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3 years ago

The lines below are perpendicular. If the green line has a slope of 2, what is

Mathematics

1 answer:

Tatiana [17]3 years ago

5 0

Answer: The slope of the red line is -1/2

Step-by-step explanation:

For perpendicular slopes, use the reciprocal of the given slope and reverse the sign (additve inverse)

The reciprocal of 2 is 1/2. Reverse from positive to negative so you have -1/2

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4 years ago

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Wally is rebuilding his fence. Each section of the fence will have 12 vertical boards that are each eight inches wide. He’s goin

Leokris [45]

Answer:

Part A)

Each diagonal is about 9.43 feet.

Part B)

In total, Wally needs about 736.02 feet of wood.

Step-by-step explanation:

Part A)

Since each vertical board has a width of 8 inches, for one section with 12 vertical boards, the total width will be 8(12) = 96 inches.

96 inches is the same as 96/12 = 8 feet.

We are also given that the horizontal pieces will be 5 feet apart.

To find the diagonal, we can use the Pythagorean Theorem. The 8 is the base and 5 is the height. Therefore:

$\displaystyle d^2=8^2+5^2$

Compute:

$d^2=89$

Taking the square root, we acquire:

$\displaystyle d=\sqrt{89}\approx9.43 \text{ feet}$

So, each diagonal is about 9.43 feet.

Part B)

For each section, we have two horizontal pieces (each 8 feet) and one diagonal piece (each √89 feet).

Therefore, for one section, we will need a total of:

$\displaystyle L=8+8+\sqrt{89}=16+\sqrt{89}$

Then for 30 sections, we will need:

$T=30(16+\sqrt{89})$

Approximate:

$T\approx 763. 02$

Wally will need about 736.02 feet of wood in total.

3 0

3 years ago

The domain and target set of functions f and g isR. The functions are definedas:(b)•f(x) = 2x+ 3•g(x) = 5x+ 7(a)f◦g?(b)g◦f?(c) (

adoni [48]

Answer:

Step-by-step explanation:

Given the domain and target set of functions f and g expressed as;

f(x) = 2x+3 an g(x) = 5x+7 we are to find the following;

a) f◦g

f◦g = f[g(x)]

f[g(x)] = f[5x+7]

To get f(5x+7), we will replace the variable x in f(x) with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Hence f◦g = 10x+17

b) g◦f

g◦f = g[f(x)]

g[f(x)] = g[2x+3]

To get g(2x+3), we will replace the variable x in g(x) with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

Hence g◦f = 10x+22

c) For (f◦g)−1 (inverse of (f◦g))

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = x-17/10

Hence the inverse of the function

(f◦g)−1 = (x-17)/10

d) For the function f−1◦g−1

We need to get the inverse of function f(x) and g(x) first.

For f-1(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = x-3/2

Hence the inverse of the function

f-1(x) = (x-3)/2

For g-1(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = x-7/5

Hence the inverse of the function

g-1(x) = (x-7)/5

Now to get )f−1◦g−1

f−1◦g−1 = f-1[g-1(x)]

f-1[g-1(x)] = f-1(x-7/5)

Since f-1(x) = x-3/2

f-1(x-7/5) = [(x-7/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f−1◦g−1 = (x-22)/10

e) For the composite function g−1◦f−1

g−1◦f−1 = g-1[f-1(x)]

g-1[f-1(x)] = g-1(x-3/2)

Since g-1(x) = x-7/5

g-1(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= x-17/10

Hence g-1◦f-1 = (x-17)/10

5 0

3 years ago