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Can you help me with my math questions

Can you help me with my math questions-example-1
User Corentor
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Answer:

1. 15/8 and -15/8

2. Yes it is a perfect square.

3. a) 2.69 in

b) 6 in

c) 17.10 in

Explanation:

1. Find the factors of 64f² - 225

64f² - 225 = 0

(8f - 15)(8f +15) = 0

8f - 15 = 0 or 8f + 15 = 0

f = 15/8 or f = -15/8


2. Find whether it is a perfect square p² + 14p + 49

p² + 14p + 49 = 0

p² + 14p = -49

p² + 14p + 7² = -49 + 7²

(p + 7)² = 0

p² + 14p + 49 = (p + 7)²

Yes it is a perfect square.

3 a)

36x² - 12x + 1 = 289

36x² - 12x = 288

x² - 1/3x + (1/6)² = 8 + 1/6

(x + 1/6)² = 49/6

x + 1/6 = ±2.8577

x = -3.02 and x = 2.69

3. b)

25x² - 50x + 25 = 1225

x² - 2x + 1 = 49

x² -2x + 1 =48 + 1

(x + 1)² = 49

x = ±√49 - 1

x = 6 and x = -8

3. c)

49x² - 56x + 16 = 289

49x² - 56x = 289 - 16

49x² - 56x = 273

x² - 1.1429x + 0.57² = 273 + 0.57²

(x - 0.57)² = 273.3265

x = ±√273.3265 + 0.57

x = 17.10 or x = -15.96

User Sreehari R
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p^2+2(7)p+7^2=(p+7)^2


Justification:

Given:
p^2+14p+49


Split the middle term;


=p^2+7p+7p+49


Factor:


=p(p+7)+7(p+7)



=(p+7)(p+7)



=(p+7)^2


QUESTION 3a

The given expression for the area of the rectangle is
36x^2-12x+1.


This is equal to the indicated area which is
289\;in^2


This implies that



36x^2-12x+1=289



\Rightarrow (6x-1)^2=289



\Rightarrow (6x-1)(6x-1)=289



\Rightarrow l=(6x-1),w=(6x-1)



This implies that, the dimensions of the rectangle are equal;


Using the square root method, we obtain


\Rightarrow (6x-1)=\pm √(289)



\Rightarrow (6x-1)=\pm 17



\Rightarrow 6x=1\pm 17



\Rightarrow 6x=18 \:or\:6x=-16



\Rightarrow x=3 \:or\:x=-(2)/(3)

We discard the negative value.

The side length of this rectangle is



\Rightarrow l=(6(3)-1)=17,w=6(3)-1=17


QUESTION 3b

The given expression for the area of the rectangle is
25x^2-50x+25.


This is equal to the indicated area which is
1225\;in^2


This implies that



25x^2-50x+25=1225



25(x^2-2x+1)=1225



(5(x-1))^2=35^2



5(x-1)5(x-1)=49



\Rightarrow l=5(x-1),w=5(x-1)



This implies that, the dimensions of the rectangle are equal;


Using the square root method, we obtain


\Rightarrow 5(x-1)=\pm √(1225)



\Rightarrow 5(x-1)=\pm 35



\Rightarrow x=1\pm 7



\Rightarrow x=8 \:or\:x=-6

We discard the negative value.

The side length of this rectangle is



\Rightarrow l=5(8-1)=35,w=5(8-1)=35



QUESTION 3c

The given expression for the area of the rectangle is
49x^2-56x+16.


This is equal to the indicated area which is
289\;in^2


This implies that



49x^2-56x+16=289





(7x-4)^2=289



(7x-4)(7x-4)=289




\Rightarrow l=(7x-4),w=(7x-4)


Applying the laws of indices gives;



(7x-4)^2=17^2


This implies that;


7x-4=17



7x=21



x=3in.


The side length of this rectangle is



\Rightarrow l=7(3)-4=17\:in.,w=7(3)-4=17\:in.


Dont forget that the square is also a rectangle.





User Toote
by
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