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Ad libitum [116K]
3 years ago
15

A triangle has vertices T(3, 7), U(6, –6), and V(5, –9). The image of the triangle has vertices T"(8, 1), U"(–5, 4), and V"(–8,

3).
Which transformations could have produced the image?

T(1, –2) ry = x
ry = x T(1, –2)

Mathematics
1 answer:
inessss [21]3 years ago
3 0
The answer:

the main rule of transformation are as follow

Reflection:a reflection in the line y = x changes the point (x; y) to (y; x)
 
the transformation T(a, b), changes changes the point (x; y) to (x+a ; y+ b)

the construction of the image is as follow:

as for T(3, 7), the image is  T"(8, 1)

so with the reflection in the line y = x, T(3, 7) becomes T' (7, 3), and with the transformation T(1, –2),  the point T' (7, 3) becomes (7+1, 3 -2) =T"(8, 1)

with the reflection in the line y = x, U(6, –6) becomes U'(-6, 6), and with the transformation T(1, –2),  the point U'(-6, 6) becomes (-6 +1, 6-2)=U"(–5, 4)

with the reflection in the line y = x, V(5, –9) becomes V'(-9, 5), and with the transformation T(1, –2),  the point V'(-9, 5)  becomes (-9 +1, 5-2)=U"(–8, 3)

so the final answer is

<span>r y = x and  then T(1, –2)</span>

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Suppose we went to choose 2 letters without replacement from 3 letters a b and c
vagabundo [1.1K]

Answer:

6 ways -  ab,ac, ba,bc and ca,cb

Step-by-step explanation:

We are given 3 letters a,b,c.

We can choose the first letter in 1 out of 3 ways.

Once the first letter has been chosen without replacement, we have two letters remaining. Another letter can be chosen from the 2 remaining letters in  2 ways. So the total number of ways of choosing the two letters is 3*2 = 6.

Listing out the possible set of choices:

Options include: ab,ac, ba,bc and ca, cb

3 0
3 years ago
What is the y intercept of c=0.05m+4.95
Burka [1]
The y intercept is where m=0. Hence, set m=0 and solve for c:
c=0.05(0)+4.95
c=4.95

7 0
3 years ago
Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
A pizza place offers 3 different cheeses and 12 different toppings. In how many ways can a pizza be made with 1 cheese and 3 top
svetlana [45]
You have to choose 1 sort of cheese from 3 ( 3 ways ). Also you have to choose 3 toppings from 12 different toppings:
12 * 11 * 10 = 1,320 ways.
In total: 3 * 1,320 = 3,960
Answer:
In 3,690 ways can pizza be made with 1 cheese and 3 toppings.
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3 years ago
A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to t
zzz [600]

Answer:

Step-by-step explanation:

D)hope it helpef

8 0
3 years ago
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