If a car travels 368.5 miles on 50 liters of gas, how many liters of gas will it take to go 691 miles if the car travels at the same rate? (Round to the nearest tenth)

The sum of the infinite geometric series is 10

From the values that we have, the first term a1 = - 20, the common ratio r = 3

From the above we can get the first 5 terms of the geometric series. We do this by multiplying each number derived by 3

this would be :

-20, -60, -180, -540 , -1650 ...

The formula for the sum of the infinite geometric series is given as

S = a1 / 1 - r

from the question we have

a1 = -20

r = 3

we would put the values into the formula

S = -20 / 1 - 3

S = -20 / -2

s = 10

Hence the sum is given as 10

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Answer:

what is this on

Step-by-step explanation:

Answer:

Each yardn is 36 inches. Multiply the number of yards. times inches and that will be the total number of inches for 8 yards.

Step-by-step explanation:

I yd = 36 inches

you have 8 yards

36 x 8 = 288 inches

Answer:

answer is 288 inches

Step-by-step explanation:

8 yards is equal to 288 inches

In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.

The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.

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The triangle that has two angles measuring 17 degrees and 107 degrees is a B. Obtuse triangle.

A triangle with sides of length 5, 6, and 7 would be a C. Scalene triangle.

There are several types of triangles and one of them is an obtuse triangle. Such a triangle would have an angle that is larger than 90 degrees, much like the triangle mentioned that has an angle with 107 degrees.

There are also Scalene triangles where all their dimensions do not have the same measurement. This is why the triangle shown has sides of 5, 6, and 7.

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The value of the equation is r = ( 1/2 ) ( A / 3L - πR )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 3L ( 2r + πR )   be equation (1)

Now , on simplifying the equation , we get

( 2r + πR ) = A / 3L

Subtracting πR on both sides of the equation , we get

2r = A / 3L  - πR

Divide by 2 on both sides of the equation , we get

r = ( 1/2 ) ( A / 3L - πR )

Therefore , the value of r is ( 1/2 ) ( A / 3L - πR )

Hence , the equation is r = ( 1/2 ) ( A / 3L - πR )

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The 3 main exponent properties are:

The product of powers property states that when you multiply two numbers with the same base, you can add the exponents to find the result. For example, (2^3) * (2^4) = 2^(3+4) = 2^7

The quotient of powers property states that when you divide two numbers with the same base, you can subtract the exponents to find the result. For example, (2^5) / (2^3) = 2^(5-3) = 2^2

The power of a power property states that when you raise a power to another power, you can multiply the exponents to find the result. For example, (2^3)^2 = 2^(3*2) = 2^6

These three properties help simplify algebraic expressions that include exponents and make it easier to solve equations and perform other mathematical operations.

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The answer is 2x-5

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here:  linear expression. −2x+5

Thus the additive inverse is -2x+5+2x-5=0

Hence, the additive inverse is 2x-5

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Transform the equation using standard form in which one side is zero is the first step to solving quadratic equations in factored form.

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Answer:

distance = (62t) + 22

Step-by-step explanation:

Distance = speed * time

distance = (62*t) + 22

Hope this helps!

Answer:

53,150 ML

Simply add both of the numbers and you have your answer.

The graph of the set of the points has the constraints  -8≤2+5t≤37 &    -25≤3-4t≤11

An inequality is an inequation separated by <,>≥,≤

Given here: The set of points (2+5t,3-4t) in the xy-plane

when -2≤t≤7 set of points (2+5t,3-4t)

then 2+5×-2≤2+5t≤2+5×7

        -8≤2+5t≤37

     Again, 3-4×-2≤3-4t≤3-4×7

             -25≤3-4t≤11

We can construct a graph using the above accordingly

Hence, The graph of the set of the points has the constraints  -8≤2+5t≤37 &    -25≤3-4t≤11

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Using simple mathematical operations, we know that we will get a change of $0.5.

An operation is a function in math that transforms zero or more input values into a strictly delineated output value.

The operation's arity is influenced by the number of operands.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "×" Finding the quotient in division ("÷)

So, we know that:

Grapes cost $1.99.

We purchased 2.25 pounds of grapes.

The change we will receive if we gave a $5 bill will be:

5 - (1.99*2.25)

5 - 4.4775

0.5225

Rounding off: $0.5

Therefore, using simple mathematical operations, we know that we will get a change of $0.5.

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Answer:  x = 1,  y = -1

Step-by-step explanation:

The elimination method is a technique for solving systems of linear equations.

1) 4x-6y=10

2) 9x+2y=7

in the second equation

it multiply with 3

then

3×(9x+2y=7)

= 27+6y= 21

We notice that the first equation has a 6y term and the second equation has a -6y term. These terms will cancel if we add the equations together—that is, we'll eliminate the x terms:

then add 1 + 2 equations

    4x-6y =  10 _____1)

   27+6y= 21   _____2)

then we will get

    31x+0  =  31

     31x= 31

     where x = 31/31= 1

          then x = 1

      if value of  x substitute in the equation ____1)

                           4x+6y =  10

                           4×1+6y =  10

                            6y = -6

                            y = -6/6

                             y = -1

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True, Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.

What is Recreational water illnesses?

Recreational water infections (RWIs) are contracted by ingesting, inhaling mists or aerosols from, or coming into touch with contaminated recreational water and are brought on by microorganisms.

                        In addition to swimming pools, hot tubs, water slides, water play zones, interactive fountains, lakes, rivers, and seas are all examples of recreational water.

What exactly is a recreational water?

Incorporated into this are swimming, diving, water skiing, and surfing. Recreation involving secondary touch, where you come into direct contact with the water but are unlikely to ingest it Paddling, wading, boating, and fishing all fall under this category.

                     without any physical interaction with the water, passive recreation.

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The graph for the inequality is attached below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each student ticket sells for $6.50 and each adult ticket sells for $11.

let the number of student ticket sold be x and number of adult ticket sold be y.

so, the inequality is

x + y < 130

and, 6.5x + 11y >1100.

Solving the inequality we get

x= 73.33 and y = 56.667

Now, if they sell at least 90 adult tickets then they sell at most 40 children ticket.

Hence, the solution is (73.33, 56.667).

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The value of x calculated by using the Pythagorean theorem is equal to 6.

This can be found by using the Pythagorean theorem to solve for the length of side bc, which is the base of the triangle. By using the two given side lengths of 8 and 12, we can find that the length of the hypotenuse (bc) is equal to the square root of 8^2 + 12^2, which is equal to 16.

Since the base is divided into two equal parts, we can divide 16 by 2 and get 8. We then subtract the given length of 2x + 1 from 8 and get 7, which means x is equal to 6.

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The width of a rectangle that has a length of 24 inches would be 60 inches.

According to the data, we can assume that all the rectangles in the table have the same ratio of measurement.

To find unknown width of the rectangle, we can use this equation:

A/B = C/D

Where:

A represents the length of the first rectangle  

B represents the width of the first rectangle

C represents the length of the second rectangle

D represents the width of the second rectangle

In this case, we are going to use 12 as the length of the first rectangle, and 30 as its width.

12/30 = 24/D

12D = (30 x 24)

12D = 720

D = 60

Thus, the width of the rectangle that has a length of 24 inches is 60 inches.

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The equation for given two points of parabola will be (x+1)^2=y-10.

What is parabola?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:

y^2 = 4ax

If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,

x^2 = 4ay

Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.

Now,

the parabola having points  (–5, 26) and (3, 26) is given in graph

and the equation will be (x+1)^2=y-10

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a) The equation of line is y = 270x + 10640.

b) The annual cost value in 2013 for age 17 is $15,320.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Points (8, 12800) and (14, 14420)

So, the slope is

= (14420 - 12800)/(14-8)

= 1620/6

= 270

and, the slope intercept form

(y - 12800) = 270 (x - 8)

y- 12800 = 270 x  - 2160

y = 270x + 10640

b) Now, x= 17

y= 270(17) +10640

y = 15, 320

Thus, In 2013 at age of 17 the amount is $15320.

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Therefore , the solution of the given problem of congruences comes out to be [FD]=[FE] and [DM]=[NE]

SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.

SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.

SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.

Here,

SSS – side, side, and side. ...

SAS – side, angle, and side. ...

ASA – angle, side, and angle. ...

AAS – angle, angle, and side. ...

HL – hypotenuse and leg.

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If algebraic expressions are a³ᵇ = x and aᵇ = y, then, by algebra properties, x / y² is equal to aᵇ.

Herein we find the following two algebraic expressions with two positive integers a and b:

a³ᵇ = x

aᵇ = y

From these equation we need to find the result associated to algebraic expression x / y² in terms of the integers given. This can be done by means of algebra properties. First, square the second expression:

(aᵇ)² = y²

Second, divide the first expression by the given formula found in previous step:

x / y² = a³ᵇ / (aᵇ)²

Third, simplify the resulting expression to a single power:

x / y² = a³ᵇ / a²ᵇ

x / y² = a³ᵇ - ²ᵇ

x / y² = aᵇ

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Answer:

I believe it is 24°F

Step-by-step explanation:

I'm just cool like that

Answer:

For each service call cost of 20$ will be added to fixed cost of 3000$.

Step-by-step explanation:

The total cost for 1 month is the sum of the fixed monthly cost and the cost of all the service calls, so we can write the equation as:

y = 3000 + 20x

This equation is already in slope-intercept form, where "y" is the dependent variable, "x" is the independent variable, 3000 is the y-intercept (the point where the line crosses the y-axis, when x=0), and 20 is the slope of the line.

This equation can be interpreted as

For each service call cost of 20$ will be added to fixed cost of 3000$.

Answer: Vertical stretch by a factor of 3.

Answer:

500 people came each day

Step-by-step explanation:

2000 divide by 4= 500

Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.

The following is the equation for a horizontal ellipse of center with coordinates (h,k):

(x - h)²/a² + (y - k)²/b² = 1.

In relation to this issue, we have that:

The origin is where the center is.

Since the major axis is 70, 2a = 70 and a = 35.

The maximum height is 20, therefore b is equal to 20.

As a result, the ellipse's equation is as follows:

x²/35² + y²/20² = 1.

It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:

25²/35² + y²/20² = 1

0.51 + y²/20² = 1

y²/20² = 0.49

y² = 20² x 0.49

y =√(20² x 0.49)

y = 14 feet.

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Erisa collected quarters. After a year he had quite a few of them. The smallest number of quarters that Erisa could have collected is 17.

Generally, Erisa collected quarters. After a year he had quite a few of them.

The smallest number of quarters that Erisa could have collected is 17.

This is because 17 is a prime number, and when it is divided into groups of 2, 3, 4, and so on, up to 16, there will always be one left over.

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The triangle problem's solution is given by the relationship amongst x,y and z, which is z²= x²+y² .

Due to its three vertices and three sections, a triangles is a polygon. It has a simple geometric form. Triangle ABC refers to a triangular with the points A, B, and C. When three factors are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By summing three triangle angles, one gets 180 degrees.

Here,

Given: In this situation, triangle XYZ is a right triangle.

Thus,

We discover:

Z, X, and Y components

They are linked in the following ways:

It being a right triangle,

So,

According to the Pythagoras Theorem,

=>z²= x²+y²

The triangle problem's solution can be found by using the relationship among z, x, and y, which is given by z2=x2+y2.

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