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3 years ago

EMERGENCY PLEASE HELP STRUGGLING! The triangles in each pair are similar.

Mathematics

1 answer:

Ludmilka [50]3 years ago

5 0

Answer: The missing length is 120 {option C}

Step-by-step explanation: What we have in the question is a triangle placed on top of another triangle and as shown in the attached diagram we can separate them into triangles BFC and GFH.

A close observation shows that line BC is parallel to line GH. Hence we have two similar triangles, and we can determine their similarity ratios as follows;

BF/FC = GF/FH

Similarly BF/BC = GF/GH

We can also express the following ratio

FC/FH = BC/GH

Therefore to calculate the missing side, which is GF, we can use the ratio

FC/FH = FB/FG

30/100 = 36/FG

By cross multiplication we now have 30 (FG) = 100 (36)

30FG = 3600

Divide both sides of the equation by 30

FG = 120

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How do I solve these problems? ln(x) = 5.6 + ln(7.5) and log(x) = 5.6 - log(7.5)

SOVA2 [1]

Use the rules of logarithms and the rules of exponents.

... ln(ab) = ln(a) + ln(b)

... e^ln(a) = a

... (a^b)·(a^c) = a^(b+c)

_____

1) Use the second rule and take the antilog.

... e^ln(x) = x = e^(5.6 + ln(7.5))

... x = (e^5.6)·(e^ln(7.5)) . . . . . . use the rule of exponents

... x = 7.5·e^5.6 . . . . . . . . . . . . use the second rule of logarithms

... x ≈ 2028.2 . . . . . . . . . . . . . use your calculator (could do this after the 1st step)

2) Similar to the previous problem, except base-10 logs are involved.

... x = 10^(5.6 -log(7.5)) . . . . . take the antilog. Could evaluate now.

... = (1/7.5)·10^5.6 . . . . . . . . . . of course, 10^(-log(7.5)) = 7.5^-1 = 1/7.5

... x ≈ 53,080.96

8 0

3 years ago

If the side length of a square pyramid is triple and the slant height is divided by 5 what would be the formula to find the modi

valentina_108 [34]

If the original side length is "s" and the original slant height is "h", the original surface area is
.. S = (base area) +(lateral area)
.. S = s² +(1/2)*(4s)*h
.. S = s(s +2h)

Now, if we make these replacements: s ⇒ 3s, h ⇒ h/5, we have
.. S' = (3s)(3s +2h/5)
.. S' = 9s² +(6/5)s*h . . . . . . . the formula for the modified area (in terms of original dimensions)

_____
Of course, in terms of the modified dimensions, the formula is the same:
.. S' = s'(s' +2h')

5 0

3 years ago

Factor completely −5x2 + 10x − 25.

garri49 [273]

5(2x-7)

Hope this helps !

Have a great day!

3 0

3 years ago

LONG WORD PROBLEM I KNOW! PLEASE ILL GIVE THANKS BRAINLIEST AND POINTS FOR THIS ANSWER! PLEASE!

11Alexandr11 [23.1K]

Answer:
5X + 8Y >= 300; intersection at (-20, 50)
Step-by-step explanation:
let t = work hours
0 < t < 30
X = time lawn mowing
Y = time babysitting.
X + Y < 30
5X + 8Y >= 300
We could solve...
X < 30 - Y
5(30 - Y) + 8Y >=300
150 - 5Y + 8Y >= 300
3Y >=150
Y >=50
then X < -20
intersection at (-20, 50)

5 0

3 years ago

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Artist 52 [7]

Answer:

lol

Step-by-step explanation:

8 0

3 years ago