Flying against the wind, an airplane travels 3800 kilometers in 4 hours. Flying with the wind, the same plane travels 3750 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer:

A) 8d^2/3c

B) 3a^2b^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

In exponent division, if base are same , subtract the exponents.

[tex]\frac{a^{m}}{a^{n}}=a^{m-n} , m>n\\\\ \frac{a^{m}}{a^{n}}= \frac{1}{a^{n-m}}, m<n[/tex]

a) 8c²d⁵ ÷ 2c³d³ = [tex]\frac{8}{2}* \frac{d^{5-3}}{c^{3-2}}= 4*\frac{d^{2}}{c}= \frac{4d^{2}}{c}[/tex]

b) 9a³b⁵ ÷ 3ab² = [tex]\frac{9}{3}* a^{3-1}*b^{5-2} = 3a^{2}b^{3}[/tex]

Answer:

in picture

Step-by-step explanation:

Brainliest please~

Answer:

1/3

Step-by-step explanation:

If it was supposed to be a negative answer, there would be negative numbers in the sequence. So that narrows it do to 3 and 1/3. And now we know that 27*3 isn't 9 but 27*1/3=9 and so on.

Answer:

your answer will have to be 3

Step-by-step explanation:

from 27 to 9, we divided by 3

from 9 to 3, we divided by 3

from 1 to 1/3, we divided by 3

from 1/3 to 1/9, we divided by 3

from 1/9 to 1/27, we divided by 3

so basically the common ratio will have to be 3

Answer:

3/8

Step-by-step explanation:

Let us represent the total fabric as an integer = 1

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines.

= 1/8, hence each section = 1/8

Then she cuts off 5 of the sections to make into placemats.

This is written as: 5 sections × 1/8 = 5/8

The fraction of the fabric that is left is calculated as:

1 - 5/8

Lowest Common Denominator = 8

Hence: 8 - 5/8 = 3/8

The fraction of the fabric that is left is 3/8

Answer:

(5 , 1)

Step-by-step explanation:

coordinate point is (2 , 9)

translation rule is

(x , y) = (x + 3 , y - 8)

here x is 2 and y is 9

so  the new coordinate will be

(x + 3 , y - 8)

(2 + 3 , 9 - 8)

(5 , 1)

Answer:

[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos\theta =-\frac{5}{13}\text{ where $\theta$ is in QII}[/tex]

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using the Pythagorean Theorem, solve for the opposite side (we can ignore the negative for now):

[tex]o=\sqrt{13^2-5^2}=12[/tex]

And since θ is in QII, sine is positive, and cosine and tangent are both negative.

Sine is the ratio of the opposite side to the hypotenuse. Therefore:

[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]

Answer:

The coordinates of the vertex is (6,4).

Step-by-step explanation:

The vertex is the highest or lowest point on the parabola (curved line).

Answer:

24 rolls

Step-by-step explanation:

12 rolls           x rolls

------------  = ------------------

4 dollars           8 dollars

Using cross products

12*8 = 4x

96 = 4x

Divide by 4

96/4 = 4x/4

24 =x

24 rolls

Answer:

False

Step-by-step explanation:

Answer:

radius = [tex]\sqrt{26}[/tex] units

Step-by-step explanation:

The radius r is the distance from the centre to a point on the circle.

Using the distance formula to calculate r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (1, - 3)

r = [tex]\sqrt{(1-2)^2+(-3-2)^2}[/tex]

  = [tex]\sqrt{(-1)^2+(-5)^2}[/tex]

   = [tex]\sqrt{1+25}[/tex]

    = [tex]\sqrt{26}[/tex]

Answer:

1/3

Step-by-step explanation:

3÷6/1 is the same thing as 3÷6

and when reducing to the lowest term gives 1÷3 or 1/3

Answer:

a line and a plan are considered parallel if they have no points in common if two parallel planes are cut by a third plane then the lines of intersection are parallel

Answer:

The population of town A = 18,000

The population of town B = 15,000

The population of town C = 20,000

Step-by-step explanation:

Given;

A:B = 6:5

B:C = 3:4

total population = 53,000

A + B + C = 53,000

[tex]\frac{A}{B} = \frac{6}{5} \\\\A = \frac{6B}{5} \\\\\Also;\\\\\frac{B}{C} = \frac{3}{4} \\\\C = \frac{4B}{3} \\\\then;\\\\\frac{6B}{5} +B+ \frac{4B}{3} = 53,000\\\\multiply \ through \ by \ "15"\\\\18B + 15B + 20B = 795,000\\\\53B = 795,000\\\\B = \frac{795,000}{53} \\\\B = 15,000[/tex]

Now solve for A and C;

[tex]A = \frac{6 \times 15,000}{5} = 18,000\\\\C = \frac{4 \times 15,000}{3} = 20,000[/tex]

Answer: hi

Step-by-step explanation: siodrifjojseidufjsoidhfidshiufhoiersdnfiojdriofjoiedsjfpoiejdpoigheroiuhgoiutrhfbiukghvioruefdhgbiuktrhdfiougkhneoiuwhsrdtifu[tex]\lim_{n \to \infty} a_n \geq \alpha \leq \sqrt{x} \\ \pi \geq \lim_{n \to \infty} a_n \left \{ {{y=2} \atop {x=2}} \right. x^{2} \frac{x}{y} \frac{x}{y}[/tex]

Answer:

oh no

Step-by-step explanation:

Answer:

1. 194

2. 189

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

1. 194 people increased.

2. Edith has 189 stamps more than Parick.

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

We want to graph:

y = -4*sin(2*x) + 1

Such that the x-axis starts at x = 30

This is trivial to do if we use a program to graph or if we graph by hand, here we just need to draw the x-axis such that it crosses the y-axis at the point (30, 0)

Then let's graph the equation in that axis, we will get an image like the one you can see below.

Answer:

12 hours

Step-by-step explanation:

pages total = pages written + pages per hour * number of hour

47 = 11 + 3*h

Subtract 11 from each side

47 -11 = 11 +3h -11

36 = 3h

Divide by 3

36/3 = 3h/3

12 = h

Answer:

9

Step-by-step explanation:

f(x) = x − 7

g(x) = x^2

Find g(4) = 4^2 = 16

Then find f(g(4)) = f(16) = 16 -7 = 9

Answer:

f(g(4)) = 9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x - 7

g(x) = x²

Step 2: Find f(g(4))

Answer:

a = 78.5 cm²

Step-by-step explanation:

a = πr²

a = 3.14 * 5²

a = 3.14 * 25

a = 78.5 cm²

Answer:

[tex](a)\ \sqrt5 <2.3 < 5.6[/tex]

[tex](b)\ \sqrt 5 <2.4 < 5.6[/tex]

[tex](e)\ \sqrt 8 <2.9[/tex]

[tex](f)\ \sqrt5 <4.5 < 5[/tex]

Step-by-step explanation:

Required

Which are true

[tex](a)\ \sqrt5 <2.3 < 5.6[/tex]

Take square root of 5

[tex]2.2 <2.3 < 56[/tex] --- This is true

[tex](b)\ \sqrt 5 <2.4 < 5.6[/tex]

Take square root of 5

[tex]2.2 <2.4 < 56[/tex]  --- This is true

[tex](c)\ 7.4 < 5 <5.5[/tex]

This is false because [tex]7.4 > 5[/tex]

[tex](d)\ \sqrt 3 <3 <3[/tex]

This is false because [tex]3 = 3[/tex] not [tex]3 < 3[/tex]

[tex](e)\ \sqrt 8 <2.9[/tex]

Take square root of 8

[tex]2.8 <2.9[/tex] --- This is true

[tex](f)\ \sqrt5 <4.5 < 5[/tex]

Take square root of 5

[tex]2.2 <4.5 < 5[/tex] --- This is true

Answer:

13328 N

Step-by-step explanation:

9.8 m/s^2 • 1360 = X

13328 N = X

Answer:

x     -1      1    3

y      -2    -4   2

Step-by-step explanation:

y=x^2-x-4

when x=-1

y=(-1)^2-(-1)-4

y=1+1-4

y=-2

when x=1

y=(1)^2-(1)-4

y=1-1-4

y=-4

when x=3

y=(3)2-(3)-4

y=9-3-4

y=9-7

y=2

Complete Question

A countertop for a kitchen is modeled with the dimensions shown below. An

18-inch by 21-inch rectangle will be removed for the installation of the sink.

8 ft

2 ft

Sink

18 in

21 in

5 ft

2 ft

What is the area of the top of the installed countertop, to the nearest square foot?

Answer:

19 square foot

Step-by-step explanation:

A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21 inch rectangle will be removed for the sink. What is the area of the top of the installed countertop to the nearest square foot.

Convert from inches to feet

18 inches

1 inch = 0.0833 feet

18 inch = x

Cross Mulitiply

x = 18 × 0.0833 feet

x = 1.5 feet

21 inches

1 inch = 0.0833 feet

21 inch = x

Cross Mulitiply

x = 21 × 0.0833 feet

x = 1.75 feet

Area 1 = 2 ft × 8 ft = 16 ft²

Area 2 = 2 ft × 3 ft = 6 ft²

Area of a sink = Length × Width

= 1.5 ft × 1.75 ft

= 2.625 square feet

Area 1 - Area of sink

= 16 ft² - 2.625 ft²

= 13.375 ft²

Area of the top installed part =

Area 2 + 13.375 ft²

= 6 ft² + 13.375 ft²

= 19.375 ft²

Approximately ≈ 19 ft²

Answer:

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Step-by-step explanation:

[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]

Apply Rational Root Theorem, our possible roots will be

plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).

I

I tried root -2 and it work so

If we apply synthetic dividon, we would be left with

[tex]15 {x}^{2} - 8x + 1[/tex]

We can factor this regularly.

Apply AC method that a number

AC will multiply to 15 but add to -8.

The answer are -5 and -3 so we write this as

[tex]15 {x}^{2} - 5x - 3x + 1[/tex]

Factor by grouping

[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]

[tex]5x(3x - 1) - 1(3x - 1)[/tex]

So our factor are

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Answer:

Conservation

Step-by-step explanation:

Conservation is the principle that an object maintains the same size and shape even if it is repositioned or divided in certain ways.

Answer:

1547

Step-by-step explanation:

10^3 is 1000 1.547 x 1000 = 1547.

Pls follow and mark answer as brainliest

Given:

The equation is:

[tex]30n-C+200=0[/tex]

To find:

The slope intercept form of the given equation.

Solution:

We have,

[tex]30n-C+200=0[/tex]

We need to write the given equation in the form of [tex]C=mn+b[/tex].

Adding C on both sides, we get

[tex]30n-C+200+C=0+C[/tex]

[tex]30n+200=C[/tex]

Interchanging the sides, we get

[tex]C=30n+200[/tex]

This equation is in the form of [tex]C=mn+b[/tex], where m is 30 and b is 200.

Therefore, the slope intercept form of the given equation is [tex]30n-C+200=0[/tex].

The angles represented by (2x - 60) and (60 - 2x) cannot be supplementary because their sum add up to zero instead of 180°.

Answer:

80n+20=total cost

Step-by-step explanation:

We don't know the value of n, but we don't need it for an expression. We know that the family has to pay $80 per night that they stay at the hotel. Modeling this would look like: 80n (80*n for nights). Also, we know that the family MUST pay a $20 fee. So, we can add that on to the expression to look like this, 80n+20=total cost.

Hope this helps!

Have a nice evening.