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Brilliant_brown [7]
3 years ago
8

A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of 24 in

ches. Complete the explanation for whether the top of the large cake has three times the area of that of the small cake.
Mathematics
2 answers:
drek231 [11]3 years ago
8 0
Large cake:
24÷2=12
12 is the radius of the large cake.
12×12×3.14=452.16

Small cake:
8÷2=4
4 is the radius of the small cake.
4×4×3.14=50.24

452.16÷3=150.72
So, The area of the large cake is not three times the area of the small cake.
Elanso [62]3 years ago
7 0
We must find the area of each cake's top.

Formula for area of a circle:

A =  \pi  r^{2} where r is the radius.

<span>small cake:
</span>Plug in 4 for r because the radius is 4. (They give us the diameter, which is 8, and the radius is half that)

A =  \pi  4^{2}

A = 16π

<span>big cake:
</span>Repeat the process: 
Plug in 12 for r because the radius is 12. (They give us the diameter, which is 24, and the radius is half that)

A = \pi 12^{2}

A = 144π

So our two radii are 144π and 16π. 
The large cake's top is not 3 times the area of the small cake's.

This makes sense because you are squaring the radius, which makes the fact that the larger cake's diameter is triple the smaller cake diameter irrelevant. 

Hope this helped! ^-^
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Solve 5x^2 - 7x + 2 = 0 by completing the square.
Reika [66]

Answer:  The correct option is (c) \dfrac{49}{100}.

Step-by-step explanation:  We are given to solve the following quadratic equation by the method of completing the square:

5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)

Also, we are to find the constant added on both sides to form the perfect square trinomial.

We have from equation (i) that

5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow  \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow  \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.

So,

x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.

Thus, the required solution is x=1,~-\dfrac{2}{5}. and the value of the constant added is \dfrac{49}{100}.

Option (c) is correct.

3 0
3 years ago
I need help with this
Llana [10]

Answer:

? = 4 units

Step-by-step explanation:

'2'  is to  ' 7+2 '     as  ?   is to   '14 + ? '

2/ 9 = ? / (14 + ?)      cross mutiply

28 + 2? = 9?

28 = 7?

? = 4

4 0
2 years ago
Katelyn and Christina are going to plant a garden together. Katelyn can plant the garden working alone in 10 hours. Together it
weeeeeb [17]

Answer:

The answer is 12 hours

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3 years ago
You have 5 pieces of wood. What is the total length of the wood? 73cm, 1.6m, 2.87m, 325cm and 4.04m
skad [1K]
First, you need to make sure that they're in the same measurement ration

1 m = 100 cm

so, now you have

73 cm + 160 cm + 287 cm + 325 cm + 404 cm

The total length would of all the wood would be be 1249 centimeters  or 12.49 meter 
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3 years ago
Given that y=6-5x which ordered pairs would graph the function that has the domain values shown on the table?
mina [271]

Answer:

option D. (-3,21),(-2,16),(0,6),(1,1),(2,-4)

Step-by-step explanation:

we have

y=6-5x

we know that

To find the values of y substitute each value of x in the equation

so

1) For x=-3

y=6-5(-3)=21

2) For x=-2

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3) For x=0

y=6-5(0)=6

4) For x=1

y=6-5(1)=1

5) For x=2

y=6-5(2)=-4

8 0
3 years ago
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