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Hatshy [7]
3 years ago
9

What number would ypu add to both sides of x^2+7x=4 to complete the square

Mathematics
2 answers:
Tcecarenko [31]3 years ago
6 0

For a monic quadratic (factor of 1 on x^2) we always add half the coefficient on the linear (x) term, so

\left(\dfrac 7 2\right)^2 = \dfrac{49}{4}

Answer: 49/4

x^2 + 7x + \dfrac{49}{4} = 4 + \dfrac{49}{4}

(x + \frac 7 2)^2 = 4 + \frac{49}{4}


Nesterboy [21]3 years ago
3 0

(*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+7x=4\\\\x^2+2\cdot x\cdot3.5=4\ \ \ \ |+3.5^2\\\\\underbrace{x^2+2\cdot x\cdot3.5+3.5^2}_{(*)}=4+3.5^3\\\\(x+3.5)^2=16.25\\\\Answer:\ 3.5^2=12.25

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Using the remainder theorem which quotient has a remainder of 20?
stealth61 [152]

Answer:

D

Step-by-step explanation:

When a polynomial f(x) is divided by (x - a) then remainder is f(a)

A

divided by (x + 4 ), then a = - 4

(-4)^{4} - 8(- 4)² + 16 = 256 - 128 + 16 = 144 ≠ 20

B

divided by (x - 2), then a = 2

3(2)³ + 7(2)² + 5(2) + 2

= 3(8) + 7(4) + 10 + 2

= 24 + 28 + 12 = = 64 ≠ 20

C

divided by (x + 5) , then a = - 5

(- 5)³ + 5(- 5)² - 4(- 5) + 6

= - 125 + 125 + 20 + 6 = 26 ≠ 20

D

divided by (x - 2), then a = 2

3(2)^{4} - 5(2)³ + 5(2) + 2

= 3(16) - 5(8) + 10 + 2

= 48 - 40 + 12 = 20 ← Remainder of 20

3 0
3 years ago
For 9 and 9A, find the slope of the line​
djverab [1.8K]

For this case we have that by definition, the slope of a line is given by:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}

Where:

(x_ {1}, y_ {1}) and (x_ {2}, y_ {2}) are two points through which the line passes.

Question 1:

According to the image, we have the following points:

(x_ {1}, y_ {1}) :( 2, -6)\\(x_ {2}, y_ {2}): (- 6,5)

Substituting we have:

m = \frac {5 - (- 6)} {- 6-2} = \frac {5 + 6} {- 8} = \frac {11} {- 8} = - \frac {11} {8}

Thus, the slope is: - \frac {11} {8}

Question 2:

According to the image, the line goes through the following points:

(x_ {1}, y_ {1}): (- 1,2)\\(x_ {2}, y_ {2}) :( 2, -2)

Substituting we have:

m = \frac {-2-2} {2 - (- 1)} = \frac {-4} {2 + 1} = \frac {-4} {3} = - \frac {4} {3}

Thus, the slope is: - \frac {4} {3}

Answer:

Slope 1: - \frac {11} {8}

Slope 2:- \frac {4} {3}

3 0
3 years ago
The following chart shows a store's records of sales of stuffed toys for two months
Dmitry_Shevchenko [17]

Answer:

None of the above answers

Step-by-step explanation:

Form a table as shown

Months         Teddy Bears    Rabbits     Cats    Horses    Others    Totals toys

September      225                275           245      260          199        1204

October           346                 308           186      297           285       1422

Trends

Cats decreased from 245 to 186

Others increased from 199 to 285,

285-199 = 86

percent increase was = increase/original quantity *100

86/199 *100 =43.22%

Total number of stuffed toys increased from 1204 to 1422

percent increase = (1422-1204)/1204 *100 = 218/1204 *100 =18.11%

7 0
3 years ago
Read 2 more answers
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Anestetic [448]
<span>A particular computer takes 12 minutes to download a 36​-minute TV show. How long will it take the computer to download a 2​-hour ​movie

that would take 40 minutes</span>
7 0
3 years ago
4(2x−3)=4(2x)−4(3) what is the proptery
Nikitich [7]

9514 1404 393

Answer:

  distributive property

Step-by-step explanation:

The <em>distributive property</em> of multiplication over addition lets you expand the product in the manner shown.

4 0
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