You must use the substitution method. 3x+2y=11 y=5x-1

I need help with this problem. Given: BC = 10 inches AC = √50 inches m∠CBD = 60° m∠CAD = 90° Calculate the exact area of the sha

Nikitich [7]

Answer:

Area of the shaded region = 23.33 in²

Step-by-step explanation:

Area of a sector = $\frac{\theta}{360}(\pi r^{2})$

Where θ = Central angle subtended by an arc

r = radius of the circle

Area of the sector BCD = $\frac{60}{360}(\pi) (10^{2})$

= 52.36 in²

Area of equilateral triangle BCD = $\frac{\sqrt{3} }{4}(\text{Side})^2$

= $\frac{\sqrt{3} }{4}(10)^2$

= $25\sqrt{3}$ in²

= 43.30 in²

Area of the shaded portion in ΔBCD = 52.36 - 43.3

= 9.06 in²

Area of sector CAD = $\frac{90}{360}(\pi)(\sqrt{50})^2$

= 39.27 in²

Area of right triangle CAD = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(\text{AC})(\text{AD})$

= $\frac{1}{2}(\sqrt{50})(\sqrt{50})$

= 25 in²

Area of the shaded part in the ΔACD = 39.27 - 25

= 14.27 in²

Area of the shaded part of the figure = 9.06 + 14.27

= 23.33 in²

8 0

3 years ago

8n^2-4(7m^3+5n^2) help

Rasek [7]

Hello there!

8m² - 4(7m³ + 5n²)

You wanna start by using the distributive property

=8n² - (-4)(7m³) + (-4)(5n²)

= 8n² - 28m³ - 20n²

= -28m³ - 12m²

7 0

3 years ago

Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line

DIA [1.3K]

Answer:

the correct answer is A.) on edg

6 0

3 years ago

Read 2 more answers

Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day

AfilCa [17]

Answer:

Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = $5\frac34 \ hrs.$

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

$5\frac34 \ hrs.$ can be Rewritten as $\frac{23}{4}\ hrs$

Number of hours rode on first day = $\frac{23}{4}\ hrs$

Also Given:

Number of hours rode on second day = $6\frac45 \ hrs$

$6\frac45 \ hrs$ can be Rewritten as $\frac{34}{5}\ hrs.$

Number of hours rode on second day = $\frac{34}{5}\ hrs.$

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = $20-\frac{23}{4}-\frac{34}{5}$

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = $\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}$

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day = $\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.$

Hence Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

3 0

3 years ago

Can you explain dot plotting?

Pepsi [2]

A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles. There are two common, yet very different, versions of the dot chart.

4 0

3 years ago