MATHEMATICS HIGH SCHOOL

3(x-2)>-3
solve each inequality

Answers

Answer 1
Answer: divide each side by the number that does not contain a variable 
answer is x>1

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If an area in the form of a circle is to be roped off by a rope 10 m long, what will be the radius of this area? Round your answer to two decimal places. A. 1.59 m
B. 2.56 m
C. 3.18 m
D. 0.31 m

Answers

Answer:

A. 1.59 m

Step-by-step explanation:

To find the radius of the area we wil; simply use the formula; C = 2π R

where C is the circumference of the circle,  π is a constant that is always 3.14 approximately, except given otherwise   and R is the radius.

From the question, since the circle is formed by roping  off  a rope 10 m long, then it implies that the circumference (c) = 10

We can now proceed to substitute our values into the formula;

C  = 2π R

10 ≈ 2×3.14×R

10 ≈ 6.28R

Divide both-side of the equation by 6.28

(10)/(6.28) = (6.28 R)/(6.28)

(At the right-hand side of the equation 6.28 will cancel-out 6.28 leaving us with just R while at the left-hand side of the equation, 10 will be divided by 6.28)

1.592≈R

R≈1.59 m

Therefore, the radius of this area will be 1.59 m
Your answer is A. 1.59 m.

Hope this helps.

The perimeter of a rectangle is 90 centimeters. The width of the rectangle can be represented by (x + 2), and its length can be represented by (3x - 5). What are the dimensions of this rectangle in centimeters?A With = 10 and length = 25
B With = 12 and length = 29
C With = 14 and length = 31
D With = 16 and length = 32

Answers

Perimeter of a rectangle=2lenght + 2width
In this case:
Perimeter=90 cm
width=(x+2)
lenght=(3x-5)
Then:

2(x+2)+2(3x-5)=90
2x+4+6x-10=90
2x+6x=90+10-4
8x=96
x=96/8
x=12

with=(x+2)=12+2=14
lenght=(3x-5)=3*12-5=31

Answer: C width=14 and lenght=31.

Find an equation of the circle that satisfies the given conditions. Endpoints of a diameter are P(-1, 1) and Q(5,9)

Answers

The equation of a circle:
(x-h)^2+(y-k)^2=r^2
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
((x_1+x_2)/(2), (y_1+y_2)/(2))
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

P(-1,1) \nx_1=-1 \n y_1=1 \n \n Q(5,9) \n x_2=5 \n y_2=9 \n \n(x_1+x_2)/(2)=(-1+5)/(2)=(4)/(2)=2 \n (y_1+y_2)/(2)=(1+9)/(2)=(10)/(2)=5

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
d=√((x_2-x_1)^2+(y_2-y_1)^2)

(-1,1) \n x_1=-1 \n y_1=1 \n \n (2,5) \n x_2=2 \n y_2=5 \n \n d=√((2-(-1))^2+(5-1)^2)=√(3^2+4^2)=√(9+16)=√(25)=5

The radius is 5.

(x-2)^2+(y-5)^2=5^2 \n\boxed{(x-2)^2+(y-5)^2=25}

What is the answer the this question​

Answers

Answer Step-by-step explanation: ITS B

8k-1=15 ? Help I have a question were we have to work this out what do I do?

Answers

8k-1=15\ \ \ \ /+1\n\n8k-1+1=15+1\n\n8k=16\ \ \ \ /:8\n\n8k:8=16:8\n\nk=2
you have to add 1 to  the -1 and you will get 0.What you have to do next is also add 1 to 15 because you want a variable on one side and a number on the other.So now you have 8k=16. So you divide 8 to 8k and you get nothing divide 8 and 16 and your answer for k =2 hope you get it right.trust mw it is very easy when you get use to it 

Solve the differential equation by separation of variables
x(dy/dx)=4y

Answers

get all your x one on side and y on the opposing sideso we have
xdy=4ydx
dy/y=4dx/x
integrate both sides
lny=4lnx+C
 y=e^(4lnx+C)
The answer is y=cx^4

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