Susan travels at a rate of 60 miles per hour for 3 hours. her car uses on average one gallon of gas per 30 miles. how many gallons of gas does she use on her trip?

Answer:

x < -2

Step-by-step explanation:

-2x + 4 > 8

     -4      -4

-2x > 4

divide both sides by -2

x < -2

Because we divided by a negative number, the sign gets flipped. So, the answer is x < -2

Hope this helps!

Answer:

The answer is it travels 180 meters.

Step-by-step explanation:

To get the answer of how many meters the frisbee traveled in 12 seconds, all you have to do is multiply the number of meters the frisbee can do in 1 second by the number of seconds it traveled. The equation would be 15 x 12 = ? which would equal 180. That is how I got the answer that the frisbee traveled 180 meters in 12 seconds.

I hope I helped!

The area of the given polygon which is a rectangle is; 28 sq. units

We are given the coordinates of the polygon as;

A(3,7)

B(5,7)

C(3,-7)

D(5,-7)

Now, by close inspection of the coordinates, we can tell that this polygon is a rectangle. Thus, we can deduce that;

AB = 5 - 3 = 2

CD = 5 - 3 = 2

BC = 7 + 7 = 14

AD = 7 + 7 = 14

Formula for area of a rectangle is;

A = Length * Width

A = 14 * 2

A = 28 sq. units

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Answer: base x height divided by 2

Step-by-step explanation:

multiple the base and height then divide by 2

Using the general recursive formula, he 25-th term in the arithmetic sequence is 29.7

Here we have an arithmetic sequence with the first term a₁ = 3.3 and the common difference is d = 1.1

Remember that the general arithmetic recursive formula is:

aₙ = a₁ + (n - 1)*d

This formula allows us to find the n-th term of the arithmetic sequence only using the first term and the common difference.

In this case, we just need to replace n by 25 and the values written above.

a₂₅ = 3.3 + (25 - 1)*1.1 = 29.7

We can conclude that the 25th term in the sequence is 29.7

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Answer: Cynthia will receive $5,400, Moses will receive $8,100, John will receive $13,500

Step-by-step explanation:

       First, we will see how many "portions" the money is broken up into.

2:3:5 can become 2 + 3 + 5 = 10

       Next, we will see how much money each "portion" is worth using division.

$27,000 / 10 = 2,700

       Finally, we will multiply to see how much each person will receive.

2:3:5

2 * $2,700 = $5,400 [Cynthia]

3 * $2,700 = $8,100 [Moses]

5 * $2,700 = $13,500 [John]

Answer:

Cynthia's money = $5,400

Moses' money = $8,100

John's money = $13,500

Step-by-step explanation:

The full ratii of the money will be 2+3+5 = 10

Cynthia's ratio = 2 × $27,000

10

= 2 × 2,700

= $5400

Moses' ratio = 3 × $27,000

10

= 3 × 2,700

= $8100

John's ratio = 5 × $27,000

10

= 5 × 2,700

= $13,500

Answer:

new position is 360 feet below sea level.

Step-by-step explanation:

see picture for reference.

The slope of the line 3x - 2y = -12  is 3/2 .

The equation of a straight line can be written as follows,

y = mx + c                                         equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 3x - 2y = -12 .

To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1. So now we will rearrange the given equation as,

  3x - 2y = -12

⇒ 2y = 3x + 12

Now on dividing this equation by 2 on both sides, we will get

⇒ y = (3/2)x + 6                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 3/2.

Intercept = c = 6

The slope of the line 3x - 2y = -12  is 3/2 .

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Answer:

something

Step-by-step explanation:

onther something

It should be noted that Tyler writing the equation x = y/65 is correct and matches the information.

It should be noted that speed is calculated as:

= Distance / Time

In this case, the car is going 65 miles per hour down the highway

x = the time traveled, in hours

y = the distance traveled,

Therefore, time = Distance / Speed

Therefore, Tyler wrote the equation x = y/65, this is correct and matches the information.

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A car is going 65 miles per hour down the highway. Tyler wrote the equation x = y/65, with x representing the time traveled, in hours, and y representing the distance traveled, in miles. Explain why Tyler's equation matches the story.

The new function is g(x) =-1(1/-x) +2.

The transformation of function f(x) to function g(x) is given by g(x)=A f(Bx+ H)+K. where the constant A scales the function vertically. (A negative A reflects the function about the x-axis B scales the function horizontally. (A negative B reflects the function on the y-axis.) H shifts the function horizontally, and K shifts the function vertically.

Convert f(x) to g(x)

where the conversion is g(x)=f(x)+2.

A perpendicular line has negative reciprocal slopes, so for g(x) to be perpendicular to f(x), we need to get the negative reciprocal of -x, which is -1(1/-x)

So, f(x)=-x-2  ; m = -1

From the above information, we get g(x) as follows.

g(x) =-1(1/-x) +2

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Answer:

find the LCM of the dimensions of the slabs

=420

Answer:

Simple Interest = Rs1560

Step-by-step explanation:

A = P (1 + rt)

A = final amount

P = initial principal balance =  Rs8000

r = annual interest rate   =  [tex]6\frac{1}{2}[/tex]% = 0.065

t = time (in years) = 3 years

A = 8000*(1 +(0.065*3)) = 8000*(1+0.195) = 8000*(1.195) = 1560

Simple Interest (A) = Rs1560

Answer:

Step-by-step explanation:

1/2

The property tax be on a house that has a market value of $420,000 is A. $9,828

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Assessed value of a house = 60% of current market value

Property tax = 3.9% of the assessment value

Now the given market value of a house is $420,000

Assessed value of a house = 60% of $420,000

⇒ Assessed value of a house = 0.60 * $420,000

⇒ Assessed value of a house = $252,000

Thus, Property tax = 3.9% of $252,000

⇒ Property tax = 0.039 *$252,000

⇒ Property tax = $9,828

Thus, the property tax be on a house that has a market value of $420,000 is A. $9,828

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As time passes, the amount of money in the account increases.

The amount in the account increases by $45.

The amount of money in the account when he started depositing is  $197.

A linear function is a function that has one independent variable and one dependent variable. A linear function increases at a constant rate over a period of time. When drawn on a graph, a linear function is usually a straight line.

The form of linear functions is:

y = a + mx

Where:

Looking at the given table, it can be seen that as time passes, the amount of money increases.

Rate of increase = (change in the amount of money) / change in the months

(557 - 467) / (8 - 6)

= 90 / 2

= $45

Amount in the account at the beginning = account balance at 6 months - (rate of increase x 6)

467 - (6 x 45)

467 - 270 = $197

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The soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.

According to the given question.

We have an equation 1/4x - 3/4 = 7/x.

As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation 1/4x - 3/4 = 7/x is given by

1/4x - 3/4 = 7/x

⇒ 1/4x - 7/x -3/4 = 0

⇒  1- 28/4x = 3/4

⇒ 27/4x = 3/4

⇒ 27  = (3/4)(4x)

⇒ 27 = 3x

⇒ 27/3  = x

⇒ x = 9

Hence, the soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.

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area of ∆PQR/ area of ∆WUV = 1/9

Answer:

(6, 2)

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\\textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Defined points:

Substitute the defined points into the formula:

[tex]\textsf{Midpoint}=\left(\dfrac{4+8}{2},\dfrac{6-2}{2}\right)=(6,2)[/tex]

Therefore, the midpoint of the two given points is (6, 2).

Answer:

129

Step-by-step explanation:

75% of 516 is 387 so we just need to subtract 387 from 516. The answer will be 129. Please mark as brainiest

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

We have to find the value in kilowatt / hours power for per year basis

So, We know

Days in one year = 365

power in 3 days = 12 kilowatt/hours

For calculate power in single day, we have to divide power in 3 days by 3.

So power in a single day  = 12/3 kilowatt/hours

                                          = 4 kilowatt/hours

Now we have to multiply days in one year with power in a single day

     power for per year basis

                              = days in one year x power in a single day

Now, putting the all values,

                            = 365 x 4 kilowatt/hours.

                            = 1460 kilowatt/hours.

Answer:

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Answer:

dnenejnejehdhsbshsbsjsnsksknsosbs

-42 is the constant for all values of x. If the given the functions f(x) = 3x - 21 and g(x) = 3x+21

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Given an arbitrary number x, lets calculate,

⇒ f(x) - g(x)

                   =  3x - 21 - (3x+21)

                   = 3x - 3x -21 -21

                   = 0 - 42

                   = -42

and thus -42 is the constant for all values of x.

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Answer:

Step-by-step explanation:

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

The range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].

We are given a function:

g(x) = - 1 / 2 | x - 6 | + 1

We need to find the range of the function.

Now, we can see that the tip of the function will be formed when | x - 6 | = 0

x - 6 = 0

x = 6

For x = 6, we have the value of g(x) as

g(x) = - 1 / 2 | 6 - 6 | + 1

g(x) = 0 + 1

g(x) = 1

Also, since - 1 / 2 is negative, the function will have range from negative infinity to 1.

So, the range of the function will become:

( - ∞, 1]

Therefore, the range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].

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Answer:

Identify angle C. It is the angle whose measure you know.

Identify a and b as the sides that are not across from angle C.

Substitute the values into the Law of Cosines.

Solve the equation for the missing side.

Step-by-step explanation:

For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.

The F-value for the interaction is [tex]3.42[/tex]. It is determined by the interaction of gender and race.

What is F-value?

The calculation of the F-value is used on statistics in analysis of variance which is denoted as ANOVA. The calculated value is determined from the ratio of explained variance to unexplained variance. When the F-values in an ANOVA is higher that means the variance is higher in the sample.

The F-statistic value is also used in the regression analysis to calculate the mean between the population. It also depends on the null hypothesis and when the null hypothesis is true. That means the F-value is always close to one most of the time. It is named as F-value after Sir Ronald Fisher. The variance is the dispersion of the value.

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   The vertex, focus and directrix of the parabola y = x²/4 are:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

y = x²/4

   We must find the canonical equation:

(y - 0)² = 1/4 (x - 0)²

(x - 0)² = 4 (y - 0)²

has the form

(x - h)² = 4p(y - k)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

4p = 4

p = 1

f = (0, 1)

d = -1

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Answer: x = - 2

Step-by-step explanation:

3 ( x + 4 ) + 3 =9

multiply into the brackets

3x + 12 + 3 = 9

3x = 9 - 12 -3

3x = -6

x = -6/3

x = - 2