If the lines in a system of equations have different slopes and the same y-intercept, how many solutions does the system have?

Mathematics

1 answer:

allochka39001 [22]3 years ago

8 0

Answer:

289819

Step-by-step explanation:

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A flagpole is located at the edge of a sheer y = 70-ft cliff at the bank of a river of width x = 40 ft. See the figure below. An

Gnom [1K]

I would solve this using tangents. Let h be height of flagpole.
Set up 2 right triangles, each with a base of 40.
The larger triangle has height of "h+70"
Smaller triangle has height of 70.

Now write the tangent ratios:
$tan A = \frac{h+70}{40} , tan B = \frac{70}{40}$

Note: A-B = 9
To solve for h we need to use the "Difference Angle" formula for Tangent
$tan (A-B) = \frac{tanA - tanB}{1+tan A tan B}$
Plug in what we know:
$tan(9) = \frac{ \frac{h+70}{40} - \frac{70}{40}}{1+ (\frac{h+70}{40})(\frac{7}{4})}$
$tan (9) = \frac{ \frac{h}{40}}{ \frac{7h +650}{160}} = \frac{4h}{7h+650}$
$h = \frac{650 tan(9)}{4-7 tan(9)}$
$h = 35.6$

7 0

3 years ago

Find the answer to zero point 73 repeating times square root of 147 end square root and select the correct answer below. Also, i

liubo4ka [24]

Answer:

$\frac{511\,\,\sqrt{3} }{99}$ which is an irrational number

Step-by-step explanation:

Recall that the repeating decimal 0.7373737373... can be written in fraction form as: $\frac{73}{99}$

Now, let's write the number 147 which is inside the square root in factor form to find if it has some perfect square factors:

$147=7^2\,3$

Then, 7 will be able to go outside the root when we compute the final product requested:

$\frac{73}{99} \,*\,7\,\sqrt{3} =\frac{511\,\,\sqrt{3} }{99}$

This is an irrational number due to the fact that it is the product of a rational number (quotient between 511 and 99) times the irrational number $\sqrt{3}$