This is the set of (unordered) class marks in an end of session maths test.

The area of a square shaped park measures 16900 square feet. How many feet of fencing would be needed to enclose that park?

sergey [27]

Answer:

520 feet

Step-by-step explanation:

The area=16900

Area formula=b^2

b^2=16900

square root of 16900=130

130*4=520

6 0

3 years ago

A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens an

Mkey [24]

Answer:

120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

x: number of pens
y: number of pencils

2. Cost

each pen costs $1, then x pens costs: x
each pencil costs $0.5, then y pencil costs: 0.5y

Then, the total cost is: x + 0.5y

The cost of the whole purchase was $ 220, then the first equation is:

x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

pencils = 80 + pens

↓ ↓

y = 80 + x ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

x + 0.5(80 + x) = 220

ii) Solve

x + 40 + 0.5x = 220

1.5x = 180

x = 180/1.5

x = 120 pens

iii) Substitute x = 120 into the equation (2)

y = 80 + 120

y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

6 0

3 years ago

Equation of the line (-6,5) and (8,14) in standard form

blsea [12.9K]

Answer:

$\huge\boxed{9x-14y=-70}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (-6, 5) and (8, 14).

Substitute:

$m=\dfrac{14-5}{8-(-6)}=\dfrac{9}{14}\\\\y-5=\dfrac{9}{14}(x-(-6))\\\\y-5=\dfrac{9}{14}(x+6)$

Thew standard form of an equation of a line:

$Ax+By=C$

transform:

$y-5=\dfrac{9}{14}(x+6)\qquad|\text{multiply both sides by 14}\\\\14y-14\cdot5=14\!\!\!\!\!\diagup^1\cdot\dfrac{9}{14\!\!\!\!\!\diagup_1}(x+6)\\\\14y-70=9(x+6)\\\\14y-70=9x+54\qquad|\text{subtract}\ 9x\ \text{from both sides}\\\\-9x+14y-70=54\qquad|\text{add 70 to both sides}\\\\-9x+14y=70\qquad|\text{change the signs}\\\\9x-14y=-70$

4 0

3 years ago

The circle below is centered at the origin and has a radius of 4. What is its equation?

Alecsey [184]

Answer:

C) x^2 + y^2 = 16

Step-by-step explanation:

<h2>Find the equation </h2>

since the radius is 4 this means that anywhere from the center of the circle to the edge of the circle is 4. hence :

place the horizontal line of the radius where y = 0 .

this means that if y = 0 , then x = 4

therefore :

x^2 + y^2

4^2 + 0^2

= 16

<h3>hence the answer is C ) x^2 + y^2 = 16</h3>

7 0

3 years ago

Look at the picture

gladu [14]

Answer:

C)

Step-by-step explanation:

- π can be added to π to get a rational number

π + (-π) = 0

0 is a rational number

6 0

3 years ago