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3 years ago

9.2 Multiplying and Factoring Polynomials 9k ( 7k+ 4 )

1 answer:

6 0

If you only want to simplify the problem, you would use the distributive property. 9k * 7k = 63 $k^{2}$ . Then, 9k * 4 = 36k. However, if you wanted to solve for k, you would want to set the equation equal to 0. This gives you 63 $k^{2}$ + 36k = 0. After factoring, k = 0 or -4/7.

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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

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3 years ago

Which answer includes a function, its inverse, and a dashed line that verifies the relationship?

just olya [345]

Answer:

the first one

Step-by-step explanation:

yellow line is an exponential graph

blue line is a log graph

the purple in the middle is a sort of "combo" of the two

3 0

2 years ago

Read 2 more answers

Can i get the answer to this question please???? and fast

lord [1]

The triangle must be isosceles, due to the perpendicular bisector. Therefore, the expression 20 - 15 can be used to yield an answer of B. 5.

Hope this helps!

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4 years ago

PLEASE HELP QUICK

valentinak56 [21]

Answer: 28 in.

Step-by-step explanation:

its simple

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4 years ago

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kherson [118]

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