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chubhunter [2.5K]

3 years ago

15

In triangle ABC, AC =24, the measure of angle A = 30 degree , and the measure of angle B = 45 degree . Find the area of this tri

angle. (Hint: Draw a picture and include the altitude from vertex C to the side AB.)

1 answer:

andriy [413]3 years ago

6 0

Answer:

142.932

Step-by-step explanation:

given that in triangle ABC, AC =24

Angle A = 30 and Angle B =45

If we draw altitude from C, we get

h = 24sin 30 = 12

Since BC = h (45, 45,90 triangle)

BC=12

By sine formula for triangle

$\frac{12}{sin30} =\frac{AB}{sin(180-45-30)} \\AB = 24 sin 105 = 23.1822$

Area of triangle

= $1/2 (23.1822)(12)\\= 142.932$

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The next number in the arithmetic sequence 15, 22, 29, is: <br><br>A) 34<br>B) 35<br>C) 36<br>D) 37

harkovskaia [24]

ANSWER: C) 36
EXPLANATION: +7 is the sequence

4 0

2 years ago

(T+10.5) + 2t + 90 = 180

Masja [62]

Answer:

x = 26.5

Step-by-step explanation:

Step 1: Write equation

(t + 10.5) + 2t + 90 = 180

Step 2: Solve for <em>t</em>

<u>Combine like terms:</u> 3t + 100.5 = 180

<u>Subtract 100.5 on both sides:</u> 3t = 79.5

<u>Divide both sides by 3:</u> t = 26.5

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

<u>Substitute:</u> (26.5 + 10.5) + 2(26.5) + 90 = 180

<u>Parenthesis:</u> 37 + 56 + 90 = 180

<u>Add:</u> 180 = 180

∴ x = 26.5

5 0

4 years ago

Read 2 more answers

A dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration

ozzi

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: Acceleration_{dog} = 0$

____________________________________

$\large \tt Solution \: :$

A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.

And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0

Henceforth, Acceleration of dog is 0 as well.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

4 0

2 years ago

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a cell phone store sells the basic model of a phone for $30 and the upgraded model for $100 when a customer signs a two-year agr

alisha [4.7K]

30b + 100u = 900
5b + 25u = 200....multiply by -6
------------------
30b + 100u = 900
-30b - 150u = - 1200 (result of multiplying by -6)
------------------add
-50u = - 300
u = 6 <== upgrated phones sold

30b + 100u = 900
30b + 100(6) = 900
30b + 600 = 900
30b = 900 - 600
30b = 300
b = 10 <== basic phones sold

8 0

3 years ago

Read 2 more answers

Find each Of change. Round to the nearest whole percent if necessary. State whether the percent Of change is an increase or 1. O

Alenkasestr [34]

Answer:

1. The percentage change is 74% and it is a percentage decrease

2. The percentage change is 15% and it is a percentage decrease

3. The percentage change is 20% and it is a percentage decrease

4. The percentage change is 43% and it is a percentage increase

5. The percentage change is 40% and it is a percentage decrease

6. The percentage change is 39% and it is a percentage decrease

Step-by-step explanation:

Given

$1.\ Original = 5; New = 1.3$

$2.\ Original = 160; New = 136$

$3.\ Original = 15; New = 12$

$4.\ Original = 7; New = 10$

$5.\ Original = $30; New = $18$

$6.\ Original = 9.6; New = 5.9$

Required

Determine the percentage change and state whether it's an increase or decrease

Percentage change is calculated as:

$\%Change = \frac{New - Original}{Original} * 100\%$

$1.\ Original = 5; New = 1.3$

$\%Change = \frac{1.3 - 5}{1.3} * 100\%$

$\%Change = \frac{-3.7}5} * 100\%$

$\%Change = \frac{-3.7 * 100\%}{5}$

$\%Change = \frac{-370\%}{5}$

$\%Change = -74\%$

<em>The percentage change is 74% and it is a percentage decrease</em>

$2.\ Original = 160; New = 136$

$\%Change = \frac{136 - 160}{160} * 100\%$

$\%Change = \frac{-24}{160} * 100\%$

$\%Change = \frac{-24 * 100\%}{160}$

$\%Change = \frac{-2400\%}{160}$

$\%Change = -15\%$

<em>The percentage change is 15% and it is a percentage decrease</em>

$3.\ Original = 15; New = 12$

$\%Change = \frac{12- 15}{15} * 100\%$

$\%Change = \frac{-3}{15} * 100\%$

$\%Change = \frac{-3* 100\%}{15}$

$\%Change = \frac{-300\%}{15}$

$\%Change = -20\%$

<em>The percentage change is 20% and it is a percentage decrease</em>

$4.\ Original = 7; New = 10$

$\%Change = \frac{10- 7}{7} * 100\%$

$\%Change = \frac{3}{7} * 100\%$

$\%Change = \frac{3* 100\%}{7}$

$\%Change = \frac{300\%}{7}$

$\%Change = 43\%$ -- (approximated)

<em>The percentage change is 43% and it is a percentage increase</em>

<em></em>

$5.\ Original = $30; New = $18$

$\%Change = \frac{18- 30}{30} * 100\%$

$\%Change = \frac{-12}{30} * 100\%$

$\%Change = \frac{-12* 100\%}{30}$

$\%Change = \frac{-1200\%}{30}$

$\%Change = -40\%}$

<em>The percentage change is 40% and it is a percentage decrease</em>

$6.\ Original = 9.6; New = 5.9$

$\%Change = \frac{5.9- 9.6}{9.6} * 100\%$

$\%Change = \frac{-3.7}{9.6} * 100\%$

$\%Change = \frac{-3.7* 100\%}{9.6}$

$\%Change = \frac{-370\%}{9.6}$

$\%Change = -39\%$ -- (approximated)

<em>The percentage change is 39% and it is a percentage decrease</em>

5 0

3 years ago