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
Natasha2012 [34]
3 years ago
5

Gracelyn has multiple sticks of different lengths to build a triangle for a class project. Which 3 lengths could Gracelyn choose

to build the triangle?
Mathematics
1 answer:
romanna [79]3 years ago
8 0
Hello

11 cm, 25 cm, 15 cm
if you add the lengths of two sides of the triangle, it must be greater than the length of the third side

therefore, the only possible lengths are 11 cm, 25 cm, 15 cm

Have a nice day
You might be interested in
we want to build a box with square base of side x and height and in such a way that the volume is 128 cubic inches. If we know t
sergij07 [2.7K]

Answer:

4 in × 4 in × 8 in or  

6.47 in × 6.47 in × 3.06 in

Step-by-step explanation:

Data:

(1)                  V = 128 in³

(2)                  l = w = x

(3) 4(l + w + h) = 64 in  (There are 12 edges)

Calculation:

The formula for the volume of the box is

(4)                 V = lwh

(5)              128 = x²h          Substituted (1) and (2) into (4)

(6)                  h = 128/x²     Divided each side by x²

          l + w +h = 16            Divided (1) by 4

          x + x + h = 16           Substituted (2) into 6

(7)          2x + h = 16           Combined like terms

     2x + 128/x² = 16           Substituted (6) into (7)

        2x³ + 128 = 16x²        Multiplied each side by x²

2x³ - 16x²+ 128 = 0            Subtracted 16x² from each side

    x³ - 8x² + 64 = 0           Divided each side by 2

According to the Rational Zeros theorem, a rational root must be a positive or negative factor of 64.

The possible factors are ±1, ±2, ±4, ±8, ±16, ±32, ± 64.

After a little trial-and-error with synthetic division (start in the middle and work down) we find that x = 4 is a zero.              

4|1   -8     0   64

 <u>|      4  -16  -64 </u>

   1  -4  -16      0

So, the cubic equation factors into (x - 4)(x² - 4x + 16) = 0

We can use the quadratic formula to find that the roots of the quadratic are

x = 2 - 2√5 and x = 2+ 2√5

We reject the negative value and find that there are two solutions to the problem.

x = 4 in and x = 2 + 2√5 ≈ 6.472 in

Case 1. x = 4 in

h = 128/x² = 128/4² = 128/16 = 8 in

The dimensions of the box are 4 in × 4 in × 8 in

Also, 4(l + w + h) = 4( 4 + 4 + 8) = 4 × 16 =  64 in

Case 2. x = 6.472 in

h = 128/x² = 128/6.472² = 128/41.89 = 3.056 in

The dimensions of the box are 6.47 in × 6.47 in × 3.06 in

Also, 4(l + w + h) = 4( 6.47 + 6.47 + 3.06) = 4 × 16.00 =  64 in

The two solutions are

(a) 4 in       × 4 in      × 8 in

(b) 6.47 in × 6.47 in × 3.06 in    

7 0
3 years ago
For the last 4.5 hours, the temperature has decreased at a rate of 2.8 Degrees Fahrenheit per hour. Which best represents the ov
myrzilka [38]

Answer:

-12.6

Step-by-step explanation:

its decreasing that eliminates 3 and 4

and the decrease is bigger than 1.6 so that eliminates 2

making the obvious answer number 1

5 0
3 years ago
Read 2 more answers
A boat can travel 64 miles on 7 gallons of gasoline. How much gasoline will it need to go 24 miles?
Oksanka [162]

Answer:192

Step-by-step explanation:

5 0
3 years ago
The sum of two numbers is 12<br> and their product is 32.<br> What are the two numbers ?
kumpel [21]

Answer:

8 and 4

Step-by-step explanation:

8 x 4= 32

8+4 = 12

8 0
3 years ago
The answer is is 26, -44, but i dont understand how to solve it. can you explain?
Anna [14]
║a+9║/7=5
you multiply 7 on both sides which cancel out 7.
now it ║a=9║=35
and now it would be a+9=35 and a+9=-35 then solve it.
35-9 and 9-(-35)= 26 and -44
hope this helped!
4 0
3 years ago
Other questions:
  • To add two numbers with the same sign, add the numbers and give the sum the __ sign.
    8·2 answers
  • Select the correct answer. In Δ``ABC, which trigonometric ratio equals `3/2`? A. sin B B. tan B C. tan C D. sin C
    11·2 answers
  • Solve for x <br> r + 23 = -22
    8·1 answer
  • How to do you divide fractions? I forgot???
    10·2 answers
  • I don't have a calculator with me and I need, rounded to 2 places, ln 4.3
    13·1 answer
  • Given A and B are vertical angles with m∠A = 20x + 10 and m∠B = 30x – 10. What is x? 3.6 4 2 9
    8·2 answers
  • 1/3 x 1/4 = ?????????
    11·2 answers
  • The ratio of solid beads to clear beads in a vase is 820. Select all the correct statements that tell if the operations will giv
    9·1 answer
  • Solve.<br> Х<br> -<br> - 5<br> - 8<br> The solution is x=
    11·2 answers
  • A. 30.3 units2<br> B. 21.61 units2<br> O C. 14.65 units2<br> D. 13.1 units2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!