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
Alla [95]
3 years ago
9

The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the

squares is 65 in squared . Find the lengths of the sides of the two squares.
Mathematics
2 answers:
Taya2010 [7]3 years ago
4 0

Answer:

L_1 = 4

And L_2 = 3 +4 = 7

Step-by-step explanation:

For this case we assume that for the first square we have the following dimensions:

A_1 = L^2_1

And we know that:

L_2 = 3 + L_1

And the area for the second square would be:

A_2 = L^2_2 = (3+L_1)^2 = 9 + 6L_1 + L^2_1

And we know that the sum of areas is 65 so then we have this:

A_1 + A_2 = 65

And replacing we got:

L^2_1 + 9 + 6L_1 + L^2_1 = 65

2L^2_1 +6L_1 - 56=0

We can divide the last expression by 2 and we got:

L^2_1 + 3L_1 -28=0

And we can factorize the last expression like this:

(L_1 + 7) (L_1 -4) =0

And we have two solutions for L_1 and we got:

L_1 = 4, L_1 = -7

Since the length can't be negative we have this:

L_1 = 4

And L_2 = 3 +4 = 7

almond37 [142]3 years ago
4 0

Answer:

4 inch and 7 inch

Step-by-step explanation:

Let the length of the smaller square=l

Since the length of each side of a square is 3 in. more than the length of each side of a smaller square,

Length of the bigger square=l+3

Area of Smaller Square=l²

Area of Larger Square=(l+3)²

The sum of their areas is 65 inch squared

Therefore: l²+(l+3)²=65

l²+(l+3)(l+3)=65

l²+l²+3l+3l+9=65

2l²+6l+9-65=0

2l²+6l-56=0

2l²+14l-8l-56=0

2l(l+7)-8(l+7)=0

(2l-8)(l+7)=0

2l-8=0 or l+7=0

l=4 or -7

l= 4 inch

The length of the larger square is (4 +3) inch =7 inch

You might be interested in
Nola purchased 2.5 pounds of cheese for $10.50. Her mother purchased 3 pounds of the same cheese for $12.60. The cost of cheese
jeka94

Answer:

cost per pound = $4.20

Step-by-step explanation:

Cheese cost per pound = ?

first for the cost per pound

cost per pound = total cost / pounds bought

cost per pound = $10.50 / 2.5 pounds

cost per pound = $4.20

to check the above answer is correct

cost per pound = total cost / pounds bought

cost per pound = $12.60 / 3 pounds

cost per pound = $4.20

Therefor, the cheese costs $4.20 per pound.

4 0
3 years ago
How many times is 3 in 43.999 than the value of the digit 3 in 42.103
Dennis_Churaev [7]

Answer:

1. 14.666 ¯ over the 3

2. 14.034 ¯ over the 3

Step-by-step explanation:

5 0
3 years ago
Justine runs 250 yards in 50 seconds.
DaniilM [7]

Answer:

a: 300 Yards

b: 10 seconds

c: 5 Yards per second

7 0
3 years ago
If the simple interest on $5,000 for 4 years is $1,600, then what is the interest rate?
matrenka [14]

Answer:

0.08, or 8%

Step-by-step explanation:

The appropriate formula is i = p*r*t, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

We want to calculate r when i, p and t are known.

                                                           i

Solving i = p*r*t for r, we get r = ------------

                                                       p*t

The interest rate in this case is

        $1600

r = ---------------- = 0.08, or 8%

      $5000*4

8 0
2 years ago
7.935 x 10 to negative 5 power
Effectus [21]

Answer:

0.00007935

Step-by-step explanation:

7.935 x 10 to negative 5 power can be written as:

7.935 x 10^(-5)

7.935*10^{-5}\\\frac{7.935}{10^5}

A trick to finding 10 to the x power, x is the number of 0's. So 10^5 = 100000

\frac{7.935}{100000}\\

When dividing by tens, move the decimal to the left by the amount of 0's

So our answer is 0.00007935

5 0
3 years ago
Other questions:
  • A function has a constant doubling time. what type of function does this represent?
    9·2 answers
  • In a triangle two angles(in degrees) are 37 and 63 find the third angle? *
    10·2 answers
  • A triangle cannot be both A. obtuse and right. B. acute and isosceles. C. equilateral and equiangular. D. scalene and acute.
    14·2 answers
  • What is 6x / 8y (6+7) =
    9·1 answer
  • The answer is A true
    5·1 answer
  • What can u hold in ur right hand but not ur left????
    5·2 answers
  • Which inequality represents the range of the relation graphed below?
    5·1 answer
  • Sergei uses 4 cups of ice cream to make 3 milk shakes.
    11·1 answer
  • Help if you see a troll report them
    13·1 answer
  • Really confused as to what I need to do. I tried to solve for Y and got 69 but that didn't work. Am I supposed to use a^2 + b^2=
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!