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Find the value of each variable. Answer in simplest radical form.

Vlada [557]

Answer:

x = 5√3; y = 5

Step-by-step explanation:

Finding y: The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:

sin 30° = 1/2 = y/10

Solve the equation of ratios

1 y

-- = ----- using cross-multiplication first: 2y = 10 → y = 5

2 10

We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:

x² + y² = 10² = 100 → x² = 100 - y² = 100 - 5² = 75

If x² = 75, then x = ±√75 = ± (√25)·(√3) → ±5√3

Since lengths are always positive, take x = 5√3 as the answer.

8 0

3 years ago

A 10-foot by 12-foot wall has two windows that measure 3 feet by 5 feet each.

musickatia [10]

12 ft maybe? i dunno im sorry if this is wrong

6 0

3 years ago

The following triangle. check all that apply

Amiraneli [1.4K]

Obtuse and isosceles

Isosceles means that at least two of the sides are congruent or equal.

Obtuse means that one angle of the triangle is greater than 90 degrees.

So, your answer is D and E

:)))

4 0

3 years ago

Read 2 more answers

A taco stand sells tacos for $3.25 each. The stands expenses for the day are $210. Define your variables and write an inequality

Julli [10]

Given:

Let P= profit
let n= no. of tacos sold per day

Sol'n:

P= 3.25n-210
the profit needs to be positive, thus

3.25n>210

n>210/3.25

n> 64.615

they can only sell whole tacos, therefore they must sell at least 65 tacos to make a profit and that profit is:

P=3.25n-210

P=3.25*65 - 210

P= 211.25 -210

P= 1.25

$1.25 profit

3 0

3 years ago

How many zeroes do we write when we write all the integers 1 to 243 in base 3?

Monica [59]

Answer:

289 numbers

Step-by-step explanation:

Above you will find the list of integers from 1 to 243 in base 3:

(1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2000, 2001, 2002, 2010, 2011, 2012, 2020, 2021, 2022, 2100, 2101, 2102, 2110, 2111, 2112, 2120, 2121, 2122, 2200, 2201, 2202, 2210, 2211, 2212, 2220, 2221, 2222, 10000, 10001, 10002, 10010, 10011, 10012, 10020, 10021, 10022, 10100, 10101, 10102, 10110, 10111, 10112, 10120, 10121, 10122, 10200, 10201, 10202, 10210, 10211, 10212, 10220, 10221, 10222, 11000, 11001, 11002, 11010, 11011, 11012, 11020, 11021, 11022, 11100, 11101, 11102, 11110, 11111, 11112, 11120, 11121, 11122, 11200, 11201, 11202, 11210, 11211, 11212, 11220, 11221, 11222, 12000, 12001, 12002, 12010, 12011, 12012, 12020, 12021, 12022, 12100, 12101, 12102, 12110, 12111, 12112, 12120, 12121, 12122, 12200, 12201, 12202, 12210, 12211, 12212, 12220, 12221, 12222, 20000, 20001, 20002, 20010, 20011, 20012, 20020, 20021, 20022, 20100, 20101, 20102, 20110, 20111, 20112, 20120, 20121, 20122, 20200, 20201, 20202, 20210, 20211, 20212, 20220, 20221, 20222, 21000, 21001, 21002, 21010, 21011, 21012, 21020, 21021, 21022, 21100, 21101, 21102, 21110, 21111, 21112, 21120, 21121, 21122, 21200, 21201, 21202, 21210, 21211, 21212, 21220, 21221, 21222, 22000, 22001, 22002, 22010, 22011, 22012, 22020, 22021, 22022, 22100, 22101, 22102, 22110, 22111, 22112, 22120, 22121, 22122, 22200, 22201, 22202, 22210, 22211, 22212, 22220, 22221, 22222, 100000)

If you count them, you will find that there are 289 numbers in total!

8 0

3 years ago