mary won £5000 in a competition .she used the money to pay for herself and 8 friends to go on a holiday. Flights cost £279 for each of them. Accommodation costs £184 for each of them. how much of the £5000 did she have left after paying for flights and accommodation for herself and the 8 friends

Step-by-step explanation:

i hope it helped you a lot. thankyou

Answer:

y = 5 + 0.9x

Step-by-step explanation:

If y is the total fee and x is the miles driven, we get following equation:

The total comprises of a constant initial rate ($5) and a charge for driven miles (0.9x)

Answer:  see proof below

Step-by-step explanation:

Use the following Power Reducing Identities:

[tex]\sin^3\theta= \dfrac{1+\cos 2\theta}{2}\\\\\\\cos^2\theta=\dfrac{3\sin \theta-\sin 3\theta}{4}[/tex]

Use the following Product to Sum Identity:

[tex]\sin A \cdot \cos B = \dfrac{1}{2}\bigg[\sin (A + B) + \sin (A - B)\bigg][/tex]

Proof LHS → RHS

LHS:                           cos² Ф · sin³ Ф

[tex]\text{Power Reducing:}\qquad \bigg(\dfrac{1+\cos 2\theta}{2}\bigg)\bigg(\dfrac{3\sin \theta-\sin 3\theta}{4}\bigg)[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}(3\sin \theta -\sin 3\theta +3\sin \theta\cdot cos 2\theta-\sin 3\theta \cdot \cos 2\theta)[/tex]

[tex]\text{Product to Sum:}\\ \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin (\theta +2\theta) +\sin(\theta -2\theta)\bigg)-\dfrac{1}{2}\bigg(\sin (3\theta+2\theta) +\sin (3\theta-2\theta)\bigg)\bigg][/tex]

[tex]\text{Simplify:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta +\sin(-\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta -\sin(\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg][/tex]

[tex]\text{Simplify:}\qquad \dfrac{1}{16}\bigg(6\sin \theta -2\sin 3\theta +3\sin 3\theta -3\sin(\theta)-2\sin 5\theta -2\sin \theta\bigg)\\\\\\.\qquad \qquad =\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)[/tex]

[tex]\text{LHS=RHS:}\quad \dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)=\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)\quad \checkmark[/tex]

Answer:

it was 4.8 degrees higher

Step-by-step explanation:

all u have to do is subtract 103.4 from 98.6

Answer:

Wouldn't it be 4.8° F ?

Step-by-step explanation:

Since you can just subtract the two numbers and you get that.

103.4°F - 98.6°F = 4.8°F

Answer:

-49

Step-by-step explanation:

-14 + -13

A + and a - is still a - , so it can be written as -14 - 13, which is -27.

Then, -27 - 22 = -49

Answer: -49

Step-by-step explanation:

-14 + -13 = -27

-27 - 22 = -49

I hope this helps

plz mark brainleist

Step-by-step explanation:

Required equation would be:

H = M + 55

Plug M = 12

H = 12 + 55

H = 67 cm

Answer:

150 square feet every half hour.

Step-by-step explanation:

Answer:

150 square feet

Step-by-step explanation:

Answer:

35% or 0.35

Step-by-step explanation

If 20 grams is 100%, that means each gram is 5% of the whole. So 7 time 5 is 35.

Answer & Step-by-step explanation:

[tex]8.5x-6.1=-7.1[/tex]

Add 6.1 to both sides:

[tex]8.5x-6.1+6.1=-7.1+6.1\\\\8.5x=-1[/tex]

Isolate the variable x. Divide both sides by 8.5:

[tex]\frac{8.5x}{8.5} =\frac{-1}{8.5}\\\\ x=-\frac{1}{8.5}[/tex]

Round to the nearest tenth. Simplify division:

[tex]-\frac{1}{8.5}=-0.11764705...=-0.1[/tex]

So, x≈-0.1

:Done

Answer:

(0+m)/2. (0+n)/2

Step-by-step explanation:

U sum both x coordinates and divide by two. U do same to the t values.

The formula used to find the midpoint of a segment with endpoints A(0, 0) and B(m, n) is x = m / 2 and y = n / 2.

What is the midpoint on a given line?

If on a straight line we have two endpoints:

- [tex](x_{1}~,y_{1})[/tex]

- [tex](x_{2},~ y_{2} )[/tex]

and the midpoint is given by ( x, y ).

Then to find the midpoint on a straight line we use the formula:

x = ( [tex]x_{2}[/tex] + [tex]x_{1}[/tex] ) / 2

y = ( [tex]y_{2}+y_{1}[/tex] ) / 2

We have,

[tex](x_{1}~,y_{1})[/tex] = ( 0, 0 )

[tex](x_{2},~ y_{2} )[/tex] = ( m, n )

[tex]x_{1}[/tex] = 0

[tex]x_{2}[/tex] = m

[tex]y_{1}[/tex] = 0

[tex]y_{2}[/tex] = n

We will use the formula :

x = ( [tex]x_{2}[/tex] + [tex]x_{1}[/tex] ) / 2

y = ( [tex]y_{2}+y_{1}[/tex] ) / 2

And substitute the values.

x = ( m + 0 ) / 2

y = ( n + 0 ) / 2

x = m / 2

y = n / 2.

The formula used to find the midpoint of a segment with endpoints A(0, 0) and B(m, n) is x = m / 2 and y = n / 2.

Learn more about midpoints here:

https://brainly.com/question/15191928

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Answer:

Step-by-step explanation:

f(x) = x − 7

g(x) = x²

To find f(g(4)) we must first find f(g(x)).

To find f(g(x)) substitute g(x) into f(x) that's for every x in f (x) replace it with g(x)

That's

f(g(x)) = x² - 7

To find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4

That's

f(g(4)) = 4² - 7

= 16 - 7

We have the final answer as

Hope this helps you

Yes

If the rectangle has sides of Square root 8 and square root 2 which are two irrational numbers but when multiplied it gives an area of 4 square units which is a rational number.

No, it is not possible for a rectangle to have rational side lengths and an irrational area, because two rational numbers are always rational.

Given that,
To figure out, is it possible for a rectangle to have rational side lengths and an irrational area.

Rational numbers can be structured in the form of the fraction of integers. Eg- 5/6, 2/3, etc.

Here,
in a rectangle, two sides have rational length and the area of the rectangle is a product of the sides of the rectangle.
Since there is a property of the rational numbers that, when two rational numbers are multiplied together the product of the rational number is always rational.

So the area of the rectangle also would be rational.

Thus,  it is not possible for a rectangle to have rational side lengths and an irrational area.

Learn more about Rational numbers here: https://brainly.com/question/17450097

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Answer:

k = 5

Step-by-step explanation:

[tex](x + 2)(x + 3) = {x}^{2} + 5x + 6[/tex]

Now comparing left hand side & right hand side ,

[tex] {x}^{2} + kx + 6 = {x}^{2} + 5x + 6[/tex]

Cancelling x^2 & 6 from both left hand side & right hand side ,

kx = 5x

=> k = 5

Answer:

The range of the function are the values of height which are from 3, 4, 5, ..., 50

Step-by-step explanation:

The given parameters are;

The height at which the ball is caught = 5 feet

The height at which the ball was hit = 3 feet

The maximum height reached by the ball = 50 feet

The height of the ball given as a function of time is f(t) s = u·t - 1/2·g·t²

Where;

s = 50 feet

g = 9.81 m/s²

Therefore, we have;

50 = u·t - 1/2 × 9.81 × t²

50 = u·t - 4.905 × t²

Therefore, the range are obtainable values for f(t) which range from 3 to 50.

Answer:

26

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

Horizontal equations are of the form

y =

The y coordinate is 8

y=8

Answer:

The answer is 2

Step-by-step explanation:

4z+2y-x

4(4)+2(-6)-2

16+(-12)-2

16-12-2

4-2

2

Step-by-step explanation:

[tex]4z + 2y - x \\ = 4 \times 4 + 2 \times ( - 6) - 2 \\ = 16 + ( - 12) - 2 \\ = 16 + ( - 14) \\ = 2[/tex]

Answer:

124°

Step-by-step explanation:

The angles CGH and AHF have the same size.

● 7x - 72 = 3x + 40

Add 72 to both sides

● 7x - 72 + 72 = 3x + 40 + 72

● 7x = 3x + 112

Substract 3x from both sides

● 7x - 3x = 3x + 112 - 3x

● 4x = 112

Divide both sides by 4

● 4x/4 = 112/4

● x = 28

■■■■■■■■■■■■■■■■■■■■■■■■■■

● < CGH = 7x - 72 = 7×28 - 72 = 124°

Answer:

25

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ;)

Answer:

22

Step-by-step explanation:

Simplify the following:

3 (2 + 7) - 5

Hint: | Evaluate 2 + 7.

2 + 7 = 9:

3×9 - 5

Hint: | Multiply 3 and 9 together.

3×9 = 27:

27 - 5

Hint: | Subtract 5 from 27.

| 2 | 7

- | | 5

| 2 | 2:

Answer: 22

Answer:22

Step-by-step explanation:

add the numbers in the  parathieses  so 2+7 and you get 9 so then your equation is 3(9)-5 or 3×9-5

then you multiply 3×9 and get 27 so then subtract 27 -5 and get 22 as your answer

Answer:

Integer

Step-by-step explanation:

The greatest integer function (as known as the floor function), is defined as to be the greatest integer less than or equal to x.

It is the function:

[tex]f(x)=\floor[x][/tex]

For instance, if x is 2, then f(x) is 2. If x is 2.7, then f(x) is still 2. 2 is the greatest integer less than or equal to 2.

You can also see this from the attached graph.

Answer:

82300000 in scientific notation = 8.23 × 107.

Step-by-step explanation:

Not sure if that's right.

Answer:

8.23×10^7

Step-by-step explanation:

to convert a number i to scientific form just drag the point to first non zero digit and write it with some multiple of 10

Answer:

105

Step-by-step explanation:

15 X 7 =105

105 is the least 3 digit multiple of 7.

12 X 7 = 84

84 + 7 = 91

91 + 7 = 98

98 + 7 = 105

or use multiplication 13 X 7= 91, 14 X 7=98

15 X 7 = 105

This is guess and check until the sum or product is a 3 digit number. It helps if you know the 7 times table at least through 7 X 12 = 84.

Answer:

6/49 or

StartFraction 6 over 49 EndFraction

Step-by-step explanation:

There are two negative fractions, the product of which results in positive.

(-2/7)* (-3/7) = 6/49

Answer:

6/7

Step-by-step explanation:

is correct

Answer:

9, 10

Step-by-step explanation:

square root of √93 is 9.64.

Thus, we see that the number 9.64 is greater than  but less than 10.

On number line it can be represented as

-∞ _____________7___8___9__9.64___10___11_______+∞

Thus, we see that  the two whole numbers between which √93 lies is 9, 10

Answer:

Negative

Step-by-step explanation:

A negative plus a negative (negative minus a positive) will give you a negative. -1.69 + (-1.69) = -3.38

-3.38 is a negative, therefore the answer is negative.

Answer:

the second choice

Step-by-step explanation:

[tex] \dfrac{1}{2}n + 3 < 5 [/tex]

Subtract 3 from both sides.

[tex] \dfrac{1}{2}n < 2 [/tex]

Multiply both sides by 2.

[tex] n < 4 [/tex]

To show n < 4 on a number line, you put an open circle on 4, and you color the line to the left of 4.

Answer: the second choice

Answer:

A) 720 possible itineraries

B) 0.5

Step-by-step explanation:

She visited 6 cities.

A)Now, to get the number of different itineraries that are possible, we will use n! = n(n-1)(n-2)(n-3)....

In this question, n is 6

Thus;

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

B) First of all, let's calculate the number of sample points in the sample space for the number of cities visited. Since we are told that she visits san francisco and Denver, we will fix the two cities to be constant. Thus, we will have 6 cities, but permutate 4 of them. Which means, we have;

Ns = P(6, 4) = 6!/(6 - 4)! = 360

Thus;

P(visits Denver before San Francisco) = Ns/number of different itineraries that are possible = 360/720 = 0.5

Answer:

[tex](-\infty ,\infty)[/tex]

[tex]y\in \mathbb{R}[/tex]

Step-by-step explanation:

[tex]$y=3-\frac{x}{3} $[/tex]

The domain is all Real numbers.

The range is all Real numbers.

Once it is a linear an equation and there's no restriction for x, both domain and range will be all Real numbers.