Write an equation and solve:
An iced cake costs 10p more than a plain cake. Sarah bought two of each cake. They cost £1 altogether. What is the cost of an iced cake?

Answer:

[tex]19 sq.\ units[/tex]

Step-by-step explanation:

The best way to approach this is to figure out the area of the overall square, then remove any gaps.

The overall square is 5 by 5 so the area is:

[tex]A_t = s * s = 5 * 5 = 25\ sq.\ units[/tex]

There are 5 gaps in the shape of triangles, we will use the formula: [tex]A = \frac{bh}{2}[/tex], and subtract from the total.

1. (Top left)

[tex]A_1 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]

2. (Top right)

[tex]A_2 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]

3. (Bottom left)

[tex]A_3 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]

4. (Bottom center)

[tex]A_4 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]

5. (Bottom right)

[tex]A_3 = \frac{bh}{2} = \frac{2 * 2}{2} = 2[/tex]

The total triangle area is:

[tex]A = 1 + 1 + 1 + 1 + 2 = 6[/tex]

Subtract from total area to actual area:

[tex]A_s = A_t - A = 25 - 6 = 19 sq.\ units[/tex]

Answer:

a straight angle

Step-by-step explanation:

the minute and hour hand are straight lined up the hour being on the six and the minute being on the twelve

Answer:

2.5 is the best deal

Step-by-step explanation:

hope this helps

Answer:

The y-intercept is (0,-3

Step-by-step explanation:

Step-by-step explanation:

to find the y intercept you simply equate x to 0. therefore, the y intercept is -4.5

and its coordinate is:

(0, -4.5)

Answer:

1089.34in²

Step-by-step explanation:

A=πr2

C=2πr

Solving for A

A=Csquared/4π = 117 squared / 4 * π = 1089.33601in²

Hope it helps

Answer:

Slope: 1

Y-Intercept: 3

Equation of the line: y=x+3

Step-by-step explanation:

1. Slope

Get two random points (eg. 0,3; -3,0)

x1-x2/y1-y2

0-(-3)/3-0

0+3/3

3/3=1

2. Y-intercept

The value of x when y=0

3. Equation of the line

y= mx+b

m= slope

b= y-intercept

y=1x+3

y=x+3

Answer:

Company A = 35 Company B = 45

Step-by-step explanation:

70x3/4 = 52.5

70x1/4 = 17.5

52.5 - 17.5 = 35

90x1/4 = 22.5

90x3/4 = 67.5

67.5 - 22.5 = 45

Hence, Company A = [tex]35[/tex] and  Company B = [tex]45[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The cumulative frequency diagram shows information about the ages of employees in two companies. Work out the IQR for both companies and compare them.

So, For the Company A

[tex]70[/tex]×[tex](\frac{3}{4})\\[/tex]

[tex]=70[/tex]×[tex](0.75)\\[/tex]

[tex]=52.5[/tex]

[tex]70[/tex]×[tex]\frac{1}{4}\\[/tex]

[tex]= 70[/tex]×[tex](0.25)\\[/tex]

[tex]=17.5[/tex]

So,

[tex]52.5- 17.5 = 35[/tex]

So, Company A is [tex]35[/tex].

For Company B,

[tex]90[/tex]×[tex]0.25 = 22.5[/tex]

[tex]90[/tex]×[tex]\frac{3}{4} = 67.5[/tex]

Then,

[tex]67.5 - 22.5 = 45[/tex]

So Company B is [tex]45[/tex].

Hence, Company A = [tex]35[/tex] and  Company B = [tex]45[/tex].

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Answer:

5.5

Step-by-step explanation:

firrst arrange them from least to greatest:

1,8,9,2,-5,-7

then cross out each side one by one until its in the middle

which leaves with 9 and 2

add both together

and get 11

divide by 2 which is 5.5

The relationship between corresponding terms in the two patterns is B(n) = 2A(n) where the A(n) and B(n) is the nth terms of the pattern A and pattern B.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have Pattern A starts at 0 and has the rule "add 3"

Pattern A:

0, 3, 6, 9, 12.....and so on

Pattern B starts at 0 and has the rule "add 6."

Pattern B:

0, 6, 12, 18, 24, 30.... and so one

In the pattern A we can find the nth term:

First term = 0, common difference = 3

A(n) = 0 + (n-1)3 = 3(n-1)

Similarly in the pattern B we can find the nth term

First term = 0, common difference = 6

B(n) = 0 + (n-1)6 = 6(n-1)

The relation can be derived between the nth term of pattern A and pattern B as follows:

B(n) = 2A(n)

Thus, the relationship between corresponding terms in the two patterns is B(n) = 2A(n) where the A(n) and B(n) is the nth terms of the pattern A and pattern B.

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73-96

For box plots, the two edges of the box represent the 25% and 75% mark, meaning everything in between those two lines is the middle 50%. In this case the lines are at 73 and 96.

Answer:

see below

Step-by-step explanation:

y = a ( x-0)^2 + 5     sub in the point given to calculate 'a'

1 = a (4)^2 + 5

-4 = 16a

a = - 1/4

y = -1/4 x^2 + 5

Answer:

18 days

Step-by-step explanation:

since 1/2 is half, u will multiple 9 by 2 to get 18 days !

Answer:

the answer is c

Step-by-step explanation:

-then+

The number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.

Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.

Dr. Orchid has 9 paintings she wants to hang side by side on her walls.

Total number of paintings is 9. She wants to arrange them side by side. Thus, the number of ways, she can arrange all 9 paintings is,

[tex]9!=9\times8\times7\times6\times5\times4\times3\times2\times1\\9!=362880[/tex]

She wants to display 4 of the paintings. The number of arrangement of 4 painting from 9 paintings is,

[tex]^9C_4=\dfrac{9!}{(9-4)!4!}\\^9C_4=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\\^9C_4=126[/tex]

Thus, the number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.

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Answer:

g(x) =  - 1/2 * (x^2 - 8x + 12)

Step-by-step explanation:

Given the information, you have provided.

Zeros: (2,0) and (6,0).

Maximum: (4,2) which is also your (h,k)

f(x) = - (x - 2)*(x - 6)

g(x) =  - 1/2 * (x^2 - 8x + 12)

I do not know how to explain this, but -1/2 makes the graph get (4,2) as the maximum.

The red graph is f(x) = - (x - 2)*(x - 6)

The blue graph is your answer g(x) =  - 1/2 * (x^2 - 8x + 12)

Answer:

Step-by-step explanation:

In this question we have given an equation that is 3 ( q - 7 ) = 27 and we have asked to solve this equation that means to find the value of q .

Solution : -

[tex] \quad \: \longmapsto \: 3(q - 7) = 27[/tex]

Step 1 : Solving parenthesis :

[tex]\quad \: \longmapsto \:3q - 21 = 27[/tex]

Step 2 : Adding 21 on both sides :

[tex]\quad \: \longmapsto \:3q - \cancel{ 21} + \cancel{21} = 27 + 21[/tex]

On further calculations we get :

[tex]\quad \: \longmapsto \:3q = 48[/tex]

Step 3 : Dividing by 3 from both sides :

[tex]\quad \: \longmapsto \: \frac{ \cancel{3}q}{ \cancel{3}} = \cancel {\frac{48}{3} }[/tex]

On further calculations we get :

[tex]\quad \: \longmapsto \: \pink{\boxed{\frak{q = 16}}}[/tex]

Verifying : -

Now we are very our answer by substituting value of q in the given equation . So ,

Therefore, our solution is correct .

Answer:

[tex] \: [/tex]

Step-by-step explanation:

So here, a equation is given and we are asked to solve the equation.

[tex] \\ \dashrightarrow \sf \qquad3(q-7)=27 \\ \\ [/tex]

For this, we have to use the Distributive property, which is :

[tex]\\ \dashrightarrow \sf \qquad3q-21=27 \\ \\ [/tex]

Transposing the constant term (-21) to the right side we get :

[tex]\\ \dashrightarrow \sf \qquad3q=27 + 21 \\ \\ [/tex]

Adding the like terms :

[tex] \\ \dashrightarrow \sf \qquad3q=48 \\ \\ [/tex]

Now, We'll divide both sides by 3 :

[tex] \\ \dashrightarrow \sf \qquad \frac{3q}{3} = \frac{48}{3} \\ \\ [/tex]

[tex]\dashrightarrow \bf \qquad \: q=16 \\ \\ [/tex]

Answer:

109.3 yard²

Step-by-step explanation:

Area of triangle = bh / 2

base is 23yd

height is 9.5yd

bh / 2 = 23 × 9.5 / 2

Area = 218.5 / 2

Area = 109.25 yd²; rounded to the nearest tenth is 109.3yd²

[tex]5^{-12} \cdot 32^{-3} \cdot 9^{-15}\\\\\\=\dfrac 1{5^{12}} \cdot \dfrac 1{32^3} \cdot \dfrac 1{9^{15}}\\\\\\=\dfrac 1{5^{12}} \cdot \dfrac 1{(2^5)^3}\cdot \dfrac 1{9^{15}}\\\\\\=\dfrac 1{5^{12} \cdot 2^{15} \cdot 9^{15} }\\\\\\=\dfrac 1{5^{12}\cdot 18^{15}}[/tex]

Answer:

[tex]\boxed{ \dfrac{1}{5^{12}} \times \dfrac{1}{32^{3}} \times \dfrac{1}{9^{15}}}[/tex]

Step-by-step explanation:

In this case, all the exponents are negative. To make them positive, take the term's reciprocal and change the exponents sign.

[tex]\implies 5^{-12} \times 32^{-3} \times 9^{-15}[/tex]

Changing the terms into it's reciprocal form:

[tex]\implies \dfrac{1}{5^{-12}} \times \dfrac{1}{32^{-3}} \times \dfrac{1}{9^{-15}}[/tex]

Changing the signs of the exponent:

[tex]\implies\boxed{ \dfrac{1}{5^{12}} \times \dfrac{1}{32^{3}} \times \dfrac{1}{9^{15}}}[/tex]

Answer:

7.11

Step-by-step explanation:

You will add all of those numbers and divide them by the amount of numbers you added. And I rounded the answer to 2 decimal places, seeing that it is a recurring decimal.

Answer:

1/2

Step-by-step explanation:

A coin has 2 sides, and it is flipped 3 times. 3 x 2 = 6. Each flip only has a head, so 3 flips would have 3 heads.

3/6 = 1/2

Answer:

x= 21

Step-by-step explanation:

[tex] \frac{x}{3} = 7 \\ \\ multiply \: both \: sides \: by \: 3 \\ \\ 3 \times \frac{x}{3} = 3 \times 7 \\ \\ \implies \cancel 3 \times \frac{x}{\cancel 3} = 21 \\ \\ \implies \: x = 21[/tex]

Answer:

Step-by-step explanation:

Let the power is x, then we have the following inequality

Solving we get

Answer:

An answer is twenty.

Step-by-step explanation:

0.35^20 is the expression the equation would be 0.35^20=7.609

or: 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times... until you multiply 0.35 times 0.35 twenty times. Not 0.35 times 20, 0.35 times 0.35 twenty times, don't forget to move the decimal! An exponent is 20.

hope this helps!

301.6 cubic meters

A cylinder is a shape with straight sides with circular or oval cross-sections. We know that the cylinder in the question must be a circular cylinder due to its radius description. 

Volume Formula

A circular cylinder has a volume of [tex]V=\pi r^2h[/tex]. In this equation, V is the volume, r is the radius, and h is the height. The question tells us that r=4m and h=6m. So, we can plug these values into the formula.

Solving for Volume

To solve plug the values into the formula and rewrite the equation.

Next, apply the exponents.

Then, multiply the constants.

Finally, multiply the remaining terms. Remember to use the pi button on the calculator and not an estimation to get a more exact value.

Make sure your answer is rounded to the correct digit. This means that the volume must be 301.6 cubic meters.

work it out you cheater lol

Answer:

885735

Step-by-step explanation:

5

x 3

15

x 3

45

x 3

135

x 3

405

x 3

1215

x 3

3645

x 3

10935

x 3

32805

x 3

98415

x 3

295245

x 3

885735

Answer:

885735

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

rotation and enlargements

Step-by-step explanation:

triangle XYZ is rotated to make triangle GHI and triangle GHI is enlarged by a scale factor of around 2.6? to make triangle MNO then triangle MNO is rotated to make triangle EDF

Answer: The three systems that would be reasonable

ΔXYZ to ΔGHI is a Rotation

ΔGHI to ΔMNO is an Enlargement

ΔMNO to ΔDEF is a Reflection

Step-by-step explanation: