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The equation for finding cost y for x liters of petrol is y = 93x

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, A liter of petrol cost £93,

Since, the unit rate of the petrol is £93 per liter

If we say let x be the number of liters we need, the total cost will have to pay will be = 93x

And, if total cost is y, then,

y = 93x

Hence, the equation for finding cost y for x liters of petrol is y = 93x

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Answer: To make the piecewise function continuous for all x, we need to make sure that the function values and the function slopes at the boundaries (-1 and 2) are the same for each piece.

For x = -1:

F(-1) = -6 (from the first piece)

F(-1) = A(-1) + 2 = -A + 2 (from the second piece)

So, to make the function continuous at x = -1, we need to set -6 = -A + 2, which gives us A = -8.

For x = 2:

F(2) = -x^2 + Bx + 14 (from the third piece)

F(2) = A(2) + 2 = 2A + 2 (from the second piece)

So, to make the function continuous at x = 2, we need to set -4 + 2B + 14 = 2A + 2, which gives us B = -5.

Now we can write the function with the constants that we found :

F(x) = -6 if x < -1

-8x + 2 if -1 ≤ x ≤ 2

-x^2 - 5x + 14 if x > 2

This function is continuous for all x and the values and slopes match at x = -1 and x = 2.

Step-by-step explanation:

The solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4

we shall write the equations as:

8x + 3y = 4...(1)

2x + y = 2...(2)

multiply equation (2) by 3 to get equation (3)

3(2x + y) = 3 × 2

6x + 3y = 6...(3)

subtract equation (1) from (3) to eliminate y

6x + 3y - 8x - 3y = 6 - 4

-2x = 2

divide through by -2

x = -1

put the value -1 for x in equation (2) to get y

2(-1) + y = 2

-2 + y = 2

y = 2 + 2 {add 2 to both sides}

y = 4

Therefore, the solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4.

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The solution to this equation: 42 +82=x² is x = 12.

A square number, also known as a perfect square, is an integer that is the square of another integer; in other words, it is the result of multiplying another integer by itself. For instance, 9 is a square number because it equals 32 and can be written as 3 3.

Instead of the product n n, the equivalent exponentiation n2, which is typically pronounced "n squared," is used to represent a number's square. The name of the shape is where the term "square number" originated. The area of a unit square (1 × 1) is the unit of area.

The solution to this equation: 42 +82=x²

x = √(42 +82)

x = √(144)

x = 12

Thus, The solution to this equation: 42 +82=x² is x = 12.

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The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.

The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:

|2x + y = 8 |

|3x - y = 7 |

This can be rewritten in matrix form as:

|2 1 | |x | | 8 |

|3 -1| |y | | 7 |

To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:

|2 1 | |x | | 8 |

|0 -2| |y | | 1 |

Then, we can divide the second row by -2 to get the coefficient of y to be 1:

|2 1 | |x | | 8 |

|0 1 | |y | |-1/2|

Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:

|2 0 | |x | | 8/2|

|0 1 | |y | |-1/2|

Therefore, the solution to the system of equations is x = 4 and y = -1/2.

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Answer: - 15 = N

Step-by-step explanation:

2 negatives make a positive so it would be -35 + 20 = -15 Have a nice day ;)

Answer:

4.725 ft

Step-by-step explanation:

well if i see this right the shadow for claire is 1.60x the person's hight

The images of the points after the transformation are (6, 1), (3, 6), (5, 2) and (-8, -4)

r(x-axis) o T(2, -3) (4, 2)

This implies that we reflect the point (4, 2) across the x-axis and then translate it by (x + 2, y - 3)

Mathematically, this is represented as

Image = (x + 2, 3 - y)

Substitute the known values in the above equation, so, we have the following representation

Image = (4 + 2, 3 - 2)

Evaluate

Image = (6, 1)

T(2, -5) o R 90 CCW (4, 2)

This implies that we translate the point (4, 2) by (x + 2, y - 5) and then rotate it by 90 degrees counterclockwise

Mathematically, this is represented as

Image = (5 - y, x + 2)

Substitute the known values in the above equation, so, we have the following representation

Image = (5 - 2, 4 + 2)

Evaluate

Image = (3, 6)

T(1, 4) o r(y-axis) (4, 2)

This implies that we translate the point (4, 2) by (x + 1, y + 4) and then reflect it across the y-axis

Mathematically, this is represented as

Image = (x + 1, 4 - y)

Substitute the known values in the above equation, so, we have the following representation

Image = (4 + 1, 4 - 2)

Evaluate

Image = (5, 2)

r(y-axis) o T(1, 4) (4, 2)

This implies that we reflect the point (4, 2) across the y-axis and then translate it by (x + 4, y + 2)

Mathematically, this is represented as

Image = (-x - 4, y + 2)

Substitute the known values in the above equation, so, we have the following representation

Image = (- 4 - 4, 2 + 2)

Evaluate

Image = (-8, 4)

Hence, the image is (-8, -4)

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Answer:

he takes a stretch every 4 miles

Step-by-step explanation: 12/3 = 4

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.

Student ID: 81725225

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

Student ID: 81725225

P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.

Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.

R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.

S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.

The resulting table is:

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.

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Step-by-step explanation:

If a company is expanding its team at a rate of 10% per year, and it currently has 200 members of staff, we can calculate the number of staff after 1 year using the formula:

number of staff after 1 year = 200 + (10/100) * 200

number of staff after 1 year = 200 + 20

number of staff after 1 year = 220

So, there will be 220 members of staff after 1 year if there are initially 200 members of staff.

The equation of plane is x - 3y - 4z = 27.

a plane produced by the application of vectors perpendicular to a normal. The implication of this is that, given a vector a, b, c, we may deduce that all planes perpendicular to it have the form ax+by+cz=d and that any surface with this form is a plane perpendicular to a, b, c.

The equation for a plane perpendicular to a given line with direction ratios a, b, and c> and passing through a point is a(x-x1) + b(y-y1) + c(z-z1) = 0. (x1, y1, z1).

The equation of the plane traveling through the points x, y, and z on a plane perpendicular to the line whose parametric equation is provided

Equation of a plane through the point (-4,-3,8) is

a(x - 4) + b(y - 3) + c(z + 8) = 0

Since it is perpendicular to the line :

x = -4+t, y=-3-3t, z= -4t,

t = x + 4 = -y - 3 / 3 = -z/4

therefore coefficients a, b, c must be proportional to 1, - 3 & (-4) respectively.

Therefore, putting the values of a, b & c in eq.(1), we get the required equation of the plane as ;

λ(x - 4) -3 λ(y - 3) - 4λ(z + 8) = 0 (λ is a constant)

⇒ x - 4 - 3y + 9 -4z - 32 = 0

⇒ x - 3y - 4z = 27

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Answer: 3 11/12

Step-by-step explanation:

Rewrite the equation with the parts seperated:

4 + 2/3 − 3/4

Find the LCD of 2/3 and 3/4

(Which is 12)

Keep going

8/12−9/12= −1/12

Finally, subtract 4 − 1/12 to get 3 11/12

Hope this helps!

The largest δ value of the given limit [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000 is calculated. The required δ value is [tex]\delta=\sqrt{1+10^{-3}}-1[/tex].

When no values are defined, a limit is used to assign values to certain functions. It is possible to assess the limits using algebraic techniques. A collection of guidelines for manipulating limits when using other operators is known as the algebra of limits. Given the expression  [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex]  and M=1000. When x>1, we write this expression as,

[tex]\begin{aligned} \frac{1}{x^2-1}& > 1000\\x^2-1& < 1000^{-1}=10^{-3}\\x^2& < 10^{-3}+1\\x& < \sqrt{1+10^{-3}}\end{aligned}[/tex]

Now, choosing, [tex]\delta=\sqrt{1+10^{-3}}-1[/tex] when we have δ > 0. Therefore, [tex]\sqrt{1+10^{-3}} > 1[/tex]. Then, [tex]x\in(1, 1+\delta)[/tex]. This is given by,

[tex]\begin{array}{ccc}1& < x& < 1+\delta\\1& < x& < \sqrt{1+10^{-3}}\end{array}[/tex]

This implies, [tex]\frac{1}{x^2-1} > 1000=M[/tex].

Therefore, the largest δ value will be [tex]\sqrt{1+10^{-3}}-1[/tex].

The complete question is -

For each limit, use graphs and algebra to approximate the largest δ or the smallest magnitude N that corresponds to the given value of ∈ or M, according to the appropriate formal limit definition.

[tex]\lim_{x\to 1^+} \frac{1}{x^2-1}=\infty[/tex], M=1000, find largest δ > 0.

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Answer: Let x be the weight of the bag over the limit in pounds.

We know that both airlines have the same weight limit and Carrie paid the same baggage fee at each airline, so we can set up the following equation:

25 + 4x = 28 + 3x

Solving for x:

x = 25

So, Carrie's bag was 25 pounds over the weight limit.

To find the fee for each airline, we can substitute x into the equations for the fees:

Fee for the first airline: 25 + 4(25) = $125

Fee for the second airline: 28 + 3(25) = $103

Therefore, Carrie paid $125 in fees for the first airline and $103 in fees for the second airline.

Step-by-step explanation:

If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.

To calculate Cp, Cpk, Pp, and Ppk using MINITAB, you would need to input the data into the software and run the appropriate statistical analysis.

Cp and Cpk are measures of a process's capability, they are calculated as follows:

Where,

Pp and Ppk are similar to Cp and Cpk, but they are calculated using the range of the data instead of the standard deviation.

Where R is the range of the data.

If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.

It is worth noting that Capability analysis can only be performed on stable and in-control processes. If the process is not in control, analyzing process capability is not meaningful.

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The measure of the missing angles are 100° and 30°

A polygon with three vertices, angles and sides.

Given is a triangle XYW, whose side WZ is extended to the point z,

We know that,

The sum of two opposite interior angles of a triangle is equal to the measure of exterior angle,

∠ 1 + 50° = 150°

∠ 1 = 100°

We know that, sum of the interior angles of a triangle is 180°

∠ 1  + ∠ 2 + 50° = 180°

150°-180° = ∠ 2

∠ 2 = 30°

Hence, the measure of the missing angles are 100° and 30°

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Answer:

Step-by-step explanation:

tha answer is 69

Answer: As Mrs Lopez required 40 ounce

Step-by-step explanation:

The slope of  following points  (3, 3) and (6,1)  is -2/3 .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given  points are (3, 3) and (6,1)

we know that slope = y2-y1 / x2-x1

y2-y1 = 1-3

The difference of y -intercept is -2

= -2

x2-x1 = 6-(3)

= 6-3

The difference of x-intercept is 3

= 3

So, slope could be y2-y1 / x2-x1  that is -2/3.

Therefore, The slope of  following points  (3, 3) and (6,1) is -2/3 .

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The slope of the least-squares line is:  0.30

The correct answer is an option (A)

We have following information:

correlation between X and Y (r) = 0.9

mean of the values of X ([tex]\bar{X}[/tex]) = 6.5

mean of the values of Y ([tex]\bar{Y}[/tex]) = 6.6

the standard deviation of the values of X ([tex]S_{X}[/tex]) = 3.6

the standard deviation of the values of Y  ([tex]S_{Y}[/tex]) = 1.2

We know that the slope of a least squares regression can be calculated by the formula,

slope m  = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex],

where, r is the correlation coefficient

Let us assume that for given scenario,  m represents the slope of of the least-squares line.

Using above formula,

⇒ m  = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex]

⇒ m  = 0.9 ×  [tex]\frac{1.2}{3.6}[/tex]

⇒ m = 0.9 ×  0.333

⇒ m = 0.2997

⇒ m ≈ 0.3

Thus, the slope is 0.30

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The complete question is:

A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least- squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities.

r = correlation between X and Y = 0.9

X = mean of the values of X = 6.5

Y = mean of the values of Y = 6.6

S_(X) = standard deviation of the values of X = 3.6

S_(Y) = standard deviation of the values of Y = 1.2

The slope of the least-squares line is: ?

A. 0.30   B. 0.88   C. 1.01   D. 2.70    E. 3.00

Answer:

9x + 7

Step-by-step explanation:

Add 4x + 1 to 5x + 6

in an algebraic expression is:

4x + 1 + 5x + 6

To simplify, combine like terms. This means add the x terms together and add the constants (plain number- - the 1 and 6) together.

4x + 1 + 5x + 6

= 4x + 5x + 1 + 6

= 9x + 7

Answer:

16.58

Step-by-step explanation:

as you can see from the graph, there's a monthly fixed cost on Y axis.  so you need to figure out 1: how much per minute. and 2. the monthly fixed fee.  you've got 2 scenarios = 2 equations, for 2 variables. so you can solve both.

assume: x=per min rate; m = monthly fixed cost.

1. 14.06 =52x+m

2. 17.18 =78x+m

use equation 2 minus equation 1 & you get

3.12 = 26 x.  so x = 0.12

plug this into equation 1: 14.06 =52*0.12 +m so m=7.82

now for 73 mins the cost = 73*0.12 +7.82 =16.58

Answer:

x =  [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

2x - 3y = 7 → (1)

- 4x + y = - 5 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

- 12x + 3y = - 15 → (3)

add (1) and (3) term by term to eliminate y

- 10x + 0 = - 8

- 10x = - 8 ( divide both sides by - 10 )

x = [tex]\frac{-8}{-10}[/tex] = [tex]\frac{4}{5}[/tex] (= 0.8 )

An equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation is y=2/3 x²+4x

A mathematical equation is a formula that uses the equals sign ('=') to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation in English is any well-formed formula consisting of two expressions related by an equals sign, while an equation in French is defined as containing one or more variables.

step 1

y=2/3+4

y=2/3 x²+4x

y=m x+ b

step 2

y= y coordinate

m=slope

x=x coordinate

b=y intercept

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X has a geometric distribution because it is the number of trials (tosses) required until a success (catching the ball) occurs.

b) The probability that it will take exactly two tosses for Sophie to catch a ball is P(x=2) = (0.2)(0.8)^1 = 0.16. This is calculated by multiplying the probability of success (0.2) by the probability of failure (0.8) raised to the power of the number of trials (2-1=1)

c) To find the probability that more than three tosses will be required, we need to find the probability that Sophie does not catch the ball on the first three tosses and then catch it on the fourth toss.

This can be found by summing the probabilities of Sophie not catching the ball on the first three tosses (0.8^3 = 0.512) and Sophie catching the ball on the fourth toss (0.8^3*0.2 = 0.1024). The probability that more than three tosses will be required is P(x>3) = 1 - P(x≤3) = 1 - (0.512 + 0.1024) = 0.3856.

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For the rectangular parking area of the shopping center shown, an equation which says that the area is 30,000 yd² is: A. x(2x + 200) = 30,000.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

From the information provided about the rectangular parking area of the shopping center shown in the image attached below, we have the following dimensions:

Length = x

Width = 2x + 200

Substituting the given points into the area of rectangle formula, we have the following;

30,000 = x × (2x + 200)

30,000 = x(2x + 200) ⇒ (required equation).

30,000 = 2x² + 200x.

2x² + 200x - 30,000 = 0.

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