by-step explanation:

I first did point-slope form which is

y+1=1/2(x-2)

Then, I converted it into slope-intercept form which is

y=1/2x

The expected gain or loss is an illustration of mean and expected values.

The expected total gain is 83 points

The given parameters are:

The probability of rolling a 6 in a fair die is 1/6.

The probability of not rolling a 6 in a fair die is 5/6.

So, the expected gain in each game is:

[tex]\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}[/tex]

[tex]\mathbf{E(x) = \frac{20}6 - \frac{15}6}[/tex]

Take LCM

[tex]\mathbf{E(x) = \frac{5}6}[/tex]

[tex]\mathbf{E(x) = 0.83}[/tex]

The number of games is 100.

So, the expected gain is:

[tex]\mathbf{Gain = 100 \times 0.83}[/tex]

[tex]\mathbf{Gain = 83}[/tex]

Hence, the expected total gain is 83 points

Read more about expected value at:

https://brainly.com/question/13499496

It looks like given matrices are supposed to be

[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]

You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:

• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues

• det(A) = determinant of A = product of eigenvalues

(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since

[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]

[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]

and

λ₁ + λ₂ = 6   ⇒   λ₁ λ₂ = λ₁ (6 - λ₁) = 5

⇒   6 λ₁ - λ₁² = 5

⇒   λ₁² - 6 λ₁ + 5 = 0

⇒   (λ₁ - 5) (λ₁ - 1) = 0

⇒   λ₁ = 5 or λ₁ = 1

To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.

• For λ = 1, we have

[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]

With v = (v₁, v₂)ᵀ, this equation tells us that

2 v₁ + 2 v₂ = 0

so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.

• For λ = 5, we would end up with

[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]

and this tells us

-2 v₁ + 2 v₂ = 0

and it follows that v = (1, 1)ᵀ.

Then the decomposition of A into PDP⁻¹ is obtained with

[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]

where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.

(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]

(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:

[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]

Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:

det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0

and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.

• For λ = 1,

[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]

tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]

tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.

• For λ = 3,

[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]

tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.

Then we have A = PDP⁻¹ for

[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]

(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,

• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃   ⇒   λ₂ + λ₃ = 7

• det(A) = 20 = 2 λ₂ λ₃   ⇒   λ₂ λ₃ = 10

and we find λ₂ = 2 and λ₃ = 5.

I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]

tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.

• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]

This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.

Then A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]

Answer:

d

Step-by-step explanation:

Answer:

0.83

Step-by-step explanation:

volume = length*height*width

1500=L*30*60

1500=1800L

1500/1800 = 0.83

length = 0.83

https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.407869.html

Answer:

Quadratic

Step-by-step explanation:

Formula: ax^2+bx+c

Answer:

if there are 2 negatives by each other it would become a postive so -5+8

Step-by-step explanation:

Answer:

-5+8

Step-by-step explanation:

minus a negative is equivalent to plus a positive

Answer:cold weather pose, there are armies that have and can conduct large-scale, ... to one inch (2.5 centimeters) per hour accumulates.

Step-by-step explanation:

Answer:

1.5 × ? = 9

9÷1.5 = 6

so the answer would be 6 hours

Answer:

decrease

Step-by-step explanation:

the percent change measures FROM the first value. A change from 50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50). A change from 75 to 50 is a change of -33.3% (25 is still the difference between the two. 25 is 33.3% of 75

Transformation involves changing the form of the function

The transformation that is not performed is (a) vertical shift

The function is given as:

[tex]\mathbf{y = cot(x)}[/tex]

From the complete question, the transformed function is:

[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]

On y = cot(x); start by translating the function 2 units left.

The rule of this transformation is:

[tex]\mathbf{(x,y) \to (x +2,y)}[/tex]

So, we have:

[tex]\mathbf{y = cot(x + 2)}[/tex]

Next, stretch the function horizontally by a factor of 1/5

The rule of this transformation is:

[tex]\mathbf{(x,y) \to (\frac 15x,y)}[/tex]

So, we have:

[tex]\mathbf{y=cot[\frac 15(x+2)]}[/tex]

Lastly, stretch the function vertically by a factor of 3

The rule of this transformation is:

[tex]\mathbf{(x,y) \to (x,3y)}[/tex]

So, we have:

[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]

From the above transformations, we have:

Hence, the transformation that is not performed is (a) vertical shift

Read more about transformations at:

https://brainly.com/question/13801312

Answer:

vertical shift

Step-by-step explanation:

edge

Answer:

a.

Step-by-step explanation:

Answer:

A, B, E

Step-by-step explanation:

I just put the number of fiction books over the number of nonfiction books. Then I plugged it into a calculator and if the answer was the same as 15/22, then it was right!

2385/3498=15/22

3945/5786=15/22

2340/3588≠15/22

2480/3410≠15/22

4650/6820≠15/22

2310/3696=15/22