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3 years ago

Cara is painting her living room. The room measures 10.6 feet by 11.6 feet. The ceiling is 10 feet

Mathematics

1 answer:

malfutka [58]3 years ago

3 0

Answer:

440 sq ft.

Step-by-step explanation:

Based on the given, the room is a rectangle with Length = 11.5 ft, width = 10.5 ft and height = 10ft. The total wall area can be calculated as the sum of the individual wall areas. The area of opposite walls can be said equal, therefore.

A = A1 + A2

A1 = (11.5 x 10) (2) since two opposite walls

A2 = (10.5 x 10) (2) since two opposite walls

Total = 440 sq ft.

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Sarah is a computer engineer and manager and works for a software company. She receives a

daser333 [38]

Answer:

a) Number of projects in the first year = 90

b) Earnings in the twelfth year = $116500

Total money earned in 12 years = $969000

Step-by-step explanation:

Given that:

Number of projects done in fourth year = 129

Number of projects done in tenth year = 207

There is a fixed increase every year.

a) To find:

Number of projects done in the first year.

This problem is nothing but a case of arithmetic progression.

Let the first term i.e. number of projects done in first year = $a$

Given that:

$a_4=129\\a_{10}=207$

Formula for $n^{th}$ term of an Arithmetic Progression is given as:

$a_n=a+(n-1)d$

Where $d$ will represent the number of projects increased every year.

and $n$ is the year number.

$a_4=129=a+(4-1)d \\\Rightarrow 129=a+3d .....(1)\\a_{10}=207=a+(10-1)d \\\Rightarrow 207=a+9d .....(2)$

Subtracting (2) from (1):

$78 = 6d\\\Rightarrow d =13$

By equation (1):

$129 =a+3\times 13\\\Rightarrow a =129-39\\\Rightarrow a =90$

Number of projects in the first year = 90

b)

Number of projects in the twelfth year =

$a_{12} = a+11d\\\Rightarrow a_{12} = 90+11\times 13 =233$

Each project pays $500

Earnings in the twelfth year = 233 $\times$ 500 = $116500

Sum of an AP is given as:

$S_n=\dfrac{n}{2}(2a+(n-1)d)\\\Rightarrow S_{12}=\dfrac{12}{2}(2\times 90+(12-1)\times 13)\\\Rightarrow S_{12}=6\times 323\\\Rightarrow S_{12}=1938$

It gives us the total number of projects done in 12 years = 1938

Total money earned in 12 years = 500 $\times$ 1938 = $969000

8 0

2 years ago

Can you help me find the slope intercept on the second one?

alexandr1967 [171]

Answer:

y= 8x + 5

Step-by-step explanation:

y = 8x + b

5 = 8(0)+b

b = 5

8 0

2 years ago

Find y when x=9 if y varies directly as the square of x, and y=100 when x=5.

sukhopar [10]

If y varies directly as the square of x, that means that y=k*x^2. Plugging y=100 and x=5 into it, we get 100=k*5^2=k*25. Dividing by both sides, we get k=100/25=4. Going back to the original equation, we now know that y=4*x^2. Plugging 9=x in, we get 4*9^2=4*81=324=y

7 0

3 years ago

Read 2 more answers

What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms? 1,842 1,844 1,846 1,848?

777dan777 [17]

$= \frac{24}{2} (2(8) + 23(6))$
$= 12(16 + 138)$
$= 12(154)$
$= 1848$

6 0

3 years ago

The equation of line AB is (y-3)=5(x-4) what is the slope of a line perpendicular to line AB

Softa [21]

Solving for y, we can start by expanding to get y-3=5x-20. Next, we can add 3 to both sides (to separate y), resulting in y=5x-17. To find the slope in the equation y=mx+b, you simply find what you multiply x by, which is 5 in this case. To find a perpendicular slope, you start by making the slope (5 in this case) negative. Next, we find the reciprocal of the number. Since -5 can be written as -5/1, the reciprocal and therefore perpendicular slope is -1/5

7 0

3 years ago