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n200080 [17]
3 years ago
5

⅓(5x-4) >x+11/12. Topic(Linear Inequalities​

Mathematics
1 answer:
Zolol [24]3 years ago
5 0

Answer:

1/3(5x_4)>x+11/12

multiply through by 12

4(5x_4)>12x+11

20x_16>12x+11

20x-12x>11+16

8x>27

x>27/8

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What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE
maks197457 [2]

Given:

The equation of a line is:

2y+3x=10

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

2y+3x=10

For x=0,

2y+3(0)=10

2y+0=10

y=\dfrac{10}{2}

y=5

For x=2,

2y+3(2)=10

2y+6=10

2y=10-6

2y=4

Divide both sides by 2.

y=\dfrac{4}{2}

y=2

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

(x,y)\to (3x,3y)

Using this rule, we get

A(0,5)\to A'(3(0),3(5))

A(0,5)\to A'(0,15)

Similarly,

B(2,2)\to B'(3(2),3(2))

B(2,2)\to B'(6,6)

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-15=\dfrac{6-15}{6-0}(x-0)

y-15=\dfrac{-9}{6}(x)

y-15=\dfrac{-3}{2}x

Multiply both sides by 2.

2(y-15)=-3x

2y-30=-3x

2y+3x=30

Therefore, the equation of the line after the dilation is 2y+3x=30.

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Read 2 more answers
The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find th
Aneli [31]

Answer:

The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of a CD player with a selling price of $110.

A. f(x) = 5 + x; $111.05

B. f(x) = 0.05x; $5.50

C. f(x) = x � 5; $108.95

D. f(x) =1.05x; $115.50  

total cost = (price) + (5% of price)

f(x) = x + 0.05x

f(x) = 1.05x

So the function is f(x) = 1.05x

Plug in x = 110 to get

f(x) = 1.05x

f(110) = 1.05*110

f(110) = 115.50

The item costs $115.50 (after tax is added on)

Step-by-step explanation:

1:    the total cost of a CD player would be 104.76

2:    Total Cost = (price) + (5% of price)

f(x) = x + 0.05x

f(x) = 1.05x

So the function is f(x) = 1.05x

Plug in x = 110 into the function

f(110) = 1.05*110

f(110) = 115.50

The item costs $115.50

3:    Answer:

f(x) = .05x; $5.50

Step-by-step explanation:

f(x) = .05x

f(110) = .05(110) = $5.50

7 0
3 years ago
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