1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ELEN [110]
3 years ago
6

Can you help me with my math questions

Mathematics
2 answers:
GrogVix [38]3 years ago
5 0

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 \sqrt{289}


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


\Rightarrow 6x=1\pm 17


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


\Rightarrow x=3 \:or\:x=-\frac{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 \sqrt{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.





Oksanka [162]3 years ago
3 0

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

Step-by-step 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

You might be interested in
QUICK I NEED FAST PLS 1. What is the mean change in the forecasted high temperatures over the next 7 days? Remember, this can be
velikii [3]

Answer:

87.7 degrees

Step-by-step explanation:

88+90+88+83+85+90+90=614

614/7=87.7

87.7 degrees is the average temp for the week

5 0
3 years ago
GIVING 100 POINTS FOR THESE 3 PROBLEMS
mart [117]

Answer:

Step-by-step explanation:

A=\frac{a+b}{2}*h=\frac{4+7}{2}*3=16.5cm^2

A=\frac{ab}{2} =\frac{4*6}{2} =12in^2

A=wl=6*5=30in^2

12+30=42in^2

A=\frac{a+b}{2}h=\frac{28+40}{2}*30=1020ft^2

Wall = A=\frac{ab}{2} =\frac{6*30}{2}=90ft^2

6 0
3 years ago
Read 2 more answers
Mr. Rahman gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to each of his 3 sons. half of the
makkiz [27]

Answer:

53760

Step-by-step explanation:

12000 x 2 = 24000

24000 x .20 = 4800 this is the amount he gave to each of his sons

4800 x 3 = 14400 this is the amount he gave to his sons in total

24000 + 14400 = 38400

38400 x .40 = 15360 this is how much he gave to his wife

15360 + 38400 = 53760

7 0
3 years ago
researchers are conducting a survey about what brand of ice cream shoppers prefer. they survey the tenth person who walks into t
RoseWind [281]
The store is conducting random sampling.
6 0
3 years ago
Read 2 more answers
I need help with this math can someone explain it please?
andreyandreev [35.5K]
There is no question
5 0
3 years ago
Other questions:
  • Steve is managing a skate park and has been analyzing the attendance data. Steve has found that the number of visitors increases
    6·2 answers
  • Plz help me asap will mark brainliest if right
    8·2 answers
  • 20 points!
    13·1 answer
  • Write this polynomial in descending order. <br> -7+8x^2-4x
    12·1 answer
  • What is the y-intercept of f^-1(x)?
    14·1 answer
  • What is the middle of a circle called
    5·1 answer
  • Help me please will mark brainliest
    15·1 answer
  • Plzzz helpppp due today
    10·1 answer
  • A race car driver's goal is to complete a 1000-kilometer auto race in 4 hours or less. The driver's average speed is 4200 meters
    7·1 answer
  • if you asked people to give their age and you collected it as &lt;5, 6-10, 11-15, 16- 20, 21-25, 26 and older, what type of vari
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!