All categories

3 years ago

If the area of the outer square is 4x2, then the area of the inner square is

1 answer:

6 0

<span>Answered by the following sums - Outer square area = 4x^2 side of the square = 2x which is equal to diameter of circle == diameter of inner square. radius of circle = x diameter of outer square = 2*sqrt(2)*x consider side of inner square = a so a^2 + a^2 = (2x)^2 2a^2 = 4x^2 a = x*sqrt(2) So area of inner square will be = 2x^2</span>

You might be interested in

The equation of the line with slope = 3, going through point (2, 4) is:

Marina86 [1]

$(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-3}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-3x+6\implies y=-3x+10$

7 0

2 years ago

Read 2 more answers

Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Anit [1.1K]

Answer:

The answer is " $\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}$ ".

Step-by-step explanation:

$\bold{\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]}$

Solve the L.H.S part:

$\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\\\\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]$

After calculating the L.H.S part compare the value with R.H.S:

$\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]} \\\\$

$\to a+2c =6....(i)\\\\\to b+2d =5....(ii)\\\\\to 3a+4c =19....(iii)\\\\\to 3b+4d = 8 ....(iv)\\\\$

In equation (i) multiply by 3 and subtract by equation (iii):

$\to 3a+6c=18\\\to 3a+4c=19\\\\\text{subtract}... \\\\\to 2c = -1\\\\\to c= - \frac{1}{2}$

put the value of c in equation (i):

$\to a+ 2 (- \frac{1}{2})=6\\\\\to a- 2 \times \frac{1}{2}=6\\\\\to a- 1=6\\\\\to a =6 +1\\\\\to a = 7\\$

In equation (ii) multiply by 3 then subtract by equation (iv):

$\to 3b+6d=15\\\to 3b+4d=8\\\\\text{subtract...}\\\\\to 2d = 7\\\\\to d= \frac{7}{2}\\$

put the value of d in equation (iv):

$\to 3b+4 (\frac{7}{2})=8\\\\\to 3b+4 \times \frac{7}{2}=8\\\\\to 3b+14=8\\\\\to 3b =8-14\\\\\to 3b = -6\\\\\to b= \frac{-6}{3}\\\\\to b= -2$

The final answer is " $\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}$ ".

4 0

4 years ago

Look at the image and please help.

dem82 [27]

How do we help u??? we can’t graph for u

8 0

3 years ago

When there is a positive trend (or positive correlation), do the y-values of the points on the scatter plot tend to increase or

Assoli18 [71]

As the y-axes decreases the x-axes increases

4 0

3 years ago

Read 2 more answers

Find the surface area of each figure. Round your answers to the nearest hundredth, if<br> necessary.

steposvetlana [31]

Answer:

1) 651.5 cm²

2) 462 cm²

3) 99 ft²

4) 1540.8 yd²

Step-by-step explanation:

1) Area of the trapezoid: (12 + 7)/2 * 6.5 = 61.75 cm²

Area of the lateral rectangles: 7*16 = 112 cm²

Area of the top rectangle: 12*16 = 192 cm²

Area of the bottom rectangle: 7*16 = 112 cm²

Area of the figure: 192 + 112 + 2*61.75 + 2*112 = 651.5 cm²

2) Area of the top and bottom squares: 11*11 = 121 cm²

Area of the lateral rectangles: 11*5 = 55 cm²

Area of the figure: 4*55 + 2*121 = 462 cm²

3) Area of the trapezoid: (3 + 7)/2 * 3.5 = 17.5 ft²

Area of the lateral rectangles: 4*4 = 16 ft²

Area of the top rectangle: 7*4 = 28 ft²

Area of the bottom rectangle: 3*4 = 12 ft²

Area of the figure: 28 + 12 + 2*17.5 + 2*12 = 99 ft²

4) Area of the lateral rectangles: 11*12 = 132 yd²

Area of the top and bottom hexagons: 3*12*10.4 = 374.4 yd²

Area of the figure: 6*132 + 2*374.4 = 1540.8 yd²

8 0

3 years ago