A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125

Answer:

A

Step-by-step explanation:

Because for A, the question is "How many weeks until the bank is full?" which is looking for X. That part is checked off. It says 100x+50=710. 710 is the total in A too so that is checked off. In the equation, the piggy bank starts with 50 coins so that is checked off. Everything is in order so A is the answer. WEAR A  MASK AND STAY SAFE DURING THIS HARD TIME! ;)

Answer:

The answer is D

Step-by-step explanation:

The original equation ..

100x +50 = 710

100x=710-50

100x=660

Divide on both sides

X =6.6

When you solve equation D in the same way, the same result will appear

Answer: B) as x→-∞, f(x) →∞ as x→∞, f(x) →-∞

Step-by-step explanation:

The expression of the line is:

To check which points are on the line we need to substitute the values of the x-coordinate into the x of the equation, and the y-coordinate into the y of the equation, and then check that the result is equal to 20.

Let's analyze our options:

(0,5)

The x-value is 0 and the y-values is 5. So we substitute x=0 and y=5 into the expression of the line

Solving the operations:

Since the result is 20, which matches the one from the original equation, that means that the point (0,5) is on the line.

(0,10)

We do the same process, substitute the x-value that in this case is 0, and the y value that in this case is 10, into the expression of the line and check if the result is 20:

The resulting expression is not correct, because 40 is not equal to 20. Thus, (0,10) is NOT in the line.

We continue doing this for the rest of the points:

(1,2)

In this point x=1 and y=2. Substituting the values:

The resulting expression is not correct because 10 is not equal to 20. Thus, (1,2) is NOT in the line.

(1,4)

The x-value is 1, and the y-value is 4, Substituting into the expression:

Since 18 is not equal to 20, the expression incorrect, and (1,4) is not on the line.

(5,0)

Substituting x=5 and y=0

Since 10 is not equal to 20, the resulting expression is not correct, and (5,0) is NOT on the line.

(10,0)

Substituting x=10 and y=0:

The resulting expression is correct, thus, (10,0) is on the line.

Answer: (0,5) and (10,0)

The area of the equilateral triangle is 36√3 square units

What is area of the equilateral triangle?

Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.

In an equilateral triangle, the center, the centroid, and the circumcenter coincide.

The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.

The side length is \(6(3)^{1/2}\), which is twice the length of the radius.

So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.

The area of an equilateral triangle with side length s is given by:

A = (s² * √3) / 4

Substituting s = 12, we get:

A = (12² * √3) / 4

= 36√3

Therefore, the area of the equilateral triangle is 36√3 square units.

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Answer:

|−0.658| < |−0.653|.

Step-by-step explanation:

Answer:

The sum of 7 and x.

Step-by-step explanation:

PLS GIVE BRAINLIEST

Answer:

B. 80, -160

Step-by-step explanation:

The common ratio between these three numbers is -2.

-10 * -2 = 20

20 * - 2 = -40

-40 * -2 = 80

80 * -2 =  -160

Answer: 6

Step-by-step explanation:

y = -3x + 6 is the linear equation of the form y = mx + c

where m is the gradient of the graph and c is the y-intercept of the graph.

Hence,

m = -3

c = 6

y-intercept of the graph = c

                                        = 6

Answer:

18/25

Step-by-step explanation:

Answer:

72%, or, 18/25

Step-by-step explanation:

I just converted 0.72 into a percentage and a fraction. I hope this helps! :P

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

146 since the angle is a central that its measure is equal to the arc

(a) There is a error in step(2) of the solution, he should multiply instead of adding the number "5",

(b) The solution is a unique solution.

Part (a) : Charlie's solution is incorrect.

In Step 2, Charlie added 5 to simplify the equation, which is incorrect.

Instead, Charlie should multiply the "5" on both sides,

The correct way to solve the equation is as follows:

Step 1: (1/5)x = 30

Step 2: (1/5)x × 5 = 30 × 5 [Multiplying both sides by 5 to isolate x]

Step 3: x = 150,

Therefore, the correct solution is x = 150.

Part (b) :  The equation has a unique-solution, which means that there is only one value of x that satisfies the equation.

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The given question is incomplete, the complete question is
Charlie solved an equation, as shown below:

Step 1: (1/5)x = 30

Step 2: (1/5)x + 5 = 30 + 5

Step 3: x = 35

(a) Is Charlie's solution correct or incorrect? If the solution is incorrect, explain why in words AND mathematically show all the correct steps to solve the equation more appropriately.

(b) What type of solution does this equation have?

Answer:

16.33

Step-by-step explanation:

I hope this was right!

The option for  sequences are arithmetic are:

From the first option we can see that -5,5,-5,5… dose not follow any sequence  of arithmetic.

if we take the  18,5.5, –7, –19.5, which are the digits from the second option and if we find their differences we will get 12.5

Then if we take the numbers from the 16, 32, 48, 64 and find the differences between the first two numbers as well as the last two numbers then we will have 16.

Therefore, since we can have constant results between consecutive numbers then it is sequence  of arithmetic.

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Answer:

i have solved them . if u can't understand. .. ask me XD

14x10x10x10x10x10x10x10x10x10x10x10x10= 14^12

The value of x in sequence of number is 10.

Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.

What is geometric series?

Geometric series is an infinite series of the form:

\(a+ar+a r^{2} +ar^{3} +..........\)

where r is known as common ratio.

Now, first term is x and each term there after is twice the previous term.

So the series will be;

x , 2x , 4x , 8x, ..........

Clearly this series is geometric series with common ratio 2.

And the nth term of geometric series is \(ar^{n-1}\)

⇒ fifth term is 160

\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)

Here, first term is x.

The value of x in sequence of number is 10.

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Answer:

\(y = 120000( {1.055}^{x} )\)

Two metal plates measuring 4.6 cm × 4.6 cm are separated by a thin piece of Teflon measuring 0.23 mm in thickness.

The setup described consists of two metal plates that are parallel to each other and separated by a thin layer of Teflon. The dimensions of each plate are given as 4.6 cm × 4.6 cm. The purpose of the Teflon layer is to provide insulation or separation between the metal plates.

Teflon, also known as polytetrafluoroethylene (PTFE), is a non-conductive material that exhibits excellent electrical insulation properties. Its low dielectric constant and high dielectric strength make it ideal for use as an insulating material. In this configuration, the Teflon layer prevents direct electrical contact between the metal plates while allowing them to remain in close proximity.

The thickness of the Teflon layer is specified as 0.23 mm, which determines the distance between the metal plates. This distance is crucial in determining the capacitance between the plates. Capacitance is a measure of the ability of the system to store an electric charge. In this case, the Teflon layer acts as a dielectric material, which increases the capacitance between the metal plates compared to if they were directly adjacent to each other.

Overall, the setup of two metal plates separated by a thin Teflon layer provides a controlled electrical environment for various applications, such as capacitors or electrical insulation in electronic circuits.

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Answer

1.) B

2.)  3 hours

Step-by-step explanation:

1.)  option B is correct I think because it shows he will either be equal to or less than how much money he wants to spend

2.) i got three because if you sent up the equal I picked in question one then you subtract 28 from 250 giving u 222 and you divide that by 65 giving you 3.4 but he only charges by the whole hour so that .4 of an hour he wouldn't charge you for

The outer function is sqrt(x) and the inner function is x^2 + 3x. the derivative of sqrt(x) is 1/(2 * sqrt(x)). The derivative of x^2 + 3x is 2x + 32f'(1) = 16. f(x) = sqrt(x^2 + 3x)

To find f'(x), we can use the chain rule. The chain rule states that the derivative of a composite function is the product of the derivative of the outer function and the derivative of the inner function. In this case, the outer function is sqrt(x) and the inner function is x^2 + 3x.

The derivative of sqrt(x) is 1/(2 * sqrt(x)). The derivative of x^2 + 3x is 2x + 3.

Therefore, f'(x) = (1/(2 * sqrt(x))) * (2x + 3) = x/(2 * sqrt(x^2 + 3x)).

To find 32f'(1), we can substitute x = 1 into the expression for f'(x) and simplify:

32f'(1) = 32 * (1)/(2 * sqrt(1^2 + 3 * 1)) = 32 * (1)/(2 * sqrt(4)) = 32 * (1)/(2 * 2) = 16

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The statement which is true about the function is that the function is negative for all real values of x where x < –3 or x > –1.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is,

\(f(x) = -(x +3)(x - 1)\)

It is positive, its value is above x-axis. For the function above, the solutions are,

\(x+3=0\\x=-3\\x-1=0\\x=1\)

The value of x is lies between,

\(-3 < x < 1\)

Thus, the statement which is true about the function is that the function is negative for all real values of x where x < –3 or x > –1.

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Since 1 multiplied by 49 equals 50, you cannot multiple anything without also multiplying by 50. while You would need to multiply by 26.5 and so on since 2 multiplied by 49 equals 51.

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.

Since 1 multiplied by 49 equals 50, you cannot multiple anything without also multiplying by 50. while You would need to multiply by 26.5 and so on since 2 multiplied by 49 equals 51.

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The correct question is -

What do you multiply to increase an amount by 49?

The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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Answer:

The answer is m = 8 + 2p.

m = 2n

n = 4 + p

m = 2(4 + p) = 8 + 2p

Therefore, the only formula that is also true is m = 8 + 2p.

Step-by-step explanation:

Answer:

From the given equation-

4(3p+2)−5(6p−1)=2(p−8)−6(7p−4)

⇒12p+8−30p+5=2p−16−42p+24

⇒−18p+13=−40p+8

⇒−18p+40p=8−13

⇒22p=−5

⇒p=

22

−5

.

Step-by-step explanation:

basicly what I said

The scale factor is the ratio of the length or size of an object in the real world to the length or size of the same object in a scale model. It is represented as a fraction or a decimal.

The missing length of a scale model can be found by multiplying the length of the corresponding object in the real world by the scale factor.

The scale factor is a mathematical concept used in scale modeling, architecture, and engineering. It is the ratio of the length or size of an object in the real world to the length or size of the same object in a scale model. The scale factor can be expressed as a fraction, such as 1/10, or as a decimal, such as 0.1. For example, a scale factor of 1/10 means that every dimension of the object in the model is one-tenth the size of the corresponding dimension in the real object.

To find the missing length of a scale model, you need to know the scale factor and the length of the corresponding object in the real world. You can then multiply the length of the object in the real world by the scale factor to find the length of the object in the scale model. For example, if the length of a car in the real world is 16 feet and the scale factor is 1/20, the length of the car in the scale model is 16 feet x 1/20 = 0.8 feet or 9.6 inches. By using the scale factor, you can create accurate models of objects that are much smaller or larger than the actual object.

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The relative maximum point is (0, 3) and the relative minimum points are (-1, 2) and (1, 2).

To find the relative maximum and minimum points of the function f(x) = x^4 - 2x^2 + 3, we need to find the values of x where f'(x) = 0.

f'(x) = 4x^3 - 4x = 4x(x^2 - 1)

Setting f'(x) = 0, we get x = 0, ±1 as critical points.

To determine the nature of these critical points, we need to use the second derivative test.

f''(x) = 12x^2 - 4

At x = 0, f''(0) = -4 < 0, so this critical point is a relative maximum.

At x = 1, f''(1) = 8 > 0, so this critical point is a relative minimum.

At x = -1, f''(-1) = 8 > 0, so this critical point is also a relative minimum.

Therefore, the relative maximum point is (0, 3) and the relative minimum points are (-1, 2) and (1, 2).

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