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3 years ago

FACTOR !!! a) 5x^2+25 b) 2x^2-3x-2

Mathematics

1 answer:

Mademuasel [1]3 years ago

3 0

Step-by-step explanation:

(a): 5x^2 + 25 = 5 * x^2 + 5 * 5 = 5(x^2 + 5).

(b): 2x^2 - 3x - 2 = 2x^2 - 4x + x - 2

= 2x(x - 2) + 1(x - 2) = (2x + 1)(x - 2).

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Answer:

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Step-by-step explanation:

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3 years ago

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

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4 years ago

Read 2 more answers

A regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. What is the area of the hexagon?

Neporo4naja [7]

<u>Answer</u>

748.23 in²

<u>Explanation</u>

Apothem a line from the centre of a regular polygon at right angles to any of its sides. This can be said to be the height of the triangle in a polygon.

The base of the hexagon = 101.8 ÷ 6

= 19.96666..

= 19.9667 inches

Area of the hexagon = 1/2 × height × base length × 6

= 1/2 × 14.7 × 19.9667 × 6

= 748.23 in²

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