A vehicle costs £17754 including vat at 20%. What was the price of the vehicle before vat was added

Answer:

R = 13/3

Step-by-step explanation:

Based on the given conditions, formulate:  2 x r - 10 = -1 1/3

Apply Multiplicative Distribution Law: 2r - 10 = -1 - 1/3

Multiply both sides of the equation by the common denominator: 2r x 3 -10 x 3 = -3 - 3/3

Reduce the fractions: 2r x 3 - 10 x 3 = -3 - 1

Multiply the monomials: 6r - 10 x 3 = -3 - 1

Calculate the product or quotient: 6r - 10 x 3 = -3 - 1

Rearrange unknown terms to the left side of the equation: 6r = -3 - 1 + 30

Calculate the sum or difference: 6r = 26

Divide both sides of the equation by the coefficient of variable: r = 26/6

Cross out the common factor: r = 13/3

Answer:  r = 13/3

Answer:

6 and 12

Step-by-step explanation:

Length= 6+w

width =w

then..

2(6+w)=24

12+2w=24

collect the like terms

24-12=2w

w =6

width=6and length=12

Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Complete Question:

Aisha reduced the size of her square driveway. she made one side 10 feet shorter and the other side 15 feet shorter. the smaller rectangular driveway will have an area of no more than 800 square feet. write an inequality to represent the area of the smaller driveway.

Answer:

The inequality that represents the area of the smaller drive way is \(x(x-25) \leq 650\)

Step-by-step explanation:

Let the original length of the sides of Aisha's square driveway be = x

She made one side 10 ft short, i.e. (x - 10) ft

She made the other side 15 ft short, i.e. (x - 15) ft

Since the sides are no longer equal, the driveway is now a rectangle

The question states that the smaller rectangular driveway will have an area of no more than 800 square feet

Area of a rectangle = length * Breadth

Area = (x - 10)*(x - 15)

\(Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150\)

Area ≤ 800

\(x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650\)

Solving the above, x = 40.9 or -15.9

Since the length of a square cannot be negative, x = 40.9 ft

Answer:

(x-10)·(x-15)≤800

Step-by-step explanation:

imagine math

Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

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Answer

Center: (1,-12)

Radius: 5

Work

\(x^{2}\)+\(y^{2}\)-2x+24y+120=0 (Subtract 120 on both sides and rearrange)

\(x^{2}\)-2x+\(y^{2}\)+24y=-120 (Then divide 2 by 2 and square it. Do the same for 24.)

\(x^{2}\)-2x+1+\(y^{2}\)+24y+144=-120+1+144 (You have to add the same numbers on both sides)

\((x-1)^{2} +(y+12)^2=25\) (Simplify)

So you would put (1,-12); r=5

Answer:

The answer is D

Step-by-step explanation:

Answer:

D) Quadrant IV (quadrant 4)

Step-by-step explanation:

Point C is in quadrant IV because its point is (4,-4)

For points that have a positive x-coordinate and a negative y-coordinate, that means they are in quadrant IV.

Another way to figure this out is by looking at this graphically:

                                    y

                                    |

         Quadrant           |          Quadrant

                II                  |                 I

                                    |

 ------------------------------|----------------------------- x

                                    |

          Quadrant          |           Quadrant

                III                 |                 IV

                                    |

I hope this helps!

The system of linear equations that can be formed to find x and y is 3x + 2y = 15.12 and 2x + 4y = 19.36. Then one can of chili costs $2.37 and one jar of salsa costs $4.005.

Let us consider  x being  the cost of one can of chili and y be the cost of one jar of salsa.
Then we can write two equations
3x + 2y = 15.12
2x + 4y = 19.36

We can multiply the first linear equation by 2 and subtract it from the second  linear equation in order to  eliminate x
(2x + 4y = 19.36) - 2(3x + 2y = 15.12)
= -4x + 0y
= -9.48

Applying Simplification to this equation
-4x = -9.48
Dividing both sides by -4 gives us:
x = 2.37

Now we can place this value of x into either of the original equations to find y
3(2.37) + 2y = 15.12
7.11 + 2y = 15.12
Subtracting 7.11 from both sides
2y = 8.01
Dividing both sides by 2
y = 4.005
Then, one can of chili costs $2.37 and one jar of salsa costs $4.005.

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Answer: No solution

Both tables have slope 2 (y increases two for every increase of 1 in x).  First has y intercept 5, second 15  (19=2(2)+b).  So our system is

y = 2x + 5

y = 2x + 15

Those are parallel lines, which never meet, so no solution.

An inequality to describe the possible values for the total area, A, of the green section can be represented as A ≥ 0 square feet. This inequality indicates that the total area must be greater than or equal to zero.

The area of a section cannot be negative since it represents a physical space. Therefore, the total area, A, of the green section must be non-negative. By using the symbol "≥" (greater than or equal to), we indicate that the area can be equal to zero or any positive value greater than zero. The inequality A ≥ 0 ensures that the total area is within the acceptable range. If the area is zero, it means there is no green section present. Any positive value represents the actual area of the green section. This inequality allows for flexibility in the size of the green section, as long as it is non-zero and non-negative. The inequality A ≥ 0 describes the possible values for the total area, ensuring that it is greater than or equal to zero square feet.

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EXPLANATION :

From the problem, since the Earth can be approximated by spherical geometries, the triangle that we will form is a spherical triangle.

Note that the sum of the angles in a spherical triangle is greater than 180 degrees.

From the options, the only angle that's greater than 180 degrees is 185 degrees.

ANSWER :

D. 185 degrees

Answer:

use distance formula

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Let's suppose "my number" is x

If you add 21 to my number: 21 + x

Multiply the result by 3: 3(21+x)

You will get 84 more than two thirds of my number

\(3(21 + x) = 84 + \frac{2}{3} x \\ 63 + 3x = 84 + \frac{2}{3} x \\ \frac{7}{3} x = 21 \\ 7x = 63 \\ x = 9\)

Therefore my number is 9

If you need any help with the algebra part feel free to let me know!

the energy use for each quarter beginning with winter in year 26 is as follows:

Winter: 121.91

Spring: 149.49

Summer: 170.44

Fall: 129.96

To determine the energy use for each quarter beginning with winter in year 26, we need to multiply the base value D = 80.0 + 0.45Q by the corresponding seasonal factors. Here are the calculations:

Winter (Q = 101): D = (80.0 + 0.45 * 101) * 0.9 = 135.45 * 0.9 = 121.91

Spring (Q = 102): D = (80.0 + 0.45 * 102) * 1.1 = 135.9 * 1.1 = 149.49

Summer (Q = 103): D = (80.0 + 0.45 * 103) * 1.25 = 136.35 * 1.25 = 170.44

Fall (Q = 104): D = (80.0 + 0.45 * 104) * 0.95 = 136.8 * 0.95 = 129.96

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Answer:

16

Step-by-step explanation:

i totally forgot how to write the equation so i did it the long way and i got with 16 shovels of dirt you get 100 pounds

Step-by-step explanation:

Q1. diameter =90yd radius=45

circumference of circle=2×pi×radius

"" =2×3.14×45

=282.6 yd

Q2 diameter =18m radius=9

area of circle=pi×(radius)

""" =3.14×9²

""" =254.34m²

Answer:

EA, EB, EC and ED are opposites rays.

Step-by-step explanation:

Given that,

Line AB and line CD intersect at point E.

According to figure,

We need to find opposite rays

Using diagram

We draw a first line AB and second line CD which is intersect of AB at point E.

Now, EA and EB is called opposite ray of first line AB.

Similarly,

EC and ED is called opposite ray of first line CD.

Hence, EA, EB, EC and ED are opposites rays.

Answer:

Girls: 7 points each

Boys: 11 points each

Step-by-step explanation:

Answer:

2$

Step-by-step explanation:

A quadrilateral is a four sided figure. It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure

A quadrilateral is a four sided figure. The images are not shown here so we don't know what the dimensionof each figure is.

It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure and find the area of the two triangles in order to obtain the area of the orginal figure.

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Answer:

law of detachment

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Plug in coordinates to see if they match the answer.

It's easier in slope-intercept form, so lets change it first.

-2x+y=7

+2x    +2x

y=2x+7

Now we can plug in the coordinates to see if they match.

Lets try A.

11=2(-2)+7

11=-4+7

11=3

A is incorrect.

Lets try B.

11=2(2)+7

11=4+7

11=11

B is a solution, therefore is on the graph.

Answer:

a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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Answer: x∈(-∞,-2√6-2)U(2√6-2,+∞)

Step-by-step explanation:

\(\displaystyle\\y=\frac{1}{4} (x+2)^2-6\\y > 0\\Hence,\\\frac{1}{4}(x+2)^2-6 > 0 \\\\\frac{1}{4}(x+2)^2-6+6 > 0+6\\\\\frac{1}{4}(x+2)^2 > 6\\\)

Multiply both parts of the equation by 4:

\((x+2)^2 > 24\)

Extract the square root of both parts of the inequality:

\(|x+2| > \sqrt{24} \\|x+2| > \sqrt{4*6} \\|x+2| > 2\sqrt{6}\)

Expand the modulus - we get a set of inequalities:

\(\displaystyle\\\left [{{x+2 > 2\sqrt{6}\ \ \ \ (1) } \atop {-(x+2) > 2\sqrt{6} \ \ \ (2)}} \right.\\\)

Multiply both parts of inequality (2) by -1 and reverse the sign of the inequality:

\(\displaystyle\\\left [ {{x+2-2 > 2\sqrt{6}-2 } \atop {x+2 < -2\sqrt{6} }} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x+2-2 < -2\sqrt{6} -2}} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x < -2\sqrt{6}-2 }} \right.\)

Thus,

\(x\in(-\infty,-2\sqrt{6}-2)U(2\sqrt{6} -2,+\infty)\)

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125