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2 years ago

10

7/12 - 1/6 in simplest form

1 answer:

juin [17]2 years ago

8 0

Answer:

5/12

Step-by-step explanation:

1/6 can be turned into 2/12

7/12-2/12=5/12

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Whitepunk [10]

Answer: it is 24 UWU

Step-by-step explanation:

4 0

3 years ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

Part 1: Use the information provided to write the standard form equation of each circle. Please show the work.

dusya [7]

Answer:

1. (x + 2)² + (y - 9)² = 64

2. (x + 6)² + (y - 9/2)² = 100

3. (x - 15)² + (y + 10)² = 1

Step-by-step explanation:

Equation of a circle:

(x - h)² + (y - k)² = r²

1. Center: (-2, 9), Radius: 8

(x - (-2))² + (y - 9)² = 8²

(x + 2)² + (y - 9)² = 64

2. Center: (-6, 9/2), Radius: 10

(x - (-6))² + (y - (9/2))² = 10²

(x + 6)² + (y - 9/2)² = 100

3. Center: (15, -10), Radius: 1

(x - 15)² + (y - (-10))² = 1²

(x - 15)² + (y + 10)² = 1

4 0

3 years ago

3 multiply by 2x - 5 = 27.

jeka94

Answer:

x=2.7

Step-by-step explanation:

27 divided by 5 = 5.4 and 5.4 divided by 2 = 2.7

8 0

4 years ago

Points are plotted at (-2, 2), (-2, -4), and (2, -4). A fourth point is drawn such that the four points can be connected to form

Marat540 [252]

Answer:24 square units

Step-by-step explanation:

7 0

3 years ago