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
Lubov Fominskaja [6]
3 years ago
6

A rope is √250 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 3:2 . What is the

length of the longer piece expressed in simplest radical form?
Mathematics
2 answers:
AVprozaik [17]3 years ago
7 0

Answer:

Length of longer piece is 15√10 units

Step-by-step explanation:

Firstly we will write √250 in the simplest radical form. i.e.

√250 = 5√10

Now we have a rope of length 5√10 and we have to divide it in ratio 3:2.

Let 3x be the length of the longer piece

and 2x be the length of the smaller piece.

So, the total length of rope is 5x.

Hence, we can write length of longer piece = \dfrac{3x \times 5\sqrt{10}}{5x}

⇒ Length of longer piece = 3 × 5√10

⇒ Length of longer piece = 15√10 units

ExtremeBDS [4]3 years ago
4 0

what we do is, simply split the whole amount by the sum of the ratios and distribute accordingly, so in this case we'll split up √250 by (3+2) and distribute to each ratio, let's do so

\bf \cfrac{\textit{longer piece}}{\textit{shorter piece}}\qquad 3:2\qquad \cfrac{3}{2}\qquad \qquad \cfrac{3\cdot \frac{\sqrt{250}}{3+2}}{2\cdot \frac{\sqrt{250}}{3+2}}\qquad \begin{cases} 250=&5\cdot 5\cdot 10\\ &5^2\cdot 10 \end{cases} \\\\\\ \cfrac{3\cdot \frac{\sqrt{5^2\cdot 10}}{5}}{2\cdot \frac{\sqrt{5^2\cdot 10}}{5}}\implies \cfrac{3\cdot \frac{5\sqrt{10}}{5}}{2\cdot \frac{5\sqrt{10}}{5}}\implies \cfrac{3\sqrt{10}}{2\sqrt{10}}~\hfill \stackrel{\textit{longer piece}}{3\sqrt{10}}

You might be interested in
Can someone please help me, please
e-lub [12.9K]
I can only help you if you give me a lot of points
5 0
3 years ago
Marley has read 112.5 pages of a book. By the end of today, she plans to have read at least a total of 360 pages. If she reads 4
Vinvika [58]
5.5 hours.  5 hours and 30 minutes

The total pages she wants to finish (360) minus the pages she has read (112.5) equals to 247.5
Then divide it by the 45 (the rate of pages she reads per hour) 
5.5 hours.

6 0
3 years ago
What is 5.38 in its expanded form
solmaris [256]
5.38 in expanded form is 5 + 0.3 + 0.08

Expanded form means you have to break it apart into addition.
5 0
3 years ago
Read 2 more answers
Jose will travel 268 km with his family this weekend. How many miles will he travel? Round to the nearest hundredth.
Vinil7 [7]
I think its 200 as if you convert to miles it's 166.527 and rounded to nearest hundredth is 200
8 0
3 years ago
Thank you in advance!
Makovka662 [10]

Vertex: (-2,1)

Maximum or Minimum: The graph has minimum point and gives minimum value because the minimum point gives the least y-value. That's why it is called minimum.

End of behavior:

When x approaches positive infinity, f(x) will approach positive infinity.

When x approaches negative infinity, f(x) will approach positive infinity as well.

Why no solution:

The graph doesn't intercept any x-axis. Therefore the graph doesn't have any solutions.

y-intercept: (0,5)

describe shape of the graph:

The graph decreases when x<0 and increases when x>0.

x<0 is concave up but decreasing

x>0 is concave up but increasing

8 0
3 years ago
Other questions:
  • Harlen has a wooden board that is 2 and one-fourth feet long. He needs to cut the board into one half-foot piece. How many can o
    9·1 answer
  • Evaluate this exponential expression. 3 • (5 + 4)2 – 42 = A. 345 B. 15 C. 227 D. 46
    6·1 answer
  • Calculate each mountain path grade to the nearest percent.
    13·1 answer
  • -6K – 3 = 39. Please solve this equation for K. Type your work in.
    11·1 answer
  • Susan ate part of a pizza. She ate more than 1/3 of the pizza. How much of the pizza might Susan have eaten?
    13·1 answer
  • 1. Bigkis o tulungan para sa kapwa kapanginabangan.
    15·1 answer
  • Solve for the roots: x3-2x2+3x-6
    11·2 answers
  • The system of equations
    8·1 answer
  • What is an equation of the line that passes through the points (4, 4) and (8, 1)?
    8·1 answer
  • A Cylinder has a base diameter of 4cm and a height of 2cm. What is it’s volume in cubic cm, to the nearest tenths place
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!