If X is a factor of Y and Y is a factor of Z then X is a factor of Z. If so then how



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Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

5 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

1

:

(x - 5) • (x - 12) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

or

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

49

Applying the quadratic formula :

17 ± √ 49

x = —————

2

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

I believe it is a because I had a question just like that in 8th grade

Answer:

130

Step-by-step explanation:

The approximate percentage of the points scored during the second part of the  game is 43%

% score in the second part  = 15/35 * 100

% score in the second part  = 1500/35

% score in the second part = 42.85 ≈ 43%

Hence the approximate percentage of the points scored during the second part of the  game is 43%

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Answer:

Answer# 1: A. 26

Answer# 2: A. 25

1. What is m + 5n where m = 1 and n = 5?

Substitute 1 for "m" and 5 for "n":

[tex]\sf (1)+5(5)[/tex]

Multiply 5*5 =25

[tex](1)+25[/tex]

Add :

[tex]\sf 26[/tex]

____________________

2. What is 5m + 5n where m = 10 and n = -5?

Substitute 10 for "m" and -5 for "n".

[tex]\sf 5\left(10\right)\:+\:5\left(-5\right)[/tex]

Multiply 5 * 10= 50

[tex]\sf 50+5\left(-5\right)[/tex]

Multiply 5 * -5 = -25

[tex]\sf 50-25[/tex]

Subtract:

[tex]\sf 25[/tex]

___________________________________

The amount of rainfall is an illustration of inverse functions, and rates.

The function is given as: R = f(t)

(a) Interpret f(6) = 4.8

This means that:

The amount of rainfall at 6 seconds is 4.8 cm

(b) Interpret f'(6) = 0.5

f'(6) represents the rate of the function

So, this means that:

The rate at which rain falls at 6 seconds is 0.5 cm per second

(c) Interpret f^-1(5) = 14

f^-1(6) represents the inverse function

So, this means that:

The time at which 5 cm of rain falls, is 14 seconds

(d) Interpret f^-1'(5) = 1.5

f^-1'(5) represents the rate of the inverse function

So, this means that:

The rate of time when 5 cm of rain falls is 1.5 seconds per cm

Read more about functions, inverse and rates at:

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Answer:

Unit rate = 4.5 mph.

Step-by-step explanation:

Unit rate: 13.5/3

=> Unit rate: 4.5 mph.

Hoped this helped.

Answer:

Infininte, Any number

Step-by-step explanation:

Simplify:

25 - 5x = 25 - 5x

Answer:

7

Step-by-step explanation:

let x be the number

3x + 11 = 32

3x = 21............subtract both sides by 11

x = 7................divide both sides by 3

Answer:

Expression-

3×r+11=32

r=7

Step-by-step explanation:

I have run this answer the calculator a million times so trust me on this one

Answer:

the answer is this sign >. it means the answer on the left is greater than the one on the right

Answer:y=2.5x+5 i thank

Step-by-step explanation:

Answer:

B. Credit that is automatically renewed as debts are paid

Hope this helps :)

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (500)(0.0125)(3)\implies \boxed{I = 18.75}[/tex]

Answer:

1. 32

3. -11

Step-by-step explanation:

(To meet character limit)

Answer:

1.) 35

2.) -20

Step-by-step explanation:

Answer:

U never showed the thing below.

Step-by-step explanation:

Answer:

Midrange Formula. Midrange in layman terms is the middle of any data set or the simply the average, mean of the data. A midrange is a statistical tool which is also known as the measure of center in statistics. Along with the existence of the midrange formula means, medium, average, mode, and range are also known as the measure of central tendency.

Step-by-step explanation:

Answer:-29

Step-by-step explanation:

(-2-4)+(5-10)-6(3)

-6+-5-18

Step-by-step explanation:

The conversion for parsecs into meters is

1 parsec (pc) = [tex]3.09×10^{16}\:\text {m}[/tex]

So if Proxima Centauri is [tex]4×10^{13}\:\text{m}[/tex] away, then in terms of parsecs, this distance is

[tex]4×10^{13}\:\text{m}×\left(\dfrac{1\:\text{parsec}}{3.09×10^{16}\:\text{m}}\right)[/tex]

[tex]\;\;\;\;\;= 1.2×10^{-3}\:\text{parsec}[/tex]

Answer:

5/4 and 7/4 are the two solutions.

Answer:

The answer is seventeen (17)

Answer:

Step-by-step explanation:

1) D

2) B

3) no solution

y ≤ 0.5x - 4 is area C including the red line

y ≥ 0.5x + 5 is area A including the blue line

Answer:

1 oz = 29.574 ml

16 oz = About 480 ml, so, yes, the answer is C.

Step-by-step explanation:

Answer:

107 adults 16 children

Step-by-step explanation:

can i get brainlest

Coding the given algorithm in python 3, the greatest common divisor of the values (124 and 244) and (4424 and 2111) are 4 and 1 respectively.

The program implementation goes thus :

def gcd(a, b):

#initialize a function named gcd which takes in two parameters

if a>b:

#checks if a is greater than b

return gcd (b, a)

#if true interchange the Parameters and Recall the function

elif a == 0:

return b

elif a == 1:

return 1

elif((a%2 == 0)and(b%2==0)):

#even numbers leave no remainder when divided by 2, checks if a and b are even

return 2 * gcd(a/2, b/2)

elif((a%2 !=0) and (b%2==0)):

#checks if a is odd and B is even

return gcd(a, b/2)

else :

return gcd(a, b-a)

A sample run if the program on the values given :

print(gcd(124, 244))

print()

#leaves a space after the first output

print(gcd(4424, 2111))

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Answer:

13:7

Step-by-step explanation:

This ratio would be 13 laptop computers for every 7 desktop computers; 13:7

9514 1404 393

Answer:

Step-by-step explanation:

The easiest way to do these is to make use of your knowledge of the decimal equivalents of fractions and percentages.

  66 2/3% of 900 = 2/3 × 900 = 600

  27 1/2% of 1200 = 0.275 × 1200 = 330

  17 1/2% of 1000 = 0.175 × 1000 = 175 . . . . move the decimal point

  33 1/3% of 600 = 1/3 × 600 = 200

     or 33 1/2% of 600 = 0.335 × 600 = 201

_____

Additional comment

The repeating decimal for 1/3 is 0.33333.... As a percentage, that is 33 1/3%. Then 2/3 = 66 2/3%.

To change a percentage to a decimal, divide it by 100%.

  17.5% = (17.5%)/(100%) = 17.5/100 = 0.175

__

The product 0.275 × 1200 can be rewritten as ...

  0.275 × 1200 = 0.275 × 1000 × 1.2 = 275 ×1.2 = 275 + 0.2×275

  = 275 +55 = 330

This is a calculation you can do in your head.

__

We suspect a couple of typos in your question. If you mean 66 2/3, not 66 2/3%, then multiply the first answer by 100 to get 60,000.

We have shown answers for both 33 1/2% as your problem says, and 33 1/3%, which would be the more usual fraction.

Answer:

Step-by-step explanation:

Given that :

x = 5-2√6

1/x = 1/(5-2√6)

The denominator = 5-2√6

The Rationalising factor of 5-2√6 = 5+2√6

On Rationalising the denominator then

⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]

⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]

⇛ 1/x = (5+2√6)/[5²-(2√6)²]

Since (a+b)(a-b) = a²-b²

Where ,

⇛1/x = (5+2√6)/(25-24)

⇛ 1/x = (5+2√6)/1

⇛ 1/x = 5+2√6

Now,

x +(1/x)

⇛ 5-2√6+5+2√6

⇛ 5+5

⇛ 10

Therefore, x+(1/x) = 10.

On squaring both sides then

⇛ [x+(1/x)]² = 10²

⇛ x²+2(x)(1/x)+(1/x)² =100

⇛ x²+2+(1/x)² = 100

⇛ x²+(1/x²) = 100-2

⇛ x²+(1/x²) = 98

Therefore, x²+(1/x²) = 98.

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Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....

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Answer:

7x - y = -7

Step-by-step explanation:

Hope this helps!