2. A laptop usually sells for £1320 (including VAT). A store is advertising a discount of 15%
if it is purchased on a Sunday and a further 10% student discount. What is the price that a
student should pay (including VAT) for a Sunday purchase?

9514 1404 393

Answer:

  √8

Step-by-step explanation:

8 is between 2² = 4 and 3² = 9. 12 is not.

√8 falls between 2 and 3.

__

Your calculator can help with this.

  √8 ≈ 2.828 . . . . . between 2 and 3

  √12 ≈ 3.464 . . . . not between 2 and 3 (between 3 and 4)

Answer:

csc x sec x

Step-by-step explanation:

csc = 1/sin

1/sin^2    /  cos/sin    =   1 / sin^2    *  sin/cos       =   1 / sin cos  = csc sec

Answer:

Step-by-step explanation:

A function can be defined as two variables (independent and dependent) which cannot have more than one output for each input.

Step-by-step explanation:

1. the first mapping is a function

2. the second mapping is not a function, because: B has 2 relations, C & E have no relations.

3. the third mapping is a function

4. the fourth mapping is not a function, because B has no relation.

Answer:

33.33%

Step-by-step explanation:

Decrease in price= Original price -- New price

= $6 - $4

= $2

Percentage decrease= $2÷$6 × 100

= 33.33%

Answer:

Step-by-step explanation:

All real number

Answer:

1000

Step-by-step explanation:

10³

= 1000

Answer:

10 * 10 * 10

Step-by-step explanation:

Cubing a number just means you are multiplying that number 3 times to itself. Since we have 10^3, we multiply 10 to itself three times.

Best of Luck!

Answer:

1. (-∞ , -10]

2. [0, ∞ )

3. [12.566, 4.242]

4. [15, 50]

5. (-∞ , 5]

6. [18, ∞)

Step-by-step explanation:

Answer:

1. The set of all numbers less than negative ten.

2. The set of all positive real numbers.

3. The set of all numbers less than 4.242 and greater than 12.566.

4. The set of all numbers that are greater than 15 and less than 50.

5. The set of all numbers that are at most 5.

6. The set of all numbers that are at least 18.

Answer:

1.3

Step-by-step explanation:

I guess it's 1.8 - 0.5

Answer:

10

Step-by-step explanation:

It 10 bucks each ticket

the ratio of students do not wear glass to total students

[tex]\frac{12}{25}[/tex]

the ratio of students wear glass to total number of students is

[tex]\frac{13}{25}[/tex]

Given

In a class of 25 students, 13 students wear glasses and 12 students do not wear glasses

The ratio of glasses to non-glasses wearing students is 13:12.

Explanation :

we need to find the ratio students wear glasses to whole students

There are total of 25 students.

13 students wear glass

So the ratio of students wear glass to total number of students is

[tex]\frac{13}{25}[/tex]

Similarly , we can find the ratio of students do not wear glass to total students

[tex]\frac{12}{25}[/tex]

Learn more :  brainly.com/question/17218035

Answers:

The coordinates of the vertices are

These coordinates are from the red points shown in the diagram below.

=============================================================

Explanation:

Because the center of dilation is at the origin, we'll multiply each coordinate of each point by the scale factor.

Specifically, we'll double the coordinate values since the scale factor is 2.

and so on

The diagram is shown below. The original preimage is in blue while the dilated enlarged image is in red. Your teacher only wants the location of the red corner points.

You can either transform this quadratic equation into a vertex form which would rather painful or use derivatives.

I'll use dervatives. We know that vertex of a quadratic function is either its maxima or its minima, since the leading coefficient [tex]-x^2[/tex] has a negative prefix that means we get a downward turned parabola with minima being the vertex.

First we take the derivative with respect to x,

[tex]\dfrac{d}{dx}-x^2-2x+3=-2x-2[/tex]

The derivative is esentially information what is the slope of a function at a particular x. When the slope is 0 we reached some sort of turning point, such as minima.

We therefore do,

[tex]-2x-2=0\implies x=-1[/tex]

So at [tex]x=-1[/tex] there appears to be a minima or x-coordinate of the vertex of the function.

Plug the coordinate into the function to get y,

[tex]y=f(-1)=-1+2+3=4[/tex]

So the vertex of the function is at [tex]\boxed{(-1,4)}[/tex].

Assuming you don't know derivatives, there is another way.

First compute the roots of the function,

[tex]-x^2-2x+3=0[/tex]

[tex]-(x-1)(x+3)=0[/tex]

[tex]x_1=1,x_2=-3[/tex]

In the middle between [tex]x_1,x_2[/tex] is an x coordinate of a vertex,

[tex]x=\dfrac{x_1+x_2}{2}=\dfrac{1-3}{2}=-1[/tex]

Just like we had before, we compute for y, [tex]h(-1)=4[/tex] and again the result is [tex]\boxed{(-1,4)}[/tex].

Hope this helps :)

Step-by-step explanation:

[tex] \frac{ \frac{8}{9} }{ - 4} \\ \frac{8}{9} \times \frac{1}{ - 4} \\ \frac{8 \times 1}{9 \times - 4} \\ \frac{8}{ - 36} \\ \frac{2}{ - 9} \\ - 0.22[/tex]

Answer:

B. [tex] - \frac{2}{9} [/tex] (second option)

Step-by-step explanation:

[tex] \frac{ \frac{8}{9} }{ - 4} [/tex]

[tex] \frac{8}{9} \div 4 = \frac{8}{9} \times \frac{1}{4} [/tex]

[tex] \frac{8 \times 1}{9 \times 4} = \frac{8}{9 \times 4} [/tex]

[tex] - \frac{2}{9} [/tex] ✅

Answer: x=41

Step-by-step explanation:

Let x be the number missing

Given expression

x - 14 = 9 × 3

Simplify by multiplication

x - 14 = 27

Add 14 on both sides

x - 14 + 14 = 27 + 14

[tex]\boxed {x=41}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

[tex]x - 14 = 9 \times 3 \\ x - 14 = 27 \\ x = 27 + 14 \\ x = 41 \\ thank \: you[/tex]

Answer:

hope it is helpful

Step-by-step explanation:

68,020-

6= 60,000

8= 8,000

0=0

2= 20

0=0

If these vectors are to be linearly independent, then there exists some not-all-zero choice for scalars [tex]c_1,c_2,c_3,c_4[/tex] such that

[tex]c_1(1,1,0,-1) + c_2(1,k,1,1) + c_3(5,1,k,1) + c_4(-1,1,1,k) = (0,0,0,0)[/tex]

We can recast this as a system of linear equations,

[tex]\begin{bmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\\c_4\end{bmatrix} = \begin{bmatrix}0\\0\\0\\0\end{bmatrix}[/tex]

This system has a solution if the coefficient matrix on the left side is not singular. So we attempt to find k such that it *is* singular, i.e. the determinant is zero:

• A cofactor expansion along the first column gives

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = \begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} - \begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} + \begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix}[/tex]

• Cofactor expansions along the first columns of the remaining 3x3 matrices give

[tex]\begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} = k \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}1&1\\1&k\end{vmatrix} + \begin{vmatrix}1&1\\k&1\end{vmatrix} = k^3-3k+2[/tex]

[tex]\begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} = \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}5&-1\\1&k\end{vmatrix} + \begin{vmatrix}5&-1\\k&1\end{vmatrix} = k^2-4k+3[/tex]

[tex]\begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix} = \begin{vmatrix}1&1\\k&1\end{vmatrix} - \begin{vmatrix}5&-1\\k&1\end{vmatrix} + \begin{vmatrix}5&-1\\1&1\end{vmatrix} = -k^2 - 6k + 7[/tex]

It follows that

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = (k^3-3k+2) - (k^2-4k+3) + (-k^2 - 6k + 7) \\\\ \begin{vmatrix}\cdots\end{vmatrix} = k^3 - 2k^2 - 5k + 6 = (k-3)(k-1)(k+2)[/tex]

which makes the coefficient matrix singular if k = 3, k = 1, or k = -2.

Then the four vectors are linearly independent for

[tex]\left\{ k\in\mathbb R \mid k\not\in\{-2,1,3\}\right\}[/tex]

Answer:

solution -2/5+1/2 =-2*2+1*5/5*2 =-4+5/10 =1/10

Answer:

153.86 ft^2

Step-by-step explanation:

π=3.14

r=7ft

πr^2=3.14*7*7

=153.86 ft^2

Area of circle = π r²

Here , We have

Area of circle = 3.14 × (7)²

Area of circle = 3.14 × 49 ft²

Area of circle = 153.86 ft²

Multiply the amount owed by 20% by changing the percent to a decimal.

20% = 0.20

200 x 0.20 = 40

The late fee is $40

Answer:

-33

Step-by-step explanation:

this math equation looks relatively simple so i assume the actual equation is -2/3x - 8 = 14

add 8

-2/3x =22

multiply by -3/2

answer is -33

Answer:

range is the y part and domain is the x so the range is the y coordinates

-6,-3,-2,-2,1,4

Step-by-step explanation:

Answer:

6.875

Step-by-step explanation:

7- (1/2)^3​ = 7-1/8 = 6.875

Step-by-step explanation:

solution :

cost of 18 drinks (is)=52

Answer:

to find midpoint add both"X" coordinates and divide by 2

also add "Y" coordinates and divide by 2

then for line of segment use distance formula which is D=√[(x2-x1)²+(y2-y1)²]

Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

To determine the midpoint of two coordinates (x₁,y₁) and (x₂,y₂ )

Midpoint = [ (x₁ + x₂)/2 + (y₁ + y₂)/2 ]

The distance between two points (x₁,y₁) and (x₂,y₂ )

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Hence "Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]".

For more about line segment,

https://brainly.com/question/25727583

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Answer:

because the points are vertical and an isosceles has vertical sides

Answer:

8 tickets

Step-by-step explanation:

To find how many tickets he bought, we can divide.

66 / 8.25 = 8

Best of Luck!

Answer:

8

Step-by-step explanation:

66 divided by 8.25, bringing it to 8.

Answer:

The equation is

[tex]{ \underline{ \sf{y = - 2 {e}^{ - 2x} + 7 }}}[/tex]

Step-by-step explanation:

[tex]{ \sf{ {e}^{2x} \frac{dy}{dx} = 1}} \\ \\ { \sf{dy = {e}^{ - 2x} dx}}[/tex]

integrate:

[tex]{ \sf{ \int dy = \int { - e}^{2x} dx}} \\ { \sf{y = - 2 {e}^{ - 2x} + c}}[/tex]

c is a constant.

when y is 5, x is 0:

[tex]{ \sf{y = { - 2e}^{ - 2x} + c}} \\ { \sf{5 = - 2 {e}^{( - 2 \times 0)} + c }} \\ { \sf{5 = - 2 {e}^{0} + c }} \\ { \sf{5 = ( - 2 \times 1) + c}} \\ { \sf{5 = - 2 + c}} \\ { \sf{c = 7}}[/tex]

therefore, equation:

[tex]y = - 2 {e}^{ - 2x} + 7[/tex]

Answer:

19,86%

Step-by-step explanation:

[tex] \frac{28}{141} = 0.198582[/tex]

➡️ [tex]0.1986[/tex]

➡️ [tex]0.1986 \times \frac{100}{100} [/tex]

➡️ [tex] \frac{0.1986 \times 100}{100} [/tex]

➡️ [tex] \frac{19.86}{100} [/tex]

➡️ [tex] = 19.86\%[/tex] ✅