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2 years ago

In ΔDEF, the measure of ∠F=90°, DF = 55, FE = 48, and ED = 73. What ratio represents the tangent of ∠D?

Mathematics

1 answer:

klemol [59]2 years ago

8 0

Answer:

$\frac{48}{55}$

Step-by-step explanation:

In problems like this, it always helps to draw a picture.

-> See attached for the picture I drew (<em>not to scale</em>)

Now, the trigonometric function tangent can be found with opposite / adjacent

When looking at ∠D, the opposite side if 48 and the adjacent side is 55.

O / A = 48 / 55

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Ghella [55]

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3 years ago

How many 3 digit numbers are possible when a) the leading digit cannot be zero and the number must be a multiple of 4?

guajiro [1.7K]

Step-by-step explanation:

I assume the digits can be repeated.

so, e.g. 555 is a valid number for this problem, right ?

that means we start with permutations with repetition :

n^r

n = the total number of items to pick from.

r = the number of items being picked per result.

we have 10 digits (0,1,2,3,4,5,6,7,8,9), and we pick 3 of them.

that gives us (with very little surprise, I hope)

10³ = 1000 different possible numbers from 000 to 999.

from these numbers we eliminate all with leading 0.

as we handled all digits the same way and with the same priority, there is the same amount of numbers for every digit in the leading position.

that means 1/10 of the total amount of numbers has a leading 0, or a leading 1, or a leading 2, ...

so, we need to subtract 1/10 × 1000 from 1000 :

1000 - 1000×1/10 = 1000 - 100 = 900

that would be the numbers 100 to 999.

and we have one more condition : the number must be a multiple of 4.

how many are there ?

well, that's the funny thing about numbers : from all numbers 1/2 of them are multiples of 2 (or divisible by 2), 1/3 of them are multiples of 3 (or divisible by 3), and ... you guessed it, 1/4 of them are multiples of 4 (or divisible by 4). and so on.

and so, 1/4 of our 900 numbers are multiples of 4 :

1/4 × 900 = 225

so, there are 225 possible 3-digit numbers that are multiples of 4 and do not start with a 0.

6 0

2 years ago

Social studies Geometry P.11 Similarity and altitudes in right triangles CEZ You have priz If SU = 28 and UV = 6, what is TU? T

Alex777 [14]

Answer:

TU ≈ 12.96

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

(leg of outer triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

TU² = UV × SU = 6 × 28 = 168 ( take square root of both sides )

TU = $\sqrt{168}$ ≈ 12.96 ( to the nearest hundredth )

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3 years ago

A hotel purchases 150 bath towels for 1,800. The hotel later purchases 40 more bath towels for x. If the unit cost remains the s

olga2289 [7]

1800/150 = 12
12*40 = 480
480 dollars

8 0

3 years ago

Read 2 more answers

•The following system of functions are shown on the graph:

Setler79 [48]

Answer:

Neither

Step-by-step explanation:

knowing that the system are y=-x+6 and y=x+2, then: x+2=-x+6; x+x=6-2; 2x=4; x=2, and replacing x in y we have: y=-2+6=4 and y=2+2=4, finally tha solution to sistem is (2,4)

7 0

3 years ago