answer pls! NEED HELP
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The given sequence the recursive function will be \(a_n = 4a_{n-1}\)

The iterative rule for the sequence is \(T_n = 8(4)^{n-1\)

Given the sequence of numbers  8, 32, 128, 512, …

From the given sequence the recursive function will be \(a_n = 4a_{n-1}\)

For the iterative sequence, we will use the common ratio and the first term as shown;

\(T_n=ar^{n-1}\\T_n=8(4)^{n-1}\)

Hence the iterative rule for the sequence is \(T_n = 8(4)^{n-1\)

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Answer:

1, -1, 3, -3, 5, -5, 15, -15

Step-by-step explanation:

The factors of negative 15 are 1, 3, 5, 15, -1, -3, -5 and -15. The solution has been obtained by using the concept of factoring.

What is factoring?

The process of determining the factors is known as factoring. Factoring is the process of determining what to multiply to produce an expression. It is comparable to "breaking" a complex phrase into a number of smaller ones.

In mathematics, the term "factorization" or "factoring" refers to the splitting apart or "factoring" of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together yield the original number, matrix, etc.

The factors of negative 15 are all the integers which can be evenly divided into 15.

The positive factors are 1, 3, 5, 15

The negative factors are -1, -3, -5, -15

Hence, the factors of negative 15 are 1, 3, 5, 15, -1, -3, -5 and -15.

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The co-ordinate of y intercept is 9 i.e. option (E)

What is Co-ordinate Geometry?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Solution:

Given the equation 6x = 2y - 18

See the attached graph below

So we can observe that on x = 0

The y intercept is equal to 9

So, the co-ordinates of the point of intercept is (0,9)

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George receives £112 based on the given data regarding the 4:5 ratio.

Felix receives 30% of £360 which is:

The total amount remaining for George and Harry is:

The ratio of the amount that the George receives to the amount that the Harry receives is 4:5. This means that the total ratio of the amount they receive is:

4+5 = 9

To find out how much George receives, we need to divide the total of the amount by the total of the ratio and then multiply by George's share of the ratio:

£252 ÷ 9 x 4 = £112

Therefore, George receives £112.

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Answer:

\(y = \frac{-3}{4}x + 36\)

Step-by-step explanation:

Data provided in the question

Height = 36 inches

Stant of the stairs followed that declines 9 inches for every 12 horizontal inches

Height = x

x =  from top of the stairs

based on the above information

Therefore the change in rate is

\(\frac{-9}{12} = \frac{-3}{4}\)

It depicts the line sloping.

Now the function would be determined by the line equation which is as follows

y = mx+c

\(m = \frac{-3}{4}\)

where,

c = 36 inches

So, the function is

\(y = \frac{-3}{4}x + 36\)

Answer:

Answer is A

Step-by-step explanation:

Answer:

The fossil is 0.254 meters long.

Step-by-step explanation:

254 millimeters is equal to 25.4 centimeters, which is equal to 0.254 meters.

To find a particular solution of the linear system x' = 3x - y and y' = 5x - 3y with initial conditions x(0) = 1 and y(0) = -1, we can use the method of integrating factors.

Step 1: Rewrite the system of equations in matrix form: X' = AX, where X = [x y] and A is the coefficient matrix [3 -1; 5 -3].

Step 2: Calculate the eigenvalues and eigenvectors of matrix A to find its diagonal form. Let λ1 and λ2 be the eigenvalues and v1 and v2 be the corresponding eigenvectors.

Step 3: Write the diagonal form of matrix A: D = [λ1 0; 0 λ2].

Step 4: Find the matrix P whose columns are the eigenvectors of A: P = [v1 v2].

Step 5: Calculate the inverse of matrix P: P^(-1).

Step 6: Write the solution of the system in diagonal form: X' = PDP^(-1)X.

Step 7: Solve for X using separation of variables and integrate to obtain the general solution: X(t) = e^(Dt)C, where C is a constant vector.

Step 8: Substitute the initial conditions x(0) = 1 and y(0) = -1 into the general solution to find the values of the constants.

Step 9: Plug in the values of the constants and simplify to obtain the particular solution of the system.

The particular solution of the linear system is x(t) = 2e^t - e^(-2t) and y(t) = 5e^t - 3e^(-2t).

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Answer:

y=-4x-8

Step-by-step explanation:

use points (0,-8) and (-2,0) and plug into slope formula.

slope formula=(y2-y1)/(x2-x1)

(0-(-8))/(-2-0)=-4

you get y=4x+b

use point (-2,0) to find b

you get y=-4x-8

Answer:

d

Step-by-step explanation:

If Mrs. Li ate 1/3 of the pie, that means there are 2/3 of the pie left. Mr. Li then ate 2/9 more than Mrs. Li. To find out how much he ate, we first need to add 2/9 to 1/3.

We can find a common denominator by multiplying the denominators of 1/3 and 2/9, which is 9. Thus, 1/3 can be rewritten as 3/9, and 2/9 can be left as is. Adding them together gives us 5/9. Therefore, Mr. Li ate 5/9 of the pie. To find out how much pie is left, we can subtract 5/9 from the 2/3 that was left after Mrs. Li ate her portion. This gives us 1/9 of the pie left, which is the answer to the question.

Mrs. Li had 2/3 of the pie left after eating 1/3.

Mr. Li ate 2/9 more pie than Mrs. Li, so he ate:

(2/9) * (1/3) = 2/27 of the pie.

Together, Mrs. and Mr. Li ate:

1/3 + 2/27 = 9/27 + 2/27 = 11/27 of the pie.

Therefore, they had 1 - 11/27 = 16/27 of the pie left.

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Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

The required scale factor  for the given line segment is 2.

In math, a line segment  is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.

Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.

We have,

QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2

Then the scale factor is of the dilation is 2 (magnification)

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Answer:

It is a producer

Step-by-step explanation:

The seagrass IS a producer and it produces energy for the manatee without taking away other animals because it has photosynthesis  

Answer:

Pfffttttt- Amateurs, it is quite simple really. Take a nice long look. In the picture is he answer. And I was just joking around, even I had to use a calculator for the answer.

Step-by-step explanation:

Put the x's together, the negatives and the positives.

Answer:

6 minutes, and 8 seconds

Step-by-step explanation:

You can simply get this answer by dividing .34 by 5.;)

Answer:

Step-by-step explanation:

Subtract 2 on both sides

7x = -56

Divide 7 on both sides

x = -8

Answer:     7 .

Step-by-step explanation:

The middle term is, +7x its coefficient is 7 . Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is

Answer:

8

Step-by-step explanation:

is the median

give email id

Answer: 3y+6

Step-by-step explanation:

Michael drinks 33.5 fl oz more fluid ounces than Lydia.

Given in question,

30 ml = 1 fl oz

  1 ml = 1/30 fl oz

1 bottle = 335 milliliters

No. of bottles of water Michael drank = 6

                                                              = 6 * 335 milliliters

                                                              = 2010 milliliters

                                                              = 2010/30 fl oz

                                                              = 67 fl oz

No. of bottles of water Lydia drank = 3

                                                           = 3 * 335 milliliters

                                                           = 1005 milliliters

                                                           = 1005/30 fl oz

                                                           = 33.5 fl oz

Therefore, 67 - 33.5 = 33.5

Hence, Michael drinks 33.5 fl oz more fluid ounces than Lydia.

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Answer:

volume of cylinder: \(\sf 396\pi \ m^3\)

Explanation:

given:

solve:

\(\hookrightarrow \sf \pi r^2h\)

\(\hookrightarrow \ \sf \pi (6)^2(11)\)

exact:

\(\hookrightarrow \ \sf 396 \pi\)

in nearest tenth:

\(\hookrightarrow \ \sf 1244.1 \ m^3\)

The x-intercept is (-9, 0) and there is no y-intercept (option b).

To determine the x- and y-intercepts for the graph defined by the equation x = -9, we need to understand the concept of intercepts. The x-intercept is the point at which the graph intersects the x-axis, and the y-intercept is the point at which the graph intersects the y-axis.

Given the equation x = -9, we can see that the value of x is fixed at -9. This means that the graph will be a vertical line passing through the point (-9, 0) on the x-axis.

Now, let's analyze the answer choices:

a. x-intercept is (-9, 0))

This statement is correct. The x-intercept is indeed (-9, 0) since the graph passes through this point on the x-axis.

No y-intercept

This statement is also correct. Since the graph is a vertical line, it does not intersect the y-axis, so there is no y-intercept.

Based on the analysis of the answer choices, the correct answer is option a: The x-intercept is (-9, 0), and there is no y-intercept.

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Answer:

Step-by-step explanation:

Given that:

cos(x) = x³

f(x) = cos (x) - x³

f(x) is continuous on the interval (0, 1)

when;

f(0) = cos (0) - (0)

f(0) = 1 - 0

f(0) = 1 > 0

f(1)  = cos (1) - 1³

f(1) = 0.5403 - 1

f(1) = -0.4597

f(1) = - 0.46

f(1) = - 0.46 < 0

Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)

such that f(c) = 0

By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)

b) Given that:

The interval length = 0.01; this implies that it is 0.005 length from its root.

f(0.865) = 0.0014

f(0.87) = - 0.013

The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.

The velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

The velocity of the cylinder when it reaches the bottom of the incline can be calculated using the principle of conservation of energy. The velocity of the cylinder is given by the formula v = sqrt(2gh/(1+I/(mr^2))), where g is the acceleration due to gravity, h is the height of the incline, and I is the moment of inertia of the cylinder.

In this case, the cylinder is released from rest at a height h on an incline without slipping, which means that all the potential energy at the top of the incline is converted to kinetic energy at the bottom of the incline. Therefore, we can write:

1/2 mv^2 = mgh

where v is the velocity of the cylinder at the bottom of the incline.

The moment of inertia of the cylinder is given as 1/2mr^2. Substituting this into the formula for v and simplifying, we get:

v = sqrt(2gh/(1+1/2)) = sqrt(4gh/3)

Therefore, the velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

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The length of A'B' = 5 units

The line segment AB is of 5 units. AB is then transformed through translation of 3 units to the right.

The translation only means change through a straight line. This transformation does not change the length of a line segment.

So the length of A'B' will also be 5 units.

But the position of A'B' will be different from that of AB on the co-ordinate plane. To be exactly, A'B' would be 3 units right to the position of AB on the co-ordinate plane.

Also the co-ordinates of A'B' will be different. Still their lengths will be same.

Thus the length of A'B' = 5 units

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Given that 70% of all Americans are homeowners. If 47 Americans are randomly selected, we need to find the probability that exactly 32 of them are homeowners.

The probability distribution is binomial distribution, and the formula to find the probability of an event happening is:

P (x) = nCx * px * q(n - x)Where, n is the number of trialsx is the number of successesp is the probability of successq is the probability of failure, and

q = 1 - pHere, n = 47 (47 Americans are randomly selected)

Probability of success (p) = 70/100

= 0.7Probability of failure

(q) = 1 - p

= 1 - 0.7

= 0.3To find P(32), the probability that exactly 32 of them are homeowners,

we plug in the values:nCx = 47C32

= 47!/(32!(47-32)!)

= 47!/(32! × 15!)

= 1,087,119,700

px = (0.7)32q(n - x)

= (0.3)15Using the formula

,P (x) = nCx * px * q(n - x)P (32)

= 47C32 * (0.7)32 * (0.3)15

= 0.1874

Hence, the probability that exactly 32 of them are homowner are 0.1874

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In the triangle, the values are p=10.3, \(\angle Q=19.5\textdegree\) and \(\angle R = 112.5\textdegree\).

The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

Here in the given triangle PQR, \(\angle P = 48\textdegree\) , q=5 and r=13.

Now using law of cosine fοrmula,

=> \(p^2=q^2+r^2-2qr.cos\angle P\)

=> \(p^2=5^2+13^2-2.5.13.cos 48\textdegree\)

=> \(p^2=25+169-130cos48\textdegree\)

=> \(p^2=107\)

=> p = 10.3

Now using law of sine then,

=> \(\frac{p}{sinP}=\frac{q}{sinQ}\)

=> \(sinQ=\frac{q sinP}{p}\)

=> \(sin Q= \frac{5sin 48\textdegree}{10.3}\)

=> sin Q = 0.344

=>\(\angle Q = 19.5\textdegree\)

Now sum οf all angles in triangle is 180°. Then,

=>\(\angle P+\angle Q+\angle R = 180\textdegree\)

=> \(\angle R = 180-48-19.5=112.5\textdegree\)

Hence the answers are p=10.3, \(\angle Q=19.5\textdegree\) and \(\angle R = 112.5\textdegree\).

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Answer:

2^2 *3^2 *19

Step-by-step explanation:

Answer:

2 x 2 x 3 x 3 x 19

also can be written as: 2² x 3² x 19

Step-by-step explanation:

draw a factor tree, and divide by prime numbers (circled), until it can no longer be divided any further