Can I have some help? I need to get done. Thank you! =)

Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 2 units up and 1 unit right. Which rule repres

Nataly [62]

Answer:

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

After the translation, the coordinates of vertex A is (-2,6).

Step-by-step explanation:

Given :

Vertices of a triangle ABC are:

A(−3, 4), B(4, −2), C(8, 3)

The triangle is translated 2 units up and 1 unit right.

To find the co-ordinates of point A after translation.

Translation rules.

For shift of $c$ units up, the translation is given as:

$(x,y)\rightarrow (x,y+c)$

For shift of $k$ units right, the translation is given as:

$(x,y)\rightarrow (x+k,y)$

So, it says the triangles is translated 2 units up and 1 unit right.

The translation statement is given by:

$(x,y)\rightarrow (x+1,y+2)$

So, co-ordinates of point A after translation is given by :

$(-3,4)\rightarrow (-3+1,4+2)=(-2,6)$

After the translation, the coordinates of vertex A is (-2,6).

4 0

3 years ago

Two triangles have side lengths 3,4,5 and 6,____10, respectively. The triangles are similar to each other.

Sergeu [11.5K]

Answer:

8

Step-by-step explanation:

3,4,5 and 6,_,10 are similar. what do you notice between the two? 6 is twice of 3. 10 is twice of 5. so then 4 would be half of 8.

hope i helped ;)

8 0

3 years ago

Describe any domain restrictions that make sense for each of these scenarios: The price of a stock fluctuates several times thro

mrs_skeptik [129]

Answer:

a) Restriction: days of the year (a discrete time)

b) The time the ball is on the air: t = 0, until the balls touchs the ground (any real value from t = 0 to t when the ball hits the ground)

c) Any positive real value: x ≥ 0

Explanation:

The domain is the set of elements that can be inputs of the function.

1. The price of a stock fluctuates several times throughout the year as a function of time.

The input variable is the time through out the year.

If you assume that the fluctuaion is recorded once a day, and not every second, the logical assumption is that the time is a day of the year.

Thus, the restricion is the days of the year.

You could represent them in different forms, like DD/MM/YY, or even as a number from 1 to 365 if it covers just one year.

2. A ball is hit into the air by a baseball player, rises until it reaches its highest point, and then falls into left field.

The domain is the time the ball is on the air, which may be any real value from t = 0, until the balls touchs the ground.

It is not restricted to integer numbers.

3. The volume of a spherical balloon increases as the balloon is blown up and decreases as air is let out of it.

The inputs of the function are amounts of air, which may be measured as number of moles.

The number of moles can be any real value equal or greater than zero.

Thus, the domain is the positive real values x ≥ 0.

8 0

3 years ago

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Use f(x) = 1/2 x and f -1(x) = 2x to solve the problems. f(2) = 1 f−1(1) = 2 f−1(f(2)) = 2 f−1(−2) = f(−4) = f(f−1(−2)) =

vampirchik [111]

Answer:

In this problem, we are given the following functions:

$f(x)=\frac{1}{2}x$

and its inverse function:

$f^{-1}(x)=2x$

First of all, we want to calculate $f(2)$ . This can be obtained by substituting

x = 2

into f(x). Doing so, we find:

$f(2)=\frac{1}{2}\cdot 2 = 1$

Then we want to calculate $f^{-1}(1)$ . We can do it by substituting

x = 1

into $f^{-1}(x)$ . Doing so,

$f^{-1}(1)=2\cdot 1 = 2$

Then we want to calculate $f^{-1}(f(2))$ , which can be found by calculating f(2) and then using it as input for $f^{-1}(x).$ We know that

f(2) = 1

Therefore,

$f^{-1}(f(2))=f^{-1}(1)=2$

Then we want to calculate $f^{-1}(-2)$ , which can be calculated by plugging

x = -2

into $f^{-1}(x)$ . Doing so,

$f^{-1}(-2)=2\cdot (-2)=-4$

Then we want to calculate $f(-4)$ ; by substituting

x = 4

into f(x), we find

$f(-4)=\frac{1}{2}\cdot (-4)=-2$

Finally, we want to find $f(f^{-1}(-2))$

We know already that

$f^{-1}(-2)=-4$

So we have:

$f(f^{-1}(-2))=f(-4)=-2$

7 0

2 years ago

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I don't understand 1/2 +1/6 what the answer

romanna [79]

Answer:

4/6

Step-by-step explanation:

1/2=3/6+1/6=4/6

3 0

2 years ago

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