An airplane makes a round-trip supply run that takes a total of 6 hours and is 350 miles each direction. The air current going to the destination is in the direction of the plane at 20 miles per hour. The air current traveling back to the starting point is against the plane at 20 miles per hour. Let x represent the speed of the airplane, in miles per hour, when there is no wind. Replace the values of a, b and c to create the equation that describes this situation.

Answer:

[tex](\frac{2}{3})^{3} (\frac{1}{5}.\frac{2}{3} )^{-3} (\frac{1}{5})^{4} =(\frac{2^{3} }{3^{3} }) (\frac{2}{8} )^{-3} (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=(\frac{2^{3} }{3^{3} }) (\frac{2^{-3} }{8^{-3} } ) (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=\frac{2^{3} .2^{-3}.8^{3}. 1 }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{1.8^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{(2^{3}) ^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{2^{9} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{512}{27.625}[/tex]

                          [tex]=\frac{512}{16875}[/tex]

The number of students that took ENG but neither BIO nor P.E is 43.

A set is a collection of well-defined objects called elements of the given set.

Analysis:

see diagram below

In conclusion, the number of students that took ENG but neither BIO nor P.E is 43

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The exponential function is P = 5.63(1.0145)ⁿ. And the population of the city in 2018 is 6.1379 million, the number of the years when the population of the city is 10 million is 40 years, and the doubling time will be 49 years.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

In​ 2012, the population of a city was 5.63 million. The exponential growth rate was 1.45​% per year.

Then the exponential function will be given as

P = 5.63 (1.0145)ⁿ

Where P is the population (in million) and n is the number of years.

Then the population of the city in 2018 will be

n = 2018 - 2012 = 6

Then we have

P = 5.63 (1.0145)⁶

P = 5.63 x 1.0902

P = 6.1379 million

The number of the years when the population of the city is 10 million.

    10 = 5.63 x (1.0145)ⁿ

1.776 = (1.0145)ⁿ

Taking log both sides, then we have

log 1.776 = n x log 1.0145

            n = 39.90

            n ≅ 40 years

Then the doubling time will be

2 = (1.0145)ⁿ

Taking log on both sides, then we have

log 2 = n x log1.0145

      n = 48.1489

      n ≅ 49 years

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Check the picture below.

[tex]\stackrel{parent}{y=x^2}\hspace{5em}y=\stackrel{A}{4}(\stackrel{B}{1}x\stackrel{C}{-2.5})^2\stackrel{D}{-3} \\\\\\ \hspace{7em} \begin{array}{llll} \textit{stretch by }4\cdot 1\implies 4\\\\ \textit{translated by }\frac{2.5}{1}\implies 2.5\textit{ to the right}\\\\ \textit{downwards shift by }3 \end{array}[/tex]

Step-by-step explanation:

you are "hiding" some more information (like how much they made together).

without that we cannot calculate the actual values.

all I can do is set up the equations expressing the given relations between the parts of the total :

a = amount Alberto made

b = amount Benjamin made

c = amount Carlota made

b = 3×a

c = 2×b = 2× 3×a = 6×a

that's it.

your see ? now we need something that "ties" all 3 together, an equation of all 3 variables, where we can use the first 2 equations (by substitution) and then solve for the remaining third variable.

and that is missing.

if it is something like "together they made x", then we would have

a + b + c = x

a + 3a + 6a = x

10a = x

a = x/10

b and c we get then from the first 2 equations by simply using the calculated value of a :

b = 3×(x/10) = 3x/10

c = 6×(x/10) = 6x/10 = 3x/5

The function f(x) =  x² + 12x is a quadratic function, and the vertex of the function is (-6,-36)

The equation of the function is given as:

f(x) =  x² + 12x

Differentiate the function

f'(x) = 2x + 12

Set the function to 0

2x + 12 = 0

Add -12 to both sides

2x = -12

Divide both sides by 2

x = -6

Set x = -6 in the function f(x)

f(-6) =  (-6)² + 12(-6)

Evaluate

f(-6) =  -36

Hence, the vertex of the function is (-6,-36)

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Answer:

the vertex of the function is (-6,-36)

Step-by-step explanation:

Pls add brainliest pls

Answer:

3/10 or 30%

Step-by-step explanation:

Add all of the marbles: 5+2+3=10

Then use a fraction to represent the three purple marbles: 3/10

That porportion is your answer

Answer:

See below under "Explanation".

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle f(x) = 3.55x - 4[/tex]

[tex]\displaystyle x = \{ 17, 21, 24, 34 \}[/tex]

Step 2: Find Profit

To find the profit the store makes each day, we input the number of customers that visited the store each day into our given function:

For the day that had 17 customers:

[tex]\displaystyle\begin{aligned}f(17) & = 3.55(17) - 4 \\& = 60.35 - 4 \\& = \boxed{56.35} \\\end{aligned}[/tex]

∴ the butcher store made $56.35 when 17 customers visited the store.

For the day that had 21 customers:

[tex]\displaystyle\begin{aligned}f(21) & = 3.55(21) - 4 \\& = 74.55 - 4 \\& = \boxed{70.55} \\\end{aligned}[/tex]

∴ the butcher store made $70.55 when 21 customers visited the store.

For the day that had 24 customers:

[tex]\displaystyle\begin{aligned}f(24) & = 3.55(24) - 4 \\& = 85.2 - 4 \\& = \boxed{81.2} \\\end{aligned}[/tex]

∴ the butcher store made $81.20 when 24 customers visited the store.

For the day that had 34 customers:

[tex]\displaystyle\begin{aligned}f(34) & = 3.55(34) - 4 \\& = 120.7 - 4 \\& = \boxed{116.7} \\\end{aligned}[/tex]

∴ the butcher store made $116.70 when 34 customers visited the store.

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Topic: Algebra I

[tex]\text{Given that,}\\\\P(x) = 2x^4 -5x^2 +3x -9\\\\P(6) = 2\cdot 6^4 -5 \cdot 6^2 +3 \cdot 6 -9 \\\\~~~~~~~=2592-180+18-9\\\\~~~~~~~=2421\\\\\text{Hence the answer is option D.}[/tex]

Answer:

9

Step-by-step explanation:

For the equation x² - 6x = 5 the coefficient of the term x is -6

(-6/2)2 = 9

The given equation can be written as

x2 - 6x + 9 = 5 + 9

x2 - 6x + 9 = 14

We can write it as

(x - 3)2 = 14

Take square root on both sides.

|x - 3| = √14

We get

x = 3 + √14

In other case,

- x + 3 = √14

x = 3 - √14

Therefore, 9 should be added to both sides of the equation to complete the square (x2 - 6x = 5).

What number should be added to both sides of the equation to complete the square (x2 - 6x = 5)?

Summary:

The number that should be added to both sides of the equation to complete the square (x2 - 6x = 5) is 9.

x + 2x + 6 = 27

3x + 6 = 27

x + 2 = 9

x = 9 - 2

x = 7

2 × 7 = 14

14 + 6 = 20

Answer:

C) 10,000,000

Step-by-step explanation:

Data provided in the question:  

- The phone number is of 7 digits

- we have choices from 0-9

meaning 10 number of choices, 0 1 2 3 4 5 6 7 8 9

we have 10 choices out of 10 for each of the 7 blanks

Therefore,

The total number of different phone numbers can there be in one area code that can be formed

= 10 × 10 × 10 × 10 × 10 × 10 × 10

= 10^7

= 10,000,000

Answer :The constant of proportionality is  K = 2/3

Answer:

3/20

Step-by-step explanation:

Take the miles that Maria walked and subtract the miles that Cody walked

3/4 - 6/10

Simplify 6/10 by dividing the top and bottom by2

3/4 - 3/5

Get a common denominator of 20

3/4 *5/5 = 15/20

3/5 *4/4 =12/20

15/20 - 12/20

3/20

Answer:

0.15(3/20) miles more than Cody

3/4 = 0.75

6/10 = 0.6

Therefore, Maria walked 0.15(3/20) miles greater than Cody.

Answer:

67.38 degrees

Step-by-step explanation:

this is a right triangle so we can use sohcahtoa

we want to calculate angle A

we know the side opposite to A as well as the hypotenuse. 13 is the hypotenuse because it is opposite the right angle

thus, sin(A) = opposite/hypotenuse = 12/13

arcsin(12/13) = A ≈ 67.38 degrees

Answer:

GCF is less than 3:

- 12 and 13

GCF is equal to 3:

- 6 and 27

- 12 and 21

- 3 and 6

GCF is greater than 3:

- 4 and 12

- 6 and 18

Step-by-step explanation:

6 and 27 GCF: 3

12 and 13 GCF: 1

4 and 12 GCF: 4

3 and 6 GCF: 3

12 and 21 GCF: 3

6 and 18 GCF: 6

Answer:

74

Step-by-step explanation:

(23-3)+(6×9)

(20) +(54)

=74

Answer: c= -8

Step-by-step explanation:

c/2=-4  

-8/2=-4

-4 +5=1

Answer: Pretty Simple; an easy equation could be 10 + 4 = 14.

Step-by-step explanation:

A more difficult equation might be (10(8) - 70) + 4 = 14

:)

Answer:

7x2=14

8+6=14

7+7=14

5x2.8=14

28/2=14

140/10=14

100-86=14

81(+-)67= 81-67=14

Answer:

√25

= √( 5 x 5 )

= 5

√25 = 5

5 is an rational number, not an irrational number.

                 [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}[/tex]

              Jillian said, "√25 is irrational because it's a square root!" Why is

she incorrect?

    [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

    First let's see if we can simplify √25.

     We can, by using either our calculator or our brains.

       Anyway, √25=5 (5×5=25)

Now, let's take a look at what irrational numbers are.

            [tex]\dagger[/tex] Irrational numbers. This set includes numbers with an infinite

           number of digits after the decimal point. Irrational numbers

           cannot be expressed as fractions (p/q form)

Can [tex]\LARGE\textbf{5}[/tex] be expressed as a fraction? Sure!

This is how it's done:-

[tex]\Large\text{$\displaystyle\frac{5}{1}$}[/tex]

As you can see, 5 is not irrational.

            [tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

The sentences here are all simple sentences and all begin with the same word.

A paragraph is used to show a complete thought. It is important that a paragraph ought to be presented in complete sentences. However the sentences here are all simple sentences and all begin with the same word.

The reasons pointed out above makes the paragraph appear clumsy and boring to read. The writer should revise the paragraph and introduce a more complex sentence structure as well as the use of pronouns where neccessary.

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Answer:

B

Step-by-step explanation:

edge 22

Answer:

[tex]P=0.71[/tex] or 71%

Explanation:

[tex]P=\frac{3.63*10^2}{1.48*10^8+3.63*10^8}[/tex]

[tex]=\frac{3.63}{5.11} =0.71[/tex] or 71%

Answer:

Ray, you need the slope-intercept formula  y=mx+b

Step-by-step explanation:

Next you'll need 2 points,  any points are fine.  Just find two easy ones along the line.  I'll just pick  Point 1  as P1 = ( 0,4)  and point 2 as P2 = (4,0) because they are easy to work with.

next use

point P1 (0,4)  in the form (x1,y1)

point P2(4,0)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

m = (0-4) / (4-0)

m = -4 / 4

m = -1

now use the point slope with one of the points,  to find the slope-intercept form.

y - y1 = m(x -x1)

y - 4 =  -1(x-0)

y -4 = -x

y = -x + 4

note:

y = mx +b

y = (-1)x + b    is the form.   see?

Answer:

y = mx + b

m = slope

b = intercept

From the graphic:

(x₁, y₁) = (0, 4)

(x₂, y₂) = (4, 0)

[tex]\frac{y-y_{1} }{y_{2} -y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} } \\\\\frac{y-4 }{0 -4} =\frac{x-0 }{4 -0 } \\\\\frac{y-4}{-4} =\frac{x}{4} \\\\(y-4)4=-4x\\\\y-4=-x\\y=-x+4\\[/tex]

The number of blocks of clay needed by Hyla is 30 blocks

Area is the region bounded by a plane shape.

To calculate the number of blocks of clay needed by Hyla, we find the area of the bottom of the box and divide it by the area of the block.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The number of blocks of clay needed by Hyla is 30 blocks

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The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.

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

Point J is at (-5, -3) while point K is at (1, 5), hence:

[tex]JK=\sqrt{(5-(-3))^2+(1- (-5))^2} =10\ units[/tex]

The distance between J(-5, -3) and K(1, 5) on the coordinate plane is about 10 units.

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Answer:

Sine: 0.94

Cosine: -0.31

Cotangent: -0.3(infinite)

Cosecant: 1.05

Tangent: -3

Secant: -3.16

Formula for finding the 6 trigonometry functions

Finding opposite and adjacent angles

Hope this helps!

Step-by-step explanation:

The six trig functions are

[tex] \sin( \alpha ) = \frac{y}{r} [/tex]

[tex] \cos( \alpha ) = \frac{x}{r} [/tex]

[tex] \tan( \alpha ) = \frac{y}{x} [/tex]

[tex] \csc( \alpha ) = \frac{r}{y} [/tex]

[tex] \sec( \alpha ) = \frac{r}{x} [/tex]

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

Where

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex]r = \sqrt{ - 2 {}^{2} + {6}^{2} } [/tex]

[tex]r = \sqrt{40} [/tex]

[tex]r = 2 \sqrt{10} [/tex]

So we just plug in -2 for x, 6 for y, and our r value into these functions.

[tex] \sin( \alpha ) = \frac{6}{2 \sqrt{10} } = \frac{3}{ \sqrt{10} } = \frac{3 \sqrt{10} }{10} [/tex]

[tex] \cos( \alpha ) = \frac{ - 2}{2 \sqrt{10} } = \frac{ - 1}{ \sqrt{10} } = \frac{ - \sqrt{10} }{10} [/tex]

[tex] \tan( \alpha ) = \frac{6}{ - 2} = - 3[/tex]

Csc is the reciprocal of sine.

[tex] \csc( \alpha ) = \frac{ \sqrt{10} }{3} [/tex]

Sec is the reciprocal of cosine

[tex] \sec( \alpha ) = - \sqrt{10} [/tex]

Cot is the reciprocal of tan

[tex] \cot( \alpha ) = - \frac{1}{3} [/tex]

The value of d at the point of equilibrium, to the nearest whole number is 54

The equations are given as:

[tex]d = \frac{-5}{9}p + 94[/tex]

[tex]s = 3p - 160[/tex]

At the point of equilibrium, d = s.

So, we have:

[tex]\frac{-5}{9}p + 94 = 3p - 160[/tex]

Multiply through by 9

-5p + 846 = 27p - 1440

Collect like terms

27p + 5p = 1440 + 846

Evaluate the sum

32p = 2286

Divide through by 32

p = 71.4375

Substitute p = 71.4375 in [tex]d = \frac{-5}{9}p + 94[/tex]

[tex]d = \frac{-5}{9} * 71.4375 + 94[/tex]

Evaluate

d = 54.3125

Approximate

d = 54

Hence, the value of d at the point of equilibrium, to the nearest whole number is 54

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Answer:

its d :)

Step-by-step explanation: