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The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:

(a - b)3.2 = 640

a - b = 200   (1)

Also:

(a + b)2 = 640

a + b = 320    (2)

The solution to equation 1 and 2 is:

a = 260, b = 60

The  airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.

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Answer:

Answer A is correct

Step-by-step explanation:

Let us use completing square method for this.

[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]

∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]

The value that remains under the radical is 2

The correct expression in the question is:

1250^4

This can be rewritten as:

[tex]\sqrt[4]{1250}[/tex]

Express 1250 as product

[tex]\sqrt[4]{(2 * 5^4)}[/tex]

Expand the expression

[tex]\sqrt[4]{2} * \sqrt[4]{5^4}[/tex]

Simplify

[tex]\sqrt[4]{2} * 5[/tex]

Evaluate the product

[tex]5\sqrt[4]{2}[/tex]

Hence, the value that remains under the radical is 2

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Answer:

Second graph

Step-by-step explanation:

See attached image.

Step-by-step explanation:

it isnot looking well here so go on geogebra. org/calculator and you will see. have a nice day :))

Answer:

C on Edge 2022

Step-by-step explanation:

Just did it and got it right

The values of the trigonometric functions are

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

[tex]cos \theta = \frac{5}{13}[/tex]

[tex]tan \theta = \frac{12}{5}[/tex]

 [tex]cot\theta = \frac{5}{12}[/tex]

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

From the question, we are to determine the values of the given trigonometric functions

From the given information,

[tex]sec \theta =\frac{13}{5}[/tex]

∴ [tex]\frac{1}{cos \theta} =\frac{13}{5}[/tex]

[tex]cos \theta = \frac{5}{13}[/tex]

Thus,

Adjacent = 5

Hypotenuse = 13

Opposite = ?

Using the Pythagorean theorem

|Opp|² = |Hyp|² - |Adj|²

|Opp|² = 13² - 5²

|Opp|² = 169 - 25

|Opp|² = 144

|Opp| = √144

|Opp| = 12

∴ Opposite = 12

Thus,

By using SOH CAH TOA

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

[tex]tan \theta = \frac{12}{5}[/tex]

[tex]cot\theta = \frac{1}{tan\theta}[/tex]

∴ [tex]cot\theta = \frac{5}{12}[/tex]

[tex]csc\theta = \frac{1}{sin\theta}[/tex]

∴ [tex]csc\theta = \frac{13}{12}[/tex]

Hence, the values of the trigonometric functions are

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

[tex]cos \theta = \frac{5}{13}[/tex]

[tex]tan \theta = \frac{12}{5}[/tex]

 [tex]cot\theta = \frac{5}{12}[/tex]

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

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Answer:

a monomial, a constant

Step-by-step explanation:

It has only 1 term, so it's a monomial.

Also, the term is a constant.

56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$

Properties of triangles are:

A triangle has three sides and three angles.

The sum of the angles of a triangle is always 180 degrees.

The exterior angles of a triangle always add up to 360 degrees.

The sum of consecutive interior and exterior angle is supplementary.

Given:

Height: ha = 7

Height: hb = 24

Height: hc = 25

Sum to sides is:

25 +7 + 24 =56 units.

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Answer:

c

Step-by-step explanation:

y = [tex]\frac{5}{2}[/tex] x + 2 → (1)

2y = 5x + 4 ( divide through by 2 )

y = [tex]\frac{5}{2}[/tex] x + 2 → (2)

the 2 equations are the same and will have infinitely many solutions

Answer:

LM

Step-by-step explanation:

Usually these problems would already be in order, so since PQ are the first 2 letters of polygon PQRS, then for LMNO, it's LM.

Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.

In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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The equation which is equivalent to the given simple interest formula is

[tex]P=\frac{A}{1+rt}[/tex].

What is an equivalent equation?

Equivalent equations are algebraic equations that have identical solutions.

According to the given question.

We have a simple interest formula.

[tex]A=P(1+rt)[/tex]

Now, the equivalent equation for the above formula can be given as

[tex]A=P(1+rt)[/tex]

⇒[tex]P=\frac{A}{1+rt}[/tex]

Hence, the equation which is equivalent to the given simple interest formula is [tex]P=\frac{A}{1+rt}[/tex].

Thus, option A is correct.

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a. The required sample size when pn and qn are unknown then n = 1844

b. The required sample size when about 10% of Californians are left-handed is n = 664

c. There would have been no effect on parts a and b if entire US has been chosen

According to statement

a. No estimate of proportion is given so we will assume:  

{p} = {q} = 0.5

For 99% confidence, z = 2.576

E = 0.03  

Hence, Required sample size  

n = (0.5)*(0.5)*(2.576/0.03)^2  

n = 1844

b. {p} = 0.10

{q} = 1 - {p}

{q} = 1 - 0.10

{q} = 0.90  

For 99% confidence, z = 2.576

E = 0.03

Hence,  Required sample size  n = (0.1)*(0.9)*(2.576/0.03)^2  = 664

c. There would have been no effect on parts a and b if entire US has been chosen because minimum sample size required is not dependent on population size.

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The false statement include:

This relationship between two variables involves them having a positive slope. This means that as volume increases, temperature also increases which isn't the case.

This cause and effect pattern also means that the volume doesn't have explanatory variables.

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Answer:

Volume is the explanatory variable

Step-by-step explanation:

because vanilla is better than chocolate

Answer:

Step-by-step explanation:

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer: 3

Step-by-step explanation:

By the intersecting chords theorem,

[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]

The first graph is the exponential function.

The exponential function serves as the  positive-valued function with respect to real variable. and  the values denoted as X which is exponential is  all real numbers.

Analyzing the first graph, moving down the graph, we can see that  x value increases.

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Answer:

First Graph

Step-by-step explanation:

Edge

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane. The positive angle that is less than 2π and is coterminal with 14π/6 is  1/3π.

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane.

The angle that 14π/6 makes from the positive x-axis is 1/3π, which is equal to 60°.

Hence, the positive angle that is less than 2π and is coterminal with 14π/6 is  1/3π.

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Answer:

Step-by-step explanation:

from the sign on the picture it is a rigth triangle

we use pythagoras

x² = 12² - 7²

x² = 144 - 49

x² = 95

x = √95

(x = 9.75)

Answer:

x = [tex]\sqrt{95}[/tex]

Step-by-step explanation:

In this problem, we need to use the Pythagorean theorem.

Pythagorean theorem is a theorem where you can find a side length in a right triangle.

The hypotenuse (The longest side) squared equals the other two side lengths added together after being squared.

In numbers, this will be: (12)^2 = (7)^2 + (x)^2.

144 = 49 + x^2.

95 = x^2

x = [tex]\sqrt{95}[/tex]

We cannot simplify [tex]\sqrt{95}[/tex], so that is the final answer.

Answer:

B

Step-by-step explanation:

[] means the endpoints are inclusive. Therefore [2,7] is equivalent to 2 <= x <= 7. So [2,7] represents graph B.

Answer:

9.62 cm²

Step-by-step explanation:

 diameter = 7 cm

              r = 7 ÷2 = 3.5 cm

             Ф = 45°

  [tex]\sf \boxed{\text{\bf Area of sector = $\dfrac{\theta}{360}*\pi r^2$}}[/tex]  

                              [tex]\sf =\dfrac{45}{360}*3.14*3.5*3.5\\\\ = 4.81 \ cm^2[/tex]

Area of the given sectors = 2 *4.81

                                           = 9.62 cm²

Hello!

Let's solve this in step

Let's find the circular region to the left of the center:

  [tex]Area = \frac{45}{360}*Area_.formuka_.of_.Circle =\\ Area = \frac{45}{360}*\pi (radius)^2\\ Area = \frac{45}{360} *\pi (3.5)^2\\Area=4.81[/tex]

Now let's find the circular region to the right of the center

 ⇒ the angle 45° by the vertical angle theorem is equal to the angle  

      opposite it in the other circular region

     ⇒ has the same area as the left region

Total Area = 4.81 + 4.81 = 9.62 cm²

Answer: 9.62 square centimeters

Hopefully that helps!

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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Answer:

3300

Step-by-step explanation:

This can be worked out using PEMDAS:

First you solve in the PARENTHESIS:

(4 × 10³) – (7 × 10²)

Then, you look at the EXPONENTS:

(4 × 10³) = (4 × 1000)

(7 × 10²) = (7 × 100)

After that, look at the MULTIPLICATION:

(4000) - (700)

Since there is only subtraction left, subtract it:

3300

Answer:

Parenthesis:

4 *1000 = 4000

7*100= 700

4000-700=3300

Step-by-step explanation:

dy/dx by implicit differentiation is cos(πx)/sin(πy)

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

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Answer:

If it is assumed that the change was constant from 2009 and 2012 , then change of population is 142 .

Step-by-step explanation:

In the question, it is given that the population of a small town increased from 1442 to 1868 between 2009 and 2012 .

It is asked to find the change of population if it is assumed that the change was constant from 2009 and 2012 .

Step 1 of 2

Population in 2012 is given to be 1868 and

Population in 2009 is given to be 1442 .

Duration of year is given by 2012-2009 which is 3 years.

Change in population is given by 1868-1442 which is 426 .

Step 2 of 2

Change in population per year is given by dividing the change in population and the duration of years it took to happen the change.

Hence, change in population per year is

[tex]$\frac{426}{3}=142$[/tex]

Hence, the population was changed by 142 per year from 2009 to 2012 .

Answer:

It must be probably √29

Step-by-step explanation:

[tex]distance = \sqrt{ { (- 4)}^{2} + {(5)}^{2} } [/tex]

hope it to be the correct...

Answer:

(x+9) and (x-4)

Step-by-step explanation:

Answer:

The third option.

Step-by-step explanation:

[tex](\frac{4xy^3}{x^2})^2\\\\=(\frac{4y^3}{x})^2\\\\=\frac{16y^6}{x^2}[/tex]

Hence the 3rd option.