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faltersainse [42]
3 years ago
7

Use matrices to determine the vertices of the reflected figure. Then graph the image and the pre-image on the same coordinate gr

id.
Triangle XYZ with vertices X(2, -9), Y(-6, 0) and Z(-5, -5), reflected over the y-axis.
A.
B.
C.
D.
(pictures below)

Mathematics
1 answer:
Amanda [17]3 years ago
3 0

Answer:

  • see below for the matrix multiplication
  • graph C

Step-by-step explanation:

Reflection across the y-axis is a left-right reflection that changes only the sign of the x-coordinate. The transformation matrix (as for any rotation and/or reflection) can be 2-dimensional, and can left-multiply the coordinate matrix that has coordinate pairs as column vectors. The transformed coordinates show up as column vectors in the result matrix.

The only graphs showing left-right reflections are those of choices C and D. Only choice C has the points properly plotted on the graph.

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Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b
Ronch [10]

Answer:

4^x-5=6 gives the solution x=\frac{\log(11)}{\log(4)}.

4^{x-5}=6 gives the solution x=\frac{\log(6)}{\log(4)}+5.

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is 4^{x}-5=6, then the following is the process:

4^x-5=6

Add 5 on both sides:

4^x=6+5

Simplify:

4^x=11

Now write an equivalent logarithm form:

\log_4(11)=x

x=\log_4(11)

Now using the change of base:

x=\frac{\log(11)}{\log(4)}.

If we assume the equation is 4^{x-5}=6, then we use the following process:

4^{x-5}=6

Write an equivalent logarithm form:

\log_4(6)=x-5

x-5=\log_4(6)

Add 5 on both sides:

x=\log_4(6)+5

Use change of base formula:

x=\frac{\log(6)}{\log(4)}+5

6 0
3 years ago
5929×2959-300+900=________
miskamm [114]

Answer:17,544,511

Step-by-step explanation: 5929 x 2959= 17,543,911

17,543,911-300= 17,543,611

17,543,611 + 900 = 17,544,511

4 0
3 years ago
Read 2 more answers
A steel worker dropped his wrench off the top of a new high rise building. How far will the wrench fall in 3 seconds?
rosijanka [135]
Using  S = ut + 1/2gt²,   from rest, u = 0

S = 1/2gt²,               g ≈ 9.8 m/s²

S = <span>1/2 *9.8*3²

</span>S = 0.5<span> *9.8*3*3 
</span>
<span>S ≈ 44.1 m</span>
6 0
3 years ago
The chorus teacher plans to arrange the students in equal rows. Only the girls or boys will be in each row. What is the greatest
emmainna [20.7K]

Answer:

2

Step-by-step explanation:

68+48=116

116÷16=7.24 (wrong)

116÷12=9.7 (wrong)

116÷4=29 (lowest even)

116÷2=58 (highest even)

If I'm wrong, let me know

8 0
2 years ago
Listed below are prices in dollars for one night at different hotels in a certain region. Find the​ range, variance, and standar
Artyom0805 [142]

Answer:

Range = 115$

Standard Deviation = 43.76$

Variance = 1915.142$

Option  A) The measures of variation are not very useful because when searching for a​ room, low​ prices, location, and good accommodations are more important than the amount of variation in the area.

Step-by-step explanation:

We are given the data for  prices in dollars for one night at different hotels in a certain region.

234, 160, 119, 131, 218, 207, 146, 141        

Range:

Sorted data: 119, 131, 141, 146, 160, 207, 218, 234

\text{Range} = 234-119 = 115\$

Standard Deviation:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{1356}{8} = 169.5

Sum of squares of differences = 4160.25 + 90.25 + 2550.25 + 1482.25 +  2352.25 + 1406.25 + 552.25 + 812.25 = 13406

\sigma = \sqrt{\dfrac{13406}{7}} = 43.76\$

Variance =

\sigma^2 = 1915.142\$

Measure of variance for someone searching for room:

Option  A) The measures of variation are not very useful because when searching for a​ room, low​ prices, location, and good accommodations are more important than the amount of variation in the area.

5 0
3 years ago
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