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zimovet [89]
3 years ago
14

Bob spent 25% more time on his research project than he had planned. He had spent an extra h hours on the project. What expressi

on could represent the number of hours Bob actually spent on the project
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
7 0

Let the projected number of work hours be w.

Then the number of hours he actually worked was 1.25w.  This represents the number of hours that Bob actually spent on the project.


Another way in which to answer this would be as follows:

Actual work hours = w + h (h hours beyond the projected w work hours).

This w + h is equivalent to 1.25w.   This means that h = 0.25w.



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You have 100$ in savings account and plan to deposit 20$ each month. Write and graph a linear equation that represents the balan
Nataly_w [17]

Answer:y=20x+100

Step-by-step explanation:

7 0
3 years ago
What is the answer?
mezya [45]

Answer:

18.1 cm

Step-by-step explanation:

AD segment breakup: 11=4+7

Pythagorean Theorem:

7^2+b^2=16^2

49+b^2=256

x^2=207

b=sqrt(207)

b=3sqrt(23)

Pythagorean Theorem:

11^2+3sqrt(23)^2=c^2

121+207=c^2

328=c^2

18.11=c

So the length of AC is around 18.1 cm

5 0
3 years ago
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
PolarNik [594]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY =  \sqrt{x^2+y^2}

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

Length CD = \sqrt{(-2)^2+5^2} =  \sqrt{29} = 5.385 units

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)|

=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2} = 10.5 units²

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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4 years ago
Can someone please show and explain how you got the answer for these please ​
Komok [63]

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3 0
3 years ago
Find the percent of the number.<br>20% of 90​
expeople1 [14]

Answer:

18

Step-by-step explanation:

90 x 0.2 = 18

7 0
3 years ago
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