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juin [17]
3 years ago
5

If you are given the graph of h(x) = log. x, how could you graph m(x) = log2(x+3)?

Mathematics
1 answer:
Agata [3.3K]3 years ago
3 0

Answer:

Option (d).

Step-by-step explanation:

Note: The base of log is missing in h(x).

Consider the given functions are

h(x)=\log_2x

m(x)=\log_2(x+3)

The function m(x) can be written as

m(x)=h(x+3)           ...(1)

The translation is defined as

m(x)=h(x+a)+b           .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

a=3,b=0

Therefore, we have to translate each point of the graph of h(x) 3 units left to get the graph of m(x).

Hence, option (d) is correct.

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Robert painted 4/8 of each tile with green paint. He painted 52 tiles. What is the total amount of tiles that he painted green?
valkas [14]

Answer:

The answer is 26

Step-by-step explanation:

All we do is multiply 4/8 by 52.

52 = 52/1

52/1 * 4/8 = 208/8

208/8 = 26

So the answer is 26.

Hope this helps! :)

3 0
2 years ago
Its worth 25 please help and show work
melamori03 [73]

9514 1404 393

Answer:

  3) y = √10

  4) x = 5√2

Step-by-step explanation:

The side ratios of an isosceles right triangle (one of the "special" right triangles) are ...

  1 : 1 : √2

So, for some multiplier k, they can be made to match the sides in your triangles.

__

3) 1·k : 1·k : k√2 = √5 : √5 : y

Clearly, k = √5, so ...

  y = (√5)(√2)

  y = √10

__

4) k : k : k√2 = x : x : 10

  k = 10/√2 = (5√2)/2

  k = x = (5√2)/2

5 0
2 years ago
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Ro
puteri [66]

Answer:

(a) P(0 ≤ Z ≤ 2.87)=0.498

(b) P(0 ≤ Z ≤ 2)=0.477

(c) P(−2.20 ≤ Z ≤ 0)=0.486

(d) P(−2.20 ≤ Z ≤ 2.20)=0.972

(e) P(Z ≤ 1.01)=0.844

(f) P(−1.95 ≤ Z)=0.974

(g) P(−1.20 ≤ Z ≤ 2.00)=0.862

(h) P(1.01 ≤ Z ≤ 2.50)=0.150

(i) P(1.20 ≤ Z)=0.115

(j) P(|Z| ≤ 2.50)=0.988

Step-by-step explanation:

(a) P(0 ≤ Z ≤ 2.87)

In this case, this is equal to the difference between P(z<2.87) and P(z<0). The last term is substracting because is the area under the curve that is included in P(z<2.87) but does not correspond because the other condition is that z>0.

P(0 \leq z \leq 2.87)= P(z

(b) P(0 ≤ Z ≤ 2)

This is the same case as point a.

P(0 \leq z \leq 2)= P(z

(c) P(−2.20 ≤ Z ≤ 0)

This is the same case as point a.

P(-2.2 \leq z \leq 0)= P(z

(d) P(−2.20 ≤ Z ≤ 2.20)

This is the same case as point a.

P(-2.2 \leq z \leq 2.2)= P(z

(e) P(Z ≤ 1.01)

This can be calculated simply as the area under the curve for z from -infinity to z=1.01.

P(z\leq1.01)=0.844

(f) P(−1.95 ≤ Z)

This is best expressed as P(z≥-1.95), and is calculated as the area under the curve that goes from z=-1.95 to infininity.

It also can be calculated, thanks to the symmetry in z=0 of the standard normal distribution, as P(z≥-1.95)=P(z≤1.95).

P(z\geq -1.95)=0.974

(g) P(−1.20 ≤ Z ≤ 2.00)

This is the same case as point a.

P(-1.20 \leq z \leq 2.00)= P(z

(h) P(1.01 ≤ Z ≤ 2.50)

This is the same case as point a.

P(1.01 \leq z \leq 2.50)= P(z

(i) P(1.20 ≤ Z)

This is the same case as point f.

P(z\geq 1.20)=0.115

(j) P(|Z| ≤ 2.50)

In this case, the z is expressed in absolute value. If z is positive, it has to be under 2.5. If z is negative, it means it has to be over -2.5. So this probability is translated to P|Z| < 2.50)=P(-2.5<z<2.5) and then solved from there like in point a.

P(|z|

7 0
3 years ago
Read 2 more answers
Why is the point ( 3, 4 ) the solution to this system of equations?<br> y= 1/3x + 3<br> y= 2x - 2
evablogger [386]

Answer:

The answer to your question is because it is a solution of each equation.

Step-by-step explanation:

Data

Point (3,4)

Equation l     y = 1/3x + 3

Equation ll     y = 2x - 2

Process

1.- To test is a point is solution to a system of equations,

-Substitute the point in both equations

Equation l            4 = 1/3(3) + 3

                            4 = 1 + 3

                            4 = 4               The point is a solution because

                                                     4 = 4

Equation ll            4 = 2(3) - 2

                             4 = 6 - 2

                             4 = 4               This point is a solution for the second

                                                     equation but not for the first one.

2.- Conclusion

As the point is a solution of each equation, it is a solution of the system.

6 0
3 years ago
☆+☆+☆=18<br>♡+♡+☆=14<br>♤+♤+♡=2<br>♡+♤+☆☆=<br><br>Genius only look closely at the details ​
Dmitriy789 [7]

Answer:

15

Step-by-step explanation:

3 stars = 18

1 star = 6

14-6=8/2 = 4

1 heart = 4

1 spade = -1

4 + -1=  3

3 + (2 stars)

3 + 12 = 15

5 0
3 years ago
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