Question 1
Find a formula for the general term an of the sequence assuming the pattern of the first few terms
continues.
Assume the first term is a₁.
an=
<
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{12, 17, 22, 27, 32,...}
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0/10 pts

Answer:

Step-by-step explanation:

The upper and lower angles are vertical angles, so congruent:

  (5x -5)° = 55°

  x - 1 = 11 . . . . . . . divide by 5°

  x = 12

_____

The 55° angle and y° are a linear pair, so are supplementary.

  y° = 180° -55°

  y = 125 . . . . . . . simplify, divide by °

Answer:

  y =  {-180, 2 8/11}

Step-by-step explanation:

I like to solve these using a graphing calculator. I generally start by writing the equation in the form ...

  f(y) = 0

This can be done by subtracting the right-side expression from both sides. The solution will be the horizontal intercepts of the graph:

  y = -180; y = 2 8/11

__

To solve this analytically, you need to recognize that this resolves into four equations, effectively two identical pairs. Each equation comes with a set of conditions (domain) for which it is applicable. Here is the expanded set of equations:

  1/3y -7 = 2/5y +5 . . . both positive: 1/3y -7 ≥ 0 and 2/5y + 5 ≥ 0

  7 -1/3y = 2/5y +5 . . . left side negative: 1/3y -7 ≤ 0 and 2/5y +5 ≥ 0

  1/3y -7 = -2/5y -5 . . . right side negative: 1/3y -7 ≥ 0 and 2/5y +5 ≤ 0

  7 -1/3y = -2/5y -5 . . . both sides negative: 1/3y -7 ≤ 0 and 2/5y +5 ≤ 0

__

The conditions resolve to ...

  1/3y -7 ≥ 0

  y -21 ≥ 0 . . . . . multiply by 3

  y ≥ 21 . . . . . . . add 21

and ...

  2/5y +5 ≥ 0

  y +25/2 ≥ 0 . . . . multiply by 5/2

  y ≥ -25/2 . . . . . subtract 25/2

Now, we are in a position to solve the equations and determine where the solution is applicable.

__

both positive

The domain will be y ≥ 21 and y ≥ -25/2, which is y ≥ 21.

Multiplying the equation by 15 gives ...

  5y -105 = 6y +75

  y = -180 . . . . . . . . . subtract 5y+75

This solution is not in the allowed domain.

__

left side negative

The domain will be y ≤ 21 and y ≥ -25/2, which is -25/2 ≤ y ≤ 21.

Multiplying the equation by 15 gives ...

  105 -5y = 6y +75

  30 = 11y . . . . . . . . . add y-75

  y = 30/11 . . . . . .  the solution is in the allowed domain

__

right side negative

The domain will be y ≥ 21 and y ≤ -25/2. This is the empty set.

__

both sides negative

The domain will be y ≤ 21 and y ≤ -25/2, which is y ≤ -25/2.

Multiplying the equation by 15 gives ...

  105 -5y = -6y -75

  y = -180 . . . . . . . . . . add 6y-105 . . . . the solution is in the allowed domain

__

Solutions to this equation are ...

  y = 30/11 = 2 8/11

  y = -180

Answer : 24 cubes

The Volume of a prism = L x w x h

Volume of the prism = 1 x 2 x 3/2

Volume of the prism = 6/2

Volume of prism = 3cm^3

Answer:

Step-by-step explanation:

Answer:

(2x−y)  

Step-by-step explanation:

Debes utilizar la fórmula de cubo binomial, a  

3 −3a 2 b+3ab 2 −b3 =(a−b)  3

donde a=2x y b=y.

Answer:

to compare -2.3 and -8/3, we need to put them in the same form. We can convert -8/3 to a decimal by dividing -8 by 3, which gives us -2.66667.

Now we can see that -2.3 is greater than -2.66667, so we can write -2.3 > -8/3.

Step-by-step explanation:

Don't worry I can help.

Mathmetics isn't easy. so study

Answer:

50 ft

Step-by-step explanation:

Every side is 5ft, add up all the sides.

The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).

An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.

Workers who complete the computer security course will each receive a reimbursement of $350.

We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.

Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.  

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Answer:

The answer is 871.285. your welcome.

Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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Answer:

96

Step-by-step explanation:

From the given information:

At 95% Confidence interval level,Level of significance \(\alpha\) 0.05, the value of Z from the standard normal tables = 1.96

Margin of Error = 0.10

Let assume that the estimated proportion = 0.5

therefore; the sample size n can be determined by using the formula: \(n =(\dfrac{Z}{E})^2 \times p\times (1-p)\)

\(n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)\)

\(n =(19.6)^2 \times 0.5\times (0.5)\)

n = 96.04

n \(\approx\) 96

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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the correct answer is negitive one hundred eighty (-180)

Answer:

2+2 is 4 4+4 is 8 8+8 is 16

Step-by-step explanation:

if you need them added up here: 4+8 =12 12+16 = 28

Congruent triangles do not conform to the side lengths given. The values of v and w that would cause the triangles to be congruent cannot be determined without more details about the triangles. 20 and 5 are the values of v and w which make △XYZ≅△FED

Congruent refers to having the same size and shape. Hence, comparing two figures is what congruent means, and comparing two phrases that are equivalent. Hence, to state that two separate segments are congruent means that the two lines' measurements are equivalent.

We can set the two triangles' respective side lengths equal to one another and find v and w if we are aware of their corresponding side lengths.

If we are aware that XY Equals FE, YZ = ED, & ZX = DF, for instance, we can construct the following equations:

XZ + ZY ≈ FD + DE XY = FE XZ + ZY

v plus w = 20 - v plus 5

When we simplify this third equation, we obtain:

2v plus w = 15

A first two equations can now be used to replace XZ, ZY, FD, & DE in terms of v & w:

FD = 5 - w DE = w XZ = v ZY Equals 20 – v - w

By simplifying this second equation and substituting these numbers, we obtain:

v + 20 – v - w = 5 - w + w

20 = 5

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Answer:

very difficult for me so ask someone

The cosine of a sum and cosine of difference identities are  (8√6-3)/25 and (8√6+3)/25 respectively

Given the trigonometry functions:

cos s = -4/5 and sint = 1/5

To find cos(s - t):

cos (s +t) =  cos s cost - sins sint

cos(s - t) = cos s cost + sins sint

Get the value of cost and sins

According to SOH CAH TOA identity;

cos s = -4/5 = adj/hyp

hyp^2 = opp^2 + adj^2

5^2 = 4^2 + opp^2

opp^2 = 25 - 16

opp^2 = 9

opp = 3

sin s = opp/hyp

sin s = 3/5

Similarly for cos t

sin t = 1/5 = opp/hyp

ad^2j = 5^2 - 1^2

adj^2 = 25 - 1

adj^2 = 24

adj = 2√6

Get cost:

cost = adj/hyp = -2√6/5 (quadrant II)

Recall that cos (s +t) =  cos s cost - sins sint

cos (s +t) =  -4/5(-2√6/5) - (3/5)(1/5)

cos(s+t) = 8√6/25 - 3/25

cos(s+t) = (8√6-3)/25

Similarly, cos(s-t) = (8√6+3)/25

Hence the cosine of a sum and cosine of difference identities are  (8√6-3)/25 and (8√6+3)/25 respectively

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Answer:

y = - 0.681 % ≈ -0.7 %

Step-by-step explanation:

Given:

                                                               April 19,1998            October 30, 1998

Value immediately prior to deposit                95                               105

                     Deposit                                       2X                                 X

amount in the account on January 1, 1999 = 115

effective dollar weighted yield = 0%

annual effective time weighted yield = y

To find:

Calculate y

Solution:

Given that the dollar weighted return is 0%

100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X

100 + 2x + x = 115

3x = 115 - 100

3x = 15

x = 15/3

x = 5

Compute y

1 + y = (95/100)(105/105)(115/110)

1 + y = 0.95 * 1 * 1.045

1 + y = 0.99318

y = 0.99318 - 1

y = - 0.0068 * 100

y = - 0.681 % ≈ -0.7 %

y = -0.7 %

I think it is (0,-1)

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The Amplitude is 1/2 and period is π/2.

We have the function as

y= 1/2 cos π/4 x

As, The general equation of a Cosine function is

y=A cos (B(x−D))+C

where A is Amplitude , D is the shift.

So, the amplitude is 1/2

Period = 2π / 4= π/2

and, the phase shift is not possible to determine.

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Answer:

x = 6, y = -2, z = 0

Step-by-step explanation:

To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.

Answer:

6, -2, 0

Step-by-step explanation:

Answer:

RA

Step-by-step explanation:

The side lengths are given as follows:

Similar triangles are triangles that share these two features presented as follows:

The similar triangles for this problem are given as follows:

ABO and DCO.

Hence the proportional relationship for the side lengths is given as follows:

AB/DC = AO/DO = BO/CO.

45/75 = AO/DO = BO/CO.

Considering the segment addition postulate, we have that:

BD = 64.

BO + DO = 64.

Since AB/DC = 45/75, BO = 3/5DO = 0.6DO, hence the length DO is obtained as follows:

0.6DO + DO = 64

DO = 64/1.6

DO = 40.

The length BO is given as follows:

BO = 0.6 x DO = 0.6 x 40 = 24.

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Using the concept of proportions and ratios, the value of BO is approximately 38.4 units

Similar triangles are triangles that have the same shape but may have different sizes. Two triangles are similar if and only if all their corresponding angles are equal and the ratios of their corresponding sides are equal. This means that if two triangles have the same angles, then they are similar, but the converse is not necessarily true.

In this problem, we can write the proportions in ratios and find the value of the unknown side.

Mathematically;

DC / AB = DB / BO

Substituting the values into the problem;

75 / 45 = 64 / BO

Cross multiply both sides and solve for BO

BO = (64 * 45) / 75

BO = 38.4units

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The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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