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Yuri [45]
3 years ago
9

For her parents' anniversary party, Sharon is considering using one of two venues. A hotel in Westford will cost $562 for a rese

rvation, plus $30 per person. A restaurant in the same city will cost $29 per person, in addition to $563 for the reservation. In order to make the best decision, Sharon figures out how many attendees it would take to have the venues cost the same amount. How many attendees would that be? What would the total cost be?
Mathematics
1 answer:
zheka24 [161]3 years ago
5 0
It will take one person for the venues to equal the same amount. This is simply done by multiplying 1 x the per person amount then adding it to the reservation cost.
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One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196
Anon25 [30]

Answer:

Option B.  24 horses and 50 humans

Step-by-step explanation:

Let

x ----> the number of humans

y ----> the number of horses

Remember that

A human has one head and two legs

A horse has one head and four legs

so

x+y=74 ----> equation A

2x+4y=196 -----> equation B

Solve the system by graphing

The solution of the system is the intersection point both graphs

The solution is the point (50,24)

see the attached figure

therefore

The number of humans is 50 and the number of horses is 24

4 0
3 years ago
Write the word sentence as an equation 54 equals 9 more than a number t
Mashutka [201]
54 = t + 9   this is your equation! 
8 0
4 years ago
Read 2 more answers
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 52 inches long and cuts it into
Ilia_Sergeevich [38]

Answer:

Steve should use:

  • 8.53 Inch of Wire to make the circle
  • 43.47 Inches of Wire to make the Square.

Step-by-step explanation:

Let Steve cut the wire so that the first piece has length x.

Therefore, the second piece will have a length of (52 - x).

The wire of length x is used to make a circle

Circumference of a Circle,

c = 2\pi r\\Therefore\\2\pi r=x\\r=\dfrac{x}{2\pi}

\text{Area of a circle, A}=\pi r^2= \pi (\dfrac{x}{2\pi})^2=\pi (\dfrac{x^2}{4\pi^2})\\A=\dfrac{x^2}{4\pi}

The wire of length (52-x) is used to make a square.

\text{Side length of the Square,} s= \dfrac{52-x}{4}

\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}

Total Area = Area of Circle + Area of Square

Area=\dfrac{x^2}{4\pi}+\dfrac{x^2-104x+2704}{16}

Let us simplify the expression

Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

$Using \: x=-\frac{b}{2a}

a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

7 0
4 years ago
What is the value of x in the diagram below?​
mel-nik [20]
You do:

130+x+5=180
x+135=180
x=45

Hope this helps!! :)
5 0
3 years ago
Read 2 more answers
Ummm help please please
zaharov [31]

Answer:

120

Step-by-step explanation:

8 0
3 years ago
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