The remainder when x^3 - 11x + 10 is divided by (x+3) isA 52
B 16
C 4
D -24

I was doing a past paper and came across this,I know one (long) way of doing this and was just wondering if anyone could show me a shorter way!!!

Answers

Answer 1

Answer: If you divide a polynomial $P(x)$ by a binomial $x-c$ , then the remainder is equal to $P(c)$ .

$c=-3\nR(x)=P(-3)\nR(x)=(-3)^3-11\cdot(-3)+10\nR(x)=-27+33+10\nR(x)=16$

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-3x+11=4x+2-(2x-4) Please solve this problem with work. Thanks!

Find the solution to the system of 5x+2y=-24 x-y=5

Answers

So to do this, we have to get rid of one of the variables by adding or subtracting the two equations together.
I will get rid of y. So, we can multiply the second equation by 2. This gives us
2x-2y=10
Now, we can add both equations
This gives us 7x=-14
Therefore, x = -2
Plug that into another equation.
-10 + 2y=-24
Therefore, y = -7

Hope this helped!! :D

5x + 2y = -24 ⇒ 5x + 2y = -24
1x - 1y = 5 ⇒ 2x - 2y = 10
      7x = -14
   7    7
   x = -2
      x - y = 5
      -2 - y = 5
      + 2    + 2
   -y = 7
   -1   -1
   y = -7
   (x, y) = (-2, -7)

Evaluate the expression if x=2 and y=4
4x+3y
a.20
b.21
c.15
d.13

Answers

The required answer would be 14 when substituting x=2 and y=4 in the expression 4x+3y which is the correct answer would be an option (A).

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have to evaluate 4x+3y when substitute x=2 and y=4

We have been given that expression as

⇒ 4x + 3y

Substitute the values of x = 2 and y = 4 in the above expression, and we get

⇒ 4(2) + 3(4)

⇒ 8+ 12

⇒ 20

Therefore, the required answer would be 20.

Learn more about the Expressions here :

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$x=2 \ny=4 \n \n4x+3y=4 * 2 + 3 * 4 =8+12=20 \Leftarrow \hbox{answer A}$

A line with a slope of 0 contains the point (3,4) . The point -2,? is also on the line. What is the missing y-coordinate?The solution is ___________

please don't use files

Answers

Answer:

Step-by-step explanation:

If the slope is 0, the line is horizontal and the y-coordinate is 4 for all x values.

Thus the missing y-coordinate is 4.

A farmer builds a rectangular pen with a perimeter of 116 feet. If the length is 5 feet more than the width, what is the width?

Answers

The formula for the perimeter of a rectangle is:
A=2l+2w.
We know the area is 116, so we can plug that in for A. Now, we cant solve the equation yet because it still has two variables. Since we know the length is 5 feet greater than the width, we can rewrite l in terms of w. So here is what our new equation will look like:
116=2(w+5)+2w
Now lets solve:
116=2w+10+2w
106=4w
w=26.5 ft.
The width is 26.5 ft.

A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm, what is the linear speed, in km/h, of a point 6 cm from the center if the disc is spinning at a rate of 6000 revolutions per minute?

Answers

The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

or approximately 135.7 km/h.

Weights of adult males.The weights of adult individuals in a certain country are normally distributed with a population mean of μ=172 pounds and a population standard deviation of σ=29 pounds. Suppose n=36 individuals are sampled.
1)
What is the mean of the sampling distribution of the means?

Answers

The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.

To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.

Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.

So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

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