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3 years ago

If possible, factor 169x^2 − y^2.

Mathematics

1 answer:

Mama L [17]3 years ago

7 0

Answer:

(13x - y)(13x + y)

Step-by-step explanation:

Both 169x^2 and y^2 are perfect squares.

The (special) rule for factoring the difference of two squares is

a^2 - b^2 = (a - b)(a + b).

Therefore, 169x^2 and y^2 = (13x - y)(13x + y)

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Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who

zmey [24]

Answer:

18.7939 m

Step-by-step explanation:

-Let x be the distance between John and clock tower.

-Let y be the vertical distance from the eyes of the two men standing to the top of the clock tower.

#Taking the right triangle ACD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5$

#Taking the right triangle ABD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5$

#We equate the two yo solve for x and y;

$(x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939$

Hence, John's distance from the tower's base is 18.7939 m

8 0

3 years ago

The mathematics faculty at a college consists of 11 professors, 12 associate professors, 7 assistant professors, and 6 instructo

Nikolay [14]

Answer:

The probability of choosing a professor or an instructor is 47.22%.

Step-by-step explanation:

Given that the mathematics faculty at a college consists of 11 professors, 12 associate professors, 7 assistant professors, and 6 instructors, if a faculty member is selected, to find the probability of choosing a professor or an instructor the following calculation must be performed:

11 + 12 + 7 + 6 = 100

11 + 6 = X

36 = 100

17 = X

17 x 100/36 = X

1700/36 = X

47.22 = X

The probability of choosing a professor or an instructor is 47.22%.

8 0

3 years ago

At the local burger restaurant, you can get 4 value meals for $20.44. How much is each value meal?

liubo4ka [24]

Answer:

the answer is 5 dollars

Step-by-step explanation:

7 0

3 years ago

Perform the indicated operation <br> 14-(-10)

lukranit [14]

24. two negatives become a positive

4 0

3 years ago

Read 2 more answers

There are 28 student desks in Ms.Johnson's.Each desk measures 26.17 inches long.If you were to line up all the desk end-to-end,h

iragen [17]

Answer:

To find the answer to this question we need to multiply the number of desks by the length of each desk.

26.17 × 28 = 732.76

So the final answer is 732.76 inches

Step-by-step explanation:

4 0

3 years ago