Which number is closest to - 102 (square root)?
A. -11.5
B. -10.0
C. -9.7
D. -11.1

Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x-3)^2[/tex] is [tex]x^2 - 6x + 9[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

For the given case, the product needed can be calculated as:

[tex](x-3)^2 = (x-3) \times(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9\\\\(x-3)^2 = x^2 - (3+3)x + 9 = x^2 - 6x + 9[/tex]

(coefficients of like terms were added)

Thus, the product result of given expression is

[tex]x^2 - 6x + 9[/tex]

Learn more about product of polynomials here:

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Answer:

x^2 - 6x + 9

Step-by-step explanation:

Hope this helps! :D

Step-by-step explanation:

I guess, the problem is to understand :

what means "average" ?

well, the average of a defined set of data points is the sum of the data divided by the number of data points (or samples).

that way you get a mean value for each time the system is "measured" (a data point is created).

each new measurement / data point changes the mean value (or average).

this is used all the time - in sports statistics (e.g. the average score of a team), in daily life (like the average height of a human being that defines sizes of clothes, beds, chairs, tables, even the typical height of ceilings and so on).

the average of these 8 data points is therefore :

(36+37+34+23+47+27+31+21)/8 = 256/8 = 32

so, if he wants to raise his average score to 35 with the results of the next 2 games, this has 2 things to be considered :

1. the number of days points will be then 8+2=10 (and not just 8).

2. we need to add 2 data points, so that the sum of all 10 data points divided by 10 is then 35.

(36+37+34+23+47+27+31+21+x+y)/10 = 35

(36+37+34+23+47+27+31+21+x+y) = 350

x + y = 350 - 256 = 94

that means, he has to score a total of 94 points in the next 2 games.

it does not matter, how many in any single game, as long as the sum of both games is 94.

since the question is phrased "how many in each of the next 2 games", we simply take the target average of these 2 games.

remember, sum/amount = 94/2 = 47.

so, he would have to score 47 points in each of the next 2 games to raise his general average score to 35.

a) [tex]x^5-x^3[/tex]

[tex]x^3\left(x^2-1\right)[/tex] ........take out x³

[tex]x^3\left(x+1\right)\left(x-1\right)[/tex] ......separated (x²-1)

b) [tex]3x^2-75[/tex]

[tex]3\left(x^2-25\right)[/tex] ........took out 3.

[tex]3\left(x+5\right)\left(x-5\right)[/tex]  .......separated (x²-25)

c) [tex]3x^5y+4x^4y-5x^2y[/tex]

[tex]x^2y\left(3x^3+4x^2-5\right)[/tex] ............takeout x²y at the front.

d) [tex]81x^3-125[/tex]

[tex]81x^3-125[/tex] ......cannot be factorised much more further.

Solution:

Part - A:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.

Part - B:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.

Part - C:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.

Part - D:

Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.

By simplifying the given expression we will get that:

18*√8 = 36*√2

Here we start with:

18*√8

We can rewrite 18 as:

18 = √324

Replacing that in our expression we get:

√324*√8 = √(324*8) = √(2,592)

Now we need to rewrite 2,592 as the product of a square number and a non-square number (such that the non-square number is the smallest possible one).

If we divide 2,592 by 2, we get:

2592/2 = 1296

Then we can rewrite:

√2592 = √(2*1296) = √2*√1296 = √2*36

So this is the expression we wanted:

18*√8 = 36*√2

If you want to learn more about square roots, you can read:

https://brainly.com/question/8952483

Answer:

[tex]36\sqrt{2}[/tex]

Step-by-step explanation:

The largest square factor under the radical is 4. This gives us the factorization [tex]\sqrt{8} =\sqrt{4} * \sqrt{2}[/tex].

Thus,

[tex]18\sqrt{8} = 18(\sqrt{4} * \sqrt{2})[/tex]

        [tex]= 18*2\sqrt{2}[/tex]

        [tex]= 36\sqrt{2}[/tex]

Hope this helps!

Answer:

-4 or -3

Step-by-step explanation:

Calculate the determinant:

D = b^2 - 4ac = 49 - 48 = 1

Apply the formula:

x = (-b +- sqrt(D))/2a = (-7 +- 1)/2 = -4 or -3

simplify

-6u>-42

switch signs when dividing negative numbers

u<7

so, u is actually smaller than 7

Answer:

no because micah started before and they are running at the same pace.

Step-by-step explanation:

If they maintain their pace, Luke will not catch up to Micah because the gap of the 2 miles will be maintained.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

It is given that Micah jogs at a 5 mph pace along a park trail. Luke begins running on the same path at a speed of five miles per hour after he has jogged two miles.

After 2 kilometers of jogging by Micah, Luke begins running along the same route. Luke moves at a 5 mph speed.

Because Micah and Luke move at the same speed. There will be a 2-mile separation between them. Luke will not catch up to Micah

Thus, if they maintain their pace, Luke will not catch up to Micah because the gap of the 2 miles will be maintained.

Learn more about the application of subtraction here:

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#SPJ2

sin = 3/7

1 = sin²0 + cos²0

cos²0 = 1 - 9/49

cos²0 = 40/49

cos0 = √(40) / 7

since its in Quadrant 2 the sin is positive and cos is negative

cos0 = - √(40) / 7

Answer:

214.50

Step-by-step explanation:

A = lw

13 x 11 = 143 (13 is a guess)

143 x 1.50 = 214.50

im not 100 % but give it a try

hope this helps

pls mark brainliest

Answer:

1. 4/5, 3/5, 4/3 || 2. x = 13.78

Step-by-step explanation:

1)

Sin = Opposite/Hypotenuse = 16/20 = 4/5

Cos = Adjacent/Hypotenuse = 12/20 = 3/5

Tan = Opposite/Adjacent = 16/12 = 4/3

So the answer is 4/5, 3/5, 4/3

2) The unknown side is the opposite, and 21 is the hypotenuse. Opposite/Hypotenuse is the sine function.

Sin(41) ≈ 0.656

0.656 = x/21

x = 13.776

The closest answer to this is 13.78

Answer:

D. [tex]256\pi\ in^2[/tex]

Step-by-step explanation:

To do this, we need to plug in the given values into the equation:

[tex]SA=2\pi rh+2\pi r^2\\SA = 2\pi 8(8)+2\pi 8^2\\SA=2\pi 64+2\pi 64\\SA=128\pi + 128\pi\\SA=256\pi \ in^2[/tex]

Answer:

[tex]x\leq 6[/tex]

Step-by-step explanation:

[tex]\frac{3x}{2} \leq 9[/tex]

multiply by 2 to cancel

[tex]3x\leq 18[/tex]

Divide by 3:

[tex]x\leq 6[/tex]

Hope this helps

Answer:

6 ducks and 13 horses

Step-by-step explanation:

x ducks

19-x horses

2x+4(19-x)=64

2x+76-4x=64

4x-2x=76-64

2x=12

x=6 ducks

19-x = horses

19-6=13 horses

6 ducks and 13 horses

Answer:

r = 2/3

Step-by-step explanation:

[tex]6^{3r} =36[/tex]

if:

[tex]36=6^{2}[/tex]

[tex]6^{3r} =6^{2}[/tex]

then:

[tex]3r=2[/tex]

[tex]r=2/3[/tex]

Hope this helps

Answer:

[tex]r=\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]6^{3r}=36\\\\log_6(6^{3r})=log_6(36)\\\\3r=2\\\\r=\frac{2}{3}[/tex]

Answer:

53.5 sec

Step-by-step explanation:

avg = 54

(56.3+52.3+x)/3 = 54

56.3+52.3+x = 54*3=162

108.5+x = 162

x = 162-108.5=. 53.5

Answer:

53.5 sec

Step-by-step explanation:

Hope its right

Answer:

r = 12

Step-by-step explanation:

Step 1: Multiply both sides by 3.

Step 2: Check if solution is correct.

Have a lovely rest of your day/night, and good luck with your assignments. ♡

Answer:

t = 12

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

[tex]3*\frac{t}{3}=3*4[/tex]

[tex]t=3*4[/tex]

Multiply the numbers

t = 12

[RevyBreeze]

Step-by-step explanation:

Use the Distributive Property:

[tex]-10(-7x^{2} +5x)[/tex]

[tex]70x^{2}-50x[/tex]

[tex]70x^{2}-50x[/tex] is your simplified expression.

Answer:

I don't think so

Step-by-step explanation:

If I remember (based on memory) it's not equivalent

Reasoning: there's a different amount of Xs

Answer:

Please answer my question if you can, and gl understanding this! <3

Step-by-step explanation:

No, for if we subtract them, when we cancel out the 5x, 2, the integer, will not be equal to 2x, for not only is 2 already there, it is also being multipled by an integer. It possibly can equal though, if x was either 0, or positive 1, but if the x is not given, then no, they're not equivalent.

Answer:

Step-by-step explanation:

143x 69

Divide 143 to both sides

143x = 69

---------------     =  2.07

143      143

Answer:

84 cm

Step-by-step explanation:

the area of a parallelogram is the how tall is it times it by the how long the base

(H x B)

the answer is 84 cm

Answer:

Length= 1616 m

Perimeter= 5656 m

= 2X L+ B

Breadth= Perimeter- Length /2

= 5656m - 1616 m

= 4040 /2

= 2020 m

Please mark as Brainliest

Answer:

Each person will get .6 of a pound

Step-by-step explanation:

If you divide 3 by 5 you get .6.

Answer:

no

Step-by-step explanation:

Doesn't add to 12

[tex] - 5x + y = 12[/tex]

Add both sides 5x

[tex] - 5x + 5x + y = 5x + 12[/tex]

[tex]y = 5x + 12[/tex]

&

[tex]y = - x[/tex]

Thus :

[tex] - x = 5x + 12[/tex]

Add both sides x

[tex] - x + x = 5x + x + 12[/tex]

[tex]0 = 6x + 12[/tex]

Subtract both sides 12

[tex]0 - 12 = 6x + 12 - 12[/tex]

[tex] - 12 = 6x[/tex]

Switch sides

[tex]6x = - 12[/tex]

Divide both sides by 6

[tex] \frac{6x}{6} = \frac{ - 12}{6} \\ [/tex]

[tex]x = - 2[/tex]

We found the x-coordinate of the solution point ; to find the y-coordinate we just need to put the value of x in one 0f the given equations :

[tex]y = - ( - 2) [/tex]

[tex]y = 2[/tex]

Thus ( - 2 , 2 ) is the solution to this system of equations.

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

the base length is 32

But we need the base angle for the x triangle so we say

[tex] \frac{32}{2} = 16[/tex]

[tex]20 = hypothenus \\ 16 = adjacent \\ [/tex]

[tex]opposite \: =[/tex]

[tex] {opp}^{2} + {adj}^{2} = {hyp}^{2} [/tex]

[tex] {opp}^{2} + {16}^{2} = {20}^{2} [/tex]

[tex] {opp}^{2} = {20}^{2} - {16}^{2} \\ {opp}^{2} = 400 - 256 \\ {opp}^{2} = 144 \\ opp = \sqrt{144} \\ opp = 12 \\ x = 12[/tex]

Answer:

7

Step-by-step explanation:

6*7=42

9*7=63

63-42

Answer:

number is 7

Step-by-step explanation:

let the number be n , then

6n = 9n - 21 ( add 21 to both sides )

21 + 6n = 9n ( subtract 6n from both sides )

21 = 3n ( divide both sides by 3 )

7 = n

That is the number is 7

Answer:

0

Step-by-step explanation:

its a straight line horizontally

Using proportions, it is found that Jade's total yearly income was of $50,600.

A proportion is a fraction of a total amount.

In this problem, Jade's income is composed by:

Hence:

[tex]T = 18000 + 50(52) + 0.025(1200000) = 50600[/tex]

Jade's total yearly income was of $50,600.

More can be learned about proportions at https://brainly.com/question/24372153