Find the nth term for the arithmetic sequence below -6, -8, -32/3, -128/9,…

Answer:

Step-by-step explanation:

(z)° + (3z + 1)° = 360° - ( 54° + 204° )

z + 3z + 1 = 360 - 258

4z = 101

z = 25.25

Answer:

Step-by-step explanation:

.

The equation of the function g(x) is g(x) =  -x² + 4 after applying the transformation.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the function f(x) = x² - 1

The equation of the function g(x) = -x² + 4

Let f(x) is the parent function.

To get the equation of the function g(x):

Applying transformation to function f(x)

f(x) → f(x) + 5 (function will shift up side by 5 units)

F(x) = x² - 1 + 5

F(x) = x² + 4

F(x) → -x²  (funtion will reflect about the line y = 4)

g(x) =  -x² + 4

Thus, the equation of the function g(x) is g(x) =  -x² + 4 after applying the transformation.

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Answer:

When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Step-by-step explanation:

\(10x + 5y = 30 \\ - 10x \: \: \: - 10x\)

\(5y = - 10x + 30\)

\( \frac{5y}{5} = \frac{ - 10x}{5} + \frac{30}{5} \)

\(y = - 2x + 6\)

y-intercept is 6. use the formula

\(y = mx + b\)

b is the y-intercept

Answer:

------------------

Simplify in below steps:

There are two elements in A' ∩ B.

The given sets are: U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, B = {1, 3, 5, 7}To find the number of elements in A' ∩ B, we first need to find the complement of A,

which is the set of all elements that are not in A.Complement of A: A' = {3, 6, 7}

Now, we need to find the intersection of A' and B.Intersection of A' and B: A' ∩ B = {3, 7}

Therefore, there are two elements in A' ∩ B, which are 3 and 7.

To summarize, we have U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, and B = {1, 3, 5, 7}. The complement of A is A' = {3, 6, 7}.

The intersection of A' and B is A' ∩ B = {3, 7}.

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we use the trigonometric identity sine, this is

answer: the missing side is 6.3 cm

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

y = (x + 6)² - 1

Step-by-step explanation:

So there are two ways of doing it, completing the square or partial factoring (which is what i prefer and will show)

so we will get x first:

x^2+12x

We are factoring x

x(x+12)

Now you do x=-12/2

x=-6

Now that you have x, you plg that back into the equation to get y

y= -6^2 +12(-6) +35

= 36-36+35

=-1

Put into vertex form

y = (x + 6)² - 1

The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.

To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.

The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.

In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.

Using the formula, we have:

P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)

C(5, 2) = 5! / (2! * (5-2)!) = 10

P(2) = 10 * (3/8)^2 * (5/8)^3

P(2) ≈ 0.164 (rounded to three decimal places)

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When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.

A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.

Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.

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The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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Answer:

bbbbbbbbbbbbbbbbbbbbbbbbb

Answer:

V=4298.0915\approx 4298.09

V=4298.0915≈4298.09

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

they only meet up once

get a new computer br.uh

Answer:

Answer = -34

Step-by-step explanation:

B = 4 ; y = -6

So,

-4 + (5) (−6)

= −4 + −30

= −34

Hope you get it :)

The value of expression will be;

⇒ - 34

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - b + 5y

And, The values are,

⇒ b = 4, y = - 6

Now,

Since, The expression is,

⇒ - b + 5y

Substitute  b = 4, y = - 6, we get;

⇒ - 4 + 5 × - 6

⇒ - 4 - 30

⇒ - 34

Thus, The value of expression is,

⇒ - 34

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9514 1404 393

Answer:

  the first is two points; the second is the interval between (and including) those two points

Step-by-step explanation:

The equation ...

  4 = |x +5|

has two solutions:

  x ∈ {-9, -1}

__

In the interval between those two solutions the absolute value expression is less than 4. So, the second expression has a solution that is a range of values. Those values are in the interval whose boundaries are -9 and -1.

  x ∈ [-9, -1]

__

The solution to the second expression can be found as ...

  4 ≥ |x +5|

  4 ≥ x+5 ≥ -4 . . . . express as a compound inequality

  -1 ≥ x ≥ -9 . . . . . . subtract 5

__

The attached graph shows the two solutions. The solution to the first equation is the pair of (black) lines, x=-9 and x=-1. The solution to the second equation is the (orange) shaded interval -9 ≤ x ≤ -1.

Answer:

\(40x+32y\leq 5,000\\x\geq 0, y\geq 0\)

Step-by-step explanation:

Let the number of acre of corn planted =x

Let the number of acre of soybeans planted =y

Seed costs for a farmer are $40 per acre for corn and $32 per acre for soybeans.

The farmer wants to spend no more than $5,000 on seed.

Therefore the linear inequality is:

\(40x+32y\leq 5,000\\x\geq 0, y\geq 0\)

Next, we graph the inequality

\(When$ x=0, y\leq156.25\\When$ y=0, x \leq 125\)

The graph is attached below.

We want to find an inequality that says how many seeds of each type the farmer can buy.

The inequality is:

$40*x + $32*y ≤ $5,000

The information given is:

Then if he buys seeds for x acres of corn and y acres of soybeans, the total cost is:

cost = $40*x + $32*y

And he wants to spend no more than $5,000, then we have the inequality:

$40*x + $32*y ≤ $5,000

Notice that there are a lot of possible solutions to this inequality, so the inequality actually describes all the different possibilities that the farmer has to not spend more than $5,000 on seeds.

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Answer:

64π

Step-by-step explanation:

Use the formula for an area of a circle
\(A = \pi r^2\)
Half of 16 is 8.
8*8 = 64.

The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.

Mathematically, the area of a circle can be calculated by using this formula:

\(\text{Area} = \pi \text{r}^2\)

Where:

\(\text{r}\) represents the radius of a circle.

\(\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.\)

By substituting the radius into the formula for the area of a circle, we have the following;

\(\text{Area of circle} = \pi \times 8^2\)

\(\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96\) square meters.

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Answer:

x is the variable!

Step-by-step explanation:

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Answer:

Step-by-step explanation:

This problem is on the mensuration of flat shapes, a rectangular shape

we are required to solve for the length and width of the rectangular ball court

we know that the perimeter is expressed as

\(P= 2(L)+2(W)\)

let the width be x

hence the length is 2x

Given data

perimeter = 64 meters

length l= 2x

width w= x

Substituting our data  and solving for x we have

\(64= 2(2x)+2(x)\\\\64= 4x+2x\\\\64= 6x\)

Dividing both sides by 6 we have

\(x=\frac{64}{6}\\\\ x= 10.66\)

Hence the width is 10.66 meters

The length is 2x= 2(10.66)= 21.33 meters

Answer:

I, 550

Step-by-step explanation:

Is the nearest hundredth

$60

Step-by-step explanation:

The unit rate can be determined by dividing $24 by 8 attendees to get

\(\dfrac{\$24}{8\:\text{attendees}} = \$3/\text{attendee}\)

so when 20 people are attending the graduation picnic, his total cost is going to be

\(20\:\text{attendees}×\dfrac{\$3}{\text{attendee}} = \$60\)

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

The question needs more information. We don't know what's the x. The number that represents the variable X in the parentheses. Or it could be like:

Step-by-step explanation:

Step-by-step explanation:

opening the bracket

5x-30=(2x+6)2

5x-30=4x+12

collecting like terms

5x-4x=12+30

x=42

Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

Answer:

All angles and opposite angle are equal;opposite sides are parallel.

Step-by-step explanation:

Answer:

they both have 4 sides and they both have paralell sides.

Step-by-step explanation: