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notsponge [240]
3 years ago
6

For f(x)=3x+1 and g(x)=x^2-6 find (fog)(4)

Mathematics
1 answer:
m_a_m_a [10]3 years ago
6 0
F(x) = 3x+1
G(x) = X^2 - 6
F(G(x)) = F(X^2 - 6) = 3(X^2 - 6) + 1 = 3X^2 - 18 + 1 = 3X^2 -17
F(G(x)) = 3X^2 - 17
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<img src="https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%209%20%2B%202x%20-%203y%20%3D%208" id="TexFormula1" title="x + y = 9 + 2x -
Vadim26 [7]

Answer:

(7,2)

Step-by-step explanation:

x + y = 9 + 2x - 3y = 8 is really two equations, and you should show this by separating x + y = 9 from 2x - 3y = 8 through the use of a comma, or the word "and," or through writing only one equation per line.

Here you have the system of linear equations

 x +   y =  9

2x - 3y = 8.

Let's solve this system by elimination.  Mult. the 1st eqn by 3, obtaining the system

3x + 3y = 27

2x - 3y =    8

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

5x = 35, so that x = 7.  Subbing 7 for x in x + y = 9, we get 7 + y = 9, indicating that y = 2.

Thus, the solution to this system of equations is (7,2).


6 0
2 years ago
Determine whether the triangles are similar. If so, write a similarity<br> statement.
Y_Kistochka [10]

Answer:

yes that are similar

Step-by-step explanation:

because the angles are both 50 degrees

similarity statement:

triangle DEF= triangle JEH

hope that helps bby<3

4 0
3 years ago
The sum of two consecutive even integers is 118. Find the smaller of the two integers.
kaheart [24]

Answer:

58 + 60

Step-by-step explanation:

Even integers are always seperated by 2.

6 0
2 years ago
Adam divides 32/8032. In which place should he write the first digit of the quotient?
kow [346]

Answer:

We have a quotient between a 2 digit number and a 4 digit number.

The usual rule for this type of problems is:

If the denominator has n more digits than the numerator, then the first digit will be in the nth position at the right of the decimal point.

If also, the denominator is larger than the numerator times 10^n, then the decimal will be moved another place to the right.

For example, if we divide 10 by 100 we have:

10/100

The denominator has one more digit than the numerator, then n = 1.

this means that the first digit of the quotient, will be on the first place at the left of the decimal point.

We can solve the quotient to get:

10/100 = 0.1

And, as we predicted, the first decimal is in the first place.

Now, with our quotient we have:

32/8032

n = 2.

and:

32*10^n = 3200

The denominator is larger than this, then we will move the first decimal to another place to the right.

Then we should expect to have the first decimal in the third place after the decimal point.

We can solve the quotient to get:

32/8032 = 0.0039

As we expected.

3 0
2 years ago
How to change the expression to a single logarithm
IrinaK [193]
First, you'll use the "Log power rule," which says that \log_ax^p=p\log_ax. In this case, you're going from the form on the right (with p in front of the log) to the form on the left (with p in the exponent position). So, the expression becomes:

\log_7x^4+\log_7y^8+\log_7z^4

Then, you'll use the "Log product rule," which says that \log_a(xy)=\log_ax+\log_ay. Again, you're going from the form on the right to the form on the left (basically, from the sum of the logs, to a log of the products). So you get:

\log_7(x^4y^8z^4)

There's your expression simplified into a simple logarithm. 
6 0
3 years ago
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