Janet rents a car while spending her vacation traveling in Argentina. When she returns the car, she has driven 1400 miles and used about 56 gallons of gas. If gas costs an average of $4.099 per gallon, estimate how much she spent on fuel.

Triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC. (Translation: Pippa was right)

Herein we find a picture a graph with two proportional right triangles, which means that the small triangle is the consequence of a rigid transformation. The kind of rigid transformation used is a dilation around the origin, whose formula is shown below:

P'(x, y) = k · P(x, y)

Where k is the scale factor.

There is a dilation if and only if each point is scaled by the same factor. If we know that A(x, y) = (3, 9), A'(x, y) = (2, 6), B(x, y) = (9, 9), B'(x, y) = (6, 6), C(x, y) = (3, 3) and C'(x, y) = (2, 2), then the scale factor for each point is:

Point A

(2, 2) = k · (3, 3)

k = 2 / 3

Point B

(6, 6) = k · (9, 9)

k = 2 / 3

Point C

(2, 2) = k · (3, 3)

k = 2 / 3

Then, triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC.

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either 1042.35 or 1.04235*10^3

Answer:

128

Step-by-step explanation:

x³y²if x = 2 and y = 4

x³*y²

[tex](2)^{3} * (4)^{2}[/tex]

(2*2*2)*(4*4)

(8)*(16)

128

Answer:

Let x = the cost of a movie

Let y = the cost of a game

Using these variables, we can set up equations.

3x + 5y = 42 eq1

9x + 7y = 72 eq2

We have here a system of equations, where we have two or more equations with two or more different variables. We use the elimination method to solve for the variables.

Multiply eq1 by 3. Keep eq2.

9x + 15y = 126 eq1

9x + 7y = 72 eq2

Subtract eq2 from eq1 to eliminate the x terms.

8y = 54

y = 6.75

This rental cost of one video game is $6.7

Substitute the value of y into eq1 to solve for x. This will give you the rental cost of one movie.

Step-by-step explanation:

pa brainly po

The cost of movie is $4.5 and cost of video game is $5.75.

Two or more expressions with an Equal sign is called as Equation.

Let x be the cost of movie and y be the cost of video game

Calvin rents 3 movies and 2 video games and spends a total of $25.

3x+2y=25...(1)

Samantha rents 2 movies and 1 video game and spends a total of $14.75.

2x+y=14.75

y=14.75-2x..(2)

Substitute (2) in equation (1)

3x+2(14.75-2x)=25

3x+29.5 -4x=25

-x+29.5 = 25

Subtract 29.5 from both sides

-x=25-29.5

x=4.5

Now let us plug in x value in equation (2)

y=14.75-2(4.5)

y=5.75

Hence, the cost of movie is $4.5 and cost of video game is $5.75.

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By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:

r = √[(√11 / 6)² + (5 / 6)²]

r = √[(11 / 36) + (25 / 36)]

r = √(36 / 36)

r = √1

r = 1

By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.

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Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.

r, the exponent of x, is: 2/3

s, the exponent of y, is: 1

According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.

³√x²y³ = x^r y^s

Cubing on both sides,

x²y³ = x^3r y^3s

As base is same, equating the powers

⇒ 2 = 3r; r = 2/3

⇒ 3 = 3s; s = 1

The expression

³√x²y³ = x^ry^s

where x and y are non-negative real numbers.

r, the exponent of X, is:

s, the exponent of y, is:

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{ 0,2,4,6,8} is  the complement of the set.

What is natural number in math?

Is zero a natural number?

u = {0, 1, 2, 3, 4, 5, 6, 7, 8}

Odd number less than 8  = { 1,3,5,7 }

complement =  {0, 1, 2, 3, 4, 5, 6, 7, 8} -  { 1,3,5,7 }

                     = { 0,2,4,6,8}

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Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

Answer:

CD= 2x-1

Step-by-step explanation:

AD = 6x-4

AC = 4x - 3

CD= AD- AC

CD=  6x-4 - (4x - 3)

CD= 6x - 4 - 4x +3

CD= 2x -1

Therefore, the value of CD= 2x-1

The equation of the line is y=x+12.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The points are

(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

We have to Write the equation of the line.

According to given question we have,

Equation of line passing through the point (-3,9) and  (-9,3).

Slope of the line=

[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]

⇒y−9=1(x+3)

⇒y-9=x+3

Add 9 on both sides we get,

y=x+12

∴ y=x+12 which is in the form y=mx +c is the required equation.

Therefore, the equation of the line is y=x+12.

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y = x + 12

What is equation of a line?

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.

y-y₁=m(x-x₁)

mm₁=-1

Points (-3,9) and  (−9,3).

Slope of the line m = (y₂ - y₁)/(x₂ - x₁)

m = (3-9)/(-9+3)

m = 1

Now  equation of line passing through two points

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

(y - 9)/(3-9) = 1*(x - 3)/(-9+3)

y - 9 = x + 3

y = x + 12

Therefore, the equation of line is y = x + 12

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The weighted average of a data set is 36.

Here,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

We have to find the weighted average of a data set.

What is Weighted Average?

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.

Now,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

The weighted average is given by the formula;

[tex]x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}[/tex]

Hence,

The weighted average of a data set;

x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2

x = 360/10 = 36

Hence, The weighted average of a data set is 36.

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-ln ( 1 - x/y - x) = c is a bernoulli equation. xdy/dx-(1 x)y=xy^2.

What is a differential equations explain?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)

[tex]\frac{-1}{y} = u[/tex]

[tex]\frac{y'}{y^{2} } = u'[/tex]

[tex]xy' - ( 1 + x )y = xy^{2}[/tex]

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

xu' + ( 1 + x )u = x

xu' + u + ux = x

 xu = s

u + xu' = s'

s' + s = x

s - x  =t

s' - 1 = t'

t' + 1 + t = 0

dt/dx = - ( 1 + t)

-∫ [tex]\frac{dt}{1 + t} =[/tex]  ∫dx

-ln ( 1+ t ) = x + c

-in ( 1 + s - x ) = x + c

-ln ( 1 + xu - x ) = x + c

-ln ( 1 - x/y - x) = c

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The value of angle B is 69°.

It should be noted that the sum of a complementary angle is 90°.

Therefore, the value will be:

x + 13 + 7x + 13 = 90

8x + 26 = 90

Collect like terms

6

8x = 90 - 26

8x = 64

Divide

x = 64/8

x = 8

Angle B = 7x + 13

= 7(8) + 13

= 56 + 13

= 69

Angle B is 69°.

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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No, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.

Here,

A function f defined on [ 4 , 5 ].

We have to find, is it possible to f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.

What is Intermediate value theorem?

Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.

Now,

A function f defined on [ 4 , 5 ].

Assume that the function,

f :  [ 4 , 5 ] → Z is a non constant continuous function.

Then, f(4) and f(5) both are integers and not equal to each other.

By, Intermediate value theorem;

Function f takes all real numbers between f(4) and f(5) at least once.

These would contain all non integers rational and irrational number between f(4) and f(5), contradicting the assumption that function takes only integer values.

Hence, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.

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Answer:

x = 4       y = 21

Step-by-step explanation:

16x - 23 = 10x + 1

16x - 10x = 23 + 1

6x = 24

24/6 = x

x = 4

16(4) - 23 = 41

41 + (180 - 62) + y = 180

41 + 118 + y = 180

y = 21

Answer:

(x-2y){5-(x-2y)}

=(x-2y)(5-x+2y)

Answer: 70

Step-by-step explanation:

2×3÷2+1+2×33

PEMDAS, do all the multiplication first.

2×3 = 6, 2×33=66

Do division next.

6÷2=3

3+1+66=70

Answer:

10e + 11

Step-by-step explanation:

12e + 6 - 2e + 5 ← collect like terms

= (12e - 2e) + (6 + 5)

= 10e + 11

Answer:

85%

Step-by-step explanation:

Total no. of matches played,

→ x = 20 matches

No. of matches they won,

→ y = 17 matches

Now the win percentage will be,

→ (y/x) × 100

→ (17/20) × 100

→ 0.85 × 100

→ 85%

Hence, the percentage is 85%.

Answer: The orthocenter and varicenter  of an equilateral triangle are the same point?

Step-by-step explanation

Answer: De nuevo, puedes ver que el baricentro, el ortocentro y el circuncentro son todos el mismo punto para un triángulo equilátero. Tenemos un centro más para comparar, el incentro. Como habrás sospechado, el incentro es el mismo punto que los otros tres para un triángulo equilátero.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

9 + 2 = 11

Best explanation I can give for this.

Answer: 11

Step-by-step explanation: bc i used a calculater

The profit shows in retained earning can be used for reinvestment into the company

There are many measures and uses of earnings. Some analysts like to calculate earnings before taxes (EBT), also known as pre-tax income. Some analysts prefer to see earnings before interest and taxes (EBIT). Still, other analysts, mainly in industries with a high level of fixed assets, prefer to see earnings before interest, taxes, depreciation, and amortization, also known as EBITDA.

Earnings that deviate from the expectations of the analysts that follow that stock can have a great impact on the stock's price, at least in the short term. For instance, if analysts on average estimate that earnings will be $1 per share and they come in at $0.80 per share, the price of the stock is likely to fall on that "earnings miss."

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The function g that is finally graphed after the transformations are applied is g(x) = -5f(-x) - 10

The function is given as:

f(x)

Next, we apply the transformations

So, we have:

(1) reflect about the x-axis;

This is represented as

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

(2) shift down 2 units;

This is represented as

(x, y) = (x, y - 2)

So, we have

g(x) = -f(x) - 2

(3) stretch vertically by a factor 5;

This is represented as

(x, y) = (x, 5y)

So, we have

g(x) = 5(-f(x) - 2)

Evaluate

g(x) = -5f(x) - 10

(4) reflect about the y-axis.

This is represented as

(x, y) = (-x, y)

So, we have

g(x) = -5f(-x) - 10

Hence, the function g that is finally graphed after the following transformations are applied is g(x) = -5f(-x) - 10

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Answer:

"If chickens make eggs, then cows make milk."

Step-by-step explanation:

Answer: A:  If chickens make eggs, then cows make milk.

Step-by-step explanation: Hope that helped

Answer: The pattern is that you -1 then -2 then -3.

Step-by-step explanation:

If you got 9, 8, 6, 3. You would be subtracting 1 then 2 then 3 then 4 then on and on.

Average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.

As given,

Total distance= 30 kilometers

Total time taken = 8 minutes

1 kilometer = 0.62137 miles

30 kilometers = 30 × 0.62137

                     = 18.641 miles

8 minutes = ( 8 / 60) hour

Average speed= total distance / total time taken

                                          = 18.641 / (8/60)

                                          = 139.8 miles/ hour

Therefore, average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.

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