Kristy bought a new tv the total cost of the tv was £360 including vat at 20% work out the cost of the tv before the vat was added

Answer:

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(f(5))=11[/tex]

Step-by-step explanation:

We are given that the table which shows some inputs and outputs of the invertible function f with domain all real numbers.

We are given that

x         f(x)

5         9

3         -2

1          -5

18          -1

0           1

9           11

We have to find

[tex]f^{-1}(f(58))[/tex] [tex]f(f(5))[/tex]

We know that

[tex]f^{-1}(f(x))=x[/tex]

Using the property

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(5)=9[/tex]

[tex]f(f(5))=f(9)[/tex]

[tex]f(f(5))=11[/tex]

Answer:

x = 3     y = 5

Step-by-step explanation:

     y=x+2

+    y=-x +8

2y = 10

y = 5

y = -x + 8

5 = -x + 8

x = 3

Answer:

There are 80 questions on the test

Step-by-step explanation:

I think this is right, but don't quote me on this.

Answer:

g(x)=f(x+3)+5

Step-by-step explanation:

Answer:

- [tex]\frac{2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Using the identity and the exact value

csc x = [tex]\frac{1}{sinx}[/tex]  and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= [tex]\frac{1}{-sin60}[/tex]

= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]

= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )

= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= - [tex]\frac{2\sqrt{3} }{3}[/tex]

The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We know that the cosecant function is defined as the reciprocal of the sine function:

cosec (θ) = 1 / sin(θ)

Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).

We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,

sin(-120°) = -sin(120°)

We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).

Using the same logic as before, we get:

sin(-240°) = -sin(240°)

Now , from the trigonometric relations , we get

Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:

sin(-240°) = -sin(-120°)

Therefore, we have:

sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)

Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:

In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.

Therefore, sin(240°) = O/H = (√3)/2.

Finally, we can use the definition of the cosecant function to find cosec(-120°):

cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.

Hence , cosec(-120°) is equal to (2√3)/3.

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

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Answer:

for (a)

Step-by-step explanation:

15 and 25 are the numbers that come in A union to B

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

Explanation:

The 90 degree counterclockwise rotation rule we use is

[tex](x,y) \to (-y,x)[/tex]

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

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

Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.

Answer:

22 cm

Step-by-step explanation:

the perimeter = AB+BG+GF+FE+ED+DC+CA

= 65 cm

7+7+7+FE+7+DC+7=65 => FE = CD

35+ 2FE = 65

2FE = 65-35

= 30

FE = 30/2 = 15

so, GE = GF + FE

= 7+15 = 22 cm

Answer:

{0,-3,-9,5,7}

Step-by-step explanation:

range = all y values

function =(x,y)

so all the second values are ranges

Answer:

see explanation

Step-by-step explanation:

Angles on the circumference subtended on the same arc are equal

Angle at the centre is twice the angle at the circumference subtended on the same arc.

Then

∠ BAC = ∠ BDC = 29°

∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°

Answer:

6:9 ÷3

2:3

Step-by-step explanation:

1st write the ratio then simplify it with dividing with the Highest common factor on both sides

Answer:

she can buy 0 to 12 bags but no more

Step-by-step explanation:

Answer:

so if its actually 1000 and that map thing is 250

250 goes into 1000 4 times so

4cm

Hope This Helps!!!

Answer:

The smallest number is 10

Step-by-step explanation:

x+y=24---equation 1

x-y=¹/6×24=>x-y=4---equation 2

Add both equations

2x=28

x=14

put x=14 into equation 1

14+y=24

y=24-14=10

Answer:

y is 4

Step-by-step explanation:

x is 3

y is 4 coordinate is (3,4)

Answer:

4

Step-by-step explanation:

Answer:

(B) 30

Step-by-step explanation:

Imagine you drew a line from Point T until it touched Line PR. Let's call that point where it touched Line PR "Point Z".

That line (called Line TZ) would be perpendicular to PR, forming a 90 degree angle.

Now, TZW is a triangle.

To find x, we need to find the angle measurment of Angle ZTW.

This is where we use the hexagon.

A hexagon's interior angle sum is 720, meaning each interior angle is equal to 120 degrees. So Angle UTS would equal 120 degrees.

However, Line TZ bisects that 120 degree angle, so Angle ZTW would equal 60 degrees (because 120/2 = 60).

Now we have two angles of the triangle: 90 & 60.

A triangle's interior angle sum is 180.

Add 90 & 60, which is 150, and subtract 150 from 180.

The result is 30, which is the angle measurement of x.

Hope it helps (●'◡'●)

Answer:

y = 7/5x + 7

Step-by-step explanation:

Answer:

x- intercept = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] and c = - 2 , then

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of line

To find the x- intercept let y = 0

0 = - [tex]\frac{1}{2}[/tex] x - 2 ( add 2 to both sides )

2 = - [tex]\frac{1}{2}[/tex] x ( multiply both sides by - 2 to clear the fraction )

- 4 = x

The x- intercept is - 4

Answer:

Kindly check attached picture

Step-by-step explanation:

Based d on the instruction given.

1.)

-3 * 6 = 18

6 * - 2 = - 12

-3 * - 2 = 6

2.)

We use logical reasoning to find 2 numbers whichbwhen multiplied gives the number in the box in between :

The answers are given in the picture attached.

Answer:

The value of P(AUB) = 0.438

Step-by-step explanation:

Given:

P(A) = 0.36

P(B) = 0.2

P(A∩B) = 0.122

Find:

The value of P(AUB)

Computation:

P(AUB) = P(A) + P(B) - P(A∩B)

The value of P(AUB) = 0.36 + 0.2 - 0.122

The value of P(AUB) = 0.56 - 0.122

The value of P(AUB) = 0.438

Answer:

[tex]9p^2-16q^2[/tex]

[tex](3p)^{2} -(4p)^{2}[/tex]

[tex]\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}[/tex]

[tex]\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)[/tex]

[tex]=\left(3p+4q\right)\left(3p-4q\right)[/tex]

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

hope it helps....

have a great day!!

Answer:

A

8.5 is the answer

If you test is going on so

all the best!

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Answer:

3, 5, 7

Step-by-step explanation:

Substitute n = 1, 2, 3 into the nth term rule

a₁ = 2(1) + 1 = 2 + 1 = 3

a₂ = 2(2) + 1 = 4 + 1 = 5

a₃ = 2(3) + 1 = 6 + 1 = 7

Answer:

3, 5, 7

Step-by-step explanation:

n = 1, 2, 3 into the nth term rule

a₁ = 2(1)+1=2+1=3

a2=2(2)+1=4+1=5

a3 = 2(3)+1=6+1=7

Answer:

Inside

Step-by-step explanation:

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of poiñt from centre is less than the radius.

Hence the point lies within the circle

Answer:

(B)

Step-by-step explanation:

Can't explain lol, but that's the answer