It took a plane 2 hours to fly from Dallas to New York with the headwind and 1.5 hours to return with the tailwind. If the speed of the wind was 30 mph, how far apart are the two cities?


Please help

The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.

Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.

First, find the least common multiple of the two denominators:

6 = 2 × 3

10 = 2 × 5

L.C.M. = 2 × 3 × 5 = 30

Second, amplify each rational number:

- (5 × 5) / (6 × 5) = - 25 / 30

- (7 × 3) / (10 × 3) = - 21 / 30

Third, compare the numerators of the fraction found in the previous step:

Since - 25 < - 21, then - 5 / 6 < - 7 / 10.

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The equation intercept at (2,3) in the graph given in the question.

Given two equations are ,

3 x - y = 3

-3 x - y = -9

to solve the equations, substract both equations ,

(3 x - y = 3) - (-3x -y = -9)

we get,  6x =12

              x = 2

by substituting value of x in any of the equation we get ,

3 x 2 -y =3

6 -y =3

-y = -3

y = 3

so x = 2 , y = 3

the points on the graph is (2,3)

Both equations are in slope intercept form.

The graph of y = mx +b, where m is the slope and b is the y intercept, is shown below.

They have the same y intercept, so they cross at (2,3).

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The expression of (f+g)(x) from the functions  f(x)=−2x2+4x and g(x)=3x+3 is (f+g)(x) = (-2x^3+7x^2 +3x ).

From the question we were given the functions that is expected to be simplified as :

f(x)=−2x^2+4x

g(x)=3x+3

And we were told to find the function  (f+g)(x) which can be written as :

(f+g)(x) = [(−2x^2+4x )+(3x+3)]x

This can be further expressed as :

(f+g)(x) = (-2x^2+4x +3x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^2+7x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^3+7x^2 +3x )

Therefore, the expression of the function (f+g)(x) is (f+g)(x) = (-2x^3+7x^2 +3x ).

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The missing part:

Find (f+g)(x).

g(x)×h(x) means we will have to multiply the two functions.

[tex]g(x) \times (h(x) = (3 {x}^{2} - 1)( {x}^{2} - x) \\ = 3 {x}^{2} ( {x}^{2} - x) - 1( {x}^{2} - x) \\ = 3 {x}^{4} - 3 {x}^{3} - {x}^{2} + x \\ g(x) \times h(x) = 3{x}^{4} - {x}^{3} - {x}^{2} + x[/tex]

ATTACHED IS THE SOLUTION

The given expression -3x²-6x+9 is quadratic expression and it is trinomial.

Classification of polynomials are given below:

A) 2x²

Degree = 2, so it is quadratic expression

Name using number of terms=monomial

B) -2

Degree = 0, it is constant

Name using number of terms=monomial

3) 3x-9

Degree = 1, so it is linear expression

Name using number of terms=monomial

4) -3x²-6x+9

Degree = 2, so it is quadratic expression

Name using number of terms=trinomial

Therefore, the given expression -3x²-6x+9 is quadratic expression and it is trinomial.

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[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 4^{\frac{2}{5}} \right)^{\frac{1}{4}}\implies 4^{\frac{2}{5}\cdot \frac{1}{4}}\implies 4^{\frac{1}{10}}\implies \sqrt[10]{4^1}\implies {\Large \begin{array}{llll} \sqrt[10]{4} \end{array}}[/tex]

g ≥ 1.8 is  the number of hours of running per day in inequality .

What are the mathematical inequalities?

Atleast means the number would be greater than or equal to given number.

g ≥ 1.8

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Answer:

65 feet

Step-by-step explanation:

[tex]3705=57h \\ \\ h=\frac{3705}{57}=65[/tex]

Answer:

first equation: Incorrect

second equation: Correct

Step-by-step explanation:

first equation:

[tex]-1 + (\frac{1}{-1}) = 1[/tex]

[tex]-1 + (-1) = 1[/tex]

[tex]-2 = 1[/tex]

negative 2 isn't the same as positive 1 which isn't true so the answer is incorrect.

second equation:

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

[tex](-1) = -1[/tex]

negative 1 is the same as negative 1 so the answer is correct

For the above question, statement 2 and 4 are true for the given data and after plotting the dot plot and histogram.

As per the question statement, data is showing the number of pieces of mail delivered to a single home address each day for three weeks.

Which is as follows: 4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2

10 for 3 days, 1 for 4 days, 2 for 4 days, 3 for 2 days, 4 for 3 days, 5 for 1 day and 6 for 1 day.

Statement 1: False because the number line of a dot plot would start at 0.

Statement 2: True

Statement 3: False as it should be 0, 1, 2, 3, 4, 5 and 6

Statement 4: True

Statement 5: False as it should show 3 bars at 0 in histogram

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Answer:

b,d

Step-by-step explanation:

The graph could be the graph of f(x) which is the correct answer would be option (B).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We are given the degree of the polynomial function f(x) to be 3; and

the roots of the equation f(x) to be 0 are -1, 0, and 4.

So we will put these values in the polynomial function of degree 3 to get:

f(x) = (x  -(-1))(x-0)(x-4)

f(x) = (x  + 1)x(x-4) = x³ - 3x² - 4x

According to this, the x-intercepts of this function on the graph will be:

(0, 0)

(-1, 0)

(4, 0)

So we will look for a graph that intercepts the x-axis at these points.

Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).

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The slope of the line passing from the two points is found as infinity.

For the given question;

The two passing points of the line is given as;

(x1, y1) = (-4, 6)

(x2, y2) = (-4, 18)

The formula for calculating the slope is;

Slope  = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (18 - 6)/ (- 4 + 4)

m = 12/0

m = ∞

It means, the line is parallel to the x axis.

Thus, the slope of the line passing from the two points is found as infinity.

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Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒[tex]r + 200 = \frac{x}{2}[/tex]

⇒[tex]x=2*(r+200)[/tex]

⇒[tex]x=2r+400[/tex]                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴[tex]3000\leq x\leq 4000[/tex]

⇒[tex]3000\leq (2r+400)\leq 4000[/tex]                             (from equation (1))

⇒[tex]3000-400\leq 2r+400-400\leq 4000-400[/tex]     (subtracting 400)

⇒[tex]2600\leq 2r\leq 3600[/tex]

⇒[tex]\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}[/tex]                                           (dividing by 2)

⇒[tex]1300\leq r\leq 1800[/tex]                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

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The equation of the line in the slope-intercept form is y = -1/4x + 9

From the question, we are to determine the equation of the line that passes through the given points.

The given points are (-4, 8) and (4, 6)

Using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

x₁ = -4

y₁ = 8

x₂ = 4

y₂ = 6

Thus,

(y - 8)/(x - -4) = (6 - 8)/(4 - -4)

(y - 8)/(x + 4) = -2 / (4 + 4)

(y - 8)/(x + 4) = -2 / 8

(y - 8)/(x + 4) = -1/4

4(y - 8) = -1(x + 4)

4(y - 8) = -x + 4

y - 8 = -1/4x + 1

y = -1/4x + 1 + 8

y = -1/4x + 9

Therefore,

The equation is y = -1/4x + 9

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3633 is the difference of these numbers.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.

Given Data

9832 - 6199

Subtracting,

= 9832 - 6199

= 3633

3633 is the difference of these numbers.

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Answer:

See below

Step-by-step explanation:

x = amount at  9.2 %             interest = .092 x

(9500 -x) = amount at 9%     interest = .09 ( 9500-x)    summed, they = 870

.092x + .09 ( 9500-x)  = 870

x = 7500   then the other amount at 9 % is 2000

Answer:

yes correct ^ ^

Step-by-step explanation:

This question is a bit confusing

Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.

c = 45 ft

a = 27 ft

b² = c² - a²

b² = (45 ft)² - (27 ft)²

b² = 2025 - 729

b² = = 1296

b = 36 ft

If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.

Using Pythagorean theorem, determine how far up the ladder is on the side of the house.

c = 45 ft

b = 39 ft

a² = c² - b²

a² = (45 ft)² - (39 ft)²

a² = 2025 - 1521

a² = 504

a = 6√14

a = 22.45 ft

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Answer:46kg

Step-by-step explanation:

23+2=25

50/25=2

2x23=46kg

Answer:

46 kg

Step-by-step explanation:

Ratio of copper to tin in the bronze alloy is 23:2

That means, as a ratio of the entire brass mass, the copper content is in the ratio of 23/(23 + 2) = 23/25

Since the mass of the bronze statue is 50 kg, the mass of copper in it must be 50  x  23/25 = 46 kg

The remaining kg (2/25 of 50 kg) is tin

Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.

What is consecutive integers ?

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the 1st sibling

Let x -2 = the second sibling

Let x -4 = the third sibling

Let x-6 = the fourth sibling.

If you add the four siblings together they equal 112

(x) +(x-2)+(x-4)+(x-6) = 112  Combine like terms

4x - 12 = 112

add 12 from both sides

4x - 12 + 12 = 112 + 12

4x = 124

divide 4 both side :

x = 31

The eldest sibling is 31, followed by siblings 29, 27 and 25

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The most appropriate choice for LCM will be given by

Smallest number of gift boxes Katy can fill is 56

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

Katy buys toys in bags of 8.

Katy buys keyrings in bags of 14.

Each gift box will contain one toy and one keyring.

Number of gift boxes Katy can fill has to be a common multiple of 8 and 14

Smallest number of gift boxes Katy can fill is the least common multiple of 8 and 14

Now,

8 = 2 x 2 x 2

14 = 2 x 7

LCM of 8 and 14 = 2 x 2 x 2 x 7

                           = 56

Smallest number of gift boxes Katy can fill is 56

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Answer:

1. 4

2. 2

3. 35

4. 96

Step-by-step explanation:

1. (6-2)÷4=4

2. 18÷(2+7)=2

3. (11-4)×5= 35

4.(4+2+6)×8= 96

Answer:

1. 1

2. 2

3. 35

4. 96

The value of x is 6 and the measure of angle LJK is 27°.

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

We have the measure of the following angles,

m∠JKL = ( 3x - 16 )°

m∠LJK = ( 2x + 15 )°

m∠KLM = ( 8x - 19)°

In ΔJKL, JL is extended through point L to point M.

At point L, the measure of angle JLK will be as,

m∠KLM + m∠JLK = 180°

m∠JLK = 180° - m∠KLM

m∠JLK = 180° - ( 8x - 19)°

m∠JLK = ( 199 - 8x )°

Now,

In triangle JKL,

By angle sum property:

m∠JKL + m∠LJK + m∠JLK = 180°

(3x – 16)° + (2x + 15)° + ( 199 - 8x )° = 180°

- 3x + 198 = 180

- 3x = - 18

x = 6°

Therefore,

m∠LJK = ( 2x + 15 )°

m∠LJK = ( 2(6) + 15 )°

m∠LJK = ( 12 + 15 )°

m∠LJK = 27°

The measure of angle LJK is 27°.

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Answer:

<KLC

Step-by-step explanation:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Both are obtuse angles and are on the opposite side of the transversal line

Answer:

∠KLC is the alternate angle of ∠BKL

Step-by-step explanation:

Alternate angles are angles that are opposite of one another and on two different parallel lines created by an intersecting line (also known as a transverse line).

In this case, the parallel lines are lines A↔B and C↔D, and the transverse line is M↔N. Therefore, the alternate angle from ∠BKL is ∠KLC.

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have slopes thst are negative reciprocals, so the slope of the line to be found is -1/4.

Substituting into point-slope form, the equation is [tex]y-4=-\frac{1}{4}(x+8)[/tex].

Rearranging into slope-intercept form,

[tex]y-4=-\frac{1}{4}(x+8) \\ \\ y-4=-\frac{1}{4}x-2 \\ \\ y=-\frac{1}{4}x+2[/tex]

The table with the situations that represent or not proportional relationships of distance and time is given at the end of the answer.

A situation represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

One example, in the context of this problem, is the relation between velocity, distance and time, as velocity is distance divided by time, hence:

v = d/t.

The relation between distance and time is given as follows:

distance = velocity x time

distance = v x t.

Hence it will only be proportional if the velocity is constant, that is, if the acceleration is of zero.

Examples of non-proportional situations in the context of this problem are:

The distance and time table (4 - 15, 8 - 30, 12 - 45) does not show enough information, we need to know if the initial point was of (0,0).

The objects are missing, and have been dragged to their correct situation on the table.

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The option that results in a graph that shows exponential decay is Option(b) f(x) = 3(0.7)ˣ.

According to the question, we have to determine the function that results in a graph that shows exponential decay.

The function will show an exponential decay if the value of b was less than 1 and greater than 0.

As we can notice in the second option, f(x) = 3(0.7)ˣ, where b is equal to 0.7 which is less than one.

So, f(x) = 3(0.7)ˣ shows exponential decay.

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The complete question is: "Which of the following options results in a graph that shows exponential decay?

a. f(x) = 0.6(2)ˣ

b. f(x) = 3(0.7)ˣ

c. f(x) = 0.4(1.6)ˣ

d. f(x) = 20(3)ˣ."