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3 years ago

The length of a rectangle is 3 m longer than its width.

1 answer:

6 0

Sometimes when you're given dimensions that differ by some amount, it is easier to work with their average value. Let x represent the average of length and width of the rectangle. The length and width differ from this average value by 1.5 m. Then the area is
.. (x +1.5)*(x -1.5) = 154
.. x^2 -2.25 = 154
.. x^2 = 156.25
.. x = 12.5
The width is 1.5 m shorter than this, or 11 m.

_____
Solved in the conventional way, you are looking for factors of 154 that differ by 3. This means you have to find the factors of 154, or use the quadratic formula.
.. 154 = 1*154 = 2*77 = 7*22 = 11*14 (the pair we want)
Once you have the factorization of 154, you have the answer. No equations are necessary, really.

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Solve the equation 3/x-4=1/5

rosijanka [135]

Answer:

The very first thing we want to do in this equation is to isolate x on one side (preferably the left side).

3/x - 4 = 1/5

We get rid of any constants first, by performing the inverse property;

The inverse property of subtraction is addition, so we add 4 to both sides:

+4 +4

3/x = 4 1/5

3 is being divided by x, so the inverse operation of division is multiplication. So we multiply by 1/3 on both sides.

x1/3 x1/3

X = 1 4/10 which simplifies to 1 2/5.

7 0

2 years ago

If m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17X-16)°, find each measure

cricket20 [7]

Answer: m∠ TUW = 38°

m∠WUV = 12°

m∠TUV = 103°

Step-by-step explanation:

Given: m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17x-16)°

Since, m∠TUV = m∠ TUW + m∠WUV

So, 17X-16 = (5x + 3) + (10x-5)

⇒ 17X-16 = 5x + 3 + 10x-5 [open parenthesis]

⇒ 17X-16 =5x + 10x +3 -5 [combine like trems]

⇒ 17X-16 =15x -2

⇒ 17X -15x = -2+16 [subtract 15x and add 16 on both sides]

⇒ 2x = 14

⇒ x= 7 [divide both sides by 2]

Now, m∠ TUW = (5(7) + 3)°= 38°

m∠WUV=(10(7)-5)° = 12°

m∠TUV=(17(7)-16)° = 103°

Hence, m∠ TUW = 38°

m∠WUV = 12°

m∠TUV = 103°

6 0

4 years ago

A pair of vertical angles has measures<br> (3x + 4) and ( 73 – 9)<br> What is the value of x?

sergij07 [2.7K]

Answer:

Step-by-step explanation:

Vertical angles are always equal to each other. So the answer is

3x + 4 = 73 - 9 Are you sure this is what the question is?

3x + 4 = 64 Subtract 4 from both sides

3x = 60 Divide by 3

3x/3 = 60/3

x = 20

6 0

3 years ago

A company knows that unit cost C and unit revenue R from the production and sale of x units are related by Upper C equals StartF

levacccp [35]

Answer:

$990 per unit.

Step-by-step explanation:

The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:

$C=\dfrac{R^2}{220000} +3221$

We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000.

Rate of Change of C,

$\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\$9, R=\$1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\$990 $ per unit$$