Divide x cubed minus 3 x squared minus 10 x 24 by x minus 2. step 1 - fill in the missing number: a vertical line and horizontal line combine to make a l shape. there is one row of entries in the shape including 1, negative 3, negative 10, 24. on the outside to the left of the l shape is k. k =

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Answer:

3x^3+2x^2+2x+5

Step-by-step explanation:

The answer is A

For given experiment, the probability of getting a multiple of 3 and 4 is 1/7

In this question we have been given an expreiment of rolling  two number cubes and multiply the numbers.

We need to find the probability of getting a multiple of 3 and 4

If two number cubes are rolled and multiply the numbers, the maximum output of multiplication would be 36

So, the sample space:

n(S) = 21

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

And the multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36

The number of outcomes for getting a multiple of 3 and 4 are:

12, 24, 36

n(A) = 3

so, the required probability would be,

p(A) = n(A)/n(S)

p(A) = 3/21

p(A) = 1/7

Therefore, the probability of getting a multiple of 3 and 4 = 1/7

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The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer:

this is just trial and error. Answer is 3

First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:

period of time in hours amount of snow in inches

0 1

from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)

from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)

from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of

hours since hour 5)

Now, using this information on a graph, we obtain:

Attached at the end hope this helps

Step-by-step explanation:

Your chart should looks something like what I attached

Answer: 45

Step-by-step explanation

31+14=45

Start from the back

4+1=5

3+1=4

Then put them together

45.

Answer:

45

Step-by-step explanation:

31 increased by 14

= 31 + 14 = 45

Hope this helps

plz mark as brainliest!!!!!!!!!!

                                    3     1

                               +    1     4  

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

                                    4     5

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

The range for the y = 2x+4 is (-∞,∞) .

The Range for a function y=f(x) is defined as set of all possible values of the dependent variable after substituting the value from domain .

For Example : the range for function y=x² is [0,∞) as x² will give only non negative values .

In the question ,

the given function is y=2x+4 ,

On comparing this with the equation of line y=mx+c

we get , slope(m)= 2 and the y intercept(c) = 4 ,

hence this function represents the straight line

So, the range of the function is (-∞,∞) .

Therefore , the range for the y = 2x+4 is (-∞,∞) .

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Answer:

V = 108

Step-by-step explanation:

B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108

Step-by-step explanation:

no, it does not.

because almost every valid value of x (from -3 to +3) has 2 associated result values of y.

like x = 0 has y = 3 and y = -3.

but for a function there can be only ONE associated y value for every valid x value.

9514 1404 393

Answer:

  y = 20·2^x

Step-by-step explanation:

Use the given points to write two equations, then solve for 'a' and 'b'.

  20 = a·b^0 = a

  5120 = a·b^8 = 20·b^8   ⇒   256 = b^8

  b = 256^(1/8) = 2

Your function is ...

  y = 20·2^x

Answer:

hi

Step-by-step explanation:

To round a number to the nearest hundredth , look at the next place value to the right (the thousandths this time). Same deal: If it's 4 or less, just remove all the digits to the right. If it's 5 or greater, add 1 to the digit in the hundredths place, and then remove all the digits to the right.

Answer:

Step-by-step explanation:

let the missing angle be x

take 65 degree as reference angle

use tan rule

tan 65=opposite/adjacent

2.14=x/7

2.14*7=x

14.98=x

The best candidate for the job based on the scores in the aptitude test is Cade. The reason behind this is because Cade got the highest score of 302.4 compared to the scores of Justin and Kaitlyn. The scores of Justin and Kaitlyn are not close to the mean of their test versions, which suggests that they did not perform well in their respective tests.

Justin got a score of 92; this version has a mean of 72.8 and a standard deviation of 12. Using the formula of the
Z-score, we can calculate Justin's Z-score:
Z = (X - µ) / σZ = (92 - 72.8) / 12Z = 1.4333
Cade got a score of 302.4; this version has a mean of 243 and a standard deviation of 27.Using the formula of the Z-score, we can calculate Cade's Z-score: Z = (X - µ) / σZ = (302.4 - 243) / 27Z = 2.2
Kaitlyn got a score of 8.83; this version has a mean of 7.5 and a standard deviation of 0.7. Using the formula of the Z-score, we can calculate Kaitlyn's Z-score:
Z = (X - µ) / σZ = (8.83 - 7.5) / 0.7Z = 1.9. From the calculated Z-scores, we can tell that Cade has the highest score, which suggests that he performed best on the test. Therefore, Cade should be offered the job.

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Answer:

6 possible intergers brainliest me

Answer:

its 7

Step-by-step explanation:

Answer:

a) x=3

y=6*3+4

=22

b) x=4

y=6*4+4

=24

c) x=6

y=6*6+4

=40

d) x=7

y=6*7+4

=46

Answer:

22 hours

Step-by-step explanation:

So, 143 equals eleven hours. 143 plus 143 would equal 243. So, you have two 143s which means you should multiply the 11 hours by two. 11x2 equals 22.

The coordinates of the endpoint is ( 5 , 20 ).

Given data:

To find the coordinates of the other endpoint, let's assume the coordinates of the unknown endpoint are (x, y).

Given the midpoint of the segment, which is (-1, 17), and one endpoint, which is (-7, 14).

Using the midpoint formula, the two equations based on the x-coordinates and y-coordinates are:

Equation 1: (x1 + x2) / 2 = x

Substituting the known values:

(-7 + x) / 2 = -1

Equation 2: (y1 + y2) / 2 = y

Substituting the known values:

(14 + y) / 2 = 17

Solving these equations will give us the values of x and y, which represent the coordinates of the other endpoint.

Let's solve the equations step by step:

Equation 1:

(-7 + x) / 2 = -1

-7 + x = -2

x = -2 + 7

x = 5

Equation 2:

(14 + y) / 2 = 17

14 + y = 34

y = 34 - 14

y = 20

Hence, the coordinates of the other endpoint are (5, 20).

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On solving the provided question, we can say that from equation \(diagonal ^2 = 8^2 + 8^2\), the answer is \(DIAGONAL = 8\sqrt(2) \\\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

\(diagonal ^2 = 8^2 + 8^2\\diagonal ^2 = 64 + 64\\diagonal ^2 = 128\\diagonal ^2 = 64 * 2\\\)

\(diagonal ^2 = 8 * sq root (2)\\Diagonal of a square = SqrRoot (2 * side^2)\\Diagonal = \sqrt{2 * 8^2} \\Diagonal = \sqrt(128)\\\)

\(\sqrt(128) = \sqrt(2 * 64) = \sqrt(2) * 8\\DIAGONAL = 8\sqrt(2) \\\)

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The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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since both sides are equal to 0, this confirms that x = 42/29 is the correct solution. To solve the equation 3/4(2-x) + 5/6(3-2x) = 1/2 for x, we can start by simplifying the equation first by multiplying each term by the least common multiple of the denominators, which is 12. This will eliminate the fractions and allow us to solve for x.

Multiplying each term by 12, we get:    

9(2-x) + 10(3-2x) = 6

Expanding the brackets, we get:

18 - 9x + 30 - 20x = 6

Combining like terms, we get:

48 - 29x = 6

Solving for x, we can subtract 48 from both sides:

-29x = -42

Dividing both sides by -29, we get:

x = 42/29

Therefore, the solution to the equation is x = 42/29.

To check if this solution is valid, we can substitute it back into the original equation and see if both sides are equal:

3/4(2-(42/29)) + 5/6(3-2(42/29)) = 1/2

Simplifying this expression, we get:

0

Since both sides are equal to 0, this confirms that x = 42/29 is the correct solution.

In summary, to solve the equation and get the variable on one side, we first simplify the equation by multiplying each term by the least common multiple of the denominators, then we expand the brackets and combine like terms to get an equation in terms of x. Finally, we isolate x by performing algebraic operations on both sides of the equation until we have x on one side and a constant on the other side.

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Answer:

x=-26

Step-by-step explanation:

6x-3x+27=2x+1

⇒3x-2x=1-27

⇒x=-26

Hope, this helps you.

Answer:

x = -26

Step-by-step explanation:

6x - 3 ( x - 9 ) = 2x + 1

6x - 3x + 27 = 2x + 1

Combine the like terms, and then you subtract 27 from each side. Hope this helps!

The linear transformation t can be represented as \(t(\vec v) = [59x - 57y]\)

To write the linear transformation t as a matrix transformation, we can use the given information to determine the matrix representation of t.

Let's denote the linear transformation t as T. We know that t([1 - 2]) = [59] and t([-2 - 1]) = [-57].

We can represent the vectors [1 - 2] and [-2 - 1] as columns and their corresponding transformed vectors as the result.

[1 -2] --> [59]

[-2 -1] --> [-57]

To obtain the matrix representation of T, we arrange the transformed vectors as columns in a matrix:

T = [[59 -57]]

Now, for any vector\(\vec v = [x y]\in\) ℝ², we can apply the linear transformation by multiplying the vector \(\vec v\) by the matrix T:

t(\(\vec v\) ) = T *\(\vec v\)

In this case, it becomes:

t(\(\vec v\) ) = [[59 -57]] * [x y]

Therefore, the linear transformation t(\(\vec v\)) is given by:

t(\(\vec v\) ) = [59x - 57y]

The coefficients in the matrix representation determine how the transformation affects the vector components.

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n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1

What is Remainder?

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.

As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.

\(n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\\)

\(k(k^2+3k+3)\) is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).

The remainder will be n= (K+1)^3

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

False

Step-by-step explanation:

Geometric series have ratios.

The ratio here is 2.

So the next term should be -8.