Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

Step-by-step explanation:

x²-xy-xy+y²

x²+2xy+y²

hope it helps

Answer:

She had 8 doubles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that [tex]x + y + z = 46[/tex]

46 hits totaled 66 bases

This means that:

[tex]x + 2y + 3z = 66[/tex]

4 times as many singles as doubles

This means that [tex]x = 4y[/tex]

So

[tex]x + 2y + 3z = 66[/tex]

[tex]4y + 2y + 3z = 66[/tex]

[tex]6y + 3z = 66[/tex]

And

[tex]x + y + z = 46[/tex]

[tex]4y + y + z = 46[/tex]

[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]

Then

[tex]6y + 3z = 66[/tex]

[tex]6y + 3(46 - 5y) = 66[/tex]

[tex]6y + 138 - 15y = 66[/tex]

[tex]9y = 72[/tex]

[tex]y = \frac{72}{9}[/tex]

[tex]y = 8[/tex]

She had 8 doubles.

Answer:

42%

Step-by-step explanation:

to find percentages, you move the decimal point twice to the right

Answer:

A is the equation in standard form

Step-by-step explanation:

Answer:

A = 16 ft^2

P = 20 ft

Step-by-step explanation:

P = perimeter

A = area

STEP 1: divide the shape into rectangles

Rectangle 1: 2ft*3ft

Rectangle 2: 2ft*5ft

STEP 2: Find the area of each rectangle

Equation for area of a rectangle = bh

Rectangle 1: b = 2, h = 3

Rectangle 2: b = 2, h = 5

(2 * 3) + (2 * 5)

6 + 10

16 ft^2

Now, we have to find the perimeter

STEP 1:  Find the unknown side lengths.

To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.

The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.

STEP 2: Add up all the side lengths

P = 2 + 5 + 5 + 2 + 3 + 3

P = 20 ft

Don't forget to label your answers!!

I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.

Answer:

[tex]hright =12[/tex]

Step-by-step explanation:

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

The formula to find the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex]  where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.

[tex]72=\frac{1}{2}(12)(h)[/tex]

[tex]72=6h[/tex]

Here, divide both sides by 6

[tex]12=h[/tex]

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

Hope this is helpful.

Answer:

height = 12

Step-by-step explanation:

.............

Step-by-step explanation:

There was originally 8 pieces of pie.

Answer:

if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.

Answer:

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]P(1) = 2[/tex]

Required

The solution

We have:

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]

Split

[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]

Divide both sides by [tex]P^\frac{1}{2}[/tex]

[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]

Multiply both sides by dt

[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]

Integrate

[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Rewrite as:

[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the left hand side

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the right hand side

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)

To solve for c, we first make c the subject

[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]

[tex]P(1) = 2[/tex] means

[tex]t = 1; P =2[/tex]

So:

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]

[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]

So, we have:

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]

Divide through by 2

[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]

Square both sides

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Answer: The answer would be D

Step-by-step explanation:

The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.

This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.

Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.

The other options from the complete text are:

Read more about adjusted trial balance here:

https://brainly.com/question/14476257

#SPJ6

Answer:

b and f

Step-by-step explanation:

====================================================

Explanation:

We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).

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

Plug n = 8 into the formula below

S = 180(n-2)

S = 180(8-2)

S = 180(6)

S = 1080

The 8 interior angles add up to 1080 degrees.

Answer:

Step-by-step explanation:

B looks like it would work.

You add speeds * time when you are travelling in opposite directions.

I don't know why you would add or subtract 1 as in A and C

120 * t = 540

t = 540/120

t = 4.5 hours.

So after 4.5 hours they are 540 miles apart.

Answer:

b

Step-by-step explanation:

Answer:

The probability is P = 0.08

Step-by-step explanation:

We have:

2 pink balls

7 purple balls

6 white balls

So the total number of balls is just:

2 + 7 + 6 = 15

We want to find the probability of randomly picking 3 purple balls (without replacement).

For the first pick:

Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)

p₁ = 7/15

Second:

Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:

p₂ = 6/14

third:

Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:

p₃ = 5/13

The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:

P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13)  = 0.08

Answer:

B) reject the null hypothesis.

Step-by-step explanation:

Answer:

Satisfaction score

Step-by-step explanation:

The dependent variable may be described as the variable which is being measured in a research experiment. In the scenario described above, the dependent variable is the satisfaction score which is used to measure preference for a one or two column textbook. The dependent variable can also seen as the variable which we would like to predict, also called the predicted variable . The predicted variable here is the satisfaction score.

Answer:

There are 256 pairs in all.

Answer:

The probability of this event is represented by a value of 1.

Step-by-step explanation:

Probability of a certain event:

The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.

You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.

This means that the probability of this event is represented by a value of 1.

Answer:

7 : 8

Step-by-step explanation:

that is the procedure above

Given:

The graph of a function.

To find:

The range of the given function using interval notation.

Solution:

Range: The set of y-values or output values are known as range.

From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.

Range [tex]=\{y|-2<y\leq 2\}[/tex]

The interval notation is:

Range [tex]=(-2,2][/tex]

Therefore, the range of the given function is (-2,2].

Answer:

m>-7

Step-by-step explanation:

expand

-10m+15-4<81

-10m+11<81

collect like terms

-10m<81-11

-10m<70

m>-7

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

19.

The numbers are m and n

Sum of m and n = m + n

Sum is multiplied by 91 = 91 x ( m + n )

20.

Let the number be = m

Six subtracted from the number = m - 6

41 times the difference = 41 x ( m - 6)

21.

Let the number be = r

Difference between 83 and 10 = 83 - 10 = 73

[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]

22.

Total of p and 23 = p + 12

[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]

23.

The product of c and 3  = 3c

Sum of 9 and 12 = 21

Product is more than Sum = 3c + 21

24.

Sum of y  and 10 = y + 10

Number x decreased by 5 = x - 5

[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]

Answer:

[tex]-5 \to -24[/tex]

[tex]-1 \to -4[/tex]

[tex]2 \to 11[/tex]

[tex]3 \to 16[/tex]

[tex]4 \to 21[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x + 1[/tex]

Required

Complete the table (see attachment)

When x = -5

[tex]f(-5) = 5 * -5 + 1 = -24[/tex]

When x = -1

[tex]f(-1) = 5 * -1 + 1 = -4[/tex]

When x = 2

[tex]f(2) = 5 * 2 + 1 = 11[/tex]

When x = 3

[tex]f(3) = 5 * 3 + 1 = 16[/tex]

When x = 4

[tex]f(4) = 5 * 4 + 1 = 21[/tex]

So, the table is:

[tex]-5 \to -24[/tex]

[tex]-1 \to -4[/tex]

[tex]2 \to 11[/tex]

[tex]3 \to 16[/tex]

[tex]4 \to 21[/tex]

Answer:

annualy=$3689.62

semiannually=$3695.27

monthly=$3700.06

weekly=$3700.81

daily=$3701.00

Continuously=$3701.03

Step-by-step explanation:

Given:

P=3000

r=3%

t=7 years

Formula used:

Where,

A represents Accumulated amount

P represents (or) invested amount

r represents interest rate

t represents time in years

n represents accumulated or compounded number of times per year

Solution:

(i)annually

n=1 time per year

[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]

On approximating the values,

A=$3689.62

(ii)semiannually

n=2 times per year

[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]

On approximating the values,

A=$3695.27

(iii)monthly

n=12 times per year

[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]

On approximating,

A=$3700.06

(iv) weekly

n=52 times per year

[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]

On approximating,

A=$3700.81

(v) daily

n=365 time per year

[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]

On approximating the values,

A=$3701.00

(vi) Continuously

[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]

On approximating the value,

A=$3701.03

Answer:

-1.28 AND 2.61

Step-by-step explanation:

[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]

use quadratic formula

x =  [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]   x =  [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

Solution/X-Intercepts: -1.28 AND 2.61    

Answer:

-  [tex]\frac{4}{\sqrt{29} }[/tex]

Step-by-step explanation:

The equations for the 1st object :

x₁ = 10 cos(2t),  and  y₁ = 6 sin(2t)

2nd object :

x₂ = 4 cos(t), y₂ = 4 sin(t)

Determine rate at which distance between objects will continue to change

solution Attached below

Distance( D )  = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]

hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]

Answer:72 [tex]cm^{2}[/tex]

Solution 1:

Step 1: Find EF use Pythagorean theorem

[tex]EF^{2} = EB^{2} + BF^{2}[/tex]

[tex]EF^{2} = 6^{2} + 6^{2}[/tex]

EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm

Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72

Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD

The area of ABCD = 12x12 = 144

Thus, the area of EFGH = 144: 2 = 72:)

Have a nice day!

Answer: [tex]n=13[/tex]

Step-by-step explanation:

Given

Sum of the first 10 terms is equal to sum of 20, 21, and 22 term

[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]

No of terms to give a sum of 960

[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]

Value of first term is less than 20

[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]

Answer:

15

Step-by-step explanation:

In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))

Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.

When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.

To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.

Then in the expression: (n÷2)×(2a+(n-1)×d)

substitute:

n = 14 (must be an even number for the equation to work)

a = 15

d = 7

This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)

substituting:

n = 15

a = 15

d = 7

This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.

I hope this has helped you.

P.S. Everything in the previous solution was right apart from the start of the last section and the answer