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3 years ago

Please please need help on these two

Mathematics

1 answer:

kati45 [8]3 years ago

6 0

Answer:

( f + g ) (x) = $2 x^{2} + x - 4$

g(x) - f(x) = $x^{2} - 2 x - 4$

Step-by-step explanation:

f(x) = 4 x - 4 and g(x) = $2 x^{2} - 3 x$

( f + g ) (x) = f(x) + g(x)

= $4 x - 4 + 2 x^{2} - 2 x$

= $2 x^{2} + x -4$

2. g(x) = $x^{2} + 1$ and f(x) = 2 x + 5

g(x) - f(x) = $x^{2} + 1 - (2 x + 5)$

= $x^{2} + 1 - 2 x - 5$

= $x^{2} - 2 x - 4$

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4 years ago

Express 3^4 = x as a logarithmic equation.

meriva

Note that the base in both the exponential form of the equation and the logarithmic form of the equation (above) is "b", but that the x and y switch sides when you switch between the two equations. If you can remember this — that whatever had been the argument of the log becomes the "equals" and whateverhad been the "equals" becomes the exponent in the exponential, and vice versa — then you should not have too much trouble with solving log equations.

Solve log2(x) = 4.

Since this is "log equals a number", rather than "log equals log", I can solve by using The Relationship:
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24 = x
16 = x

Solve log2(8) = x.

I can solve this by converting the logarithmic statement into its equivalent exponential form, using The Relationship:log2(8) = x
2 x = 8But 8 = 23, so:2 x = 23
x = 3

Note that this could also have been solved by working directly from the definition of a logarithm: What power, when put on "2", would give you an 8? The power 3, of course!

If you wanted to give yourself a lot of work, you could also do this one in your calculator, using the change-of-base formula:

log2(8) = ln(8) / ln(2)

Plug this into your calculator, and you'll get "3" as your answer. While this change-of-base technique is not particularly useful in this case, you can see that it does work. (Try it on your calculator, if you haven't already, so you're sure you know which keys to punch, and in which order.) You will need this technique in later problems.

Solve log2(x) + log2(x – 2) = 3I can't do anything yet, because I don't yet have "log equals a number". So I'll need to use log rules to combine the two terms on the left-hand side of the equation:log2(x) + log2(x – 2) = 3 
log2((x)(x – 2)) = 3 
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8 = x2 – 2x 
0 = x2 – 2x – 8 
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x = 4, –2But if x = –2, then "log2(x)", from the original logarithmic equation, will have a negative number for its argument (as will the term "log2(x – 2)"). Since logs cannot have zero or negative arguments, then the solution to the original equation cannot be x = –2.The solution is x = 4.

Keep in mind that you can check your answers to any "solving" exercise by plugging those answers back into the original equation and checking that the solution "works":

log2(x) + log2(x – 2) = 3 
log2(4) + log2(4 – 2) ?=? 3 
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Since the power that turns "2" into "4" is 2 and the power that turns "2" into "2" is "1", then we have:

log2(4) + log2(2) ?=? 3 
log2(22) + log2(21) ?=? 3 
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Solve log2(log2(x)) = 1.This may look overly-complicated, but it's just another log equation. To solve this, I'll need to apply The Relationship twice:log2(log2(x)) = 1
21 = log2(x) 
2 = log2(x) 
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3 years ago

Read 2 more answers

The sum of the measures of the angles of any triangle is 180 degrees. in triangle abc, angles a and b have the same measure, w

frutty [35]

Its given that the sum of the values of total angles of a triangle is 180. It is also given that angles a and b are equal and that value of c is 72. Thus we get the following equation:

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2a = 108

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3 years ago

The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d re

alexandr1967 [171]

Answer: A ,C,G and H are correct statements. Look into the step by step for more understanding.

Step-by-step explanation:

To solve for this problem let's find the actually numbers.

so we know that c + d=58 and also c= 1/2d-8

We have two systems of equations

c+d = 58

c= 1/2d - 8

Solve for c by substitution. Substitute the second equation into the first one.

1/2d -8 + d = 58 Add 8 to both sides

1/2 +d = 66

3/2d =66 Divide both sides by 3/2

d=44 Now we know the d which is the second number is 44 so subtract it from 58 to find the first number.

58 - 44 = 14

we will represent the statements by letters from A going.

A. The equation c + d = 58 represents the sum of the two numbers

B. The equation c+d=58 represents the sentence "The first number is 8 less than half the second number."

C.The equation c= 1/2d -8 represents the relationship between the two numbers.

D. The equation c= 1/2d - 8 represents the sum of the two numbers.

E. The number d is 14.

F. The number c is 44.

G. The number c is 14.

H. The number d is 44.

Now looking at the statements, A ,C,G and H are all correct.

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3 years ago

Determine if The square root of 9 is rational or irrational and give a reason for your answer.

Mademuasel [1]

Answer:

As square root of 9 can be written in the required form for being a rational number, so it is a rational number

Step-by-step explanation:

First of all we'll define rational numbers.

A number that can be written in the form p/q where p and q are integers and q≠0 is called a rational number.

Now we have to check if $\sqrt{9}$ is rational or not, we will check if it can be written in the form p/q

$\sqrt{9} => \frac{\sqrt{9}}{1} => \frac{3}{1}$

As square root of 9 can be written in the required form for being a rational number, so it is a rational number

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3 years ago