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
Leno4ka [110]
3 years ago
5

A new community Wellness Complex is being built in Madison. The perimeter of the rectangular playing field is 446 yards. The len

gth of the field is 7 yards less than quadruple the width. What are the dimensions of the playing field?
Mathematics
1 answer:
vovikov84 [41]3 years ago
7 0

Answer:

The length of the rectangular playing field is 177 yards and the width is 46 yards

Step-by-step explanation:

Let

x -----> the length of the rectangular playing field

x -----> the width of the rectangular playing field

we know that

The perimeter of the  rectangular playing field is

P=2(x+y)

P=446 yd

so

446=2(x+y) ------> equation A

x=4y-7 -----> equation B

Solve the system by substitution

Substitute equation B in equation A and solve for y

446=2(4y-7+y)

223=5y-7

5y=223+7

5y=230

y=46

Find the value of x

x=4(46)-7

x=177

therefore

The length of the rectangular playing field is 177 yards and the width is 46 yards

You might be interested in
Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩
klemol [59]

\mathbf r'(t)=\langle\sin9t,\sin6t,9t\rangle


\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt


\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle


\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1

\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2

\displaystyle\int9t\,\mathrm dt=\frac92t^2+C_3


With the initial condition \mathbf r(0)=\langle4,6,3\rangle, we find


\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9

\dfrac16\cos0+C_2=6\implies C_2=\dfrac{35}6

\dfrac92\cdot0^2+C_3=3\implies C_3=3


So the particular solution to the IVP is


\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle

4 0
3 years ago
24) sin x = 1/3<br> Find cos x.
liq [111]

Answer:

\frac{2\sqrt{2} }{3}

Step-by-step explanation:

The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;

sin x = ( opposite / hypotenuse)

The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;

The adjacent side would be;

\sqrt{9-1}=\sqrt{8}=2\sqrt{2}

The cosine of an angle is given as;

cos x = (adjacent side / hypotenuse)

Therefore, the cos x would be;

\frac{2\sqrt{2} }{3}

6 0
3 years ago
Read 2 more answers
The radius of a sphere is 1/3 ft what is the approximate volume of the sphere
Katen [24]

Answer:

0.16 ft

Step-by-step explanation:

v = 4/3 πr³

v = 4/3 × 3.142 × 1/3 × 1/3 × 1/3

v = 0.16 ft

7 0
2 years ago
4(x + 2) = 2 (x – 6)
andreev551 [17]
The correct answer for this would be -10
6 0
3 years ago
Read 2 more answers
ABCD is a parallelogram and this figure is NOT drawn to scale.
dimulka [17.4K]
The angle does not matter. Think of it as finding the other side to a triangle. Use a ^{2} +b^2 =c^2

a=39 (line AB)
b=b (the leg we need to find)
c=89 (line BD)

39^2 + b^2 = 89^2
1521 + b^2 = 7921
(subtract the 1521 from both sides)
b^2 = 6400
(square root both sides)
\sqrt{(b^2)} =  \sqrt{6400} &#10;

b = 80
AD=80
7 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone help me on this please? thanks
    14·2 answers
  • Please tell me the answer to #22
    7·1 answer
  • Jack says 0.90 is between 0.9 and 0.91. Is he correct? Explain.
    5·1 answer
  • Find (10)<br> f(x) = 3x - 2<br> a. 1<br> b. 0<br> C.-8<br> D.-1
    8·1 answer
  • Help two helpless triangles?
    9·2 answers
  • The formula V=lwh is used to calculate the volume of a rectangular prism. What is the equation solved for h?
    15·2 answers
  • Evaluate y(y-x); use x =1, and y=4​
    13·1 answer
  • Find the value of 3v- 10 given that 2v- 7 = 9
    8·2 answers
  • Write an Equation given the point (1, -1) and a rate of 2.
    15·2 answers
  • Kate multiplied two binomials using the distributive property. She made a
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!