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ale4655 [162]
3 years ago
14

The length of a rectangle is 4 units greater than its width w. Write an expression for the length of the rectangle.

Mathematics
1 answer:
Shkiper50 [21]3 years ago
6 0
If the length is four units greater than w, then it is equal to w+4.
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Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
PLEASE HELP!!!!!!!!!
stiv31 [10]

Answer:

The Best answer choice is D

Step-by-step explanation:

This one is the best choice because it fits the shape the best. The other ones don't complete the shape but D does.

Hope that helps!

5 0
3 years ago
Martha is late for class, so she races her 75 kg body up a 4.0 meter flight of stairs in only 2.3 seconds. What is Martha’s powe
vovangra [49]

Answer:

1.3\cdot 10^3\text{ J}

Step-by-step explanation:

Power is defined by work over time. In physics, work can be defined as the energy transferred over from an applied force over some distance. As a formula:

W=Fd, where F = force applied and d = distance that force is applied over.

*It is worth noting that F must be parallel to the distance travelled. If it is perpendicular, no work is done, and if it is at an angle, find the parallel component and use that for F.

In this case, the force applied must counter the force of gravity on Martha, which is given by F_g=mg, where m = Martha's mass and g = gravitational constant 9.8 m/s/s. Therefore, F_g=75\cdot 9.8=735\text{ N}. Since she raises her body 4.0 meters, the work done must be W=Fd=735\cdot 4=2940\text{ J}.

Since power is equal to work over time and t = 2.3 seconds, we have:

\displaystyle P=\frac{W}{t}=\frac{2940}{2.3}=\boxed{1278\text{ J}}\approx \boxed{1.3\cdot 10^3\text{ J}} (to two significant figures)

7 0
2 years ago
PLEASE HELP ASAP! need answer now!
BARSIC [14]

Answer:

i have the same question

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
HELPPPPP
mart [117]

answer is the first one and the last 2

7 0
3 years ago
Read 2 more answers
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