A dog won a race at the local fair by running 7 1/4 miles in exactly 2 hours. At this constant rate, how long does it take the same dog to run the 26 1/10 mile state fair race? Use ratio reasoning to solve. Use the unit rate found below.

In each solution, n is an arbitrary integer.

1. Nothing fancy, just take the inverse tangent.

tan(x) = -5

x = arctan(-5) + nπ

x = -arctan(5) + nπ

2. Recall the identity cos(2x) = 2 cos²(x) - 1, then factorize:

cos(2x) - 3 cos(x) + 2 = 0

(2 cos²(x) - 1) - 3 cos(x) + 2 = 0

2 cos²(x) - 3 cos(x) + 1 = 0

(2 cos(x) - 1) (cos(x) - 1) = 0

2 cos(x) - 1 = 0   or   cos(x) - 1 = 0

cos(x) = 1/2   or   cos(x) = 1

[x = arccos(1/2) + 2nπ   or   x = -arccos(1/2) + 2nπ]

…   or   x = arccos(1) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ   or   x = 2nπ

3. By definition, csc(x) = 1/sin(x) :

csc(2x) + √2 = 0

csc(2x) = -√2

1/sin(2x) = -√2

sin(2x) = -1/√2

2x = arcsin(-1/√2) + 2nπ   or   2x = π - arcsin(-1/√2) + 2nπ

2x = -π/4 + 2nπ   or   2x = 5π/4 + 2nπ

x = -π/8 + nπ   or   x = 5π/8 + nπ

4. More factorization:

2 sin²(x) - sin(x) = 0

sin(x) (2 sin(x) - 1) = 0

sin(x) = 0   or   2 sin(x) - 1 = 0

sin(x) = 0   or   sin(x) = 1/2

x = arcsin(0) + 2nπ

…   or   [x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ]

x = 2nπ   or   x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

5. Yet more factorization. Also recall that |cos(x)| ≤ 1 for all x.

4 cos²(x) - 8 cos(x) + 3 = 0

(2 cos(x) - 3) (2 cos(x) - 1) = 0

2 cos(x) - 3 = 0   or   2 cos(x) - 1 = 0

cos(x) = 3/2   or   cos(x) = 1/2

The first case gives no solution since 3/2 > 1.

x = arccos(1/2) + 2nπ   or   x = -arccos(1/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

6. Recall the identity sin(a - b) = sin(a) cos(b) - cos(a) sin(b).

sin(2x) cos(x) - cos(2x) sin(x) = -√3/2

sin(2x - x) = -√3/2

sin(x) = -√3/2

x = arcsin(-√3/2) + 2nπ   or   x = π - arcsin(-√3/2) + 2nπ

x = -π/3 + 2nπ   or   x = 4π/3 + 2nπ

Answer:

The total number of different suits consisting of a jacket, shirt, tie, and pants are possible is 576 ways and this can be determined by using the given data.

Given :

A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants.

The following steps can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible:

Step 1 - The arithmetic operations can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible.

Step 2 - According to the given data, the total number of shirts is 6, ties is 8, suit jackets is 3, and pants is 4.

Step 3 - So, the total number of different suits consisting of a jacket, shirt, tie, and pants are possible is:

= 576 ways

Step-by-step explanation:

Answer:

I think it is 100

Answer:

Step-by-step explanation:

The answer is 50 ounces

Because 30% silver is right in between 20% silver and 40% silver, it would have to be the same amount to be 30%

Answer:

Your Estimated Equations and Answers: 6+9= 15 ; 16+12 = 28

Step-by-step explanation:

Estimating can be equivalent to rounding. This is because you're trying to find an approximate number or sum.

6.48 + 9.34 is your first question.

You should round it to the nearest whole number.

6.48 ~ 6 and 9.34 ~ 9

*Rounding rules applied here*

(~ this sign is the approximate or rounded to symbol)

Now, do 6+9 =

6+9= 15

______________________________________________

15.71 + 12.2 is your next question.

Same as last, round to the nearest whole number.

15.71 ~ 16 and 12.2 ~ 12

Now, do 16+12

16+12 = 28

Shaded area = area of square - area of a circle.

[tex] \\ \\ [/tex]

For this we have to find area of both square and circle which is visible in the picture.

[tex] \\ [/tex]

Part one :

In this part we'll find area of circle.

Given :

To find :

Solution:

We know :

[tex] \boxed{ \rm Area \: of \: circle =\pi {r}^{2} }[/tex]

Steps :

[tex] \dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2} [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\ [/tex]

[tex] \\ [/tex]

Part 2

As it's visible diameter of circle = side of square.

So we have to find diameter of circle.

We know :-

[tex] \boxed{ \rm Diameter \: of \: circle =2 \: radius}[/tex]

[tex] \\ [/tex]

Steps:-

[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Diameter \: of \: circle =18 \: ft[/tex]

We have :

To find:

Solution:

We know :

[tex] \boxed{ \rm Area \: of \: square= {side}^{2} }[/tex]

Steps :

[tex] \dashrightarrow\sf Area \: of \: square= {side}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: square= {18}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: square= {18} \times 18[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2} [/tex]

Part three:

Remember the first line of answer ? :)

So let's insert here:-

[tex] \boxed{ \text{Shaded area = area of square - area of a circle}}[/tex]

Steps :-

[tex] \dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\textsf{Shaded area = 324 - 254.57} \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\ [/tex]

Answer:

The point [tex](3,8)[/tex] will transform into [tex](7,9)[/tex]

Step-by-step explanation:

When you move the unit right, you make the number larger. right and left deal with the X value. you add 4 to 3, and you get 7. Now you move 1 point up, which is just 8+1, which is 9. You get your answer, [tex](7,9)[/tex].

Hope This Helps! :)

Answer:

Number of 7th grade = 360 - X

Step-by-step explanation:

As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from &th grade. As we know: Total number of students on the A honor roll = 360 We are asked to calculate, number of students from 7th grade on the A honor roll. So, let's assume that "X" represents the all the students who are on the A honor roll except 7th grade. Mathematical Expression: Number of 7th Graders = Total number of students on the A honor roll - X Number of 7th Graders = 360 - X So, if you know the value of X, you can easily calculate the number of students which are from 7th grade on the A honor roll.

Answer:

There are 126 8th grade A honor roll students.

Step-by-step explanation:

Since there are 14 8th grade A honor roll students out of 40 A honor roll students. That means that the fraction is 14/40. After that we do 14/40x360 which results in 126.

Answer A: 45 5/16

B: The present of the area as 83%

Step-by-step explanation:

(a)

35= 3+3+3.2x+3.2x+3.2x+3.2x

35= 6 + 12.8

29/12.8 +12.8x/12.8

X=2.265625 = 2/12/64

1x = 2 17/64 * 4 + 9 1/16

P = 45 5/16

(b)

The present of the area as 83%

35 – the bases or 6 = 29

29/35 + 0.82857142857

0.82857142857 * 100 = 82.8571428571

Rounded to the nearest whole number is 83%

Answer:

[tex] {x} = - 4 \pm \: 2\sqrt{5} [/tex]

Step-by-step explanation:

[tex] {(x + 4)}^{2} - 4 = 16 \\ \\ \implies \: {(x + 4)}^{2} = 16 + 4 \\ \\ \implies \: {(x + 4)}^{2} = 20 \\ \\ \implies \: {(x + 4)} = \pm \: \sqrt{20} \\ \\ \implies \: {x + 4} = \pm \: 2\sqrt{5} \\ \\ \implies \: {x} = - 4 \pm \: 2\sqrt{5} [/tex]

Answer:

Step-by-step explanation:

a whole number can be ANY counting number

10 to the 5th power =  × 10 × 10 × 10 × 10 × 10

when you multiply by any positive power of ten, you are making it really big

23 × 10 × 10 × 10 × 10 × 10 = 2,300,000

30 × 10 × 10 × 10 × 10 × 10 = 3,000,000

100 × 10 × 10 × 10 × 10 × 10 = 10,000,000

the pattern is the whole number followed by 5 zeros that show 5 place values

Answer:

Step-by-step explanation:

This is like volume!

Equation:

Solve:

Simplify:

Answer is 216 sq. ft³.

Answer:

Step-by-step explanation:

Given

We need to subtract the 2nd polynomial from the 1st.

Answer:

  $2418.07

Step-by-step explanation:

Problems involving the time-value of money are conveniently solved using a TVM app on a suitable calculator or spreadsheet. The result of doing that is shown in the attachment.

__

If you would like to compute the value of Emily's account by hand, the annuity formula is the one you want.

  A = Pn((1 +r/n)^(nt) -1)/r . . . . where r is the annual interest rate, n is the number of times per year it is compounded (12), t is the number of years (1/2), and P is the periodic payment into the acccount (400).

Using the given values in the formula, we have ...

  A = 400(12)((1 +0.036/12)^(12/2) -1)/0.036 = 4800×(1.003^6 -1)/0.036

  A ≈ 2418.07

At the end of 6 months, Emily will have saved $2418.07.

Answer:

About 154 Square

Explanation:

To find an area of a circle you multiply pi by the radius squared so 7² = 49 and 49 x 3.14 = 153.86 which is the closest to 154.

Answer:

A) 64

Step-by-step explanation:

16/2=8

8^2= 64

x^2 +16x +64= 69

(x +8)^2= 69

Answer:

y=(x−3)2−2

Step-by-step explanation:

The vertex form of a quadratic function isy=x^2-6x+7 , where x, y, are constants. of the parabola is at (x, y).

Answer:

[tex]\log_5 8^{M}[/tex]

Step-by-step explanation:

[tex]\text{We know that,}~ b\log_a c = \log_a c^b[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{3}[/tex] =1.73205 In between 1 and 2 closer to 2

[tex]\sqrt{8}[/tex]=2.82842  In between 2 and 3 closer to 3

[tex]\sqrt{23}[/tex]=4.7958  In between 4 and 5 closer to 5

Answer:

2. Elana's Family. Elana's Family.

3. 8 minutes 4 seconds

4. Elena's family will have driven 2.76 miles while Andre's family will have driven which is farther.

Step-by-step explanation:

Answer:

I got f^-1 (x) = -7x + 21

Step-by-step explanation:

180° hope it's correct and really helps....!!!!

Answer:

How might the situation lead to bullying?

Step-by-step explanation:

How might the situation lead to bullying?

the answer B

Answer:

-3/2

Step-by-step explanation:

6=|x|+3-x

move the terms

-|x|+x=3-6

-|x|+x=-3

-x+x=-3 , x > 0 (put a line under >)

-(-x)+x=-3 , x < 0

-3/2 , x < 0 find the intersection

x= -3/2

if you dont want it as a fraction you can do -1.5 in decimal form

Answer:

2898

Step-by-step explanation:

number of people * number of pages in each book they read =total

mystery bookclub:

5 * 1,296 = 6480

fantasy bookclub:

9 * 398 = 3582

mystery - fantasy = difference in books between the two groups

6480 - 3582 = 2898

possible equation:

(1296 x 5) - (398 x 9) = x

x = answer

Answer:

Step-by-step explanation:

hey i got a couple (10) calculus questions in my profile and im pretty desperate right now

can u pls help

Answer:

P1:40% P2:47500 P3:10%

Step-by-step explanation:

2/5 = 0.4 =40%

5/8= .625

.625 x 76000 =

47500

Hey there!

3x = 27
DIVIDE 3 to BOTH SIDES

3x/3 = 27/3

CANCEL: 3/3 because it give you 1

KEEP: 27/3 because it help solve for the x-value

NEW EQUATION: x = 27/3

SIMPLIFY IT!

x = 9

Good luck on assignment & enjoy your day!

~Amphitrite1040:)