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klio [65]
3 years ago
11

ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Mathematics
1 answer:
Allushta [10]3 years ago
6 0
The triangle is drawn and is shown in the image attached with.

We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same. 

D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:

AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units

So,

4 :x = 8 : 6 \\  \\ 
 \frac{4}{x} = \frac{8}{6}  \\  \\ 
x=4* \frac{6}{8}=3 


Therefore, the length of DE will be 3 units

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An angle measures 78° less than the measure of its supplementary angle. What is the
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Answer:

Step-by-step explanation:

Supplementary angles add up to 180°.

If the angle is x, its supplement is 180°-x.

x = (180°-x) - 78°

x = 51°

supplement = 180°-x = 129°

The angles are 51° and 129°

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3 years ago
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IrinaK [193]

Equation step-by-step:

y = \sqrt{-9} - 2

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Hope it helped,


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<em>(If you have any questions feel free to ask them in the comments)</em>

8 0
3 years ago
What is the multiplicity of each of the roots of the graph of f(x)=−-x^3+2x^2+3x?
DerKrebs [107]

Answer:

A. -1, multiplicity 1; 0, multiplicity 1; 3, multiplicity 1.

Step-by-step explanation:

Let f(x) = -x^{3}+2\cdot x^{2} + 3\cdot x, to determine its roots and multiplicities we proceed to factorize the polynomial:

1) -x^{3}+2\cdot x^{2} +3\cdot x Given

2) x\cdot (-x^{2}+2\cdot x + 3) Distributive property

3) x\cdot (x-3)\cdot (x+1) Quadratic formula/Result

The roots and multiplicities of f(x) = -x^{3}+2\cdot x^{2} + 3\cdot x are:

<em>0 (multiplicity 1)</em>

<em>3 (multiplicity 1)</em>

<em>-1 (multiplicity 1)</em>

Therefore, the correct answer is A.

4 0
3 years ago
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I WILL GIVE INSTANT BRANLEIST
Vsevolod [243]
The ratio is 5:12

Glad I help you
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Write an equation of a line with the given slope and y-intercept.<br><br> m = , b = 2
Vlad [161]

Answer:

<u>Equation</u><u> </u><u>is</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>mx</u><u> </u><u>+</u><u> </u><u>2</u>

Step-by-step explanation:

General equation of line:

{ \boxed{ \bf{y = mx + b}}}

Substitute in considerance of the question:

{ \sf{ y = mx + 2}}

If m is given, substitute for m to the answer.

3 0
3 years ago
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