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telo118 [61]
2 years ago
10

The functions fand g are defined as follows:

Mathematics
1 answer:
LuckyWell [14K]2 years ago
6 0

Step-by-step explanation:

Given

f(x) = -5x - 1

and

g(x) = 2x + 2

Now

f(3) = - 5 * 3 - 1

= -15 -1

= -16

Also

g(-4) = 2 * (-4) + 2

= - 8 + 2

= - 6

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PRACTICE ANOTHER A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an
sergejj [24]

Answer:

Step-by-step explanation:

We have the equations

4x + 3y = 18   where x = the side of the square and y = the side of the triangle

For the areas:

A = x^2 + √3y/2* y/2

A = x^2  + √3y^2/4

From the first equation x = (18 - 3y)/4

So substituting in the area equation:

A = [ (18 - 3y)/4]^2 + √3y^2/4

A = (18 - 3y)^2 / 16 + √3y^2/4

Now for maximum / minimum area the derivative = 0 so we have

A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0

-3/8 (18 - 3y) + √3 y /2 = 0

-27/4 + 9y/8 + √3y /2 = 0

-54 + 9y + 4√3y = 0

y = 54 / 15.93

= 3.39 metres

So x = (18-3(3.39) / 4 = 1.96.

This is a minimum value for x.

So the total length of wire the square  for minimum  total area is 4 * 1.96

= 7.84 m

There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.

3 0
3 years ago
I’ll mark brainliest what’s 1228822882-1228822882?
xxMikexx [17]

0

Subtract

Answer is 0

Hope this helps

God bless!

4 0
2 years ago
Read 2 more answers
The hypotenuse of a right triangle is 10 ft long. the shorter leg is 2ft shorter than the longer leg. find the side lengths of t
Gwar [14]
Since we have two possible pieces of information and 2 items to solve for, we know this is a system of equations.
Our first piece of information is that our shorter leg (s) is 2 feet shorter than our longer leg (l). This can be written as s=l-2.
Our second piece of information is that using the Pythagorean theorem that our shorter leg squared plus our longer leg squared is equal to our hypotenuse squared. This can be represented by s^2+l^2=10^2. Now we can solve.
We have already isolated for s in our first equation, so we can substitute l-2 in.
(l-2)^2+l^2=10^2
l-2+l=10
2l-2=10
2l=12
l=6
Now we can substitute in for s in our simpler equation
s=6-2
s=4
We now know that using our knowledge of systems of equations, the side lengths of this right angle triangle are 6 and 4.
5 0
3 years ago
Solve for g:<br> 3/16=(-5/4)+g
Musya8 [376]

Answer:

g = 23/16

Step-by-step explanation:

3/16 = (-5/4) + g

g = 5/4 + 3/16

g = 23/16

7 0
2 years ago
If f(x) = x² - 2x, find:<br> ƒ(6) = [ ? ]
zhannawk [14.2K]

<u>Answer:</u>

24

<u>Step-by-step explanation:</u>

To find ƒ(6), we have to substitute x = 6 into the expression for ƒ(x):

ƒ(6) = (6)² - 2(6)

      = 36 - 12

      = 24

7 0
1 year ago
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