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chubhunter [2.5K]
3 years ago
10

A builder needs to cover 10 square yards of floor with tile. red tile costs $60 per square yard, and white tole costs $40 per sq

uare yard. if the builder spends exactly $480 on tile, how much of the floor will be overed with RED tile?
Mathematics
1 answer:
dsp733 years ago
6 0

Answer:40 square yards

Step-by-step explanation:

Given

Floor area A=10 square yards

Red tile costs \$ 60 per square yards

White tile costs \$40 per square yards

Total money spent=\$480 on tiles

Suppose red tiles cover an area of x square yards

So, we can write

60\times x+40\times (10-x)=480\\60x+400-40x=480\\20x=80\\x=40\ \text{square yards}

Red tiles cover an area of 40 square yards  

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Step-by-step explanation:

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let x1,x2, and x3 be linearly independent vectors in R^(n) and let y1=x2+x1; y2=x3+x2; y3=x3+x1. are y1,y2,and y3 linearly indep
Nutka1998 [239]

Answer with Step-by-step explanation:

We are given that

x_1,x_2 and x_3 are linearly independent.

By definition of linear independent there exits three scalar a_1,a_2 and a_3 such that

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We have to prove that y_1,y_2 and y_3 are linearly independent.

Let b_1,b_2 and b_3 such that

b_1y_1+b_2y_2+b_3y_3=0

b_1(x_2+x_1)+b_2(x_3+x_2)+b_3(x_3+x_1)=0

b_1x_2+b_1x_1+b_2x_3+b_2x_2+b_3x_3+b_3x_1=0

(b_1+b_3)x_1+(b_2+b_1)x_2+(b_2+b_3)x_3=0

b_1+b_3=0

b_1=-b_3...(1)

b_1+b_2=0

b_1=-b_2..(2)

b_2+b_3=0

b_2=-b_3..(3)

Because x_1,x_2 and x_3 are linearly independent.

From equation (1) and (3)

b_1=b_2...(4)

Adding equation (2) and (4)

2b_1==0

b_1=0

From equation (1) and (2)

b_3=0,b_2=0,b_3=0

Hence, y_1,y_2 and y_3 area linearly independent.

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3 years ago
There are 30 books on the library shelf, Sam noted that 1/6 of them are non fiction. Dan notes that 3/5 of the books are fiction
ehidna [41]

Answer:

7

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23 of the books are either fiction or non fiction.

30 - 23, or 7, of the books remain (are neither fiction nor non-fiction).

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3 years ago
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