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2 years ago

If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]?

1 answer:

3 0

<span>If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]? f[g(-5)] means substitute -5 for x in the right side of g(x), simplify, then substitute what you get for x in the right side of f(x), then simplify. It's a "double substitution". To find f[g(-5)], work it from the inside out. In f[g(-5)], do only the inside part first. In this case the inside part if the red part g(-5) g(-5) means to substitute -5 for x in g(x) = (x - 3)/2 So we take out the x's and we have g( ) = ( - 3)/2 Now we put -5's where we took out the x's, and we now have g(-5) = (-5 - 3)/2 Then we simplify: g(-5) = (-8)/2 g(-5) = -4 Now we have the g(-5)] f[g(-5)] means to substitute g(-5) for x in f[x] = 2x + 3 So we take out the x's and we have f[ ] = 2[ ] + 3 Now we put g(-5)'s where we took out the x's, and we now have f[g(-5)] = 2[g(-5)] + 3 But we have now found that g(-5) = -4, we can put that in place of the g(-5)'s and we get f[g(-5)] = f[-4] But then f(-4) means to substitute -4 for x in f(x) = 2x + 3 so f(-4) = 2(-4) + 3 then we simplify f(-4) = -8 + 3 f(-4) = -5 So f[g(-5)] = f(-4) = -5</span>

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Solve the question: (-4)+(-1)+2+5+...+x=437

Alex Ar [27]

The sequence is an arithmetic sequence with
a₁ = -4

d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3

an = x

Sn = 437

General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)

We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7

Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874

Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.

Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50

The solution is 50

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2 years ago

Answer ?? It’s multiplicity

EleoNora [17]

I think A is the answer

3 0

2 years ago

Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of

Shalnov [3]

Answer:

$Owl= 67.14ft$

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

$(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})$

$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

The height of the owl is:

$Owl= H + 5$

$Owl= 62.14 + 5$

$Owl= 67.14ft$

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2 years ago

1/3v= -5 What is the value if v?

beks73 [17]

Given:

$\frac{1}{3}v=-5$

To get rid of the fraction, we can multiply both sides by the denominator, which is 3. This will cancel the fraction:

$3(\frac{1}{3}v)=3(-5)$

We are left with:

$v=-15$

3 0

2 years ago

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RideAnS [48]

Answer:

1.) The product of 12 and 3/4 is less than 12. This is because you are multiplying 12 by a number less than 1.

2.) The product of 5 and 1/2 is less than 5, this is because you are multiplying 5 by a number less than one.

Step-by-step explanation:

If multiplied by a number less than one then it will be smaller than original

If multiplied by one will be the same as original

If multiplied by a number greater than one it will be greater than original

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2 years ago