In ΔSTU, s = 1.6 cm, u = 9.5 cm and ∠U=24°. Find all possible values of ∠S, to the nearest 10th of a degree.

Answers

Answer 1

Answer:

Final answer:

In triangle STU, the possible values for ∠S, derived by using the law of sines, are approximately 10.2° and 169.8°.

Explanation:

The student wants to find all possible values of ∠S in ΔSTU, s=1.6 cm, u = 9.5 cm and ∠U=24°. This is a problem involving the laws of sines and cosines in trigonometry. By using the law of sines, we can find ∠S = sin⁻¹ ((sin U * s) / u) ≈ 10.2° or 169.8° (since sinx is positive in both the 1st and 2nd quadrants). It is important to note that ∠S and ∠U are not complimentary angles in a right triangle, therefore, both possible values of ∠S are valid if they meet the condition that the sum of ∠S, ∠T and ∠U should be equal to 180° in ΔSTU.

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Answers

$(4)/(2+\sqrt3+\sqrt7)\cdot(2-(\sqrt3+\sqrt7))/(2-(\sqrt3+\sqrt7))=(8-4\sqrt3-4\sqrt7)/(2^2-(\sqrt3+\sqrt7)^2)=(8-4\sqrt3-4\sqrt7)/(4-3-2√(3\cdot7)-7)\n\n=(8-4\sqrt3-4\sqrt7)/(-6-2√(21))=(-2(2\sqrt3+2\sqrt7-4))/(-2(3+√(21)))=(2\sqrt3+2\sqrt7-4)/(3+√(21))\cdot(3-√(21))/(3-√(21))\n\n=(6\sqrt3-2√(63)+6\sqrt7-2√(147)-12+4√(21))/(3^2-(√(21))^2)=(6\sqrt3-2√(9\cdot7)+6\sqrt7-2√(49\cdot3)-12+4√(21))/(9-21)$

$=(6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4√(21))/(-12)=(-8\sqrt3+4√(21)-12)/(-12)=(-4(2\sqrt3-√(21)+3))/(-12)\n\n=(2\sqrt3-√(21)+3)/(3)$

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$(4)/(2\sqrt3+\sqrt5)\cdot(2\sqrt3-\sqrt5)/(2\sqrt3-\sqrt5)=(8\sqrt3-4\sqrt5)/((2\sqrt3)^2-(\sqrt5)^2)=(8\sqrt3-4\sqrt5)/(4\cdot3-5)=(8\sqrt3-4\sqrt5)/(12-5)\n\n=(8\sqrt3-4\sqrt5)/(7)$

$(1) (4)/(2+√(3) +√(7)) \n \n or, (4)/(2+√(3) +√(7)) * (2 - √(3) -√(7))/(2-√(3)-√(7)) \n \n => \frac{ \sqrt[2]{3} - √(21)+3}{3} \n \n \n (2) \frac{4}{\sqrt[2]{3} + √(5)} \n \n or, \frac{4}{\sqrt[2]{3} + √(5)} * \frac{\sqrt[2]{3}-√(5)}{\sqrt[2]{3}-√(5)} \n \n => \frac{\sqrt[8]{3}-\sqrt[4]{5}}{7}$

Someone Help please?!?!

Answers

A is true statement.

4+2(5*7) please help me do this, km in year 10!

Answers

$4+2\cdot(5\cdot7)\n\nfirst:5\cdot7=35\n\n4+2\cdot35\n\nnext:2\cdot35=70\n\n4+70\n\nfinish:4+70=74$

First do 5*7 = 35
This is what the equation looks like then 4+2(35)
Since the 2 is next to the ( ) that means you multiply. So 35*2 = 70
Then the last part is 70+4 = 74 !

A restaurant sells tea for $1.50 plus 0.50 per refill. The restaurant brews enough tea for 4 refills per customer . The linear function that represents the total cost of rtea refills is C(r) = 0.5r + 1.5 . Describe an appropriate domain of this function . Make sure to identify the set of numbers appropriate to the domain

Answers

4.50Answer:

Step-by-step explanation:

If f(x)=x^2-11 for what values of x is f(x) < 25

Answers

The range of values for which f(x) < 25 are -6 < x < 6. The correct answer choice is e).

To find the values of x for which f(x) < 25, we substitute the expression for f(x) into the inequality and solve for x.

Given f(x) = x² - 11, we need to find the values of x that make f(x) less than 25.

x² - 11 < 25

Adding 11 to both sides, we have:

x² < 36

To determine the values of x that satisfy this inequality, we take the square root of both sides. Since the squareroot of a number can be positive or negative, we consider both positive and negative solutions.

x < √36

x > -√36

Simplifying, we get:

x < 6

x > -6

Therefore, the correct answer choice is e) -6 < x < 6, as it represents the range of values for which f(x) < 25. This means that x can take any value between -6 and 6 (excluding -6 and 6) for the inequality to hold true.

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Answer: D

Step-by-step explanation:

5²-11=14

6^2-11= 25

14>25

as the question asks for something lower than 25 not lower/equal to the answer is D.

How many triangles can be constructed with angles measuring 35º, 62º, and 83º?A. 0

B. 1

C. 2

D. an infinite number

Answers

B)OPTION B only 1 is your answer.

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