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Ulleksa [173]
3 years ago
8

Matt invests £1800 for 2 years at a simple interest rate of 10%.

Mathematics
1 answer:
Snezhnost [94]3 years ago
6 0

Answer:

Step-by-step explanation:

P = 1800

R = 10%

T = 2 years

I = PRT

= 1800 * 10/100 * 2

= 1800 * 0.1 * 2

I = £360

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A spherical ball has a radius of 4 inches. What is the volume of this sphere, to the
stealth61 [152]

Answer:

V = 267.9 in^3

Step-by-step explanation:

V = 4/3 * (pi) * r^3

V = 4/3 * 3.14 * 4^3

V = 4/3 * 3.14 * 64

V = 256/3 * 3.14

V = 803.84/3

7 0
2 years ago
Stan’s Car Rental charges $35 per day plus $0.25 per mile. Denise wants to rent one of Stan’s cars, keeping the total cost of th
Greeley [361]
$55-$35=20
$20 divide by $0.25=80 miles.
therefore denise can drive the car for 1day 80 miles to stay within her budget
4 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
oee [108]

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.

7 0
2 years ago
Equalivent fraction of 2/3
LiRa [457]
2/3 could equal 4/6 , 6/9, 8/12 , 10/15 , 12/18 ETC
6 0
3 years ago
Read 2 more answers
A cone has a diameter of 18 units and height of 8 units. What is its volume?
sveta [45]
The radius of your cone is half of 18 units = 9 units.

The volume of any cone is      <span><span>V = (1/3) · (pi) · (radius)² · (height) </span>
</span>
-- Take that formula for the volume of any cone.
-- Write '8' in place of 'height'.
-- Write '9' in place of 'radius'.
-- Write '3.142' in place of 'pi'.
-- Complete the arithmetic.
-- Bada-bing, you've got the volume.
6 0
2 years ago
Read 2 more answers
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