write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...

a. a_n= 2n-2
b. a_n= 2n+2
c. a_n=4n+2
d. a_n = 6n-4

Answer:

Final simplified expression is 6.

Step-by-step explanation:

We have been given an expression [tex]216^{\frac{1}{3}}[/tex].

Now we need to simplify [tex]216^{\frac{1}{3}}[/tex] So let's do that by factoring 216 first so that we can have same repeating factor thrice

[tex]216^{\frac{1}{3}}[/tex]

[tex]=(6*6*6)^{\frac{1}{3}}[/tex]

[tex]=(6^3)^{\frac{1}{3}}[/tex]

Apply formula [tex](x^m)^n= x^{m*n}[/tex]

[tex]=6^{3*\frac{1}{3}}[/tex]

[tex]=6^{1}[/tex]

[tex]=6[/tex]

Hence final simplified form is 6.

Answer:

60

Step-by-step explanation:

Since it turns 30 degrees each hour, it is simply 2 * 30 which is 60.

Answer:

y = -3

Step-by-step explanation:

First, subtract 44 from both sides of the equation to set it equal to 0. This will give you 6 + 2y = 0. Then, subtract 6 from both sides, leaving you with 2y = -6. Then just divide both sides by 2 to isolate the y and give you your answer. -6 divided by 2 is -3. y = -3

Answer:

y = -1/2 x

Step-by-step explanation:

Follow the directions "Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k."

y = kx substitute y = -4 and x = 8.

-4 = k*8

-4/8 = k

-1/2 = k

So the equation is y = -1/2(x).

Answer:

1. Start with the equation of direct variation y = kx.

2.Substitute in the given values for x and y to get: -4=k(8)

3. Solve for k to get: -1/2

4. Write the direct variation equation with the value found for k. The equation is: y=(-1/2)x

Step-by-step explanation:

I just did it on e2020

Answer:

The value of x = -0.46

Step-by-step explanation:

∵ [tex]4e^{5x}-e^{-x}=-3e^{2x}[/tex] ÷ [tex]e^{-x}[/tex]

∴ [tex]\frac{4e^{5x}}{e^{-x}}-\frac{e^{-x}}{e^{-x}}=\frac{-3e^{2x}}{e^{-x}}[/tex]

* Subtract the power of the same bases

∴ [tex]4e^{6x}-1=-3e^{3x}[/tex]

* Let [tex]e^{3x}=y[/tex]

∴ [tex]e^{6x}=y^{2}[/tex]

∴ 4y² - 1 = -3y

∴ 4y² + 3y - 1 = 0 ⇒ factorize

∴ (4y - 1)(y + 1) = 0

∴ y + 1 = 0 ⇒ y = -1

∴ 4y - 1 = 0 ⇒ 4y = 1 ⇒ y = 1/4

∵ [tex]y=e^{3x}[/tex]

∴ y = -1 refused ([tex]e^{ax}[/tex] never gives -ve value)

∴ [tex]e^{3x}=1/4[/tex] ⇒ insert ln in both sides

∵ [tex]lne^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1

∴ 3xln(e) = ln(1/4)

∴ 3x = ln(1/4)

∴ x = [ln(1/4)] ÷ 3 = -0.46

Answer:

B) A rectangle with a length of 15 cm and a width of 9 cm

Step-by-step explanation:

we know that

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

Verify each cases

case A) A rectangle with a length of 9 cm and a width of 6 cm

[tex]\frac{10}{9}\neq \frac{6}{6}[/tex]

therefore

The rectangle case A) is not similar to rectangle A

case B) A rectangle with a length of 15 cm and a width of 9 cm

[tex]\frac{10}{15}=\frac{6}{9}[/tex]

[tex]\frac{2}{3}=\frac{2}{3}[/tex]

therefore

The rectangle case B) is  similar to rectangle A

case C) A rectangle with a length of 14 cm and a width of 7 cm

[tex]\frac{10}{14}\neq \frac{6}{7}[/tex]

therefore

The rectangle case C) is not similar to rectangle A

case D) A rectangle with a length of 12 cm and a width of 8 cm

[tex]\frac{10}{12}\neq \frac{6}{8}[/tex]

therefore

The rectangle case D) is not similar to rectangle A

Answer:

A rectangle with a length of 15 cm and a width of 9 cm.

Step-by-step explanation:

In similar rectangles, the ratios of the corresponding sides are equal.In similar rectangles, the ratios of the corresponding sides are equal.

[tex]\frac{length}{width}[/tex] → [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]  and [tex]\frac{15}{9}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

D

Step-by-step explanation:

I got it right

There infinitely many solutions are possible. Option D is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
For two intersecting lines, it is not possible that the lines have only two solutions, either the lines have one solution or the lines have infinitely many solutions,

In our case line have infinitely many solutions,
Because the equations of the lines are the same.

Now,
The equation of the line is given as,
y - y₁ = m (x - x₁)
y - 5 = [7-5 / 3-1] (x - 1)
y = x - 1 + 5
y = x + 4

Thus, there infinitely many solutions are possible. Option D is correct.

Learn more about simultaneous equations here:

https://brainly.com/question/16763389

#SPJ5

Answer:

6.63 cm

Step-by-step explanation:

The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.

a² + b² = c²

Here a is unknown, b = 10 and c = 12.

a² + 10² = 12²

a² + 100 = 144

a² = 44

a = √44 = 6.63

Answer is C

If x=0, f(x) (or y) is 2^(0+2)=2²=4

So find the graph that runs through the point (0,4)

Graph C is the graph that represents the exponential function f(x) = 2ˣ⁺²

Which graph matches the function?

We want to find the graph that matches the function:

f(x) = 2ˣ⁺²

First, we can see that when x = 0 we have:

f(0) = 2² = 4

So we need to find the graph that intercepts the y-axis at y = 4. From the given options we can see a single graph that does that, which is option B, so we can conclude that B is the correct option.

Answer:

Step-by-step explanation: If w is hours at Westside, then (18-w) is the number of hours taken at Pinewood.

Cost to westside = 98w. Cost to Pinewood = 115(18-w).

Total cost = 98w + 115(18 - w) = 2070 - 17w.

[I guess there should be some constraints like 0 > w > 18]

I put it as "greater than" rather than "greater than or equal" because the problem states he takes classes at both schools, hence he has to take at least something at Westside, and similarly he has to take something at Pinewood so he would not take all 18 hours at Westside.

Answer:

98 × w + $115(19-w)

Step-by-step explanation:

We are given that Alan takes classes at both Westside Community College, where class fees are $98 per credit hour, and Pinewood Community College, where class fees are $115 per credit hour.

If Alan is taking a total of 19 credit hours at the two mentioned schools, we are to write an expression for the combined total dollar amount he paid for his class fees.

Considering the fees per credit hour mentioned for each school, we can write the total payed fees as:

[tex]98 \times w + $115(19-w)[/tex]

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

[tex]r=\frac{k}{1-4sin(theta)}[/tex]

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

Answer:

B

Step-by-step explanation:

edge

did you mean to put. y= -1/2x+2 for choice b? because that's what I got as a solution

Answer:

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Answer:

A) 0.335; B) 0.343; C) 0.599

Step-by-step explanation:

For part A,

To find the probability that the user has more than one infection per year, we can either add together the probabilities for 2, 3, 4 and 5; or we can add together the probabilities for 0 and 1 and subtract them from 1:

1-(P(X = 0)+P(X = 1))

= 1-(0.343+0.322) = 1-0.665 = 0.335

For part B,

The probability that the user has no infections per year is P(X = 0); this is 0.343.

For part C,

The probability that the user has between 1 and 3 infections (inclusive) per year is

P(1 ≤ X ≤ 3) = 0.322+0.201+0.076 = 0.599

The probabilities are as follows: A. An echinacea user is likely to experience more than one infection per year with probability 0.335. B. The likelihood of an echinacea user having no infections per year is 0.343. C. The probability that an echinacea user has between one and three infections, inclusive, is 0.599.

This question relates to probability distribution in mathematics. Here's how to find the probabilities:

https://brainly.com/question/32733554

#SPJ3

Answer:

p:a

Step-by-step explanation:

given: AB=c, BC=a, CA=b

          PQ=r, QP=p, PR=q

  also , ∠CAB ≅ ∠RPQ,--------- (1)

          , ∠ABC ≅ ∠RQP,---------(2)

    and, ∠ACB ≅ ∠QRP,---------(3)

FROM (1), (2) AND (3),

we can say that a=p, b=q, c=r

therefore, the triangles are congruent (S.S.S congruence criteria),

also then, r:c=1

then the ratio equal to r:c, will be p:a ( since p=a and p:a would be =1)    

Answer:

i believe that the answer is P:A if it is not I'm sorry

Step-by-step explanation:

Answer:

1.172

Step-by-step explanation:

1.954

-1.563

=0.391

So you must minus 0.391 from 1.563

1.563-0.391= 1.172

Answer:

Unknown scale is 1.25

Step-by-step explanation:

Here size of fonts have been enlarged with a scale factor. Scale factor means a common factor by which a sequence is formed.

The given sequence will be a geometric sequence.

So common ratio between 3rd and 4th fonts = [tex]\frac{1.954}{1.563}=1.25[/tex]

This ratio will be same in 1st and second fonts = [tex]\frac{1.25}{1}=1.25[/tex]

So unknown scale size is 1.25

Answer:

1,400 bracelets in 3 and a half hours

Step-by-step explanation:

First you have to find how many minutes are in 3 and a half hours. 1 hour is 60 minutes, so 60 + 60 + 60 is 3 hours or 180 minutes and 30 minutes is a half an hour. Therefore 3 and a half hours equals 210 minutes. Set up an equal proportion: 100 bracelets / 15 min = x bracelets / 210 min. Use algebra to solve: 100 * 210 = 15x → 21000 = 15x → 1400 = x.

1400 bracelets can the factory produce in three and a half hours.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A factory can produce 100 bracelets every 15 minutes.

So, In one minutes the factory produced

= 100 /15

= 20/3

Now, In three and a half hours ( 210 minutes) the factory can make

= 20/3 x 210

= 20 x 70

= 1400

Hence, In three and a half hours 1400 bracelets can be made.

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ2

Answer:The Time (period) is 0.003 s

Step-by-step explanation:

The period is equal to Time.

the formula for calculating Time (period) is:

Time (period)= 1/frequency

frequency= 293 hz

Time (period) = 1/293

                      = 0.003 s

Answer:

Period = 0.0034 seconds

Step-by-step explanation:

It is given that,

The d string on a violin has a frequency of 293 Hz when it is in tune. We have to find its period. The relationship between the time period and the frequency is given by :

[tex]T=\dfrac{1}{\nu}[/tex]

Here, [tex]\nu=293\ Hz[/tex]

So,

[tex]T=\dfrac{1}{293\ Hz}[/tex]  

T = 0.0034 seconds

Hence, the period of the d string on a violin is 0.0034 seconds.

See the attached picture:

1<x<6 or its x>1 and x>6

The solution to the compound inequality is given by:

                       [tex]1\leq x<6[/tex]

The compound inequality is given by:

[tex]3x-8\geq -5[/tex] and

[tex]2x-7<5[/tex]

[tex]3x-8\geq -5[/tex]

on adding both side of the inequality by 8 we get:

[tex]3x\geq -5+8\\\\i.e.\\\\3x\geq 3[/tex]

Now on dividing both side of the inequality by 3 we get:

[tex]x\geq 1[/tex]

[tex]2x-7<5[/tex]

On adding both side of the inequality by 7 we get:

[tex]2x<5+7\\\\i.e.\\\\2x<12[/tex]

on dividing both side of the inequality by 2 we get:

[tex]x<6[/tex]

Hence, the solution of the compound inequality is:

                    [tex]1\leq x<6[/tex]

the next step would be add x to both sides to get x isolated

Answer:

i thought it was a but its b

Step-by-step explanation:

got it right on my test

First set up birds is +3 than 2x the number of birds Rhonda saw

Rhonda's birds = r

Current set of birds = c

c = 2r + 3

Current birds are equal to three more than double the amount of birds rhonda saw

360 is the answer for sure

Answer:

Part 1) [tex]m<ECF=90\°[/tex]

Part 2) [tex]m<AKB=77.5\°[/tex]

Part 3) [tex]m<ACF=75\°[/tex]

Step-by-step explanation:

Part 1) Find the measure of angle ECF

we know that

CF is tangent at point C

so

the radius EC is perpendicular to the tangent CF

therefore

[tex]m<ECF=90\°[/tex]

Part 2) Find the measure of angle AKB

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

[tex]m<AKB=\frac{1}{2}(arc\ AB+arc\ DC)[/tex]

substitute the values

[tex]m<AKB=\frac{1}{2}(50\°+105\°)=77.5\°[/tex]

Part 3) Find the measure of angle ACF

we know that

The inscribed angle is half that of the arc it comprises

[tex]m<ACF=\frac{1}{2}(arc\ AB+arc\ BF)[/tex]

substitute the values

[tex]m<ACF=\frac{1}{2}(50\°+100\°)=75\°[/tex]

Answer:

∠ ECF = 90°

∠AKB = 77.5°

∠ACF = 75°

Step-by-step explanation:

The given figure is a circle E.

Line CF is tangent at point C.

(1) To find measures of angle ECF

Since line FC is tangent at point C and radius ECis always perpendicular to the tengent.

So ∠ ECF = 90°

(2) Measure of angle AKB

By theorem of angle formed by two interesting chords.

∠ AKB = [tex]\frac{1}{2}[/tex] (arc AB + arc CD)

= [tex]\frac{1}{2}[/tex] (50 + 105) = [tex]\frac{1}{2}(155)[/tex]

∠AKB = 77.5°

(3) Measure of angle ACF

Since tangent chord angle = [tex]\frac{1}{2}[/tex] (intercepted arc)

m (∠ACF) = [tex]\frac{1}{2}[/tex] (m arc AB + m arc BC)

= [tex]\frac{1}{2}(50+100)[/tex]

[tex]\frac{1}{2}(150)[/tex]

∠ACF = 75°

Answer:

b. ellipse; [tex]4x^2+5y^2-40x+60y+260=0[/tex]

Step-by-step explanation:

The graph of [tex]4x^2+5y^2=20[/tex] an ellipse because the coefficients of the quadratic terms are not the same.

This ellipse is centered at the origin. If this ellipse is translated  so that its center is now at [tex](5,-6)[/tex].

Then the translated ellipse will now have equation.

[tex]4(x-5)^2+5(y+6)^2=20[/tex]

We expand to get;

[tex]4(x^2-10x+25)+5(y^2+12y+36)=20[/tex]

[tex]4x^2-40x+100+5y^2+60y+180=20[/tex]

[tex]4x^2+5y^2-40x+60y+100+180-20=0[/tex]

[tex]4x^2+5y^2-40x+60y+260=0[/tex]

Answer:

B

Step-by-step explanation:

just took it on edge and it was right :)

Answer:

13 / 204; No, they are dependent events

Step-by-step explanation:

Total number of cards in the deck = 52

Total number of spades in the deck = 13

Total number of hearts in the deck = 13

Part 1: Calculating the Probability

Picking up the first card:

When picking the first card i.e spade, we have the option to pick 13 cards out of 52. So the probability will be 13/52

When first card is picked, the total number of cards will be reduced to 51 because we are not placing the card back in the deck

Picking up the second card:

When picking up the second card i.e. heart, we have the option to pick 13 cards out of 51. So the probability will be 13/51

The probability of picking a spade and then a heart is = 13/52 x 13/51 = 13/204

Part 2: Independent or Not

Note that, picking up a spade and not replacing it back is changing the probability of picking up a heart. In normal cases, picking up a heart from a deck will have the probability of 13/52, but since the we are not placing the card back the probability is changed to 13/51

Since, the probability of picking a heart is being changed by the previous event, we say that the two events are dependent.

Therefore, the correct answer will be final option: 13 / 204; No, they are dependent events

Answer:

5 foot 8

Step-by-step explanation:

Answer:

The number of adult tickets sold is a=202\ tickets

The number of student tickets sold is c=310\ tickets

Step-by-step explanation:

c------>  the number of student tickets sold

a----->  the number of adult tickets sold

we know that

a+c=512 -----> equation A

5c+10a=3,70-----> equation B

therefore

the solution is

the number of adult tickets sold is a= 202 tickets

the number of student tickets sold is c= 310 tickets

Answer:

tan(x) = 1

Step-by-step explanation:

The red curve(s) are y=tan(x). The horizontal line is y=1, so the point(s) of intersection are where tan(x) = 1.

_____

Sine and cosine do not have infinite range.

The range of secant excludes (-1, 1), so the only remaining possibility for the red curve is tan(x).

Answer:

4

Step-by-step explanation:

Given in the question a logarithm expression

[tex]7^(log_{49}16 )[/tex]

We will use Exponent of Log Rule

[tex]b^(log_{b}k ) = k[/tex]

here b = 7

        k = 16

So suppose

[tex]7^(log_{49}16 ) = x\\Take square on both sides\\(7^(log_{49}16 ) )^{2} = x^2\\49^(log_{49}16)= x^2[/tex]

Now, according to the rule

16 = x²

to find x only take square root on both sides of the equation

x = √16

x = 4

so [tex]7^(log_{49}16 )[/tex] = 4