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2 years ago

8

Factor -1/2 out of -1/2 X +6=?

1 answer:

solong [7]2 years ago

8 0

The solution to the problem is as follows:

Since -1/2 is the greatest common factor of the two terms,

(-1/2)x + 6 = (-1/2) (x - 3)

The factored form therefore is (-1/2) (x - 3). I hope my answer has come to your help. God bless and have a nice day ahead!

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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.

8 0

3 years ago

Read 2 more answers

A model car is 7.5 inches long made with a scale of 2 inches = 48 inches. How long is the actual car?

slava [35]

Answer:

360

Step-by-step explanation:

3 0

2 years ago

Item 13<br> Factor out the coefficient of the variable.<br><br> The expression 14y+38 factored is

klemol [59]

Answer:

2(7y+19)

Step-by-step explanation:

14y+38=2(7y+19)

8 0

3 years ago

The diameter of a circle endpoints are A(-1, 5) and B(4,-3). Use the midpoint formula to find the coordinates of the center of c

mina [271]

Answer:

centre = ( $\frac{3}{2}$ , 1 )

Step-by-step explanation:

using the midpoint formula

midpoint = [ $\frac{1}{2}$ (- 1 + 4), $\frac{1}{2}$ (5 - 3) ] = ( $\frac{3}{2}$ , 1 )

6 0

3 years ago

If i spend $ 101.65 at kohls,but have 30% off how much is my total show work please

Juliette [100K]

101.65 x .30= 30.50 saving
so take 101.65 - 30.50= 71.15

6 0

3 years ago