one friday night, two large groups of people called wildgrove taxi service. the first group requested 1 sedan and 2 minivans, which can seat a total of 13 people. the second group asked for 3 sedans and 2 minivans, which can seat a total of 19 people. how many passengers can each type of taxi seat?

Answer:

Below

Step-by-step explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x       then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

The curve will get shifted left side by four units. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = g(x)

If the g(x) is replaced with g(x + 4). Then the curve will get shifted left side by four units.

Thus, the correct option is A.

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The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

50L of diesel from Sasol costs R 799.59. Then the rate is given as,

⇒ 799.59 / 50

⇒ R 15.9918 per liter

40L of diesel from Shell costs R 619.60. Then the rate is given as,

⇒ 619.60 / 40

⇒ R 15.49 per liter

The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.

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The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses, then combine like terms: 6b 4r - 2b r = 4b + 3r.

The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses. To correctly simplify the expression, first distribute the negative sign, then combine like terms. Start by distributing the negative sign: 6b 4r - 2b r = 6b 4r + (-2b) (-r). Then, combine like terms: 6b 4r + (-2b) (-r) = 6b + (-2b) + 4r + (-r) = 4b + 3r. This is the correct answer.  It is important to note that when subtracting within parentheses, you must distribute the negative sign to each term. Once the negative sign has been distributed, you can then combine like terms. This method can be used to simplify any expression with parentheses and subtractions.

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Using the linear relationship the height of the candle after 17 hours is 22.3 cm.

As it is given that the height of the candle is linear to the amount of time. The linear relationship is the relationship between two variables such that it follows a straight line.

Now, let the time be on the x-axis and the y-axis is the height of the candle. therefore, the slope of the linear relationship can be represented as,

(x₁, y₁) = (7, 23.3)

(x₂, y₂) = (23, 21.7)

Since we know the two points of the linear relationship, therefore, the slope can be written as,

m = (y₂ - y₁)/(x₂ - x₁)

m = (21.7 - 23.3)/(23 - 7)

m = -1.6/16

m = -1/10

Now, the equation of the linear relationship can be written as,

y - y₁ = m( x - x₁)

y - 23.3 = (-1/10)(x - 7)

10y - 233 = -x + 7

x + 10 y = 240          --(1)

We are asked to determine the height of the candle after 17 hours. So, put x = 17 and find y

17 + 10y = 240

10y = 223

y = 22.3

Hence, the height of the candle after 17 hours is 22.3cm.

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Answer:right angles, two sets of parallel sides, and opposite sides equal.

Step-by-step explanation:

Answer:

5.83 x 10^13.

Step-by-step explanation:

5.3x10^6 x 1.1x10^7

= 5.3 x 1.1 x 10^(6+7)

= 5.83 x 10^13.

Answer:

There is no given price so lets say I need something that is 85$ and I have a 10% off coupon well I will be saving 8.50$ and only needing to pay 76.50.

4$ would not take that much off only would be paying 81$

Step-by-step explanation:

85 divided by 100 x10 = 8.50

85$-4=81

Answer: function A is linear

Step-by-step explanation:

Answer:

15√2

Step-by-step explanation:

3[tex]\sqrt{50}[/tex] = 3√25·2 = 3·5√2 = 15√2

Answer:

1 2/3 sq ft

Step-by-step explanation:

2/1 x 5/6 = 10/6 = 1 4/6 = 1 2/3

you turn 2 into a fraction 2/1 then multiply by 5/6, then you get 10/6so you simplify and you get the answer 1 2/3

According to the question we have (5, 2) isn't a response of the linear equation system because one of equations is erroneous.

Salt water, rub whiskey, and sucrose dissolved in water are a few examples of solutions. When you watch hard after combining salt and water, you can no longer see the sodium chloride, indicating that the combination is uniform.

In chemistry, a solution containing of two or more compounds in their relative proportions. The composition of the solution can be continually changed up to the solubility limit. Although solution of gas and solids are possible, the term "solution" is most frequently used to refer to the liquid condition of matter.

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A new dog park is enclosed by a fence and shaped like a parallelogram. So, the area and perimeter of the dog park is 2125 m² and 202.5 m.

Pictures can be seen in the attachment.

These are the specified parameters:

Coordinate points in the image = (-8, 0), (5, 5), (9, 0), and (-4, -5).

1 unit = 5 m

The area of the parallelogram of the dog park

Triangular base (b) = (9 - (-8)) × 5 m = 85 m

Triangle height (h) = (0 + 5) × 5 = 25 m

A = 2 × 1/2 × b × h

  = 2 × 1/2 × 85 m × 25 m

  = 2125 m²

Perimeter of the dog park

The line a goes through the point (-8, 0) and (5, 5)

a² = (5 - (-8))² + (5 - 0)²

   = 13² + 5²

   = 169 + 25

   = 194

a = √192

a = 13.85

Length a = 13.85 × 5 m = 69.25 m

The line b goes through the point (5, 5) and (9, 0).

b² = (9 - 5)² + (0 - 5²

   = 4² + (-5)²

   = 16 + 25

   = 41

b = √41

b = 6.4

Length b = 6.4 × 5 m = 32 m

Perimeter = 2 × (a + b)

                = 2 × (69.25 m + 32 m)

                = 2 × 101.25 m

                = 202.5 m

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Answer:

Below

Step-by-step explanation:

The solution(s) to a system of equations is where the equations' graphs cross (intersect) ....for this system, that is at -1, -1

the answer is 1040

your welcome

Answer:

1/2 base * height = 16 in^2

1/2 * 8 in * H = 16 in^2

H = 32 in^2 / 8 in = 4 in         Equation # 4

The length to the nearest tenth of a meter is, 0.8 meter.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A pendulum's period in seconds, P, is related to the length of the pendulum in meters, L, by the following equation:

⇒ P = 2√9.8 L

Now, For a pendulum in a grandfather clock has a period of 1.7 seconds , its length is,

⇒ P = 2√9.8 L

⇒ 1.7 = 2√9.8 L

⇒ L = 1.7 / 2×√9.8

⇒ L = 1.7 / 2.26

⇒ L = 0.75

⇒ L = 0.8 meter

Thus, The length is, 0.8 meters.

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The average of any two real numbers is not greater than both of the two numbers, and is less than or equal to at least one of the two numbers.

The proof by contradiction of the theorem begins by assuming the opposite of the theorem, that the average of any two real numbers is greater than both of the two numbers. This can be expressed mathematically as follows:

Let a and b be two real numbers.

Average of a and b = (a + b)/2

Assume that (a + b)/2 > a and (a + b)/2 > b

This can be rewritten as

(a + b)/2 - a > 0  and  (a + b)/2 - b > 0

Subtracting a from both sides of the first equation and subtracting b from both sides of the second equation yields

b - a > 0  and  a - b > 0

Since b - a and a - b are both positive, the two equations cannot be true simultaneously. This is a contradiction and therefore our initial assumption must be false. Therefore, the average of any two real numbers is not greater than both of the two numbers, and is less than or equal to at least one of the two numbers.

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Answer:

Step-by-step explanation:

Using the properties of a kite:

Measure of 1, 2, 3 and 4:- each of these = 90 degrees.

Measure of:

5 = 53 degrees.

6 = 27 degrees.

7 = 90 - 27 = 63 degrees.

8 = 90 - 53 = 37 degrees.

9 = m < 7 = 63 degrees.

10 = 90 - 53 = 37 degrees.

As per the linear equation the system has one solution, which is x = 1 and y = 1.

A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.

The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.

It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.

When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.

For example, consider the following system of linear equations:

2x + 3y = 6

4x + 6y = 12

This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.

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It would cost R451.4 to buy an item that was priced at £37

During 2012, the article was priced at £15 to R183

Therefore the cost of the item in rand when the article is priced at £37 can be calculated as follows

£15= R183

£1= x

cross multiply both sides

15x= 183

x= 183/15

x= 12.2

£1= R12.2

£37= Y

Cross multiply both sides

y= 12.2 ×37

= 451.4

Hence the price of the item when it was priced at £37 is $451.4

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Step 1: To calculate the cost of 5kg of breakfast cereal, we need to multiply the cost of 1kg by 5.

Step 2: R36 x 5 = R180

Step 3: Therefore, 5kg of breakfast cereal will cost R180.

A regular hexagon can be divided into six equilateral triangles by drawing lines from the center of the hexagon to each of its vertices.

Each of these equilateral triangles has an area that is one-sixth of the total area of the regular hexagon.

When the midpoints of the sides of the regular hexagon are joined to form a smaller regular hexagon, it can be seen that the smaller hexagon is made up of six equilateral triangles, each of which has half the area of the equilateral triangles in the larger hexagon. This is because the sides of the smaller hexagon are half the length of the sides of the larger hexagon.

Therefore, the fraction of the area of the larger hexagon that is enclosed by the smaller hexagon is:

[tex]6 * (1/2)^2 = 6 * 1/4 = 3/2[/tex]

This means that the smaller hexagon encloses 3/2 of the area of the larger hexagon.

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The five number summary of the data is: 9, 43, 46, 79, 81. It means 50% of the data is between 43 and 79.

The five number summary of a set of data consists of:

In this problem, the five number summary is  9, 43, 46, 79, 81. Hence,

43 is the first quartile, while 79 is the third quartile. We know that quartiles are percentile. Q1 is the 25th percentile, which means 25% of data is below Q1. Similarly, 50% of data is below Q2 and 75% of data is below Q3. Therefore, between 43 and 79 means between Q1 and Q3, there will 75% - 25% = 50%  of data falls in this range.

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The expression for the total bill is { (Ap + B) x 0.09 } x 0.10.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The cost per person p = $A.

Room charge = $B.

Tax = 9%.

Tip = 10% of the total bill, including tax.

Now,

Total bill.

= { (Ap + B) x 9% } x 10%

9% = 9/100 = 0.09

10% = 10/100 = 0.10%

So,

= { (Ap + B) x 0.09 } x 0.10

Thus,

The total bill is { (Ap + B) x 0.09 } x 0.10.

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The ouput at x = 2 is 3 and the input at y = -1 is 0

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(2) = 3

This means that the output is 3

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(0) = -1

This means that the input is 0

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The equations which are represents in the graph are  y  = 0.86x & y =  -2.4x + 6

The equation of a straight line is a relationship between x and y coordinates, The two points form of equation of a straight line is y-y₁ =  y₂-y₁/x₂-x₁(x-x₁),

Given that,

A graph, In which two lines are given,

Line 1 is passing through following points,

(0, 0) and (1.75, 1.5)

Line 2 is passing through following points,

(2.5, 0) and (0, 6)

Equation of line 1

y - 0 =  (1.5-0)/(1.75-0) (x - 0),

y  =  0.86(x - 0),

y  = 0.86x,

Equation of line 2,

y - 6 =  (0 - 6)/(2.5 - 0)(x - 0),

y - 6 =  -2.4 (x - 0),

y - 6 =  -2.4x

y =  -2.4x + 6

Hence, the equations are y  = 0.86x & y =  -2.4x + 6

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Answer:

To write equivalent fractions with a common denominator, we need to find the least common multiple (LCM) of the denominators of the fractions and then write each fraction with the LCM as the denominator. Here's a step by step guide:

1. To find the LCM of 3 and 6, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 3: 3, 6, 9, 12, 15, 18, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, ...

The LCM of 3 and 6 is 6, so we write 2/3 and 3/6 with 6 as the denominator:

2/3 = 4/6 and 3/6 = 1/2

2. To find the LCM of 4 and 12, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, ...

The LCM of 4 and 12 is 12, so we write 3/4 and 5/12 with 12 as the denominator:

3/4 = 9/12 and 5/12 = 5/12

3. To find the LCM of 5 and 10, we list the multiples of each number and find the smallest one that is common to both:

Multiples of 5: 5, 10, 15, 20, 25, 30, ...

Multiples of 10: 10, 20, 30, 40, 50, 60, ...

The LCM of 5 and 10 is 10, so we write 3/5 and 7/10 with 10 as the denominator:

3/5 = 6/10 and 7/10 = 7/10

You can use this process to find the LCM and write equivalent fractions with a common denominator for the rest of the problems.

The required equation of the line is y = 5x + 3.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

From the given table we have slope(m) = (3 + 2)/(0 + 1) = 5/1 = 5.

Now, - 2 = 5(-1) + b.

- 2 = - 5 + b.

b = 3.

Therefore, y = 5x + 3 is the required equation of the line.

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The first four terms are 35, 50, 65, 80.

And the recursive formula:

aₙ = aₙ₋₁ + 15

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

The sequence defined by the explicit formula g(n)=15n + 35

The first term,

g(0) = 0 + 35 = 35.

g(1) = 15 + 35 = 50

g(2) = 30 + 35 = 65

g(3) = 45 + 35 = 80.

The common difference is 15.

The recursive formula:

aₙ = aₙ₋₁ + 15

Therefore, the formula is aₙ = aₙ₋₁ + 15.

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