Emma changed £500 into rand before going on holiday to South Africa.
The rate of exchange at the time was £1 = 10.4 rand.
Emma spent 4000 rand on holiday. When she got home, she changed her leftover rand into pounds.
The exchange rate was now £1 = 9.8 rand. How much money did she get back in pounds?

Hey there! I'm happy to help!

PART A

Let's look at our two equations.

y=3x-5

y=6x-8

We will solve this with substitution because we have two different values for y, so it will be be very easy to substitute.

We know that y is equal to 6x-8. This means that we can replace the y in the first equation with 6x-8 and then solve for x.

6x-8=3x-5

We add 8 to both sides.

6x=3x+3

We subtract 3x from both sides.

3x=3

We divide both sides by 3.

x=1

We can plug this x-value into either of our equations to figure out what y is.

y=6(1)-8

y=6-8

y=-2

Therefore, our solution is x=1 and y= -2.

PART B

When graphing the two equations in a systems of equation, the point where they intersect is the solution. We already have our solution, so now we will just write it as a point, which is (1,-2).

Have a wonderful day! :D

Answer:

see below

Step-by-step explanation:

y = 3x − 5

y = 6x − 8

I will use substitution by substituting for y in the first equation

y = 3x − 5

6x -8 = 3x-5

Subtract 3x from each side

6x-3x -8 = 3x-5-3x

3x-8 = -5

Add 8 to each side

3x-8+8 = -5+8

3x =3

Divide by 3

3x/3= 3/3

x =1

Now find y

y = 3x − 5

  = 3(1) -5

  =3-5

  = -2

( 1,-2)

The two lines will intersect at ( 1,-2)

The solution to the two equations is where the lines intersect.

Let the age will be x

4x+2x-28 years

6x-28

x-28 by 6 -4.66

SO THE ANSWER IS 4.66

Answer:

Noi = x

Noy = y

x+y = 26 ... (1)

4x-2y= 28 ... (2)

Solve:

x+y= 26

x= 26-y (keep it)

4x-2y= 28

4(26-y)-2y=28

104-4y-2y= 28

-6y= 28-104

-6y=-76

y= 12,6 (12 years 6 mouths)

x+y= 26

x + 12.6 = 26

x= 26-12.6

x= 13, 4 ( 13 years 4 mouths)

Answer:

Length = 34 feet

Breadth = 30 feet

Step-by-step explanation:

Perimeter= 128 ft

Let the breadth be = [tex]x[/tex]

Let the length be = [tex]x+4[/tex]

∴by the problem ,

2(length+breadth)= perimeter

[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]

Therefore, length of the garden = 30+4= 34 feet

breadth of the garden = 30 feet  

Answer:

The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)

Please find diagram with the arrangements

Step-by-step explanation:

The horizontal width of an hyperbola

For

1) [tex]\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1[/tex]

h = 2, k = 11

The widths are;

Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide

(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide

2)

[tex]\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1[/tex]

h = 7, k = 1

(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide

(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide

3) [tex]\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1[/tex]

h = 6, k = -1

a = 8, b = 3

The widths are;

(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16

(6, -1 - 3) to 6, -1 + 3) width = 6

4) [tex]\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1[/tex]

h = 4, k = -2, a = 2, b = 5

(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4

(4, -2 - 5) to (4, -2 + 5) width = 10

5) [tex]\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1[/tex]

h = -4, k = -5, a = 2, b = 3

(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4

(-4, -5 - 3) to (4, -5 + 3) width = 6

6) [tex]\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1[/tex]

h = 1, k = -1, a = 2, b = 9

(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4

(1, -1 - 9) to (1, -1 + 9) width = 18

7) [tex]\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1[/tex]

h = -7, k = 9, a = 4, b = 9

(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8

(-7,  9 -9) to (-7, 9 + 9) width = 18

Answer:

[tex]\large \boxed{\mathrm{All \ real \ numbers}}[/tex]

Step-by-step explanation:

The domain of a function is all possible values of x for which the function is real and defined.

[tex]f(x)=-15x^2 +6000[/tex]

The function has no undefined points nor any restrictions on the value of x.

[tex]- \infty < x < \infty[/tex]

The domain of the function is all real numbers.

Answer:

All real numbers

Step-by-step explanation:

The domain is the set of all possible values for x.

f(x) = -15x² + 6000

There are no restrictions on the value of x.

The domain is all real numbers.

Answer:

12 cm is the right answer pls mark me brainliest

The height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles is 12 cm.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:

Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

Given:

Three sides are: 15cm, 25 cm and 2 cm

Now, Using Heron's formula

semi-perimeter= (25+ 20 + 15)/2

s= 30 cm

Now,

Area of triangle

=√s(s-a)(s-b)(s-c)

=√30* 5 * 10* 15

=√5*2*3*5*2*5*3*5

=5*5*2*3

=150 cm²

Again, area of triangle= 1/2* b* h

150= 1/2* 25* x

12cm= x

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Answer:

When you roll a 6-sided cube, numbered 1 to 6, the probability of rolling a 2 is 1:6. This is an example of theorectical probability.

Step-by-step explanation:

The probability of rolling a 2 on a 6-sided dice is  

1

6

The probability of rolling two 2s on two 6-sided die is, by the multiplication principle,  

1

6

×

1

6

=

1

36

Subjective is something that is based on personal opinion, so I think the answer is actually theoretical probability! Theoretical probability is a method to express the likelihood that something will occur. It is calculated by dividing the number of favorable outcomes by the total possible outcomes.

Hope this helps, have a good day :)

(brainliest would be appreciated?)

Step-by-step explanation:

[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } [/tex]

To rationalize the surd multiply both the numerator and the denominator by

2 + √11

That's

[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } \times \frac{2 + \sqrt{11} }{2 + \sqrt{11} } [/tex]

Multiply the numerators and the denominator separately

That's

[tex] \frac{(5 - 5 \sqrt{3} )(2 + \sqrt{11} )}{(2 - \sqrt{11})(2 + \sqrt{11} ) } [/tex]

Simplify

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5\sqrt{33} }{?} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33} }{4 - 2 \sqrt{11} + 2 \sqrt{11} - 11} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{4 - 11} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{ - 7} [/tex]

We have the final answer as

[tex] - \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{7} [/tex]

Hope this helps you

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is

[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values

[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

the triangles are all similar, because they have proportional sides and equal angles.

if you assume the smallest, equal part of side to be x

the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .

since they're similar, ratio of their corresponding sides is constant or equal.

[tex] {BK\over BC}={JK \over AC}[/tex]

BK/BC=3/5

and AC=40

so JK = 40*3/5=24

Answer:

greater than or equal to -36

Step-by-step explanation:

2x >= -36-16

2x >= -52

x >= -26

Answer:

x = -9

Step-by-step explanation:

2x + 8 = -10

2x = -8 -10

2x = -18

x = -9

Answer:

Numer 1

A) (-5, -4), (-4, -3), (-3, -2), (-2, -1) Is a function

Number 2

C) (-5, -1), (-2, -1), (1, -1), (4, -1) is a function

in a function, all elements in domain "x" should have a pre-image "y" and they should be unique (one x can have only one value of y, but more than one x can have same same value of y) for all ordered pair (x,y)

it's not clearly possible to tell without knowing the actual set but with given information,

1. A

2. C

Answer: Hi!

The only thing we're able to do to simplify this equation is combine our like terms. We have two like terms in the equation: 7.5 and 9.63.

7.5 + 9.63 = 17.13

Our equation now looks like this:

n + 17.13

We have nothing left to simplify, so we're done!

Hope this helps!

Answer:

Segment addition postulate

Step-by-step explanation:

It’s the Segment addition postulate.

ab+bc=ac

Answer:

7 2/5

Step-by-step explanation:

7.08 to improper fraction:

708/100

= 7 2/25

Answer:

3x3÷2= 4.5cm^2

The formula is 1/2×base×slanted height

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = ¹/₃•(¹/₂•10•9)•10 = ¹/₃•45•10 = 15•10 = 150 in²

Answer:

6 sacks

Step-by-step explanation:

Buying Price = $1200

Selling Price = $1500

Total profit = Selling price - Buying Price

= $1500 - $1200

= $300

Given that the profit on each sack of tea is $50

Number of Sacks of Tea = Total Profit ÷ profit per sack

= $300 ÷ 50

= 6 sacks

The number of sacks of tea he has is 6.

The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.

Profit = selling price - cost price

$1500 - $1200 = $300

The second step is to divide the total profit by the profit made per sack of tea.

Number of sacks = $300 / $50 = 6

To learn more about division, please check: https://brainly.com/question/194007

Answer:

10 hours for the month

Step-by-step explanation:

What you know: The total amount Jorge was charged for the month was $25

The base rate is $15

He gets charged $1 per each hour

Setting it up:

15+1h=25

(the 15 is the base rate, plus the 1 dollar per hour (h) which both add to the total of 25 dollars for the month)

Subtract 15 from both sides of the equation to get your variable by itself

1h=10

then divide the 1 on both sides to get h (hours) by itself

h=10

And there's your answer, 10 is the number of hours that Jorge was charged for the month

Hopefully this helped :))

Answer:

10

Step-by-step explanation:

$25 - $15 = $10

and its $1 per hour so the answer is 10hrs

Answer:

f(x) = 5x² + 3

Step-by-step explanation:

Exponential Function: [tex]a(b)^x+c[/tex]

Logarithmic Function: [tex]alog_bx+c[/tex]

5x² + 3 is a quadratic function. Therefore, it is not an exponential or logarithmic function and is incorrect.

log₅x is a logarithmic function. Therefore, it is correct.

5log₃x + 3 is a logarithmic function. Therefore, it is correct.

5ˣ + 3 is an exponential function. Therefore it is correct.

Answer:

34.7

Step-by-step explanation:

First Step: Multiply.

3 × 10 = 30

4 × 1 = 4

7 × 1/10 = 7/10

Second step: Add.

30 + 4 + 7/10= 347/10

Final step: Make it a decimal.

347 ÷ 10 = 34.7

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[tex]3\times 10+4\times 1+7\times 1/10[/tex]

[tex]= \frac{347}{10}[/tex] (Decimal: 34.7)

Step by Step Explanation.

[tex](3) (10) + (4) (1) + \frac{(7)(1)}{10} \\= 30 + (4) (1) + \frac{(7)(1)}{10} \\= 34 + \frac{(7)(1)}{10} \\= 34 + \frac{7}{10} \\= \frac{347}{10}[/tex]

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If this helped you, could you maybe give brainliest..?

❀*May*❀

Answer:

[tex] \boxed{\sf Time \ taken = 15 \ minutes} [/tex]

Given:

Initial speed (u) = 65 km/h

Final speed (v) = 85 km/h

Acceleration (a) = 80 km/h²

To Find:

Time taken for car to achieve a speed of 85 km/h in minutes

Step-by-step explanation:

[tex]\sf From \ equation \ of \ motion:[/tex]

[tex] \boxed{ \bold{v = u + at}}[/tex]

By substituting value of v, u & a we get:

[tex] \sf \implies 85 = 65 + 80t[/tex]

Substract 65 from both sides:

[tex] \sf \implies 85 - 65 = 65 - 65 + 80t[/tex]

[tex] \sf \implies 20 = 80t[/tex]

[tex] \sf \implies 80t = 20[/tex]

Dividing both sides by 80:

[tex] \sf \implies \frac{ \cancel{80}t}{ \cancel{80}} = \frac{20}{80} [/tex]

[tex] \sf \implies t = \frac{2 \cancel{0}}{8 \cancel{0}} [/tex]

[tex] \sf \implies t = \frac{ \cancel{2}}{ \cancel{2} \times 4} [/tex]

[tex] \sf \implies t = \frac{1}{4} \: h[/tex]

[tex] \sf \implies t = \frac{1}{4} \times 60 \: minutes[/tex]

[tex] \sf \implies t = 15 \: minutes[/tex]

So,

Time taken for car to achieve a speed of 85 km/h in minutes = 15 minutes

[tex](a+b+c)^2=a^2 + 2 a b + 2 a c + b^2 + 2 b c + c^2\\a^2+b^2+c^2=(a+b+c)^2-2ab-2ac-2bc\\a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)\\\\a^2+b^2+c^2=9^2-2\cdot26=81-52=29[/tex]

Answer:

0 points

Step-by-step explanation:

So first we see that she gets 2 questions correct,

2 * 5 = 10

Then we see that she gets 5 questions wrong,

5 * -2 = -10

Then we see that she doesn't attempt three questions,

3 * 0 = 0;

Now we add up the points,

10 - 10 + 0 = 0 points

Answer:

Heena gets 2 correct and 5 incorrect. She attempts only 7 questions so for the remaining 3 questions she will score zero marks.

So total marks scored by Heena is 5×2−5×2+0  i.e 0marks

Step-by-step explanation:

Answer

Equation : x + 1 + 3x = 7

Miles Lissette biked : 3/2 miles

Step-by-step explanation:

Step 1: Determine the total number of miles biked.

From my understanding. 7 miles is the total number of miles biked by both.

Step 2: Assume the values

Miles Lissette biked = x

Miles Shane biked = 1 + 3x

Step 3: Add miles biked by Lissette and Shane which will be equal to total miles.

Equation for miles Lissette biked: x + 1 + 3x = 7

4x + 1 = 7

x = 6/4

Step 4: Simplify

x = 6/4

x = 3/2

Therefore, the equation for miles Lissette biked is x + 1 + 3x = 7 and Lissete biked for 3/2 miles.

Hope it helped if yes mark me BRAINLIEST

Tysmm

Answer:

7 = 3x - 1

Step-by-step explanation:

Miles Shane biked = y

Miles Lissette biked = x

The equation is

(x ⋅  3) - 1 = y

And we know y = 7, so

(x ⋅  3) - 1 = 7

3x - 1 = 7

Answer:

98.1km²

Step-by-step explanation:

The name of the Triangle in this question is: WXV

In the question, we have:

Angle W = ? Unknown

Angle X = 119°

Angle V = 34°

Side w =?

Side x = 26km

Side v = ?

Step 1

We have to find the missing third angle = Angle W

Sum of angles in a triangle = 180°

= Angle W = 180° - (119 + 34)°

= 180° - 153°

Angle W = 27°

Step 2

Find the sides w and v using the sine rule

Sine rule =

a/ sin A = b/ Sin B

Hence for triangle WXV

w/ sin W = x/ sin X = v/ sin V

We have the following values

Angle W = 27°

Angle X = 119°

Angle V = 34°

We are given side x = 26km

a) Finding side w

w/ sin W= x/ sin X

w/sin 27 = 26/sin 119

Cross Multiply

sin 27 × 26 = w × sin 119

w = sin 27 × 26/sin 119

w = 13.49587km

w = 13.5km

b) Finding side v

x / sin X= v/ sin V

26/ sin 119 = v/sin 34

Cross Multiply

sin 119 × v = 26 × sin 34

v = sin 34 × 26/sin 119

v = 16.62324km

v = 16.62km

Step 3

Detemine the area of triangle WXV

We make use heron formula

= √s(s - w) (s - x) (s - v)

Where s = w + x + v/ 2

s = (13.5 + 26 + 16.62)/2

s = 56.12/2

s = 28.06

Area of the triangle = √28.06× (28.06 - 13.5) × (28.06 - 26 ) × (28.06 - 16.62)

Area of the triangle = √9628.137559

Area of the triangle = 98.123073530337km²

Approximately to the nearest tenth =98.1km²

Answer:

XS is 9 inches long.

Step-by-step explanation:

Given that

YS is the perpendicular bisector of XZ.

Length of XZ = 18 inches

To find:

Length of XS = ?

Solution:

First of all, let us learn about the perpendicular bisector.

Perpendicular bisector of a line AB is a line PQ, which divides the line AB in two equal parts and is at an angle of [tex]90^\circ[/tex] with the line AB.

If B is on the line PQ, then [tex]BP = BQ = \frac{PQ}{2}[/tex] and

[tex]\angle ABP = \angle ABQ = 90^\circ[/tex]

Applying the above property in our given question.

Kindly refer to the attached image for the given dimensions.

S is on the line XZ.

[tex]XS = SZ = \frac{XY}{2} = \dfrac{18}{2} \\\Rightarrow \bold{XS = 9\ inches}[/tex]

So, the answer is XS is 9 inches long.

Answer: what table? u need to add an attachment

Step-by-step explanation:

The table containing whole number express 2.8 as the sum or difference.

To express 2.8 as the sum or difference of whole numbers.

There are three different ways to do it:

1. As a sum of whole numbers:

  2 + 0.8 = 2.8

2. As a difference of whole numbers:

  4 - 1.2 = 2.8

3. Another way as a sum of whole numbers:

  1 + 1.8 = 2.8

The table will be:

Representation             Whole Number 1        Whole Number 2      Result

          1                                      2                               0.8                       2.8

          2                                      4                               1.2                       2.8

          3                                      1                               1.8                        2.8

As each row represents a different way to represent the number 2.8 using whole numbers.

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Answer:

4 maximum extrema

Step-by-step explanation:

5th degree means that it can change direction 5 times, therefore creating a maximum of 4 extrema

Answer:

-47/8.

Step-by-step explanation:

If the line has a slope of -1/8, that means the equation y = mx + b will be y = -1/8x + b.

In this case, we are given a point: (9, -7). That means that x = 9 and y = -7.

-7 = (-1/8)(9) + b

b - 9/8 = -7

b = -56/8 + 9/8

b = -47/8 = -5.875 = -5 and 7/8, which is your y-intercept!

Hope this helps!

Answer:

A

Step-by-step explanation:

Both angles together are supplementary, or they add up to 180 degrees.

(3x+12)+x=180 degrees

Answer:A. (3x+12)+x=180

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

There are ₁₃C₃ ways to choose 3 diamonds from 13.

There are ₃₉C₁ ways to choose 1 non-diamond from 39.

There are ₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

The approximate probability that exactly three of the cards are diamonds is 4%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.

Since we can see that there are ₁₃C₃ ways to choose 3 diamonds from 13.

₃₉C₁ ways to choose 1 non-diamond from 39.

₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

Therefore, the answer could be 4 percent.

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