use synthetic division to divide the polynomial and find p(x)

Answer:

$12.50

Step-by-step explanation:

$50/4 = $12.50

Answer:

option a is the correct answer

Step-by-step explanation:

bye

Answer:

  45

Step-by-step explanation:

You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.

From the first point, 9 segments can be drawn.

From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)

From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:

  9(10)/2 = 45

45 line segments can be drawn.

__

Additional comment

This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.

Answer:

yes it is The answer is C

Step-by-step explanation:

Answer:

The answer is y=3x+4

Step-by-step explanation:

Answer: 3/4  / 7/8

Step-by-step explanation:

= 3/4  * 8/7  = 24/28 = 6/7 gallons

This is the volume of juice  when the jar is full.

Answer:

6/7

Step-by-step explanation:

Answer:

Total is 23 times 7 which is 161 pounds

Step-by-step explanation:

you do 7 × 23 and u get 161

and thats how you figure it out

Answer:

3,600

Explanation:

There's nine thousand numbers here, 4,500 of which are even, you will need to subtract mutiples of five from this number, making it even smaller.

subtract the non-even five's (exactly half of the 1800 hundred fives that fit in our little original number, (900!) ) 4,500-900= 3,600. Which should be your answer. :D

Step-by-step explanation:

Answer:

7 is 1/3 of 21 hens

Step-by-step explanation:

7/21 = 3

Answer:

7/21 and simplifies, its 1/3

Step-by-step explanation:

Answer:

471.24

Step-by-step explanation:

This should be surface area.

2 π r h + 2 π r^2

2 π 5 (10) + π 5^2

471.24

Answer:

A

Step-by-step explanation:

because he is rich

Answer:

483.8

Step-by-step explanation:

the 18% of 590 is 106.2

Answer:

the answer is negative 135

Step-by-step explanation:

this question is kinda tricky

The solution to the initial value problem is \(y(t) = e^{(-t)} + 4e^{(-5t)} + 24e^t.\)

As per the question given,  

To solve the initial value problem using Laplace transformation, we need to apply the Laplace transform to both sides of the equation and use the initial conditions to solve for the unknown constants.

Taking the Laplace transform of the equation, we get:

\(L{y''} + 6L{y'} + 5L{y} = 24L\)\(e^{t}\)

Using the properties of Laplace transform, we can simplify this to:

\(s^2\) \(Y(s) - sy(0) - y'(0) + 6sY(s) - 6y(0) + 5Y(s) = 24/(s-1)\)

Substituting the initial conditions, we get:

\(s^2Y(s) - 2s - 6 + 6sY(s) - 12 + 5Y(s) = 24/(s-1)\)

Simplifying further, we get:

\((s^2 + 6s + 5)Y(s) = 24/(s-1) + 2s + 6\)

\(Y(s) = [24/(s-1) + 2s + 6] / (s^2 + 6s + 5)\)

To find the inverse Laplace transform of Y(s), we need to factor the denominator and use partial fractions:

\(Y(s) = [24/(s-1) + 2s + 6] / [(s+1)(s+5)]\)

\(Y(s) = [A/(s+1) + B/(s+5)] + [24/(s-1)]\)

Multiplying both sides by (s+1)(s+5)(s-1), we get:

\(24 = A(s+5)(s-1) + B(s+1)(s-1) + 24(s+1)(s+5)\)

Substituting s = -1, we get:

24 = 6B

B = 4

Substituting s = -5, we get:

24 = 24A

A = 1

Therefore, the partial fraction decomposition is

\(Y(s) = [1/(s+1) + 4/(s+5)] + [24/(s-1)]\)

Taking the inverse Laplace transform of each term, we get:

\(y(t) = e^{(-t)} + 4e^{(-5t)} + 24e^t\)

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When a rational number is expressed as a decimal, the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors in the denominator.

For example,

If we consider the fraction 1/7, the decimal representation is 0.142857142857..., and the repeating section has a length of 6 digits. This is because the denominator 7 is a prime number, and there is only one distinct prime factor.

Similarly, for the fraction 1/6, the decimal representation is 0.1666..., and the repeating section has a length of 1 digit. The denominator 6 has two distinct prime factors (2 and 3), but since the prime factor 2 is repeated, it contributes to a repeating section of length 1.

In general, if a rational number can be expressed in the form p/q, where p and q are coprime integers (they have no common factors other than 1), and q has prime factors p1^a1 * p2^a2 * p3^a3 * ..., then the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors, which is a1 + a2 + a3 + ...

It's important to note that not all rational numbers have repeating decimal representations. For example, the fraction 1/2 can be expressed as the terminating decimal 0.5.

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(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

sus

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

x = 6

Step-by-step explanation:

From the figure attached,

∠AFB ≅ ∠EFC [Vertically opposite angles]

Since, ∠AFB and ∠EFC are the central angles subtended by arcs EC and AB.

Therefore, (21x - 9) = m(∠EFC)

(21x - 9) = m∠EFD + m∠CFD

(21x - 9) = 90° + 27°

21x = 9 + 117

21x = 126

x = 6

Therefore, x = 6 will be the answer.

Answer:

ask the teacher

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

derivate of 7x = 1(7)x⁰, or 7

derivate of 4 is 0

derivative of 7x + 4 = 7

Answer:

2.8888888888889

Step-by-step explanation:

I hope this helps

Answer:

2.8889 I searched it and I found this I hope this is what you're looking for

Answer: The measure of angle 4 is 95 degrees.

Step-by-step explanation:

Knowing that the lines are parallel that means the alternate exterior angles are congruent. The alternate exterior angle of the angle marked with 95 degrees is angle 1. That means angle one is 95 degrees. Angle 1 and Angle 4 are vertical angles. All vertical angles are congruent so this mean angle 4 is also 95 degrees.

Therefore, the middle term is equal to: twice the product of the first term and the second term

Answer:

10.4880885 or 10.5

Step-by-step explanation:

The square root of 110 is a decimal ... 10.4880885

If we round up it will be 10.5

Answer:

10.488 to nearest thousandths

Step-by-step explanation:

If you mean using a calculator, sqrt(110) is approximately 10.488.

If you mean by hand (unlikely), there are methods such as Newton-Raphson method that converge quite quickly (after around 10 iterations it's basically no different than your calculator)

For the given statement option C  increase, wider and decrease , narrower is correct.

What is confidence interval?

A confidence interval is computed at a designated confidence level; the  95% confidence level is most common, but other levels, such as 90% or  99%, are sometimes used.

When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.

Hence  Increase; wider is the correct answer.

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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