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olya-2409 [2.1K]
3 years ago
12

If ADE ABC in this diagram, which pair of ratios must necessarily be equal?

Mathematics
2 answers:
ad-work [718]3 years ago
8 0

Answer:

\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}

Step-by-step explanation:

we know that

Triangle ADE and Triangle ABC are similar

therefore

the ratio of their corresponding sides are equal

so

\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}

solong [7]3 years ago
4 0
From the diagram, the the pair of ratios that should be equal is the ratio between the sides of each triangle. For instance,

AE/EC = AD/DB

This ratio of the lengths should be equal so that the figure can be true. Hope this answers  the question.
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3 years ago
Two numbers whose sum is 44 and whose product is a maximum
Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x)                    Remove the brackets

Max = 44x - x^2                   Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x )               Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done  is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.


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