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Alenkinab [10]
2 years ago
14

Please answer question attatched thanks :)

Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
7 0

Answer:

(a) 6.01 (b) 57.33

Step-by-step explanation:

(a) DF² = 10² + 12² - 2 · 10 · 12 · cos(30°)

=> DF² = 244 - 240 · cos(30°)

=> DF² = 36.154

=> DF = √36.154

=> DF ≈ 6.01

(b) \frac{12.8}{sin(63)} = \frac{12.4}{sin (B)}

=> sin (B) = sin (63) × 12.4 ÷ 12.8

=> B = sin^-1 (sin (63) × 12.4 ÷ 12.8)

=> B = 59.67355245

180 - 63 - 59.67355245 ≈ 57.33

Law of cosines & sines:

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carter has 7,500 in a bank account that earns 3% simple interest per year. how much will be in the account after 5 years
allsm [11]

Answer:

11.25

Step-by-step explanation:

7500 times 0.03 times 5 = 1125

1125 divided 100 = 11.25

simple interest formula = Amount times Rate times Time

                                                         Divide 100

8 0
3 years ago
Help me answer pls thanks.Dont answer if ur just put nothing or you dont know. ​
raketka [301]
Hi I want the points thanks
8 0
2 years ago
The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect
ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}

Now the points  A(−3, 4) and  B(7, 2)

AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}

AB = \sqrt{(10)^{2} +(-2)^{2}}

AB = \sqrt{100+4}

AB = \sqrt{104}

AB = 2\sqrt{26}\units

Thus

CD= 2\sqrt{26}\units

Now the points

A (−3, 4) , D (−4, −1)

AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}

AD = \sqrt{(-1)^{2} +(-5)^{2}}

AD = \sqrt{1 + 25}

AD = \sqrt{26}\units

Thus

BC = \sqrt{26}\units  

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

Length = 2\sqrt{26}\ units

Breadth = \sqrt{26}\ units  

Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})

Perimeter\ of\ rectangle = 2(3\sqrt{26})

Perimeter\ of\ rectangle = 6\sqrt{26}

\sqrt{26} = 5.1 (Approx)

Perimeter\ of\ rectangle = 6\times 5.1

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

8 0
3 years ago
In 10 seconds, Lauren counts 5 vehicles passing by her house. At that rate, how many vehicles would pass by in one hour?
Anna007 [38]
6 x 60 x 5 would be the equation and all of that put together would be 1,800 vehicles would pass by in an hour.
7 0
3 years ago
The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the r
zysi [14]

Answer:

a cone with a base circumference of about 126 mm

Step-by-step explanation:

Rotating a triangle about a line results in a cone created by the rotation.  This is because the segment at the bottom forms a circle, and the point at the top stays there; the three-dimensional figure with a circular base and a point at the top is a cone.

Since we rotate the segments about a line, this makes the length of the base the radius of the circle. This means the circumference would be

C = 2πr = 2(3.14)(20) = 125.6 ≈ 126 mm

3 0
3 years ago
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