MATHEMATICS HIGH SCHOOL

Billy invests £800 for 5 years in a savings account.By the end of the 5 years he has received a total of £96 simple interest.
Work out the annual rate of simple interest.

Answers

Answer 1

Answer:

Answer:

2.4%

Step-by-step explanation:

Simple interest (I) is calculated as

I = $(PRT)/(100)$

where P is the principal, R the rate of interest and T time in years

Here I = 96, P = 800 and T = 5, thus

96 = $(800R(5))/(100)$ = $(4000R)/(100)$ = 40R ( divide both sides by 40 )

R = $(96)/(40)$ = 2.4%

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Which of the following is equivalent to 6x 2 + x - 12 ?A. (2x + 3)(3x - 4) B. (2x - 3)(3x - 4) C. (2x + 3)(3x + 4) D. (6x + 3)(x - 12) E. (x + 3)(2x - 12) Please show me step by step how to solve this problem Thanks
Fill in the blanks so the solution of the system is (5,5) x+y=5 x+y
Find the area of the green sector if m∠ A = π 6 and the circle has a radius of 10 inches.

Suppose a triangle has sides 3 4 and 5, which of the following must be true

Answers

You haven't given any options to select.
However, if this is the way of values we can check pythagoras theorem .

5^2 = 25

3^2 + 4^2
9 + 16
25

25 = 25

therefore we can say it is the right angle triangle

Suppose you have 52 feet of fencing to enclose a rectangular dog pen. where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

Answers

Answer:

Width which gives maximum area = 13 feet

Maximum Area = 169 $feet^2$

Step-by-step explanation:

Given: 52 feet of fencing means Perimeter of rectangular dog pen.

If Total length of the boundary of rectangle (.i.e., Perimeter) is fixed then the rectangle with equal sides has the maximum area.

Width = x (given)

∴ for maximum area let length = x

Perimeter of rectangle = 52 feet

2 × (Length + Width) = 52

2 × ( x + x ) = 52

2 × ( 2x ) = 52

4x = 52

x = $(52)/(4)$

x = 13 feet.

Maximum Area = Length × Width

= 13 × 13

= 169 $feet^2$

Width which gives maximum area = 13 feet

Maximum Area = 169 $feet^2$

Maximum Area = 169 feet^2

Y = 3x + 10
y = -7x - 20

Answers

Answer:

x = -3

Step-by-step explanation:

3x + 10 = -7x -20

3x + 7x = -20 -10

10x = -30 /: (10)

x = -3

Solve equation e^{2x} + 2e^{x} −3 = 0

Answers

$e^(2x)+2e^x-3=0\n\n\underbrace{\left(e^x\right)^2+2e^x\cdot1+1^2}_((*))-1^2-3=0\n\n(e^x+1)^2-1-3=0\n\n(e^x+1)^2-4=0\n\n(e^x+1)^2=4\iff e^x+1=\sqrt4\to e^x+1=2\n\ne^x=2-1\n\ne^x=1\n\ne^x=e^0\iff x=0$