All categories

3 years ago

Which sequence of transformations produces R’S’T’ from RST?

Mathematics

1 answer:

inn [45]3 years ago

6 0

Answer:

A translation 2 units right and then a reflection over the x-axis

Step-by-step explanation:

The given vertices of ΔRST are R(0, 0), S(-2, 3), and T(-3, 1)

The vertices of triangle ΔR'S'T' are (2, 0), (0, -3), (-1, -1)

The points are plotted with the aid of MS Excel, and by observation, we have that the image of ΔRST is located on the other side of the x-axis with each coordinate on ΔR'S'T' shifted 2 units to the right of ΔRST

A translation of ΔRST 2 units right gives;

(0 + 2, 0) = (2, 0), (-2 + 2, 3) = (0, 3), and (-3 + 2, 1) = (-1, 1), to give;

(2, 0), (0, 3), and (-1, 1)

A reflection of the point (x, y) across the x-axis gives (x, -y)

A reflection of the above points across the x-axis gives;

(2, 0) reflected about x-axis → (2, 0) reflected about x-axis → (0, -3), and (-1, 1) reflected about x-axis → (-1, -1), which are the points of ΔR'S'T'

Therefore, the sequence of transformations that produces R'S'T' from RST are;

A translation 2 units right and then a reflection over the x-axis

You might be interested in

Drake wants to save $750 so that he can take a class on computer analysis for cars. The class is being held on various dates ove

STatiana [176]

C. Both options A and B will allow him to meet his goal.

Looking at Drake's situation after 4 weeks, he only has $470 saved. By his original plan, he should have had $500 saved. So he's $30 short of his goal and has 2 weeks until his originally planned class. If he goes with option A and takes the later class, he will save an additional $125 which is more than enough to make up the $30 short fall. So option A will work for him to save enough money for his class. With option B, he will save $140 for the last 2 weeks of his plan giving him a savings of $280 for the last 2 weeks. Adding the $470 he's already saved will give him a total savings of $470 + $280 = $750 which is enough for him to attend his class. So option B will also allow Drake to attend his desired class. Both options A and B allow him to meet his goal. Hence, the answer is "c".

8 0

3 years ago

One ounce of olive oil costs $0.23. How much does the whole bottle cost if it contains 32 ounces?

Gwar [14]

Answer:$7.36

Step-by-step explanation:

Just multiply 0.23 with 32

7 0

2 years ago

Read 2 more answers

Please help, I need this quickly. Fairly easy, help pleasee

ahrayia [7]

-4x-3y-9=0
|| m1 = - ( - 4)/-3= - 4/3
_|_ m2 = -1/m1= 3/4

2x+4y-3=0
|| m1= -2/4= -1/2
_|_ m2= 2

12x-y-17=0
|| m1= -12/-1=12
_|_ m2 = -1/12

x-y=0
|| m1= -1/-1=1
_|_ m2= -1

8x - 3y - 2=0
|| m1= -8/-3= 8/3
_|_ m2 = -3/8

-2x + y - 5=0
|| m1= -(-2)/1=2
_|_ m2= -1/2

3 0

3 years ago

What is the probability of rolling a four then a three

spayn [35]

Answer:

$\frac{1}{36}$

Step-by-step explanation:

Total possibilities when we a roll a die at a time are 6

given we should have four for first time and then three

let us assume we rolled the dice we may get 1,2,3,4,5,6(any of these) the probability to get 4 is

PROBABILITY= $\frac{\textrm{FAVOURABLE CHANCES}}{\textrm{TOTAL CHANCES}}$

Favourable chances=1

Total chances=6

Probability= $\frac{1}{6}$

the prabability to get 4 in first roll is $\frac{1}{6}$ .

let us assume we rolled the dice for second time again we may get 1,2,3,4,5,6(any of these) the probability to get 3 is

Favourable chances=1

total chances=6

probability= $\frac{1}{6}$

the probability to get 3 in second roll irrespective of first one is $\frac{1}{6}$

the probability to get 4 in first time and then 3 is

The probability to occur both events at a time is multiplication of individual probabilities

So,

probablility to get 4 in first roll= $\frac{1}{6}$

probability to get 3 in second roll= $\frac{1}{6}$

probability to occur both at a same time is = $\frac{1}{6}$ $\times$ $\frac{1}{6}$ = $\frac{1}{36}$

6 0

2 years ago

Is anybody else here to help me ??

Akimi4 [234]

Answer:

$\cot(x)+\cot(\frac{\pi}{2}-x)$

$\cot(x)+\tan(x)$

$\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}$

$\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})$

$\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})$

$\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}]$

$\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}]$

$\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]$

$\csc(x)[\frac{1}{\cos(x)}]$

$\csc(x)[\sec(x)]$

$\csc(x)[\csc(\frac{\pi}{2}-x)]$

$\csc(x)\csc(\frac{\pi}{2}-x)$

Step-by-step explanation:

I'm going to use $x$ instead of $\theta$ because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

$\cot(x)+\cot(\frac{\pi}{2}-x)$

I'm going to use a cofunction identity for the 2nd term.

This is the identity: $\tan(x)=\cot(\frac{\pi}{2}-x)$ I'm going to use there.

$\cot(x)+\tan(x)$

I'm going to rewrite this in terms of $\sin(x)$ and $\cos(x)$ because I prefer to work in those terms. My objective here is to some how write this sum as a product.