Find the area of the triangle.<br> a. 620 sq. m<br> b. 270 sq. m<br> C. 540 sq. m<br> d. 980 sq.m

Simplify the complex fraction.

lilavasa [31]

Given:

$$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}$

To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

$$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}$

Step 2: Simplify the denominator

$$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}$

Step 3: Using step 1 and step 2

$$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}$

Step 4: Using fraction rule:

$$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$

$$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}$

Cancel the common factor r and t², we get

$$=\frac{64 r^{2} \cdot 9 }{16 \cdot 15 t^2 }$

Cancel the common factors 16 and 3 on both numerator and denominator.

$$=\frac{4 r^{2} \cdot 3 }{ 5 t^2 }$

$$=\frac{12 r^{2} }{ 5 t^2 }$

$$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2} }{ 5 t^2 }$

The simplified fraction is $\frac{12 r^{2} }{ 5 t^2 }$ .

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I just used a fraction calculator lol

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The quotient of a number and 6decreased by 10 is equal to 2??

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Someone please help asap! I will mark as brainliest, thank you!!

madreJ [45]

Answer:

19 square units

Step-by-step explanation:

Hello!

Step 1: Plot the points

We are first going to plot the points on the coordinate graph and connect the points to create a shape.

Refer to attachment titled "Step 1"

Step 2: Box the shape

Since this is an irregular shape, I'm going to make a box around the shape and subtract the area of the empty spaces to find the area of the original polygon.

Refer to attachment titled "Step 2"

Step 3: Area of Edges

We are going to find the area of the shapes A, B, and C and subtract them from the area of the big box to find the area of the polygon.

Area of a triangle = 1/2(base x height)

Area of Box = 6 un x 7 un
Area of Box = 42 un²

Area of A:

Area A = 1/2(4 un x 2 un)
Area A = 1/2(8 un²)
Area A = 4 un²

Area of B:

Area B = 4 un x 4 un
Area B = 16 un²

Area of C:

Area C = 1/2(2 un x 3 un)
Area C = 1/2(6 un²)
Area C = 3 un²

Step 4: Area of the polygon

Now, we can simply subtract the values of A, B, and C from the box to get the area of the polygon.

Area Polygon = Box - A - B - C
Area Polygon = 42 un² - 4 un² - 16 un² - 3 un²
Area Polygon = 38 un² - 16 un² - 3 un²
Area Polygon = 22 un² - 3 un²
Area Polygon = 19 un²

The area of the polygon is 19 un²

-Chetan K

6 0

2 years ago

Find the area of the triangle. a. 620 sq. m b. 270 sq. m C. 540 sq. m d. 980 sq.m