Solve for b.
7
b
12
b= ✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter

Answer:

A

Step-by-step explanation:

side opposite to smallest angle is smallest=1

Hypotenuse=2

sin 30=1/2

It looks like you have to find the value of the sum,

[tex]C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}[/tex]

so that the n-th term in the sum is

[tex]\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}[/tex]

for 1 ≤ n ≤ 180.

We can then write the sum as

[tex]\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}[/tex]

Break up the summand into partial fractions:

[tex]\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}[/tex]

Combine the fractions into one with a common denominator and set the numerators equal to one another:

[tex]1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)[/tex]

Expand the right side and collect terms with the same power of n :

[tex]1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c[/tex]

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==>   a = 1/2, b = -1, c = 1/2

Now our sum is

[tex]\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)[/tex]

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

Answer:

75 - 35y / 3 + 2y = -4

( 75 - 35y + 6y ) / 3 = -4 [ Taking LCM ]

( 75 - 29y ) / 3 = -4

75 - 29y = -12

29y = 75+12

29y = 87

y = 3

hope that helps ✌

3(y+11) y=12

3(12+11)=?

12+11=23

3x23=69

Answer = 69

I hope this helps :)

5y=-2x-10

y=-2/5x-2

Rewriting the equation to slope intercept form, you get that the slope is -2/5 and the y intercept is -2. The graph that matches that is line d.

Answer:

Line D (-5,-2)

Step-by-step explanation:

I usually just use the website, demos graphing calculator.

Answer:

opposite side of an angle

hypotenuse

Answer:

no A

Step-by-step explanation:

sqrt13 is the ans

hope it helps

Answer:

x         -2     3     8     13

f^-1(x)  -1    0     1        2

Step-by-step explanation:

The inverse function has the input as the output and the output as the input

x         -2     3     8     13

f^-1(x)  -1    0     1        2

Answer: C

Step-by-step explanation: In this problem, we're given a function

in the form of a chart and we're asked to find the inverse of the function.

To find the inverse of a function, we simply switch

the x and y values in each point.

In other words, the point (-1, -2) becomes (-2, -1),

the point (0, 3) becomes (3, 0), the point (1, 8) becomes (8, 1),

and the point (2, 13) becomes (13, 2).

Answer:

32is the answer to yours questions

Answer:

7/6

Step-by-step explanation:

p=3/4*q

q=14/9*r

so p=3/4*14/9r=7/6r

Answer:

D

Step-by-step explanation:

380

Answer:

Sorry if i'm wrong.

=6x² + 16x - 2

[tex](4.2 \times {10}^{5}) \times (3.2 \times {10}^{6}) = 15.54 \times {10}^{11} = 1.554 \times {10}^{12} [/tex]

I hope I helped you ^_^

Option C

Corresponding angles along parrellel lines are conguerent.

Answered by Gauthmath must click thanks and mark brainliest

Answer:

x=15.73292

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 70 = x / 46

46 cos 70 =x

x=15.73292

Answer:

15.73

Step-by-step explanation:

cos(x) = adjacent leg / hypotenuse

cos(70) = x / 46

0.342 = x / 46

0.342 x 46 = x

x = 15.73

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

Answer:

im not sure but i got 30.1

Step-by-step explanation:

[tex] \cos(x) = \frac{45}{52} \\ x = 30.1[/tex]

Answer:

a. linear pair 5 & 6

b. pair of vertical angles 5 & 2

c. pair of angles that are congruent 3 & 8

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect.

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines.

If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. All right angles are congruent.

Answer:

x = 5

<AED = <AEC = 37

Step-by-step explanation:

<AEF = <AEC (Vertical angles)

6x+7=8x-3

or, 8x-6x=7+3

or, 2x=10

or, x=5

6x+7 = 37

Answered by GAUTHMATH

Answer:

x=5

AED =37

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

6x+7 = 8x-3

Subtract 6x from each side

6x+7-6x = 8x-6x-3

7 = 2x-3

Add 3 to each side

7+3 = 2x-3+3

10 =2x

Divide by 2

10/2 =2x/2

5 =x

We want the AED = 6x+7 = 6*5+7 = 30+7 = 37

Answer:

-44, -42, -40, -38, -36

Step-by-step explanation:

"preceding" requires an indication of the direction.

but I assume the usual left to right direction. in that sense the provided 5 even numbers are directly preceding -35

Answer:

can you translate in english,would be better...

answer maybe wrong because of the language but stil....

9x(2+6x+1)

=9x(9x)

81x..

Answer:

20 days

Step-by-step explanation:

10kg= 10,000g

10,000g/500g= 20 days

Answer:

20 days

Step-by-step explanation:

1 kg=1000 grams

10 kg=10000 grams

10000÷500

=20 days

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]4x + 2 = 2(x + 6)[/tex]

[tex]4x + 2 = (2 * x) + (2 * 6)[/tex]

[tex]4x + 2 = 2x + 12[/tex]

Step 2:  Subtract 2 from both sides

[tex]4x + 2 - 2 = 2x + 12 - 2[/tex]

[tex]4x = 2x + 10[/tex]

Step 3:  Subtract 2x from both sides

[tex]4x - 2x = 2x - 2x + 10[/tex]

[tex]2x = 10[/tex]

Step 4:  Divide both sides by 2

[tex]2x / 2 = 10 / 2[/tex]

[tex]x = 5[/tex]

Answer:  [tex]x = 5[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x = 5[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\4x + 2 =2(x+6)\\------------\\\rightarrow 4x + 2 = 2x + 12\\\\\rightarrow4x - 2x +2 = 2x - 2x + 12\\\\\rightarrow 2x + 2 = 12\\\\\rightarrow2x + 2 - 2 = 12 - 2\\\\\rightarrow 2x = 10\\\\\rightarrow \frac{2x=10}{2}\\\\\rightarrow \boxed{x = 5}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

-8 and 3, or -3 and 8

Step-by-step explanation:

xy = -24

x - y = 11

x = y + 11

y(y + 11) = -24

y^2 + 11x + 24 = 0

(y + 8)(y + 3) = 0

y = -8 or y = -3

x = 3 or x = 8

the numbers are -8 and 3, or -3 and 8

9514 1404 393

Answer:

  after 89 years

Step-by-step explanation:

For principal p, interest rate r, and number of years t, the two account balances are ...

  a = p·e^(rt) . . . . continuous compounding

  a = p(1+r)^t . . . . annual compounding

Using the given values, we have

  3000·e^(0.07t) . . . . . compounded continuously

  20000·1.05^t . . . . . . compounded annually

We want to find t so these are equal.

  3000·e^(0.07t) = 20000·1.05^t

  0.15e^(0.07t) = 1.05^t . . . . divide by 20,000

  ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms

  ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t

  t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t

  t ≈ 89.4 ≈ 89

The two accounts will have the same balance after 89 years.

Answer:

six x squared y over 3 x y

Answer: 4x/y

Step-by-step explanation:

6x^2y. (2/3xy^2)= (6x^2y.2)/(3xy^2)= (12x^2y)/(3xy^2)= 4x/y

Answer:

I think it's the zero property

Step-by-step explanation:

Answer:

Cost of a play station game = $11.3

Cost of each water ride = $22.6

Step-by-step explanation:

Entrance tickets = $89.97

Royal meal = $10.85

Cost of a play station game = x

Cost of each water ride = 2x

Find the cost of a water ride

Entrance tickets = Royal meal + 1 play station game + 3 water rides

89.97 = 10.85 + 1(x) + 3(2x)

89.97 = 10.85 + x + 6x

89.97 = 10.85 + 7x

89.97 - 10.85 = 7x

79.12 = 7x

x = 79.12/7

x = 11.302857142857

Approximately to the nearest tenth

x = $11.3

Cost of a play station game = x = $11.3

Cost of each water ride = 2x

= 2(11.3)

= $22.6

Her dad = 36

Sarah = 5

After 31 years sarah = 36

And her dad = 67

Answered by Gauthmath must click thanks and mark brainliest