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IgorC [24]
2 years ago
10

Under a dilation, the point (2, 6) is moved to (6, 18).

Mathematics
1 answer:
Sergio039 [100]2 years ago
4 0

Answer:

3

Step-by-step explanation:

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Find the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest in
prohojiy [21]
<h2>Answer:</h2>

55°

<h2> Step-by-step explanation:</h2>

To solve this, follow these steps:

i. <em>Make a sketch of the problem</em>.

The sketch has been attached to this response.

ii. <em>Label the sketch properly</em>

As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).

iii. <em>Solve using the tangent trigonometric ratio</em>

With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being  5 units and 7 units respectively.

Using the tangent formula,

tan θ = opposite / adjacent

tan θ = 7 / 5

θ = tan⁻¹ (7/5)

θ = tan⁻¹ (1.4)

θ = 54.46

θ = 55° to the nearest integer.

Therefore, the angle  made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°

3 0
2 years ago
Suppose the radius of a circle is 5.what is its diameter
Gnom [1K]
The diameter would be twice 5, or 10
8 0
3 years ago
Read 2 more answers
Tim plays a computer game. each game is a win or loss
Drupady [299]

Answer:

If the rest of the question is:

Each game is a win or a loss.

He wins three fifths of his first 40 games.

He then wins his next 12 games.

For all 52 games, work out the ratio wins : losses

Give your answer in its simplest form.​

then the answer is below ↓

Step-by-step explanation:

9:4

of his first 40 games:     3/5 *40=3*8=24  wins

=> of his first 40 games: 24 wins and  40-24=16 losses

next 12 games: 12 wins

so,  for all  52 games: 24+12=36 wins and 16 losses

36 wins and 16 losses

wins: losses=> 36:16=> 9:4

7 0
3 years ago
-23
Dvinal [7]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
Find f(g(x)). State the domain of the composite function.<br> f(x) = 3x-2/x+1<br> g(x) = x+5/2x-3
AnnyKZ [126]

Answer:

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

g(x)=\dfrac{x+5}{2x-3}\Longrightarrow 2x-3\neq 0\iff \boxed{x\neq\dfrac{3}{2}}

- Domain of f(g(x)): We'll find its expression:

f(x) = \dfrac{3x-2}{x+1}\\\\f(g(x)) = \dfrac{3g(x)-2}{g(x)+1}\\\\f(g(x)) = \dfrac{3\cdot\dfrac{x+5}{2x-3}-2}{\dfrac{x+5}{2x-3}+1}=\dfrac{~~~\dfrac{3(x+5)-2(2x-3)}{2x-3}~~~}{\dfrac{(x+5)+(2x-3)}{2x-3}}\\\\f(g(x)) =\dfrac{3(x+5)-2(2x-3)}{(x+5)+(2x-3)}=\dfrac{3x+15-4x+6}{x+5+2x-3}\\\\\boxed{f(g(x)) =\dfrac{21-x}{3x+2}}

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

f(g(x)) =\dfrac{21-x}{3x+2}\Longrightarrow 3x+2\neq0\iff \boxed{x\neq-\dfrac{2}{3}}

Lastly, we may write the domanin of f(g(x)):

D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[

or, just writing in a shorter way:

\boxed{D(f(g(x)) = \mathbb{R}-\left\{-\dfrac{2}{3},\dfrac{3}{2}\right\}}

7 0
2 years ago
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