Find the distance between (3, -3) and (2, 7). Round to the nearest hundredth if necessary. * 10 points

Short Response

garik1379 [7]

Answer:

(a)2(89x+84)

(b) $2(89x+84-x^2\pi)$

Step-by-step explanation:

The dimensions of the larger rectangular field are:

Length=5x + 12; Width = 9x + 14.

The dimensions of the smaller rectangular soccer field are:

Length=5x; Width = 9x.

(a)Area of the part of the field that is outside the soccer field

=Area of the larger rectangular field - Area of the Soccer Field

=(5x+12)(9x+14)-5x(9x)

=(5x)(9x)+70x+108x+168-5x(9x)

=178x+168

=2(89x+84)

(b)Radius of the Semicircular Fountain =2x

From Part (a),

Area of the larger rectangular field - Area of the Soccer Field=178x+168

Area of the Semicircular Fountain = $\dfrac{\pi r^2}{2} =\dfrac{\pi (2x)^2}{2} =\dfrac{4x^2\pi}{2} =2x^2\pi$

Area of the Field that does not include the soccer field or the fountain.

=Area of the larger rectangular field - Area of the Soccer Field-Area of the Semicircular Fountain

$=178x+168-2x^2\pi\\=2(89x+84-x^2\pi)$

8 0

4 years ago

Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming poo

kolezko [41]

Let x and y be the unit rates at which one large pump and one small pump works, respectively.

Two large/one small operate at a unit rate of

(1 pool)/(4 hours) = 0.25 pool/hour

so that

2x + y = 0.25

One large/three small operate at the same rate,

(1 pool)/(4 hours) = 0.25 pool/hour

x + 3y = 0.25

Solve for x and y. We have

y = 0.25 - 2x ==> x + 3 (0.25 - 2x) = 0.25

==> x + 0.75 - 6x = 0.25

==> 5x = 0.5

==> x = 0.1

==> y = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05

In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.

Now, if you have four each of the large and small pumps, they will work at a rate of

4x + 4y = 4 (0.1) + 4 (0.05) = 0.6

meaning they can fill 3/5 of a pool in one hour. If it takes time t to fill one pool, we have

(3/5 pool/hour) (t hours) = 1 pool

==> t = (1 pool) / (3/5 pool/hour) = 5/3 hours

So it would take 5/3 hours, or 100 minutes, for this arrangement of pumps to fill one pool.

6 0

3 years ago

Find y Solve the simultaneous equations 3x + 2y = 27 3x - Y = 9

lutik1710 [3]

Answer:

$y = 6$

Step-by-step explanation:

To find $y$ , we need to eliminate $x$ in this system of equations:

$3\cdot x + 2\cdot y = 27$ (1)

$3\cdot x - y = 9$ (2)

From (1) and (2):

$x = \frac{27-2\cdot y}{3}$

$x = \frac{9+y}{3}$

Then, we equalize both expressions and solve for $y$ :

$\frac{27-2\cdot y}{3} = \frac{9+y}{3}$

$27-2\cdot y = 9 + y$

$3\cdot y = 18$

$y = 6$

6 0

3 years ago

-2x+5/-5x-7 simplify

Yakvenalex [24]

Hello from MrBillDoesMath!

Answer:

-3x - 7

Discussion:

The order of operations states that multiplication and division are done before addition\subtraction. So

-2x +5/-5x - 7 =

-2x + (5/-5x) - 7 -

-2x -x -7 =

-3x - 7

Thank you,

MrB

3 0

3 years ago

What is 25% of 10....

Gekata [30.6K]

Answer: 2.5

10 X 25%

25% = 25/100 = 0.25

10x0.25 = 2.5

Hope this helps!!

8 0

3 years ago

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