Do 7, 8, and 9 form a right triangle?

Answer:

The sum converges at: [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sum\limits^{\infty}_{n =2} \frac{8}{n^2 - 1}[/tex]

Express the denominator as difference of two squares

[tex]\sum\limits^{\infty}_{n =2} \frac{8}{(n - 1)(n+1)}[/tex]

Express 8 as 4 * 2

[tex]\sum\limits^{\infty}_{n =2} \frac{4 * 2}{(n - 1)(n+1)}[/tex]

Rewrite as:

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{2}{(n - 1)(n+1)}[/tex]

Express 2 as 1 + 1 + 0

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+0}{(n - 1)(n+1)}[/tex]

Express 0 as n - n

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+n - n}{(n - 1)(n+1)}[/tex]

Rewrite as:

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)-(n - 1)}{(n - 1)(n+1)}[/tex]

Split

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)}{(n - 1)(n+1)}-\frac{(n - 1)}{(n - 1)(n+1)}[/tex]

Cancel out like terms

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]

In the above statement, we have:

[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{6})][/tex]

[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{6})][/tex]

Add [tex]a_7[/tex]

[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{7 - 1} - \frac{1}{7+1})][/tex]

[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{8})][/tex]

[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{8})][/tex]

Notice that the pattern follows:

[tex]a_3 + a_5 + a_7 + ...... + a_{k}= 4[(\frac{1}{2} - \frac{1}{k+1})][/tex]

The above represent the odd sums (say S1)

For the even sums, we have:

[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]

In the above statement, we have:

[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{7})][/tex]

[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{7})][/tex]

Add [tex]a_8[/tex] to both sides

[tex]a_4 + a_6 +a_8 = 4[(\frac{1}{3} - \frac{1}{7}) + \frac{1}{7} - \frac{1}{9}][/tex]

[tex]a_4 + a_6 +a_8 = 4[\frac{1}{3} - \frac{1}{9}][/tex]

Notice that the pattern follows:

[tex]a_4 + a_6 + a_8 + ...... + a_{k}= 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]

The above represent the even sums (say S2)

The total sum (S) is:

[tex]S = S_1 + S_2[/tex]

[tex]S =4[(\frac{1}{2} - \frac{1}{k+1})] + 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]

Remove all k terms

[tex]S =4[(\frac{1}{2}] + 4[(\frac{1}{3}][/tex]

Open bracket

[tex]S =\frac{4}{2} + \frac{4}{3}[/tex]

[tex]S =\frac{12 + 8}{6}[/tex]

[tex]S =\frac{20}{6}[/tex]

[tex]S =\frac{10}{3}[/tex]

The sum converges at: [tex]\frac{10}{3}[/tex]

Answer:

8

Step-by-step explanation:

eight letters

there is only one who has 8 letters in the name

Answer:

a = 2

Step-by-step explanation:

Use Pythagorean Theorem:

[tex]a^2+b^2=c^2\\a^2+2.1^2=2.9^2\\a^2+4.41=8.41\\a^2=4\\\sqrt{a^2}=\sqrt{4}\\a=2[/tex]

Therefore, a is 2 meters.

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

This question may be relatively tricky. Since no specific order is stated or implied, it does not matter whether the vendor chooses vanilla or strawberry first, as long as the vendor chooses both.

Therefore, for the first flavor the vendor can either choose vanilla or strawberry. There is a [tex]\frac{2}{4}=\frac{1}{2}[/tex] chance of this happening.

For the second flavor, the vendor must choose the one they didn't pick for the first flavor (either strawberry or vanilla). There is a [tex]\frac{1}{4}[/tex] chance they do so.

Therefore, there is a [tex]\frac{1}{2}\cdot \frac{1}{4}=\boxed{\frac{1}{8}}[/tex] chance that vanilla and strawberry are chosen.

Answer:

.169

Step-by-step explanation:

I hoped I helped you solve sorry if I'm wrong

Answer:

x-10x=100

-9x=100

-9x÷-9=100÷-9

x=-11,1

Answer:

5/8

Step-by-step explanation:

Make denominators equal

1/4 = 2/8 (Multiply both sides by 2 to get a common denominator)

2/8 + 3/8 = 5/8

Answer:

x = 3

Step-by-step explanation:

Given the linear equation :

1/4(x-5)+4=1/3(2x+7)-5/6

(x-5)/4 + 4 = (2x+7)/3 - 5/6

Take the lcm and sum

(x-5+16)/4 = (4x+14-5)/6

(x+11)/4 = (4x+9)/6

Cross multiply

6(x+11) = 4(4x+9)

6x + 66 = 16x + 36

Collect like terms

6x - 16x = 36 - 66

-10x = - 30

x = 30/10

x = 3

Answer:

neither, since the gradients are not the same, as well as the c value

Step-by-step explanation:

First line : y = -4x + 7

Second line : y = -4x + 3

We know that the standard form of equation of a line is y = mx + c

where :

m is the slope

c is the y intercept

Comparing both line equations with the standard form, we can notice that :

⊕  Slope of the first line = -4

⊕  Slope of the second line = -4

We know that Slopes of parallel lines are same

So, We can conclude that the given two lines are parallel to each other

Answer : Parallel because the slopes are the same

Answer:

Step-by-step explanation:

Parallel lines have the same slope. The slope of the given line is 3. The easy way to do this, the one that uses our logical brains as opposed to our mathematical brain, tells us that since there is only one choice that has a given slope of 3, that is the one that we want. The second choice down is the only one that has a slope of 3.

Mathematically,

[tex]y-2=3(x-3)[/tex] and

[tex]y-2=3x=9[/tex] and

[tex]y=3x-9+2[/tex] so

y = 3x - 7 (the second choice)

There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

In this question we have a triangle with two known sides and a known angle. By the law of sines we find the possible values of the angle D:

410/sin 120° = 440/sin D

Please notice that the sum of the internal angles of triangles equals 180°. Then,

sin D = (440/410) · sin 120°

sin D ≈ 0.929

There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

To learn more on law of sines: https://brainly.com/question/17289163

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Answer:

C. The probability of choosing a blue marble after a red marble has been removed is 0.6.

Step-by-step explanation:

P(B|A)

P(B|A) states the probability of event B happening, given that event A has happened.

In this question:

Event A: First marble is red.

Event B: Second marble is blue.

P(B|A) = 0.6

This means that the probability that the second marble is blue, considering that the first marble was red, is of 0.6, and thus, the correct answer is given by option C.

Answer:

18.67 ft

Step-by-step explanation:

     |\

     |   \

     |      \

h    |         \     20 ft

     |            \

     |               \

     |--        69°  \

     ---|----------------

For the 69° angle, h is the opposite leg, and 20 ft is the hypotenuse.

sin A = opp/hyp

sin 69° = h/20

h = 20 * sin 69°

h = 18.67

Answer: 18.67 ft

Three consecutive integers that add up to 27 are 8, 9, and 10

Hope this helps =)

First represent your 3 consecutive integers as x, x + 1, and x + 2.

Since their sum is 27, our equation reads x + (x + 1) + (x + 2) = 27.

Now simplifying on the left side we get 3x + 3 = 27.

You should be able to easily solve for x and find that x = 8.

Make sure you list all your answers.

If x is 8, then x + 1 is 9 and x + 2 is 10.

Answer:

Your answer should be 647.51

Explanation : the price was 215.949 in December, 2009.

the price was 233.049 in December, 2013.

divide 233.049 by 235.949 and got 1.079185363.

multiply that by 600 and got 647.5112179.

The cost of the TV in 2010 is $647.5

Given that the complete information contains the Consumer Price Index values:

To find the CPI,

CPI= [tex]\frac{C_t}{C_0}[/tex]

Where C_t= cost of the market basket in the current period

C_0 = cost of the market basket in the base period

In December 2009, the price was 215. 949

In December 2013, the price was 233.049

Hence,

215. 949/233.049

= 1.079185363.

Then we would multiply by the base selling price

[tex]1.079185363 * 600 = 647.5112179.[/tex].

Read more about the consumer price index here:

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9514 1404 393

Answer:

  7x^3y^4z^2

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{343x^9y^12z^6}=\sqrt[3]{(7x^3y^4z^2)^3}=\boxed{7x^3y^4z^2}[/tex]

Answer:

[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]

Step-by-step explanation:

[tex] \small \sf \leadsto \: \sqrt[3]{343 \: x {}^{9} \: y{}^{12} \: z {}^{6} }[/tex]

[tex] \small \sf \leadsto \: \sqrt[3]{7x {}^{3}y {}^{6}z {}^{2} } [/tex]

[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]

Answer:

C 6

Step-by-step explanation:

Pythagoras

c² = a² + b²

117 = x² + (x+3)² = x² + x² + 6x + 9 = 2x² + 6x + 9

=>

108 = 2x² + 6x

54 = x² + 3x

0 = x² + 3x - 54 = (x-6)(x+9)

just think by what numbers can we divide 54 without any remainder (so that when multiplying we get 54) ? and which pair of these have a difference of 3 (so that with +/- combination we get "3x" in the multiplication)?

the solutions for x are the 2 numbers that would make one of the bracket expressions 0, as this turns the whole expression to 0.

x = 6 and x = -9

a negative number does not make any sense for a side length.

so, the only possible solution is x = 6

x^2 + 13x + 22 = 0

( x + 11 )( x + 2 ) = 0

x = - 11 Or x = - 2

Answer:

Step-by-step explanation:

eq. of any circle with center (h,k) and r=1 is

(x-h)²+(y-k)²=1²

points (-18,15) and (-20,15) lie on it.

(-18-h)²+(15-k)²=1

(15-k)²=1-(-18-h)²

and (-20-h)²+(15-k)²=1

(15-k)²=1-(-20-h)²

so 1-(-18-h)²=1-(-20-h)²

-(18+h)²=-(20+h)²

324+36h+h²=400+40h+h²

40h-36h=324-400

4h=-76

h=-19

(15-k)²=1-(-18-(-19))²=1-1=0

k=15

so center is (-19,15)

Answer:

Area = 20yd

Perimeter = 23 yd

Step-by-step explanation:

Area = 1/2 ×bh

b, which I the base = 10yd

h, which is the height = 4yd

Note: 5yd is the base because when you turn the triangle you will see that 10yd is the base and 5yd is the height not 8yd because 8 yd is not a straight line at a right angle

Therefore;

Area = 1/2× 10 × 4

= 1× 5 × 4

= 20yd

Perimeter = 8yd +5yd +10yd

= 13yd + 10yd

= 23yd

Answer:

It is D...........nnnnnnn

Answer:

A.// He has the side lengths in the wrong place in the cosine ratio.

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

a strange question, as 2 answer options are actually possible, as they define valid domains for this function.

and if the range of the function would include imaginary numbers ("i"), all 4 would be correct.

the problem statement has to be much more precise. you can tell your teacher that.

but I assume, we base just on real numbers and want the biggest domain range. and that is A.

A. for x=1 we get sqrt(0) + 2, which is absolutely valid.

B. a square root of a negative number is undefined in the works of real numbers. we would need "i", the imaginary numbers, to make this a valid function.

C. is also valid. no bad values and expressions involved. it is just a snake range than A.

D. the same a for B.

The domain of the function [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]

The function is given as:

[tex]f(x) = \sqrt{x - 1} + 2[/tex]

Set the radicand greater than or equal to 0

[tex]\sqrt{x - 1} \ge 0[/tex]

Take the square of both sides

[tex]x - 1 \ge 0[/tex]

Add 1 to both sides

[tex]x \ge 1[/tex]

This means the possible values of x starts from 1 till infinity

Hence, the domain of [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]

Read more about domain at:

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