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OleMash [197]
3 years ago
11

The area of a rectangle is 14 m2 , and the length of the rectangle is 3 m less than double the width. find the dimensions of the

rectangle.
Mathematics
1 answer:
muminat3 years ago
3 0
Width =3.5, length = 4

Let's make a few equations to summarize what we know.:
a = 14
l = 2w -3
a = wl

Now let's substitute the expression for l into the expression for area and solve.
a = w(2w - 3)
a = 2w^2 - 3w
14 = 2w^2 - 3w

0 = 2w^2 - 3w - 14

which factors into
(2w - 7) (w + 2)

Solving for w
2w - 7 = 0
2w = 7
w = 3.5

w+2 = 0
w = -2

So w can be either 3.5 or -2. Since a negative width doesn't make sense, w = 3.5

Let's verify
w = 3.5
l = 2w - 3
l = 2*3.5 - 3
l = 7 - 3
l = 4
a = wl
a = 3.5 * 4
a = 14

So the width is 3.5 and the length is 4.

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iris [78.8K]

Answer:

The U.S. PPF rotates​ outward (abticlockwisely), increasing the ​x-axis intercept with no change in the y-axis intercept

Step-by-step explanation:

Fracking is a method of improving production capabilities on oil and gas production. Although, it usually leads to environmental pollution later, it does bring in higher yields of oil and gas.

If the oil and gas production on the x-axis increases without a simultaneous, almost equal increase in production of other goods and services (on the y-axis), the data points for the x-axis shift more to the right and the PPF rotates more anti-clockwisely outward, thereby increasing the intercept on the now improved x-axis and not too much change on the intercept of the y-axis.

8 0
3 years ago
What is the solution to 31|-3x + 9|=-18
Kisachek [45]

Answer:

No solutions

Step-by-step explanation:

31 times any positive number cannot be a negative number.

8 0
3 years ago
Find the sum of the following series. Round to the nearest hundredth if necessary,
Aneli [31]

Answer:

sum =   \frac{a( {r}^{n - 1} )}{r - 1}   \\  : but \: l = a( {r}^{n - 1} ) \\ 49152 = 3( {2}^{n - 1} ) \\ 16384 =  {2}^{n - 1}  \\  {2}^{n}  = 32768 \\  {2}^{n}  =  {2}^{15}  \\ n = 15 \\  \therefore \: sum =  \frac{3(2 {}^{15 - 1}) }{15 - 1}  \\  =  \frac{49152}{14}  \\  = 3510.9

3 0
3 years ago
Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 53 minutes. Billy could mow the lawn by himself
podryga [215]
5353 minutes = 89.22 hours
Maybe the figures should be 53 and 20??

Let's let Billy = A
The formula to use for work problems is
Time = (A*B) / (A+B)

53 = ( (A +20)* A) / (A +20 + A) )
53 = ( A^2 + 20A ) / (2A + 20)
A^2 + 20A -106A -1060
A^2 -86A -1060
A = 96.935
Bobby Mows in 116.935 minutes

3 0
4 years ago
What is 4855/200 simplified
EleoNora [17]

Answer:

The answer is 2427.5

Step-by-step explanation:

The fraction consists of two numbers and a fraction bar: 4,855/200

The number above the bar is called numerator: 4,855

The number below the bar is called denominator: 200

The fraction bar means that the two numbers are dividing themselves.

To get fraction's value divide the numerator by the denominator:

Value = 4,855 ÷ 200

To calculate the greatest common factor, GCF:

1. Build the prime factorizations of the numerator and denominator.

2. Multiply all the common prime factors, by the lowest exponents.

Factor both the numerator and denominator, break them down to prime factors:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

4,855 = 5 × 971;

4,855 is a composite number;

In exponential notation:

200 = 2 × 2 × 2 × 5 × 5 = 23 × 52;

200 is a composite number;

3 0
3 years ago
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