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3 years ago

If f(x)=7x-3 and g(x)=x^2-4x-8, Find (f+g)(x)

Mathematics

2 answers:

IrinaK [193]3 years ago

6 0

For this case we have the following functions:

$f (x) = 7x-3\\g (x) = x ^ 2-4x-8$

We must find $(f + g) (x):$

By definition we have to:

$(f + g) (x) = f (x) + g (x)\\(f + g) (x) = 7x-3 + x ^ 2-4x-8$

We add similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

$(f + g) (x) = x ^ 2 + 3x-11$

Answer:

$(f + g) (x) = x ^ 2 + 3x-11$

Xelga [282]3 years ago

3 0

Answer:

Step-by-step explanation:

The value of (f+g)(x) is x^2 + 3x - 11

You can combine this by simply adding the like terms. Start by adding together all of the x^2 terms. Since only g(x) has one of those, we use that in its entirety.

x^2

Next we add together the x terms. f(x) has 7x and g(x) has -4x.

7x + -4x = 3x

Finally, we add together the constants. f(x) has -3 and g(x) has -8.

-3 + -8 = -11

With all of the like terms combined, we simply take the answers and put them together.

x^2 + 3x - 11

Read more on Brainly.com - brainly.com/question/10711144#readmore

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(9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

asambeis [7]

Answer:

3 roots

Step-by-step explanation:

(9x+7)(4x+1)(3x+4)=0

x=-7/9 or - 1/4 or - 4/3

3 0

2 years ago

Toa has 4 dimes a 12 nickels.Gail has 2 dimes and 3 nickels. What would be the ratio of dimes to nickels if they put these toget

Free_Kalibri [48]

Answer:

2 : 5

Step-by-step explanation:

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

We are to determine the ratio of dimes to nickels

total sum of nickels = 3 + 12 = 15

total sum of dimes = 4 + 2 = 6

6 : 15

three can divide each of the numbers

2 : 5

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2 years ago

Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and

Natali [406]

Answers:

Total equation: x+y = 80
Legs equation: 2x+4y = 248
How many ducks? 36
How many cows? 44

====================================================

Further explanation:

x = number of ducks
y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

2x = number of legs from all the ducks only
4y = number of legs from all the cows only
2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

5 0

2 years ago

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Oliga [24]

Answer:

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Step-by-step explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

$V_{C}=(10)^3=1000\text{ cm}^3$

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

$V_R=h(25)(20)=500h\text{ cm}^3$

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

$500h=1000$

Therefore:

$h=2$

So, the height of the water level in the rectangular vessel is 2 centimeters.

To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

$A_{R_M}=20(25)(10)=5000 \text{ cm}^3$

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

$(5000-1000)\text{ cm}^3=4000\text{ cm}^3$

Sincer 1000 cubic centimeters is 1 liter, this means that we will need four more liters of water in order to fill the rectangular vessel.

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3 years ago

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A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned i

olganol [36]

Answer:

Point C at (-18/7)

Step-by-step explanation:

Point A is at -6 and point B is at 2.

So, the distance between A and B = 2 - (-6) = 8

point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4.

Let the distance AC = x

∴ BC = 8 - x

AC : CB = 3 : 4

∴ $\frac{AC}{CB} =\frac{3}{4} = \frac{x}{8-x}$

Using cross multiplication

3 (8-x) = 4x

24 - 3x = 4x

24 = 7x

x = 24/7

So, Point C = -6 + 24/7 = -18/7

Point C at (-18/7)

7 0

3 years ago

Read 2 more answers