If your car gets 33 miles per​ gallon, how much does it cost to drive 370 miles when gasoline costs ​$2.80 per​ gallon?

Answer:

[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]

Step-by-step explanation:

The division between functions is defined as:

[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]

So:

[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]

Since [tex]g(x) \neq0[/tex] , let's find its roots:

[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]

For (2)

[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]

Therefore the roots are:

[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]

Finally the complete answer is:

[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]

Answer:

C. 124.3 ft

Step-by-step explanation:

Let h represent Nick's distance from ground.

We have been given that Nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. The angle of elevation from nick's mom to nick is 73 degrees.

Nick, his mother and angle of elevation forms a right triangle with respect to ground, where, h is opposite side and 38 feet is adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{tan}(73^{\circ})=\frac{h}{38}[/tex]

[tex]\text{tan}(73^{\circ})*38=\frac{h}{38}*38[/tex]

[tex]3.270852618484*38=h[/tex]

[tex]h=3.270852618484*38[/tex]

[tex]h=124.292399502392[/tex]

[tex]h\approx 124.3[/tex]

Therefore, Nick is 124.3 feet above the ground.

The term that describes the relationship the three points must have is known as: collinear.

Collinear points are points positioned on a shared straight line, forming a linear arrangement.

In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.

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Answer:

The measure of angle YUV is equal to [tex]m<YUV=42\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we have that

[tex]arc\ UV=84\°[/tex] -----> given problem

so

[tex]m<UZV=84\°[/tex] ------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

[tex]ZU=ZV=radius[/tex]

so

[tex]m<ZUV=m<ZVU[/tex] -----> bases angle of the isosceles triangle

Remember that

The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]

so

[tex]m<ZUV+m<ZVU+m<UZV=180\°[/tex]

[tex]2m<ZUV+m<UZV=180\°[/tex]

substitute and solve for m<ZUV

[tex]2m<ZUV+84\°=180\°[/tex]

[tex]m<ZUV=(180\°-84\°)/2=48\°[/tex]

[tex]m<ZUV+m<YUV=90\°[/tex] ------> by complementary angles

solve for m<YUZ

[tex]48\°+m<YUV=90\°[/tex]

[tex]m<YUV=90\°-48\°=42\°[/tex]

Answer: A. 42

Step-by-step explanation: trust i got a 100% on the quiz

The result of the sum of the three numbers is: [tex]\frac{-767}{60}[/tex]

The numbers are given as:

Start by calculating the sum of numbers 2 and 3 as follows:

[tex]Sum = -8\frac 34 -2\frac 56[/tex]

Express the numbers as improper fraction

[tex]Sum = -\frac{35}4 -\frac{17}6[/tex]

Take LCM

[tex]Sum = \frac{-3 \times 35 - 2 \times 17}{12}[/tex]

[tex]Sum = \frac{-139}{12}[/tex]

The opposite of number 1 is: -1 1/5

So, the overall sum is:

[tex]Sum = -1\frac 15 - \frac{139}{12}[/tex]

Express as improper fraction

[tex]Sum = -\frac 65 - \frac{139}{12}[/tex]

Take LCM

[tex]Sum = \frac{-72 - 695}{60}[/tex]

[tex]Sum = \frac{-767}{60}[/tex]

Hence, the result of the sum is: [tex]\frac{-767}{60}[/tex]

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Answer:

(A)[tex]G(F(x))=(x-5)^2[/tex]

Step-by-step explanation:

Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].

To find: [tex]G(F(x))[/tex]

Solution:

It is given that  [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:

[tex]G(F(x))=G(x-5)[/tex]

⇒[tex]G(F(x))=(x-5)^2[/tex]

Thus, it matches with the option A of the given options.

The numbers between 61 and 100 are given as 80 and 100.

The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.

The required numbers between 61 and 107 are given as follows,

The LCM of 2,4 and 5 is 20.

Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.

Now, the multiples of 20 are 20, 40, 60, 80 and 100.

80 and 100 lies between 61 and 107.

Hence, the numbers that Ali can choose are given as 80 and 100.

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Answer:

[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]

Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]

The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by

x+a=0

x= -a

(-a,0).

So, vertex of the given parabola is , at (-5,0).

The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.

Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).

So, the equation of line is : x= -5

Area of sector= \frac{\Theta}{360}\times \Pi \times r^{2}

Area =\frac{10\Pi }{7 }\times \frac{1}{360}\times \Pi \times (18.4)^{2}

Area = \frac{1800 }{7 }\times \frac{1}{360}\times (3.14) \times (18.4)^{2}

So, Area of the given sector= 759.34 square meters.

Answer:

759.34 m²

Step-by-step explanation:

Answer:

C. Fernando incorrectly found the product of -2 and -5.

Step-by-step explanation:

We have been given an image, which represents work of Fernando's evaluation of an expression. We are  asked to find the error in Fernando's work.

[tex]\frac{5(9-5)}{2}+(-2)(-5)+(-3)^2[/tex]

Let us evaluate our given expression using order of operations (PEMDAS).

[tex]\frac{5(4)}{2}+(-2*-5)+9[/tex]

[tex]\frac{20}{2}+10+9[/tex]

[tex]10+10+9[/tex]

[tex]29[/tex]

Since we know that product of two negative numbers is always positive, therefore, the product of negative 2 and negative 5 will be positive 10.

Therefore, Fernando incorrectly found the product of -2 and -5 and option C is the correct choice.

The probability that the tourist will visit the cities in alphabetical order is 0.00020.

There are a total of 7! ways to visit 7 different cities, but there is only one way to visit them in alphabetical order. So, the probability that the tourist will visit the cities in alphabetical order is:

1/7! = 1/5040 = 0.0002

To five decimal places, the probability is 0.00020.

Here is a step-by-step explanation of the calculation:

We can think of the route as a permutation of 7 letters, with no of the letters being identical.

The number of permutations of 7 letters is 7!.

So, the number of ways to visit the cities in alphabetical order is 1.

The probability that the tourist will visit the cities in alphabetical order is 1/7!.

Here are some additional things to consider:

The probability that the tourist will visit the cities in alphabetical order is very small, because there are many other possible routes.

The probability would be 1 if there were only one city to visit.

The probability would be 0 if there were 7 cities and the tourist had to visit them all in alphabetical order.

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The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.

A data set is a set of information that corresponds to one or more database tables in the case of tabular data,

The maximum value is 12

The minimum value is 4

The range of  the data set will be;

R = M-m

R=12-4

R=8

Hence the range of this data set will be 8.

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Answer:  [tex]x-100[/tex]

Step-by-step explanation:

Given : Phil received a prize of x dollars from a poker tournament.

The tournament cost him 100 dollars to enter.

To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.

Thus, the expression to show Phil's net winnings from the tournament :-

[tex]x-100[/tex]

The domain of a function is the set of all possible input values, while the range is the set of possible output values. In the given example, the function's domain is {-3, 0, 2}, which means the input data will be either -3, 0, or 2. Similarly, the function's range is {3, 0, -2}, which means the output data will be either 3, 0, or -2.

In mathematics, the domain of a function refers to the set of all possible input values (often represented as 'x' values) that the function can accept without producing an undefined result. Similarly, the range of a function refers to the set of all possible output values (often represented as 'y' values) that the function can produce.

To address your examples: for a function with domain {-3, 0, 2} and range {3, 0, -2}, it means all input data ('x' values) will be either -3, 0, or 2; and all output data ('y' values) will be either 3, 0, or -2.

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