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KonstantinChe [14]

2 years ago

9

Matilda needs at least $112 to buy a new dress. She already has saved $40. She earns $9 an hour by babysitting. Write an inequal

ity that can be used todetermine how many hours, X, Matilda will need to buy the dress?

1 answer:

Ymorist [56]2 years ago

6 0

Answer:

8

Step-by-step explanation:

9*8 = 72 + 40 = 112

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State the number of possible triangles that can be formed using the given measurements.

romanna [79]

Answer: 39) 1 40) 2

41) 1 42) 0

<u>Step-by-step explanation:</u>

39) ∠A = ? ∠B = ? ∠C = 129°

a = ? b = 15 c = 45

Use Law of Sines to find ∠B:

$\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o$

If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°

If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°

Since ∠A cannot be negative then ∠B ≠ 165°

∠A = 36° ∠B = 15° ∠C = 129° is the only valid solution.

40) ∠A = 16° ∠B = ? ∠C = ?

a = 15 b = ? c = 19

Use Law of Sines to find ∠C:

$\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o$

If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°

If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°

Both result with ∠B as a positive number so both are valid solutions.

Solution 1: ∠A = 16° ∠B = 144° ∠C = 20°

Solution 2: ∠A = 16° ∠B = 4° ∠C = 160°

41) ∠A = ? ∠B = 75° ∠C = ?

a = 7 b = 30 c = ?

Use Law of Sines to find ∠A:

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o$

If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°

If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°

Since ∠C cannot be negative then ∠A ≠ 167°

∠A = 13° ∠B = 75° ∠C = 92° is the only valid solution.

42) ∠A = ? ∠B = 119° ∠C = ?

a = 34 b = 34 c = ?

Use Law of Sines to find ∠A:

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o$

If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°

If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°

Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°

There are no valid solutions.

6 0

3 years ago

Calculate the scale factor of ALMN to AOPQ. Enter answer as a whole

Troyanec [42]

Step-by-step explanation:

the scale factor is 1

1/1

both triangles are similar and the scale factor is 1/1

....................

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3 years ago

What does 27.75n represent

Phoenix [80]

Answer:

There is $27.75 and n is the number of books.

<h2><em>hope this helped</em></h2>

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3 years ago

Xinran walks 3 mi/h uphill, 4 mi/h on flat land and 5 mi/h downhill. If he walks one mile uphill, then one mile on flat land and

Dmitriy789 [7]

Given :

Xinran walks 3 mi/h uphill, 4 mi/h on flat land and 5 mi/h downhill.

To Find :

If he walks one mile uphill, then one mile on flat land and then returns by the same route to his starting point, how many minutes does he walk.

Solution :

Time taken to walk one mile uphill is :

$t_1 = \dfrac{1}{3}\ hours$

Time taken to walk two mile on flat land( one on going and one or returning ) is :

$t_2 = \dfrac{2}{4}\ hours\\\\ t_2 = \dfrac{1}{2}\ hours$

Time taken to walk one mile downhill is :

$t_3 = \dfrac{1}{5}\ hours$

Total time taken :

$T = t_1 + t_2 + t_3 \\\\T = \dfrac{1}{3} + \dfrac{1}{2}+\dfrac{1}{5}\\\\T = \dfrac{10 + 15 + 6}{30} \\\\T = \dfrac{31}{30}\ hours = \dfrac{31}{30}\times 60 \ minutes\\\\T = 62\ minutes$

Therefore, time taken un 62 minutes.

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3 years ago

Zita made 1 5/8 quarts of punch. then she made 1 7/8 more quarts how much punch did she make in all?

katrin [286]

<span>5.5 cups hopes that helps you</span>

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3 years ago