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maks197457 [2]
3 years ago
9

What is the length of DE in the right triangle below

Mathematics
1 answer:
liraira [26]3 years ago
8 0

The answer is B

Step-by-step explanation:

As shown in the given figure, ΔDEF is a right-angles triangle, where ∠DFE = 90°, DF = 15 units and EF = 20 units.

We are to find the length of DE.

ΔDEF is right-angled at ∠DFE.

So, using Pythagoras theorem, we have

\begin{lgathered}DE^2=DF^2+EF^2\\\\\Rightarrow DE^2=15^2+20^2\\\\\Rightarrow DE^2=225+400\\\\\Rightarrow DE^2=625\\\\\Rightarrow DE^2=25^2\\\\\Rightarrow DE=25.\end{lgathered}

DE

2

=DF

2

+EF

2

⇒DE

2

=15

2

+20

2

⇒DE

2

=225+400

⇒DE

2

=625

⇒DE

2

=25

2

⇒DE=25.

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The value 5 is an upper bound for the zeros of the function shown below. f(x)=x^4+x^3 -11x^2-9x+18
Inessa [10]
Answer: True

Explanation:
According to the rational zeros theorem, if x=a is a zero of the function f(x), then f(a) = 0.

Given:  f(x) = x⁴ + x³ - 11x² - 9x + 18
From the calculator, obtain
f(5) = 448
f(4) = 126
f(3) = 0
f(2) = -20
f(1) = 0
f(0) = 18
f(-1) = 16
f(-2) = 0
f(-3) = 0

The polynomial is of degree 4, so it has at most 4 real zeros.
From the calculations, we found all 4 zeros as x = -3, -2, 1, and 3.
Therefore
f(x) = (x+3)(x+2)(x-1)(x-3).

For x>3, f(x)increases rapidly. Therefore there are no zeros for x>3.
The statement that x=5 is an upper bound for the zeros of f(x) is true.



7 0
3 years ago
Read 2 more answers
Find the value of x<br> x° <br> 66°<br> 117°
pogonyaev

Answer:

x = 51 degrees

Step-by-step explanation:

Keep in mind, the angles of a triangle add up to 180 degrees.

A flat line also equals 180 degrees.

First, we should find the lower left angle. We know that 117 plus that angle is going to be 180, since it's a flat line.

180 - 117 = 63

Now, we just need to find angle x. (All 3 of our angles should add up to 180, knowing this, we can put it in an equation)

63 + 66 + x = 180

Then, you solve for x:

(63+66) + x = 180

129       + x = 180

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Hope this helps :)

5 0
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Lelechka [254]
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3 years ago
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son4ous [18]
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2 years ago
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A tetrahedron is a triangular pyramid with 4 equilateral faces. Han has a box of tetrahedrons with each of the 4 vertices marked
Daniel [21]

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If this is so, then the tetrahedron is a fair tetrahedron otherwise not.

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