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Mkey [24]
3 years ago
10

A ballroom in a hotel has the shape shown. The manager needs to determine how much carpet is needed to recarpet this area. All a

ngles are right angles. What is the area of the ballroom?
Question 3 options:

42 sq yds


72 sq yds


82 sq yds


100 sq yds

Mathematics
1 answer:
Mars2501 [29]3 years ago
7 0
Area of a rectangle=length x width


You have two rectangles:


First rectangle (the biggest):
length=9 yd
width=12 yd-6 yd=6 yd

Area of the biggest rectangle=(9 yd)(6 yd)=54 yd²

Second rectangle (the smallest)
length=6 yd
width=3 yd

Area of the smallest rectangle=(6 yd)(3 yd)=18 yd²

Area of the ballroom=area of the biggest rectangle + area of the smallest rectangle.

area of the ballroom=54 yd² +18 yd²=72 yd²
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WILL GIVE BRAINLIEST.
Elena L [17]

Answer:

\tan(\theta) = undefined

Step-by-step explanation:

Given

\sin(\theta) = -1

Required

Determine \tan(\theta)

We know that:

\sin^2(\theta) + \cos^2(\theta) = 1

This gives:

(-1)^2 + \cos^2(\theta) = 1

1 + \cos^2(\theta) = 1

Collect like terms

\cos^2(\theta) = 1 -1

\cos^2(\theta) = 0

Take square roots

\cos(\theta) = \sqrt 0

\cos(\theta) = 0

By tan identity

\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}

\tan(\theta) = \frac{-1}{0}

\tan(\theta) = undefined

6 0
3 years ago
ASE
eimsori [14]

Answer:

128 deg

Step-by-step explanation:

The sum of the measures of the angles of a polygon of n sides is

(n - 2)180

A trapezium has 4 sides, so the sum of the measures of the angles is

(4 - 2)180 = 2(180) = 360

<em>m<CBE + m<C + m<D + m<DEB = 360</em>

Angles ABC and CBE are a linear pair so the sum of their measures is 180 deg.

m<ABC + m<CBE = 180

115 + m<CBE = 180

m<CBE = 65

m<C = x

m<D = 90

Angles DEB and DEF are a linear pair so the sum of their measures is 180 deg.

m<DEB + m<DEF = 180

m<DEB + m<103 = 180

m<DEB = 77

<em>m<CBE + m<C + m<D + m<DEB = 360</em>

65 + x + 90 + 77 = 360

x + 232 = 360

x = 128

Answer: 128 deg

<em />

3 0
3 years ago
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Ratios and rates are ways to relate different quantities. For example, for every 1 car, there are 4 tires. This is a ratio. What
Olenka [21]

Cookies I make make sugar is 1 cup for every 2 cups of flour so it is 1 to 2


3 0
3 years ago
Carry out three steps of the Bisection Method for f(x)=3x−x4 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine w
ELEN [110]

Answer:

a) There's a zero between [1,2]

b) There's a zero between [1.5,2]

c) There's a zero between  [1.5,1.75].

Step-by-step explanation:

We have f(x)=3^x-x^4

A)We need to show that f(x) has a zero in the interval [1, 2]. We have to see if the function f is continuous with f(1) and f(2).

f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(2)=3^2-(2)^4=9-16=(-7)

We can see that f(1) and f(2) have opposite signs. And f(1)>f(2) and the function is continuous, this means that exists a real number c between the interval [1,2] where f(c)=0.

B)We have to repeat the same steps of A)

For the subinterval [1,1.5]:

f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13

f(1) and f(1.5) have the same signs, this means there's no zero in the subinterval [1,1.5].

For the subinterval [1.5,2]:

f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(2)=3^2-(2)^4=9-16=(-7)

f(1.5) and f(2) have opposite signs, this means there's a zero between the subinterval [1.5,2].

C)We have to repeat the same steps of A)

For the subinterval [1,1.25]:

f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5

f(1) and f(1.25) have the same signs, this means there's no zero in the subinterval [1,1.25].

For the subinterval [1.25,1.5]:

f(x)=3^x-x^4\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13

f(1.25) and f(1.5) have the same signs, this means there's no zero in the subinterval [1.25,1.5].

For the subinterval [1.5,1.75]:

f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)

f(1.5) and f(1.75) have opposite signs, this means there's a zero between the subinterval [1.5,1.75].

For the subinterval [1.75,2]:

f(x)=3^x-x^4\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)\\\\f(2)=3^2-(2)^4=9-16=(-7)

f(1.75) and f(2) have the same signs, this means there isn't a zero between the subinterval [1.75,2].

The graph of the function shows that the answers are correct.

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3 years ago
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