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3 years ago

Find the area of the following figure:

Mathematics

2 answers:

Sidana [21]3 years ago

4 0

Answer: 15cm^2

Step-by-step explanation:

0.5*10*3=15

tia_tia [17]3 years ago

4 0

Answer: 15 cm²

Step-by-step explanation:

Let x represent the length of the base of the smaller right angle triangle (drawn in broken lines).

The base of the full triangle would be (10 + x) cm. To determine x, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

12² = 3² + (10 + x)²

144 = 9 + (10 + x)²

(10 + x)² = 144 - 9 = 135

Taking square root of both sides

10 + x = √135 = 11.62

x = 11.62 - 10

x = 1.62

The total base of the triangle is 11.62cm

The formula for determining the area of a triangle is expressed as

Area = 1/2 × base × height

Area of the full triangle is

Area = 1/2 × 11.62 × 3 = 17.43 cm²

Area of the smaller triangle (with broken lines) is

Area = 1/2 × 1.62 × 3 = 2.43 cm²

Area of the given figure is

17.43 - 2.43 = 15 cm²

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Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

g100num [7]

Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

=> $k =109.6 \ miles$

4 0

3 years ago

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yuradex [85]

Answer:

13 and 6

Step-by-step explanation:

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2 years ago

Help MOI for the Third time PLS<br> Solve for t.<br><br> –9t − 19t + 9t − –18t − t = 14

Lorico [155]

Answer:

–9t − 19t + 9t − –18t − t = 14

t = -7

Step-by-step explanation:

Hope this helps!!

3 0

3 years ago

Find the coordinates of the point (a, b).

Leviafan [203]

Answer:

a = $\frac{1}{\sqrt{2} }$ and b = $\frac{\sqrt{2} }{2}$

Step-by-step explanation:

As we know, the radius of the unit circle is 1 unit (it is the hypotenuse in the right triangle, the blue line)

We use trigonometric formulas to find out a and b

Sin(45) = opposite side / hypotenuse

<=> Sin(45) = b / 1

<=> b= Sin(45)*1 = $\frac{\sqrt{2} }{2}$

Cos(45) = adjacent side / hypotenuse

<=> Cos(45) = a / 1

<=> a = Cos(45)*1 = $\frac{1}{\sqrt{2} }$

So: a = $\frac{1}{\sqrt{2} }$ and b = $\frac{\sqrt{2} }{2}$

5 0

3 years ago

What is the simple interest of a note that has a face value of $12,000, a rate of 8%, and a term of 1 year?

Tju [1.3M]

Solution:

Given:

$\begin{gathered} P=\text{ \$}12,000 \\ R=8\text{ \%} \\ T=1year \end{gathered}$

Using the simple interest formula,

$\begin{gathered} I=\frac{PTR}{100} \\ I=\frac{12000\times1\times8}{100} \\ I=\text{ \$}960 \end{gathered}$

Therefore, the simple interest is $960.

8 0

1 year ago