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taurus [48]
3 years ago
7

Tim Worker expects Social Security benefits of $937 per month. His wife, Mary, is eligible for a wife's benefit of 50 percent of

Tim's benefit. How much will Mary receive?
A.) 187.40
B.) 468.50
C.) 1405.50
D.) 1874.00
Mathematics
2 answers:
dimulka [17.4K]3 years ago
4 0

Answer:

B.) 468.50

Step-by-step explanation:

Mary will receive 50% of what Tim receives. The 100% is $937, to calculate the 50% we have to divide $937 by half (because 50% = 50/100 = 1/2).

$937/2 = $468.50

Mary will receive $468.50.

We are assuming that she doesn't receive social security benefits on her own, she just have the wife's benefit of 50% of Tim's benefit.

Anestetic [448]3 years ago
3 0
Hi there

Mary receive
937×0.5
=468.5

Hope it helps
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The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo
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The perimeter of polygon ABCD, to the nearest thousandth units is

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Step-by-step explanation:

The coordinates forming the polygon are

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Therefore, the length between points AB is

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

= \sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2}  = \sqrt{20}  = 4.472 units

Similarly, length BC is given by

Length BC =  \sqrt{(-4)^2+1^2} =  \sqrt{17} = 4.123 units

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Length DA = \sqrt{(8)^2+(-2)^2} =  \sqrt{68} = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A =  \sqrt{(7)^2+(0)^2} =  \sqrt{49} =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

 S_{\bigtriangleup} = (\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|

= (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

S_{{\bigtriangleup}ABC} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|

= =(\frac{1}{2})|-4-6 -8|= 9 units^2

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

S_{{\bigtriangleup}ACD'} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

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Area of polygon =   S_{{\bigtriangleup}ABCD'} = S_{{\bigtriangleup}ABC} + S_{{\bigtriangleup}ACD'} = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

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