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2 years ago

11

You and six friends play on a soccer team. a sponsor paid $100 for the league fee, x dollars for each player's t/shirt and $68.2

5 for trophies. write an expression for the total amount the sponsor paid.

1 answer:

Ratling [72]2 years ago

4 0

100+x (s)+68.25(t)=a
S=shirts
T=trophies
A=amount paid

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A rectangular lawn, 100 feet long by 50 feet wide, is to have two sidewalks installed that will cut the lawn in half both ways,

Damm [24]

Answer:

3.41 feet

Step-by-step explanation:

Area = Length × Breath

Area of the rectangular lawn = 100 × 50

= 5000 feet²

The sidewalk must occupy an area no more than 10% of the total lawn area.

So, the area of the sidewalk would be not more than = 10% × 5000

= 0.10 × 5000

= 500 feet²

Let the width of the sidewalk = x feet

area of the side walk = (L×W of the long way) + ((L-x)×W of the short way)

(100 × x) + ((50 - x) × x) < 500

100x + (50-x)(x) < 500

-x² + 150x < 500

-x² + 150x = 500

-x² + 150x - 500 = 0

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\frac{(-150)\pm\sqrt{(150)^2-4(-1)(-500)} }{2(-1)}$

$x=\frac{-150\pm \sqrt{20500} }{-2}$

$x=75-5\sqrt{205}$ or $x=75+5\sqrt{205}$

x = 3.41089 ≈ 3.41 feet or x = 146.58

Therefore, width of the sidewalk would be 3.41 feet.

5 0

3 years ago

A 1400 kg car moving +13.7 m/s makes an elastic collision with a 3200 kg truck, initially at rest. What is the velocity of the c

Kamila [148]

Answer:

The velocity of the car after the collision is -5.36 m/s

Step-by-step explanation:

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

let the following:

m₁ = mass of the car = 1400 kg

m₂ = mass of the truck = 3200 kg

u₁ = velocity of the car before collision = 13.7 m/s

u₂ = velocity of the truck before collision = 0 m/s

v₁ = velocity of the car after collision

v₂ = velocity of the truck after collision

v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

= [ 13.7 * (1400 - 3200) + 0 * 2 * 3200 ]/ (1400 + 3200)

= - 5.36 m/s

So, <u>the velocity of the car after the collision is -5.36 m/s</u>

7 0

3 years ago

Select the correct answer.

White raven [17]

Answer:

c is the best answer of this question

6 0

3 years ago

Read 2 more answers

In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to

brilliants [131]

If he got 5 points in the first round and he needed at least thirty he would score 9 points in the next three rounds

8 0

3 years ago

Question<br> (X-5y/y3)-1=

Ilia_Sergeevich [38]

Answer:

$x = y^3+5y$

Step-by-step explanation:

Complete question

$\frac{x - 5y}{y^3} - 1=0\\$

Required

Solve for x

We have:

$\frac{x - 5y}{y^3} - 1=0$

Collect like terms

$\frac{x - 5y}{y^3} = 1$

Multiply through by $y^3$

$x - 5y = y^3$

Make x the subject

$x = y^3+5y$

8 0

2 years ago