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spin [16.1K]
3 years ago
14

Which value of x would make ? 1 6 8 10

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
3 0

Answer:

x=8\ in

Step-by-step explanation:

we know that

If NO is parallel to KJ

then

Triangles LNO and LKJ are similar by AA Similarity Postulate

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{LO}{LJ}=\frac{LN}{LK}

substitute the values

\frac{x-4}{x-4+x}=\frac{x-3}{x-3+x+2}

\frac{x-4}{2x-4}=\frac{x-3}{2x-1}\\ \\(x-4)(2x-1)=(x-3)(2x-4)\\ \\2x^{2}-x-8x+4=2x^{2}-4x-6x+12\\ \\-9x+4=-10x+12\\ \\10x-9x=12-4\\ \\x=8\ in

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Express the sum in the simplest form.
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The answer would be the third one because you cannot change the denominator and you can only add the numerators
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The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc
masya89 [10]

Answer:

Therefore the angle of intersection is \theta =79.48^\circ

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

r_1(t)=(2t,t^2,t^4)

and r_2(t)=(sin t , sin5t, 2t)

To find the tangent of a carve , we have to differentiate the carve.

r'_1(t)=(2,2t,4t^3)

The tangent at (0,0,0) is     [ since the intersection point is (0,0,0)]

r'_1(0)=(2,0,0)      [ putting t= 0]

|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2

Again,

r'_2(t)=(cos t ,5 cos5t, 2)

The tangent at (0,0,0) is    

r'_2(0)=(1 ,5, 2)        [ putting t= 0]

|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}

If θ is angle between tangent, then

cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}

\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }

\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }

\Rightarrow cos \theta =\frac{1}{\sqrt{30} }

\Rightarrow  \theta =cos^{-1}\frac{1}{\sqrt{30} }

\Rightarrow  \theta =79.48^\circ

Therefore the angle of intersection is \theta =79.48^\circ.

8 0
3 years ago
Can someone please help me please?
Iteru [2.4K]

Answer: D

Step-by-step explanation:

Proof see picture

5 0
3 years ago
Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
notka56 [123]

A function assigns the values. The correct option is D.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.


The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

Learn more about Function:

brainly.com/question/5245372

#SPJ1

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2 years ago
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