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2 years ago

7

Peter bought 90 boards for $270.

1 answer:

Vesnalui [34]2 years ago

8 0

The algebraic expression would be
n=$270/90
the value of n to the expression is equal to 3 meaning that 20 boards would cost $60

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The length of a rectangle is 3 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 264 feet, f

Digiron [165]

L = 2w - 3

p = 264

2(L + w) = p

2(2w - 3 + w) = 264

2(3w - 3) = 264

6w - 6 = 264

6w = 270

w = 270/6

w = 90/2

w = 45

L = 2w - 3

L = 2(45) - 3

L = 90 - 3

L = 87

The length is 87ft, and the width is 45ft

7 0

3 years ago

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Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

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$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

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Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

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(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

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3 years ago

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PIT_PIT [208]

Let's start with a picture.

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If we look at the difference of points (technically called vectors but we don't have to go there) we get

C-B=(-2,2)

T-S=(1,-1)

Without further calculation we can see T-S is half the length of C-B.

The problem asks for a dilation followed by a reflection. We know the dilation scale is k=1/2 because the new triangle is half the size.

After dilation we get A'B'C':

A'(3,2), B'(-1,0), C'(-2,1)

We see now we need a reflection that flips the coordinates x and y. That's the +45° line through the origin, namely y=x.

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3 years ago

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krok68 [10]

Answer:

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2. 7/8

3. 1/2

4. 5/4

5. 4/5

6. 5/4

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8. 5/2

9. 11/12

10. 2/3

11. 13/20

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14. 7/18

15. 2/3

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17. 5/12

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4 years ago

Susy has 14 dogs and 9 cats. How many pets does she have

Naily [24]

Answer:

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Step-by-step explanation:

If Susy has 14 dogs and 9 cats she has 23 pets in all.

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9 cats

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Therefore, Susy has 23 pets.

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3 years ago

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