Classify the following polynomials. Combine any like terms first. x²+ 3x + 2x – 2x² x³+ 4x – 4x – 4x² x³+ 2x – x³ – 2x² + 3

Answer:

k=-63

Step-by-step explanation:

multiply both sides by -9

k=7*-9

k=-63

Answer:

-63

Step-by-step explanation:

by simplifying both sides of the equation, then isolating the variable.  k= -63

-9 x 7 = -63

Answer:

AC = 13.3

Make proportional relationship:

\(\dfrac{\text{AB}}{\text{AC}} =\dfrac{\text{AM}}{\text{AN}}\)

Insert values

\(\rightarrow\dfrac{10}{\text{AC}} =\dfrac{6}{8}\)

Cross multiply

\(\rightarrow \text{AC}=\dfrac{10(8)}{6}\)

Simplify

\(\rightarrow \text{AC}=13.3\)

The interest rate that was calculated using the data that we have here is 1 %

The formula for simple interest is:

I = Prt

Where:

I = interest earned

P = principal (initial amount deposited)

r = interest rate (expressed as a decimal)

t = time (in years)

Given that Sidney deposited $60,000 in a savings account and earned $1,200 in interest after 2 years, we can plug these values into the formula:

1200 = 60000 * r * 2 years

1200 = 120000 r

divide through by 120000

1200 / 120000 = r

r = 0.01

= 1 %

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Answer: 4.8

Step-by-step explanation:

when we power the number i to a odd number, we obtain the same i, but when we power i to a even number we obtain 1 instead.

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

Step-by-step explanation:

1)

total area = rectangle area + 2 triangle area

                =  length * width = 2 ( \(\frac{1}{2}\) * base * height )

                =  7.5 * 6 + 2 (  \(\frac{1}{2}\) * 3 * 4 )

                = 57 ft²

2)

separate it into two rectangles:

length * width + length * width

  6  *   2  +  9 * 4

      48 cm²

3)

parallelogram area =  base * height

                                = 20 * 25

                                 = 500 in²

A. The signal of each coefficient is given by:

B. The coefficient closest to zero is of B.

C. The coefficient with the least value is of C.

The transformations are vertical stretch/compression of the absolute function.

Then the signal is defined as follows:

The coefficient closest to zero is for the biggest vertical compression, which is of B, for which the graph stretches horizontally and compresses vertically.

The least value is for the biggest reflected stretching, which is in item c, in which the curve has a larger vertical stretch than in item d.

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Answer:

Step-by-step explanation:

There are 50 children, and 18 children have red shirts. 18 out of 50 children are wearing red shirts. So, 18/50 children have red shirts.

Answer:

Increases by 71% to the nearest whole number

Step-by-step explanation:

=((12-7) /7 )x100

=57×100

=0.714286×100

=71.4286%change

=71.4286%increase

Answer:

14

-83

-43

these anwrers when you make it with different ways.

You nees to get more than one answer with this problem I guess.

13-7+8 = 14

13(-7) + 8 = -83

13-7(+8) = -43If this not what you asked please delete my answer, if not kindly give me brainliest if you like.

Answer:

THERE IS NO OTHER ANSWER THAN 14

Step-by-step explanation:

Only 1 answer can be found by doing this problem in any order:

If we do 13-7 first:
(13-7)+8=

6+8=

14

So 1 answer is 14

If we do -7+8 first:

13+(-7+8) =

13+1=

14

So either way you do it you get the same answer. This is why it doesn't matter whether you do addittion or subtraction first before the other.

THERE IS NO OTHER ANSWER THAN 14

By using the power rule for derivatives, we get dy/dx = 3/(2√(3x + 9)).

It is defined as the limit of the ratio of the change in the function to the change in its input, as the change in the input approaches zero.

To find dy/dx, we can use the power rule for derivatives and the chain rule as follows:

y = √(3x + 9)

Inferring the derivative from x, we obtain:

dy/dx = d/dx [√(3x + 9)]

Using the chain rule, we can write:

dy/dx = d/du [√u] * du/dx, where u = 3x + 9

Taking the derivative of √u with respect to u using the power rule, we get:

d/dx [√u] = 1/2 \(u^(-1/2)\)

Substituting back u = 3x + 9 and multiplying by du/dx, we get:

dy/dx = 1/2 \((3x + 9)^(-1/2)\) * d/dx [3x + 9]

Taking the derivative of 3x + 9 with respect to x, we get:

d/dx [3x + 9] = 3

Reentering the preceding equation, we obtain:

dy/dx = 1/2 \((3x + 9)^(-1/2)\) * 3

Simplifying, we get:

dy/dx = 3/(2√(3x + 9))

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Answer:

0.125 gallon

Step-by-step explanation:

Answer:

The answer is 0.125.

Step-by-step explanation:

Nobody wants an explanation. Get to the point.

Answer:0.25 tons

Step-by-step explanation:

I looked it up on the internet

Answer:

what is the expressio

Step-by-step explanation:

Answer:

still need help

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

I took the test :)

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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The common difference is 4 and the sum of the first 20 terms is 880

Let's use the formula for the nth term of an arithmetic sequence to solve the problem:

a_n = a_1 + (n - 1) d

where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.

From the given information, we have:

a_18 = 5 a_2 (1)

a_11 = 52 (2)

We can use equation (1) to substitute for a_18 in terms of a_2:

a_18 = a_2 + 16d (3)

where d is the common difference. Substituting equation (3) into equation (1), we get:

a_2 + 16d = 5 a_2

4 a_2 = 16d

a_2 = 4d

Substituting this into equation (3), we get:

a_18 = 68d

Now, we can use the formula for the sum of the first n terms of an arithmetic sequence:

S_n = n/2 (a_1 + a_n)

Substituting a_1 and a_n in terms of d, we get:

S_n = n/2 [a_1 + (a_1 + (n - 1)d)]

Simplifying, we get:

S_n = n/2 [2 a_1 + (n - 1)d]

We know that a_11 = 52, so we can use the formula to find a_1:

a_11 = a_1 + 10d = 52

Subtracting 10d from both sides, we get:

a_1 = 52 - 10d

Substituting this into the formula for the sum of the first 20 terms, we get:

S_20 = 20/2 [2 (52 - 10d) + 19d]

Simplifying, we get:

S_20 = 10 (52 + 9d)

We still need to find the value of d to calculate S_20. We can use the equation we derived earlier, a_2 = 4d, to solve for d:

a_2 = a_1 + d = 52 - 9d

Substituting a_2 = 4d, we get:

4d = 52 - 9d

13d = 52

d = 4

Substituting this into the formula for S_20, we get:

S_20 = 10 (52 + 9d) = 10 (52 + 36) = 880

Therefore, the sum of the first 20 terms of the arithmetic sequence is 880.

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Answer:

I am pretty sure its A sorry if its incorrect

Answer:

point B

Step-by-step explanation:

hope it helps you

Answer:

57

Step-by-step explanation:

Given:

x = 4

y = 5

w = -3

Work:

3xy + w

3(4)(5) + (-3)

12(5) - 3

60 - 3

57

Step-by-step explanation:

d = √(15-10)²+(-6-3)²

=√5²+(-9)²

= √25+81

=√106

10.3 units

The sum we want is

\(\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots\)

where \(T_n=\frac{n(n+1)}2\) is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as

\(\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)\)

For convenience, I'll use the abbreviations

\(S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}\)

\({S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}\)

for m ∈ {1, 2, 3, …, 7}, as well as the well-known series

\(\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}\)

We want to find \(S_1-S_3-S_5+S_7\).

Consider the periodic function \(f(x) = \left(x-\frac12\right)^2\) on the interval [0, 1], which has the Fourier expansion

\(f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}\)

That is, since f(x) is even,

\(f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)\)

where

\(a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}\)

\(a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}\)

(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)

Expand the Fourier series to get sums resembling the \(S'\)-s :

\(\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)\)

which reduces to the identity

\(\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'\)

Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution

\(\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}\)

It turns out that

\({S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7\)

so we're done, and the sum's value is \(\boxed{\dfrac{\pi^2}{8\sqrt2}}\).

Answer:

6x^2 - 32x + 10

Step-by-step explanation:

I used the FOIL method of factoring. Hope this helps!

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Answer:

f(x) =5x -6 and g(x) = x + 1

Step-by-step explanation:

5x^2 - x - 6

finding the product of AC where A is 5 and C is -6 equals -30

factors of -30 whose sum eqjals -1 are +5 and -6

substitute into the expression

5x^2 + 5x -6x - 6

group the expression

(5x^2 + 5x) (-6x - 6)

take out the common factors in each bracket

5x(x + 1) -6 (x + 1)

(5x - 6) (x + 1)

Answer:a

Step-by-step explanation:

Question: What's the joint frequency a 9th grader liked math?

Explanation:

Check out the attached image below. I've filled in the table with the missing values. The upper left corner is 3 because 7+3 = 10 in the first column. You'll fill in the other values in a similar fashion. Once we filled out the table, we can answer all of these questions. There are 3 ninth graders who like math out of 100 people total. So the final answer is 3/100 = 0.03 = 3%.

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

Question: What's the marginal relative frequency of 9th graders surveyed?

Explanation:

Again, refer to the table to find that there are 10 ninth graders out of 100 total. So 10/100 = 0.10 = 10% is the answer.

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

Question: Given a student was in 10th grade, what's the likelihood the student preferred English?

Explanation:

We only focus on the 10th graders because of the "given". There are 23 people in this row who like English out of 50 total sophomores. So 23/50 = 0.46 = 46% of the tenth graders liked English.

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

Question: Given the subject was science, what's the likelihood the student was a freshman?

Explanation:

Focus on the science column only. There are 29 freshmen out of 40 students total. We get the percentage of 29/40 = 0.725 = 72.5%

Answer:

Parallel lines have the same slope, so the slope would be 1/3. It would need a different y intercept though or it would be the same line.