Answer:
area of circle having radius 3
is πr²=π*3²=9π square units
area of circle having radius 2
=πr²=π×2²=4π square units
again
area of big circle having radius [3+2]=5 units
=πr²=π×5²=25π square units
Now
area of shaded region=25π-4π-9π=12π or 37.7square units.
Answer:
(4) (M∠1 + m∠2) = 180 and (m∠3 + m∠4 + m∠2) = 180
Step-by-step explanation:
Given the equations:
![\begin{gathered} \frac{4y+11x}{4}=x+2 \\ \\ 3x-7y=7x+10 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4y%2B11x%7D%7B4%7D%3Dx%2B2%20%5C%5C%20%20%5C%5C%203x-7y%3D7x%2B10%20%5Cend%7Bgathered%7D)
Let's determine if the lines are parallel or perpendicular.
Rewrite both equations in slope-intercept form:
y = mx + b
Where m is the slope.
Rewrite each equation for y.
• Equation 1:
![\begin{gathered} \frac{4y+11x}{4}=x+2 \\ \\ 4y+11x=4(x+2) \\ \\ \text{ Apply distributive property:} \\ 4y+11x=4x+8 \\ \\ \text{ Subtract 11x from both sides:} \\ 4y+11x-11x=4x-11x+8 \\ 4y=-7x+8 \\ \text{ Divide all terms by 4:} \\ \frac{4y}{4}=-\frac{7}{4}x+\frac{8}{4} \\ \\ y=-\frac{7}{4}x+2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4y%2B11x%7D%7B4%7D%3Dx%2B2%20%5C%5C%20%20%5C%5C%204y%2B11x%3D4%28x%2B2%29%20%5C%5C%20%20%5C%5C%20%5Ctext%7B%20Apply%20distributive%20property%3A%7D%20%5C%5C%204y%2B11x%3D4x%2B8%20%5C%5C%20%20%5C%5C%20%5Ctext%7B%20Subtract%2011x%20from%20both%20sides%3A%7D%20%5C%5C%204y%2B11x-11x%3D4x-11x%2B8%20%5C%5C%204y%3D-7x%2B8%20%5C%5C%20%5Ctext%7B%20Divide%20all%20terms%20by%204%3A%7D%20%5C%5C%20%5Cfrac%7B4y%7D%7B4%7D%3D-%5Cfrac%7B7%7D%7B4%7Dx%2B%5Cfrac%7B8%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20y%3D-%5Cfrac%7B7%7D%7B4%7Dx%2B2%20%5Cend%7Bgathered%7D)
• Equation 2:
![\begin{gathered} 3x-7y=7x+10 \\ \\ Subtract\text{ 3x from both sides:} \\ 3x-3x-7y=7x-3x+10 \\ \\ -7y=4x+10 \\ \\ \text{ Divide all terms by -7:} \\ -\frac{7y}{-7}=\frac{4}{-7}x+\frac{10}{-7} \\ \\ y=-\frac{4}{7}x-\frac{10}{7} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203x-7y%3D7x%2B10%20%5C%5C%20%20%5C%5C%20Subtract%5Ctext%7B%203x%20from%20both%20sides%3A%7D%20%5C%5C%203x-3x-7y%3D7x-3x%2B10%20%5C%5C%20%20%5C%5C%20-7y%3D4x%2B10%20%5C%5C%20%20%5C%5C%20%5Ctext%7B%20Divide%20all%20terms%20by%20-7%3A%7D%20%5C%5C%20-%5Cfrac%7B7y%7D%7B-7%7D%3D%5Cfrac%7B4%7D%7B-7%7Dx%2B%5Cfrac%7B10%7D%7B-7%7D%20%5C%5C%20%20%5C%5C%20y%3D-%5Cfrac%7B4%7D%7B7%7Dx-%5Cfrac%7B10%7D%7B7%7D%20%5Cend%7Bgathered%7D)
Therefore, we have both equations in slope-intercept form:
![\begin{gathered} y=-\frac{7}{4}x+2 \\ \\ y=-\frac{4}{7}x-\frac{10}{7} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D-%5Cfrac%7B7%7D%7B4%7Dx%2B2%20%5C%5C%20%20%5C%5C%20y%3D-%5Cfrac%7B4%7D%7B7%7Dx-%5Cfrac%7B10%7D%7B7%7D%20%5Cend%7Bgathered%7D)
• The slope of equation 1 is: -7/4
,
• The slope of equation 2 is: -4/7
Parallel lines have equal slopes.
Perpendicular lines have slopes that are the negative reciprocal of each other.
Since both slopes are neither equal nor negative reciprocals, then both lines are neither parallel nor perpendicular.
• ANSWER:
Neither
A. There is no mode; no numbers are used twice
B. 1+3+0+2+4=10
10/5= 2
I hope this helps. :)
Answer:
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Step-by-step explanation: