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3 years ago

Logan has 22 blue marbles and eight red marbles what is the ratio of red marbles to the total Of marbles

Mathematics

1 answer:

Lunna [17]3 years ago

5 0

Answer:

it is 8/30

Step-by-step explanation:

first you have to add the red and blue marbles together to get the total of marbles which is 22 so then you create a fraction of 8/30 8 is the red marbles and 30 is the total number of marbles

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The perimeter of the rectangle below is 68 cm. The perimeter of the triangle is 60 cm. Find the length of the hypotenuse of the

Inessa05 [86]

The right triangle is assumed to be inscribed in the rectangle, such that

hypotenuse is the diagonal of the rectangle.

The length of the hypotenuse of the triangle is 26 cm.

Reasons:

Let x and y represent the length of the sides of the rectangle

Whereby the base and height of the right triangle are the same as the

length and width of the rectangle, we have;

Perimeter of the rectangle = 2·x + 2·y = 68

Therefore;

$\displaystyle x + y = \frac{68}{2} = 34$

x + y = 34

The base of the right triangle = x

The height of the right triangle = y

By Pythagoras's theorem, the length of the hypotenuse side = √(x² + y²)

Therefore; Perimeter of the right triangle = x + y + √(x² + y²) = 60

Which gives;

∴√(x² + y²) = 60 - (x + y) = 60 - 34 = 26

The length of the hypotenuse side, √(x² + y²) = 26 cm

Learn more about Pythagoras's theorem here:

brainly.com/question/8171420

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2 years ago

Given △ABC. m∠A>m∠B>m∠C. Perimeter=30. Which side of △ABC may have length 7?

lisabon 2012 [21]

Solution-

As given in △ABC,

$m\angle A>m\angle B>m\angle C$

As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e

$\sin A>\sin B>\sin C$

According to the sine law,

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.

$\Rightarrow a>b>c$

Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.

Case-1. Length of a is 7

As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.

Case-2. Length of b is 7

As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.

Case-3. Length of c is 7

As this is the last case, this must be true.

Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.

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3 years ago

The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3 inches from th

LiRa [457]

The area of the rectangular base is the amount of space on the rectangular base

The area of the rectangular base is 60 square inches

<h3>How to determine the area of the rectangular base?</h3>

The question is incomplete; as the diagram is not given.

So, I will apply the concept of similar shapes to determine the area of the rectangular base

To determine the area of the rectangular base, we make use of the following equivalent ratio:

Ratio = Height : Area

This gives

3 : 36 = 5 : Area

Express as fraction

36/3 = Area/5

Evaluate the quotient

12 = Area/5

Multiply both sides by 5

Area = 60

Hence, the area of the rectangular base is 60 square inches