At Rental Company A, a rental car costs $55.50 and every
kilometer costs $14.40. At Rental Company B, a rental car
costs $91.50 and every kilometer costs $10.80.
At how many kilometers will they cost the same, and how
much will it cost?
kilometers
dollars

For the quadratic equations -

1) f(x) = x² - 16x + 3 → Vertex form is y = 3(x - 8)² - 61 and vertex is (8,-61).

2) f(x) = 4x² + 24x - 7 → Vertex form is y = 4(x + 3)² - 43 and vertex is (-3,-43).

3) f(x) = -2x² - 8x + 9 → Vertex form is y = -2(x + 2)² + 17 and vertex is (-2,17).

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic equation is written in the form ax² + bx + c = 0.

The vertex form of a quadratic equation is -

y = a(x - h)² + k

The first equation is - f(x) = x² - 16x + 3.

Here, a = 1, b = -16 and c = 3

The formula for h is -

h = -b/2a

h = -(-16)/2(1)

h = 16/2

h = 8

The formula for k is -

k = c - (b²/4a)

k = 3 - [(-16)²/4(1)]

k = 3 - (256/4)

k = 3 - 64

k = -61

So, the vertex form is -

y = a(x - h)² + k

y = 3(x - 8)² - 61

The vertex is written as (h,k).

The vertex is (8,-61).

Therefore, the vertex form and vertex is y = 3(x - 8)² - 61 and (8,-61) respectively.

The second equation is - f(x) = 4x² + 24x - 7.

Here, a = 4, b = 24 and c = -7

The formula for h is -

h = -b/2a

h = -(24)/2(4)

h = -24/8

h = -3

The formula for k is -

k = c - (b²/4a)

k = -7 - [(24)²/4(4)]

k = -7 - (576/16)

k = -7 - 36

k = -43

So, the vertex form is -

y = a(x - h)² + k

y = 4(x + 3)² - 43

The vertex is written as (h,k).

The vertex is (-3,-43).

Therefore, the vertex form and vertex is y = 4(x + 3)² - 43 and (-3,-43) respectively.

The third equation is - f(x) = -2x² - 8x + 9.

Here, a = -2, b = -8 and c = 9

The formula for h is -

h = -b/2a

h = -(-8)/2(-2)

h = 8/-4

h = -2

The formula for k is -

k = c - (b²/4a)

k = 9 - [(-8)²/4(-2)]

k = 9 - (64/-8)

k = 9 + 8

k = 17

So, the vertex form is -

y = a(x - h)² + k

y = -2(x + 2)² + 17

The vertex is written as (h,k).

The vertex is (-2,17).

Therefore, the vertex form and vertex is y = -2(x + 2)² + 17 and (-2,17) respectively.

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The y-coordinate for the solution to the system of equations is -3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations. The intersection of two lines represents the system of equations' solution.

Given system of equations are,

6x + 11y = -3

4x + y = 17

To solve these equations, we must first remove x or y terms.

To do this we must make the removing term's coefficients the same.

In this case, let's remove y.

We are multiplying the second equation by 11. Then,

6x + 11y = -3

44x + 11y = 187

Now we will subtract the second equation from the first.

- 38x  = -190

x = 5

Now to find y, substitute x in any one of the equations.

6 * 5 + 11y = -3

11y = -33

y = -3

Hence the y-coordinate for the solution to the system of equations is -3.

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An expression that calculates how much greater Alphaville's annual budget surplus is than Betaville's for a particular amount of tax revenue is, -3x² + 600x - 10000.

And the value is -$16830010000.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Alphaville's Budget Surplus Model is,

-2x² + 500x.

Betaville's Budget Surplus Model is,

x² - 100x + 10000.

The tax revenue that year in each town is $75,000.

An expression that calculates how much greater Alphaville's annual budget surplus is than Betaville's for a particular amount of tax revenue:

-2x² + 500x - x² + 100x - 10000,

= -3x² + 600x - 10000

Now, x = 75000

Then,

= -$16830010000

Hence, an expression is -3x² + 600x - 10000.

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Answer:

[tex]10.3x-10.3y[/tex]

Step-by-step explanation:

Distribute 10.3 to x and -y

[tex]10.3x-10.3y[/tex]

Answer:

Step-by-step explanation:

2nd one because if you use logic it works

btw this is a real answer

Step-by-step explanation:

There are 6 + 1 + 3 = 10 marbles in total.

Out of these, 6 are yellow, so the fraction of yellow marbles is 6/10 = 3/5.

Answer:

40 miles per hours

Step-by-step explanation:

We know

A truck driver drove 350 miles in 8 3/4 hours.

8 3/4 = 35/4 = 8.75

So, the truck driver drove 350 miles in 8.75 hours

What is the speed of the truck in miles per hour?

We take

350 divided by 8.75 = 40 miles per hours

So, the speed of the truck is 40 miles per hour.

The probability of being no blue marble in the experiment is given as follows:

P(no blue) = 27/100.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of outcomes for this problem is given as follows:

100.

The desired outcomes are those with only white marbles, which are of:

27.

Hence the probability of being no blue marble in the experiment is given as follows:

P(no blue) = 27/100.

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Sum of coordinates, S + T = (9 , -7)

A coordinate is an address, which helps to locate a point in space. For a two-dimensional space, the coordinates of a point are (x, y). Here let us take note of these two important terms.

Abscissa: It is the x value in the point (x, y), and is the distance of this point along the x-axis, from the origin

Ordinate:  It is the y value in the point (x, y)., and is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.

Given,

S = (4 , -6)

T = (5 , -1)

S + T = (4 , -6) + (5 , -1)

        = (4 + 5 , -6 + -1)

        = (9 , -7)

Hence, S + T = (9 , -7) is sum of coordinates of point S and T

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An equivalent expression  of x² - 8x + 5 is  (x - 4)² - 11

To convert this quadratic expression x² - 8x + 5 into the form (x - a)² - b we will use completing the square method.

Comparing expression  x² - 8x + 5 with ax² + bx + c we get,

a = 1, b = -8 and c = 5

First we find the value of the expression (b/2a)² is:

(b/2a)²

= [-8/(2 × 1)]²

= (-8/2)²

= (-4)²

= 16

Now, we add and subtract the value of the term (b/2a)² in the expression  x² - 8x + 5

So the expression  x² - 8x + 5 becomes,

x² - 8x + 5

= x² - 8x + 5 + 16 - 16        

= x² - 8x  + 16 + 5 - 16       ......(commutative property of addition)

= (x - 4)² - 11                      ......(since (x - 4)² = x² - 8x  + 16)

Therefore, the required expression is:  (x - 4)² - 11

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Answer:

[tex]x = \frac{y + c}m[/tex]

Step-by-step explanation:

[tex]y = mx - c \text{ // Add c}\\y + c = mx - c + c\\\to y + c = mx \text{ // Divide by m}\\\\\frac{y + c}m = \frac{mx}m\\\\\to \frac{y + c}m = x[/tex]

Hi there, here's your answer:

From the question,
Given:

Weight limit for the lift = 1000kg

Mean weight of 10 people = 70kg

Therefore, the total weight of 10 people inside the lift is 70 × 10 = 700kg.

Now, remaining weight that can fit in the lift is 1000 - 700 = 300kg.

Assuming the mean weight of the people who get inside the lift is constant, we find the closest number of people who can get inside the lift to be:

300 ÷ 70 = 4.285
Or
Roughly 4 more people.

Hope it helps!

The equation that represents the apex angle is x + 15° + 15° = 180°. And the measure of the apex angle is 150°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

If the base angle of an isosceles triangle measures 15°. And the angle of 15° is an isosceles angle.

Let the third angle be 'x'. Then the equation is given as,

x + 15° + 15° = 180°

x = 180° - 15° - 15°

x = 180° - 30°

x = 150°

The equation that represents the apex angle is x + 15° + 15° = 180°. And the measure of the apex angle is 150°.

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Answer:The Attachment

Step-by-step explanation:

8.75 cm  length can Nuka weave in 5 minutes.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

they can weave 7 cm of the strip in 4 minutes

so, Nuka weave in 5 minutes = 7/4 *5

                                                = 8.75 cm

Hence, 8.75 cm  length can Nuka weave in 5 minutes.

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The number of solutions that this system of equations shown above has is: A. no solution.

In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

This ultimately implies that, an equation would have no solution when both sides of the equal sign are not the same and the variables cancel out, which can be demonstrated through this system of equation;

x + y = 4

x + y = 6

4 - y + y = 6

4 = 6 (no solution).

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It take 4 hours to paint a house working alone.

Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 8 hours to paint a house alone. How long does it take karen to paint a house working alone?

According to the problem, when Betty and Karen work together, they can paint a house in two-thirds the time it takes Karen to paint a house alone, so t * 2/3.

Let k = time it takes Karen to paint the house alone

then

(2/3)(k)(1/k + 1/8) = 1

(2k/3)(1/k + 1/8) = 1

(2k)(1/k + 1/8) = 3

(2 + k/4) = 3

K=4

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The total value of Mr. Liling's shares at the end of 2016 was $1388.50.

The value of a share, also known as the stock price, represents the price per unit of ownership in a company. It is determined by supply and demand for the stock in the stock market and can fluctuate based on a variety of factors such as the company's financial performance, industry trends, and overall market conditions.

At the beginning of 2016, Mr. Liling bought 10 shares of stock in QIZ Software for $198.58 per share, so the total cost was 10 * $198.58 = $1985.80.

In 2016, the stock price of QIZ Software changed by -$59.73, so the value of Mr. Liling's shares at the end of 2016 was $1985.80 - 10 * $59.73 = $1985.80 - $597.30 = $1388.50.

So, the total value of Mr. Liling's shares at the end of 2016 was $1388.50.

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Answer:

2

Step-by-step explanation:

Start at the bottom of the graph.  It starts at (8,0).  From that point go up 2 and one to the right.  You will be back on the line at the point (9,2)

Slope is your rise over your run.  2/1 = 2

9.  The area of the triangle is  17. 5 square units

10. The area of the rectangular shaded (lavender) area that lies behind the triangle is 72 square units

11. By counting the dots around the shapes.

The formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Given that the parameters are;

From the diagram, we have;

Area = 1/2 × 5 × 7

Area = 17. 5 square units

The formula for area of a rectangle is expressed as;

Area = lw

Substitute the values

Area = 9 × 8

Multiply the values

Area = 72 square units

Hence, the values are 17. 5 square units and 72 square units

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The amount in the new account (future value) after 7 years will be D. $3,207.40.

The future value of the investment is determined in two stages.

The first stage compounds the present investment semiannually at 2.5%.

Using the determined future value of the first stage, we can determine the second stage's future value.

To determine the future values, we deploy an online finance calculator.

N (# of periods) = 24 semiannual periods (12 years x 2)

I/Y (Interest per year) = 2.5%

PV (Present Value) = $1,800

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $2,425.23

Total Interest = $625.23

N (# of periods) = 84 months (7 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $2,425.23

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,207.40

Total Interest = $782.17

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There are 105 odd numbers with a middle digit of 5 between 40000 and 69999 with no repeating digits.

We must first take into account the limitations of the issue in order to determine this.

∴,

There are three options for the first digit: 4, 5, and 6.

There are five options for the units digit: 1, 3, 5, 7, and 9.

There are seven possible outcomes for the remaining digits: 0, 2, 4, 6, 7, 8, and 9.

According to the multiplication principle, the total number of numbers having the needed qualities is:

3 × 5 × 7 = 105

Thus, there are 105 odd numbers between 40000 and 69999 that have a middle digit of 5 but no repeated digits.

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Answer: maybe go to quizly

Step-by-step explanation: just type geometric formulas quizly in the search bar

answer you can go to kahn acadamy

Step-by-step explanation:

please add me on brainlist

Answer:

The function displayed in the table is best described as an Exponential Decay Function.

Step-by-step explanation:

            First, the main difference between a linear and an exponential function is the shape of its graph, as well as the presence of either a constant ratio or a constant rate of change.

            Linear functions are functions with a base function of  [tex]f(x)=mx+b[/tex], which has a constant rate of change ([tex]m[/tex]), and the shape of its graph will be a straight line.

            Exponential functions on the other hand use the base function [tex]f(x)=a^x[/tex], where [tex]a[/tex] is the constant ratio of the function, and its graph is curved and has a horizontal asymptote that the graph will approach but never touch as it either increases or decreases to positive or negative infinity respectively.

            The function in the problem gives you four points that are on its graph: (-2, 540), (-1, 270), (0, 135), and (1, 67.5). Using these points, you can determine whether it is a linear or exponential function. You can tell that when the x-value increases by 1, the f(x) value is divided by 2, or multiplied by [tex]\frac{1}{2}[/tex]. Since there is a constant ratio instead of a constant rate of change in the function, you would know that the function in the table is an exponential function. Since the function is also constantly decreasing, the function would be best described as an Exponential Decay Function.

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The result of the long division of the polynomial (6x³ - 2x² + 10x -25) ÷ (2x - 2) is   3x²  + 2x + 7 ( - 11 / 2x - 2 ).

A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.

The quotient of the polynomial is obtained by using long division method as shown below.

                          3x²  + 2x + 7

                     ---------------------------------

            2x - 2  √ ( 6x³ - 2x² + 10x -25 )

                           - (6x³  - 6x² )

                          -------------------------

                                      4x² + 10x -25

                                  - ( 4x² - 4x )

                                ------------------------------

                                             14x - 25

                                          - ( 14x - 14 )

                                      -------------------------------

                                                      - 11

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The probability that the sequence of tosses is HTHT is 1/16, which can also be written as 0.0625 rounded to four decimal places.

The probability of getting a specific sequence of coin tosses, such as "htht", in four tosses of a fair coin can be calculated by finding the probability of getting each individual outcome and multiplying them together. The probability of getting heads in a single fair coin toss is 1/2 and the probability of getting tails is also 1/2.

So, the probability of getting the sequence "HTHT" in four tosses of a fair coin is:

= (1/2) * (1/2) * (1/2) * (1/2)

= 1/16

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A dot plot is a graphical representation of data that shows the frequency of each data value on a number line by plotting dots above the values. A box plot is a graphical representation of data that depicts data distribution using five key values: minimum, first quartile, median, third quartile, and maximum.

The box plot in this case depicts the distribution of points awarded to dance teams in a competition. The minimum value is zero, the first quartile is fifty, the median is seventy, the third quartile is ninety, and the maximum value is one hundred.

"dot plot titled Dance Competition Points with Points on the x axis and Number of Teams on the y axis with 2 dots over 50, 1 dot over 70, 2 dots over 90, 1 dot over 100," is the dot plot that best represents the box plot data. This dot plot accurately reflects the data distribution in the box plot.

It shows two dots over 50 (representing two teams), one dot over 70 (representing one team), two dots over 90 (representing two teams), and one dot over 100 (representing one team) (representing 1 team). These values correspond to the box plot values and accurately represent the data distribution.

The other dot plots do not accurately reflect the distribution of the data as they either have incorrect values or incorrect frequencies for each value.

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The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.

A: the x-axis.

Answer:

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

For RIGHT triangles

Cos (21°) = adjacent leg / hypotenuse

cos ( 21°) = x / 21

re-arrange to

21 * cos (21°) = x      then use calculator to find x = 19.6 units

( it may not look like it from the picture...but the picture is not drawn to scale :  a 21° angle is much smaller than pictured)