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worty [1.4K]
3 years ago
10

Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (2,-2)

Mathematics
2 answers:
ZanzabumX [31]3 years ago
4 0

Answer:

y=\log_{\frac{1}{2}}(x+2).

Step-by-step explanation:

Find the equation of the transformed logarithm as y=\log_a (x-b).

For the point (-2,0):

0=\log_a (-2-b).

For the point (2,-2):

-2=\log_a (2-b).

Solve the system of equations:

\left\{\begin{array}{l}0=\log_a (-2-b)\\-2=\log_a (2-b)\end{array}\right.\Rightarrow \left\{\begin{array}{l}b=-2\\-2=\log_a 4\end{array}\right.

Then

a^{-2}=a^{\log_a 4} \Rightarrow \dfrac{1}{a^2}=4,\ a=\dfrac{1}{2}.

The equation of the function is y=\log_{\frac{1}{2}}(x+2).

Art [367]3 years ago
3 0

The correct answer is: f(x)=\frac{-2log(x+3)}{log(5)}

(In compact form: f(x) = -2log_5(x+3))

Explanation:

Follow these steps...

1. As it is a logarithmic graph, but reflected along x-axis, the general form of the function will be the following:

f(x) = -a*log(x) + k --- (A)

Where <em>a</em> represent the scale of the logarithmic graph, and <em>k </em>represents whether the graph is shifted down or up.

The negative sign indicates that the graph is reflected along the x-axis.

2. The vertical asymptote is at x = -3, the equation (A) will now become the following:

f(x) = -a*log(x + 3) + k --- (B)

The (x+3) part of the above equation shows that the graph is shifted 3 units towards left.

3. Now we need to find <em>k</em> and <em>a</em>. For finding <em>k, </em>plug in the point (-2,0) in equation (B):

0 = -a*log(-2+3) + k

0 = -a*0 + k

k = 0

4. For finding <em>a</em>, plug in the point (2,-2) and the value of k=0 in equation (B):

-2 = -a*log(2+3) + 0

a = 2/log(5)


Now plug in the values of <em>a</em> and <em>k </em>in equation (B), you will get the answer:

f(x) = -(2/log(5))*log(x+3) + 0


Therefore, the correct answer is:

f(x)=\frac{-2log(x+3)}{log(5)}

or, in compact form:

f(x) = -2log_5(x+3)


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Tara wants to weigh her three stuffed animals. They will only fit on the scale two at a time. Together Addie and Missy weight 18
Pepsi [2]

Answer: Addie weighs 4 ounces

Missy weighs 14 ounces

Corky weighs 8 ounces

Step-by-step explanation:

Let a represent the weight of Addie.

Let m represent the weight of Missy.

Let c represent the weight of Corky.

Together Addie and Missy weigh 18 ounces. This means that

a + m = 18 - - - - - - - - - 1

Missy and Corky weigh 22 ounces. This means that

m + c = 22

m = 22 - c - - - - - - - - - - 2

Addie and Corky weigh 12 ounces. This means that

a + c = 12

a = 12 - c - - - - - - - - - - - 3

Substituting equation 2 and equation 3 into equation 1, it becomes

22 - c + 12 - c = 18

34 - 2c = 18

- 2c = 18 - 34 = - 16

c = - 16/ - 2 = 8

Substituting c = 8 into equation 2, it becomes

m = 22 - 8

m = 14

Substituting c = 8 into equation 3, it becomes

a = 12 - 8

a = 4

3 0
3 years ago
(x+3)^2 + 16/(x+3)^2 = 92 <br><br> x + 1/(x+3) = ??
Irina-Kira [14]
One
Remark

This is very complicate unless you pick the right method. It's very handy o know about substitutions.

Method
Let z = (k + 2)^2

Now the problem becomes
z + 16/z = 92           Multiply through by z 

Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer. 

Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.

Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9  + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828  Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803


It looks that way from the second question. If I'm wrong about that, put a comment down below.

Two
 Put over a common denominator and expand
\frac{(x + 3)^2 + 1}{(x + 3)^2}  =  \frac{x^2 + 6x + 9 + 1}{x^2 + 6x + 9} =  \frac{x^2 + 6x + 10}{x^2 + 6x + 9}
3 0
3 years ago
Alex buys a subscription to a streaming site. The function describes the 5.50m c=3+2 cost of the yearly subscription,c, in terms
azamat

Answer:

5.50 = c = 3 + 5 = 7c \\  \\ then \: divide \: 5.50to \: the7 \\  \\

Step-by-step explanation:

the answer u will get after

3 0
3 years ago
50 POINTS NO JOKE IM DYING I NEED HELP
Effectus [21]

Answer:

9 x 7 = 63 is cost of 9 people

3 x 9

6 x 8

8 x 8

9 x 7

3 0
3 years ago
James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The
Brrunno [24]

Answer:

The correct option is 4.

Step-by-step explanation:

Given information:

Bring lunch : 46 males, 254 females

Buy lunch   : 176 males, 264 females

Total number of peoples is

46+254+176+264=740

Total number of males is

46+176=222

The probability of male is

P(Male)=\frac{Males}{Total}=\frac{222}{740} =0.3

Since probability of males is 0.3, therefore options A and C are incorrect.

Total number of persons who buys lunch is

176+264=440

The probability of persons who buys lunch is

P(\text{Buys lunch})=\frac{\text{Buys lunch}}{Total}=\frac{440}{740} =\frac{22}{37}

We need to find the probability of P(male | buys lunch).

According to the conditional probability, we get

P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}

P(male | buys lunch)=\frac{P(\text{male }\cap \text{ buys lunch})}{P(\text{buys lunch})}

P(male | buys lunch)=\frac{\frac{176}{740}}{\frac{22}{37}}

P(male | buys lunch)=\frac{2}{5}=0.4

Therefore the correct option is 4.

8 0
3 years ago
Read 2 more answers
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