PLEASE HELP ASAP
A shop sells a washing machine for £236.25, making a profit of 5%. At what wholesale price did the shop buy the washing machine?
Original price = £

Answer:

A = 36√3 - 12π

Step-by-step explanation:

Make 2 identical 30-60-90 triangles out of the "wedge"

For each 30-60-90 triangle:

Since the short leg is 6 the long leg is 6√3

short leg is the base and long leg is the height

a = (1/2)bh

a = (1/2)(6)(6√3)

a = 3(6√3)

a = 18√3

Since there are 2 triangles

a = 36√3

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

Then subtract off the area of the 120º sector

a = (120/360)πr^2

a = (1/3)π(6^2)

a  = (1/3)π(36)

a = 12π

Shaded area

a = 36√3 - 12π

Step-by-step explanation:

we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).

since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.

basically, the area of a triangle is

1/2 × b×c × sin(A)

A being the angle between the 2 sides b and c. for any 2 sides of the triangle.

one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.

we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.

remember, the sum of all angles in a triangle is 180 degrees.

so, via the law of sines we can then calculate all sides :

a/sin(A) = b/sin(B) = c/sin(C)

with the angles being opposite of the sides.

6/sin(30) = baseline/sin(90)

6/0.5 = baseline/1

12 = baseline

top side² + 6² = 12²

top side² = 12² - 6² = 144 - 36 = 108

top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.

the area of the 2 triangles is then

6×sqrt(3)×6×sin(90) = 36×sqrt(3)

and the circle segment to be deducted is

pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12

so, the complete answer is

A = 36×sqrt(3) - 12×pi

Answer:

y > -2

Step-by-step explanation:

-5y-2<8

= -5y<8+2

= -5y<10

= y > 10/-5

∴ y > -2

Note: Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.

Answer:

{0}

Step-by-step explanation:

{0} is not because 0 is not an element of set {1, 2, 3}

The null set is a subset of every set, so Ø is.

A set is a subset of itself.

Answer:

71/50

Step-by-step explanation:

Answer:

Im soooooo hungry ughhh

Step-by-step explanation:

Hi

Answer:

124.72

Step-by-step explanation:

Answer:

Step-by-step explanation:

4% of 128.72 = 0.04 * 128.72

                    = 5.1488

A linear function is one of the most simplest form of functions. As the name "linear" indicates, a linear function is simply a line, more precisely a straight line.

So it is in the form of f(x) = ax + b.

Lets now check the possible answers : (second answer :) "a curved line", not correct.

(third answer:) "a parabola", this is not a straight line, so not correct.

(fourth answer:) "a wavy line", not a straight line, so not correct.

The only correct answer is the first one : a line passing through the x axis at negative 2 and the y axis at negative 6.

Answer:

f(x) = [tex]8^{x}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{512} = 8\\\sqrt[4]{4096} = 8\\\sqrt[5]{32768} = 8[/tex]

which means 8 to the power of 3 will give you 512, to the fourth power will give you 4096.

So the exponential function is f(x) = [tex]8^{x}[/tex]

Answer:

0, 11/6 , 8/7

Step-by-step explanation:

Answer:

[tex]0, \frac{11}6, \frac87[/tex]

Step-by-step explanation:

Good thing it's already written as a product, which spares us the most complicated (and boring) part.

We know that a product is zero if it's 0 any of the factors.

From the first one [tex]x^2=0 \rightarrow x=0[/tex]

from the second factor [tex]6x-11=0 \rightarrow x=\frac{11}6[/tex]

and finally, for the third one, [tex]7x-8 =0 \rightarrow x = \frac87[/tex]

Answer:

we know that

perimeter =2*(l+b)

20=2*(l+2)

20=2l+4

2l=20-4

2l=16

l=16/2

l=8

Answer:

-1

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

Using the points on the line  (-2,0) and (0,-2)

m = ( -2-0)/(0- -2)

   = (-2-0)/(0+2)

   -2/2

   -1

Answer:

5, 7, and 12

Step-by-step explanation:

First we can make and equation

x + z + y = 24

we can plug in the numbers you gave us giving us

y = x + z

z = y - x

x = (y - 2) ÷ 2

Once, were done we get that x = 5 ≈ smallest number

z = 7 ≈ second largest number

y = 12 ≈ largest number

Answer:

1

Step-by-step explanation:

there are 3 people and 1 boat holds three people

Answer:

x=12 y=4

Step-by-step explanation:

x=y+8

x=3y

x=y+8 times 3

3x=3y+24

x=3y

3x=3y+24 - x=3y

2x=24

x=24

24-8=4

4 times 3 =12

Answer:

C

Step-by-step explanation:

put x^5=u

Answer:

[tex]u=x^{5}[/tex]

Step-by-step explanation:

[tex]x^{10} - 13x^{5} + 12 = 0\\\\(x^{5})^{2} - 13x^{5} + 12 = 0\\\\u^{2}-13u+12=0[/tex]

Answer:

x = 3

Step-by-step explanation:

1 - 6x = - 17 ( subtract 1 from both sides )

- 6x = - 18 ( divide both sides by - 6 )

x = 3

Answer:

Your answer is All of the Above.

Hope this helps!

Step-by-step explanation:

OA is the radius

OC is the radius

and OB is the radius

( They are all half length of the circle )

Answer:

-4/3x-7=1

Step-by-step explanation:

just combine like terms

Answer:

Ms. Brown needs 0.18 more cents to afford the pounds of granola and cranberry mix.

Step-by-step explanation:

Ms. Brown = $10 limit

Purchases 1.75 lbs of granola and 2.9 lbs of cranberry mix

Cranberry per lb = $3.25

Granola per lb = $2.19

1.75 x 2.19 = 3.8325 (Cost of granola)

2.9 x 2.19 = 6.351 (Cost of cranberry)

3.8325 + 6.351 = 10.1835 (Total cost of both cranberry and granola)

10.1835 rounded to nearest cent = 10.18

10 < 10.18

Ms. Brown doesn't have enough money to buy the pounds of granola and cranberry mix.

Using the normal distribution, there is a 0.9515 = 95.15% probability of a bone density test score greater than −1.66.

The graph is given by option B.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the mean and the standard deviation of the scores are given as follows:

[tex]\mu = 0, \sigma = 1[/tex]

The probability of a bone density test score greater than −1.66 is one subtracted by the p-value of Z when X = -1.66, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (-1.66 - 0)/1

Z = -1.66

Z = -1.66 has a p-value of 0.0485.

1 - 0.0485 = 0.9515, which is the probability.

The graph of the probability is given at the end of the answer, and in the context of this problem, is given by option B.

More can be learned about the normal distribution at https://brainly.com/question/4079902

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Answer:

Let the hours when they equalize=h, then we have:

12.25 + .13h=13 - .09h

.13h + .09h=13 - 12.25

.22h=.75 divide both sides by .22

h=.75/.22

h=3 9/22, hours, when they will equalize.

The stock prices will be the same in 3.4 hours.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

At 9 a.m., the price of Stock A was $12.73. Since then, the price has risen at a pace of $0.06 per hour. Stock B was trading at 13.48 at midday. It starts to fall at a pace of $0.14 each hour.

Let's assume the hours would be h when to equalize,

As per the given question, we can write the equation as:

12.25 + 0.13h = 13 - 0.09h

Rearrange the terms of h in the above equation,

0.13h + 0.09h = 13 - 12.25

Combine the likewise terms in the above equation,

0.22h = 0.75

Divide both sides by 0.22

h = 0.75/0.22

h = 3.4

Thus, the stock prices will be the same in 3.4 hours.

Learn more about the equation here:

brainly.com/question/13947055

#SPJ2

Answer:

To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. ...

To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Answer:

x=-2

Step-by-step explanation:

6(x+1)=-2(3x+9)

Distribute the 6.

6x+6=-2(3x+9)

Distribute the -2.

6x+6=-6x-18

Move the variable to the left-hand side and change the sign.

6x+6+6x=-18

Collect like terms

12x=-18-6

Calculate the difference.

12x=-24

Divide both sides by 12.

x=-2

Hope this helps :)

Answer: s= -8

Step-by-step explanation:

The gradient of the ski slope can ge used as the slope (literally) of a line equation:

y = mx + b,

where m is the slope and b the y-intercept (the value of y when x = 0).

The first slope would be y = -(1/3)x + b.

The slope is (-1/3) since the ski run is headed downhill.  The second ski slope is assumed to have the same gradient ("two parallel straight ski slopes").

y' = -(1/3)x' + b

We may assume that b is the same for both slopes - they start and end at the same point.

We can find b by using the given point (2,-3):

y' = -(1/3)x' + b

-3 = -(1/3)(2) + b

-3 = -(2/3) + b   [Add -(2/3) to both sides: (-3 + 2/3 = -9/3 + 2/3 = -7/3]

-7/3 = b

b = -(7/3)

The second ski slope, y', thus has the equation

y' = (1/3)x' -(7/3)

We want the value of s in (s, -5).

y' = (1/3)x' -(7/3)

-5 = (1/3)s -(7/3)

(1/3)s = -5 +(7/3)    [-15/3 + 7/3 = -8/3]

(1/3)s = -(8/3)    [Multiply both dies by 3]

s = -(24/3)  

s = -8