It is 2.7 from Salma's house to the nearest mailbox. How far is it in meters?

A rectangle has a length of 12 yards less than 3 times its width. If the area of the rectangle is 135 square yards, find the len

Aleonysh [2.5K]

Answer:

The length is 15 yards

Step-by-step explanation:

Given

Represent the width with W and length with L: So

$Area = 135yd^2$

$L=3W - 12$

Required

Determine the length of the rectangle:

Area is calculated as thus:

$Area = L * W$

Substitute 3W - 12 for L and 135 for Area

$135= (3W - 12) * W$

$135= 3W^2 - 12W$

Reorder:

$3W^2 - 12W - 135= 0$

Divide through by 3

$W^2 - 4W - 45 = 0$

Expand:

$W^2 - 9W + 5W - 45 = 0$

$W(W - 9) + 5(W - 9) = 0$

$(W + 5)(W-9) = 0$

$W + 5 = 0$ or $W - 9 = 0$

$W = -5$ or $W = 9$

But width can't be negative

So:

$W = 9$

Recall that: $L=3W - 12$

$L = 3 * 9 - 12$

$L = 15$

<em>Hence, the length 15 yards</em>

4 0

3 years ago

Add<br>(4-4i)+(3-2i)<br>Write as complex number in standard form

Viefleur [7K]

Answer: (4-4i)+(3-2i) = 7-6i

Step-by-step explanation:

To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. For instance, the sum of 4 -4i and 3 - 2i is 7 -6i. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part.

8 0

3 years ago

What are the distances from the point (x,y) to the focus of the parabola and the directrix, select two answers

yulyashka [42]

Answer:

3,5

Step-by-step explanation:

axis

6 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

Which number is between 1/6th and 1/4th

bazaltina [42]

1/5...
This question should be relatively easy for a high schooler...

3 0

4 years ago

Read 2 more answers