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
nlexa [21]
3 years ago
10

The area of a rectangular rug is given by the trinomial r squared minus 4 r minus 77r2−4r−77. What are the possible dimensions o

f the​ rug? Use factoring.
Mathematics
2 answers:
Alina [70]3 years ago
7 0
R2-4r-77 = (r-11)(r+7)
r has to be greater than 11 in order for the formula to represent the area of a rug since a side length cannot be less than or equal to 0.
olchik [2.2K]3 years ago
6 0

Answer:

r>\frac{4 +\sqrt{23732} }{154}  \approx1.03\\

Step-by-step explanation:

The area of the rectangular rug is given by this equation:

77r^2-4r-77

The area must be a number greater than 0 since a negative area, or an area equal to 0 wouldn't have much sense. So:

77r^2-4r-77>0

Let's find the roots of this equation using the quadratic formula:

r=\frac{-b\pm \sqrt{b^2-4ac} }{2a} =\frac{-(-4)\pm\sqrt{(-4)^2-(4)(77)(-77)} }{2(77)} \\\\r=\frac{4 \pm \sqrt{23732} }{154} \\\\r_1=\frac{4 +\sqrt{23732} }{154} \approx1.03\\\\r_2=\frac{4 - \sqrt{23732} }{154} \approx-0.97

Now, let's evaluate the area for r>r_1 for example r=1.05:

A=77(1.05)^2-4(1.05)-77=3.6925>0

The result is greater than zero, so for r>r_1 the values make sense.

Now let's evaluate the area for r_2 for example r=0.5 and r=-0.7:

A=77(0.5)^2-4(0.5)-77=-59.75

The result is less than zero, so for r_2 the values don't make sense.

Now, let's evaluate the area for r for example r=-1:

A=77(-1)^2-4(-1)-77=4>0

The result is greater than zero, so for r the values make sense

However, since negative values of r wouldn't make much sense (I never heard about of -8 inches for example) the possible dimensions of the​ rug are just:

r>\frac{4 +\sqrt{23732} }{154}  \approx1.03\\

You might be interested in
Geometric mean of 5 and 405
Anvisha [2.4K]
45.2216762184
It is the square root of
405x5
6 0
3 years ago
The map shows the location of the mall, library, and school in the city; Brittany travels from the school to the mall and then f
Shkiper50 [21]

Answer:A) 8 miles

Step-by-step explanation:

8 miles

7 0
3 years ago
I need help, help me plz !!!!! Match the verbal expression (term) with its algebraic expression (definition). Match Term Definit
Talja [164]

Answer:

Four less than an unknown value E) y-4

Quotient of a variable and four B) \frac{z}{4}

Some number to the power of four A) a^4

Four times an unknown value D) 4x

Four more than some number C) b+4

Step-by-step explanation:

Let's analyze each statement separately:

- Four less than an unknown value --> this means that we have to subtract 4 to an unknown value. Calling y the unknown value, it means we have to write

y-4

- Quotient of a variable and four --> this means we have to divide a variable by 4. Calling z the unknown variabl, it means we have to write

\frac{z}{4}

- Some number to the power of four --> this means that we have to write the power of a number, in the form a^m, where m in this case is equal to 4. Calling a the unknown number, it means we have to write

a^4

- Four times an unknown value --> this means that we have to multiply an unknown value by 4. Calling x our unknown values, we have to write

4x

- Four more than some number --> this means we have to add 4 to an unknown number. Calling b the unknown number, it means we have to write

b+4

7 0
3 years ago
Read 2 more answers
Walmart is selling 24 bars Gatorade for $8.44 what is the price per bottle​
Eva8 [605]

Answer:

About $0.35 per bottle.

Step-by-step explanation:

8.44 / 24 = .3516

3 0
3 years ago
Read 2 more answers
Find the Volume. Plz Help
koban [17]

Answer:

B

Step-by-step explanation:

V = \frac{l*w*h}{2} = \frac{18*12*9}{2} = \frac{1944}{2} = 972

3 0
3 years ago
Read 2 more answers
Other questions:
  • Simplify 3x + (-12x) - 5x. -14x -9x 10x 20x
    14·2 answers
  • Find the roots of the parabola given by the following equation <br> 2x^2+5X-9=2x
    13·1 answer
  • Which of the following describe an angle with a vertex at A?
    12·1 answer
  • Please help will name brainiest<br> 6n+11=-13 what in n
    14·1 answer
  • If f(x) = 2x, which of the following shows the graph of f(x) = 2(x) + 2?
    10·2 answers
  • Susie's bakery is having a sale on all cookies. The bakery is offering a sale pack of 4 cookies for $2.80. What is the unit pric
    8·1 answer
  • Please help me with this homework
    11·2 answers
  • Help!!<br><br><br> For question just posted
    15·1 answer
  • The cost in dollars of producing x vehicles for a company is given by C(x)=1200x+5500
    10·1 answer
  • Please explain this to me step by step. Thanks!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!