A truck driver can travel 560 miles on 28 gallons of gas. How far can he travel on 35 gallons of gas?

Inequality is a statement of an ordered relationship

The value of x as inequality is less than -3.

x < -3 is our answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

Example:

x > 3

y < 5

x ≤ 6

y ≥ 2

We have,

-32 > -5 + 9x

Add 5 on both sides.

-32 + 5 > -5 + 9x + 5

[ -32 + 5 = -27 ]

-27 > 9x

Divide both sides by 9.

-27/9 > 9x/9

-9 x 3 / 9 > 9x / 9

-3 > x

This can be written as:

x < -3

Thus,

The value of x as inequality is less than -3.

i.e x < -3

Learn more about inequality here:

https://brainly.com/question/22010462

#SPJ2

The complete expression for the given equation is x^2 - 6x + 9= -13 +9

Given the quadratic expression x^2 - 6x = -13

In order to complete the square, we will follow the steps

Coefficient of x is -6

Half of the coefficient. = (-6/2) = -3

Square of the result = (-3)^2 = 9

Add 9 to both sides of the equation

x^2 - 6x + 9= -13 +9

Hence the complete expression for the given equation is x^2 - 6x + 9= -13 +9

Learn more on complete the square here: https://brainly.com/question/13981588

#SPJ6

Answer:

Speed of current = 5 mph

Step-by-step explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph

The equation of the line that passes through the point (-1,5) and has a slope of 3 in point-slope form is y = 3x + 8.

The subject of this question relates to Mathematics, specifically algebra and line equations. The line equation in point-slope form is given by y - y1 = m(x - x1). In this equation, (x1, y1) represents the point that the line passes through and m represents the slope of the line. In our case, we know that the line passes through the point (-1,5) and has a slope of 3.

By substituting these values into the point-slope formula, we get the following:y - 5 = 3(x - (-1)), or, after simplifying, y - 5 = 3x + 3. So, the equation of the line that passes through (-1,5) and has a slope of 3 is y = 3x + 8.

https://brainly.com/question/35689521

#SPJ3

10-3 =7

 each term increases by 7

 so 24 +7 = 31

31+7 = 38

 next 2 terms are 31 & 38

To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.

To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m):

Therefore, the slope (m) is $1.50 / 10 = $0.15.

Next, let's find the y-intercept (b):

$1.75 = $0.15(2003) + b

b = $1.75 - $0.15(2003)

b = $1.75 - $300.45

b = -$298.70

Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.

https://brainly.com/question/32634451

#SPJ11

I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.

We will get that the distance is 3.22

So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)

That distance is:

[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]

Now we want to minimize this, which is equivalent to minimize d^2, then we can define:

D = d^2

and write:

[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]

Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).

Remember that for a parabola like:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then for our parabola, the vertex will be at:

x = -(-44)/(2*10) = 44/20 = 2.2

Thus the minimum distance is given by:

[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]

If you want to learn more, you can read:

https://brainly.com/question/12082741

I believe that the correct word here is correlation. Correlation is the term that we use when we want to say that something is strong related to the other. Correlation must be however differentiated from causality. Correlation is when two things occur at the same time. Causality is when one results in the occurrence of the other.

Correlation coefficient has a maximum value of 1 which indicates strong relationship.

The quotient of  4+2i/6-i is (11/4-4i)/*1/5.

Quotient is a result obtained by dividing one quantity by another.

explanation;

(4-2i)/(6-i)

Multiply and divide by the denominator = (6+i)

=>(4-2i)/(6-i)/(6+i)(6+i)

=> (4*6 + 4i - 12i - 2i^2)/[6^2 - (2i)^2]

=>  (24 - 8i -2)/ [36 + 4]                            [since i^2 = -1]

=> (22-8i) /40

=> 22/40 - 8i/40

=> 11/20 - i/5

Hence, the quotient of 4+2i/6-i is (11/4-4i)/*1/5.

A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer identical zero. A proportion is an equation wherein ratios are set equal to each other. The share components is used to depict if two ratios or fractions are same. we can find the lacking fee by dividing the given values. the proportion formula can be given as a: b::c : d = a/b = c/d wherein a and d are the acute terms and b and c are the mean phrases.

The quantitative relation among two quantities showing the number of times one cost consists of or is contained inside the other. The indicated quotient of two mathematical expressions. b : the connection in quantity, quantity, or size among  or more matters.

A ratio can be defined as the connection or assessment among two numbers of the same unit to check how larger is one variety than the alternative one. as an instance, if the quantity of marks scored in a take a look at is 2 out of 5, then the ratio of marks received to the total range of marks is written as 2:5.

Learn more about quotient here:-https://brainly.com/question/673545

#SPJ2

multiply 5.5 cm by 11.5 km

5.5 * 11.5 = 63.25

 rounded to nearest tenth = 63.3 km

The operation results on the matrices representing relations r1 and r2 are beautiful illustrations of how relations are manipulated in set theory. Given the limitations imposed by the data available, only three of the five stipulated operations can be carried out.

In the given question, the student needs to perform different operations on the matrices that represent relations r1 and r2. Here is the solution:

https://brainly.com/question/16956653

#SPJ11

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.

What is the percentage?

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".

Here given information:-

Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.

So,

[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]

[tex]=0.125[/tex]×[tex]100[/tex]

[tex]=12.5[/tex]%

Hence, Sharon has [tex]12.5[/tex]% of the credits required.

To know more about the percentage

https://brainly.com/question/13244100

#SPJ2

For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.

Here's how to solve a similar problem based on the given examples:

Let the first train's speed be 50 mph and the second train's speed be 55 mph.

The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).

The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.

Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.

So, the second train will overtake the first train after 5 hours.