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3 years ago

What is the width of Averi's area model? (See picture)

Mathematics

1 answer:

shepuryov [24]3 years ago

8 0

Answer:

Width = x² + 5x - 4

Step-by-step explanation:

By the definition of an area model,

Area = Width × greatest common factor

Since, Area = 4x² + 20x - 16

And greatest common factor = 4

4x² + 20x - 16 = 4(Width)

By dividing both the sides of the equation by 4,

$\frac{4x^2+20x-16}{4}=\frac{4(\text{Width})}{4}$

x² + 5x - 4 = Width

Therefore, width = (x² + 5x - 4) will be he answer.

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Blake is driving home from the water park. He drives for 60 miles and stops to rest before driving 20 more miles. Unfortunately,

7nadin3 [17]

Mathematically its 60+20-36+70

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3 years ago

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If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the

Oduvanchick [21]

Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.

Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?

Explanation:-

Let the radius of the right circular cylinder be r units

Let the radius of the right circular cylinder be h units

Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)

If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units

The height of the new right circular cylinder

= (1/4)×h units

⇛ h/4 units

Curved Surface Area of the new cylinder

= 2π(2r)(h/4) sq.units

⇛ 4πrh/4 sq.units

⇛ πrh sq.units --------(ii)

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder

⇛ πrh : 2πrh

⇛ πrh / 2πrh

⇛ 1/2

⇛ 1:2

Therefore the ratio = 1:2

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2

6 0

2 years ago

Consider 8x2 - 48x = -104.

ki77a [65]

Answer:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$

Step-by-step explanation:

Quadratic Equation Solving

We have the equation:

$8x^2-48x=-104$

Divide by 8:

$x^2-6x=-13$

Now complete the squares so the left side is a perfect square of a binomial:

$x^2-6x+9=-13+9=-4$

Factoring the perfect square:

$(x-3)^2=-4$

Taking the square root:

$x-3=\sqrt{-4}$

The square root of a negative number is an imaginary number:

$x-3=\pm 2\mathbf{i}$

Solving for x:

$x=3\pm 2\mathbf{i}$

The solutions are:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$

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3 years ago

Michael has two more apples than Ann does. Together, Michael and Ann have no more than 9 apples. If Ann has at least one apple,

fiasKO [112]

Answer:

ann has 1 apple and Michael has 8 apples

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3 years ago

Of 560 marbles in a bag, 65% are red and the rest are blue. After 28 red marbles are replaced with blue ones, how many blue marb

jonny [76]

Answer: The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

$n_b=560-364=196.$

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

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3 years ago

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