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3 years ago

Let

Mathematics

1 answer:

Roman55 [17]3 years ago

8 0

The right answer is: g(x) is translated 2 units up from f(x)

Step-by-step explanation:

Given functions are:

$f(x) = 4x\\g(x) = 4x+2$

In order to shift the functions upward or downward, an integer is added or subtracted from the original function's output.

We can see by comparing both functions that 2 can be added to f(x) to make function g.

As 2 is added to the function, not the input, it is a vertical shifting.

As the integer is positive, the shift is upward.

So,

The right answer is: g(x) is translated 2 units up from f(x)

Keywords: Functions, shifting

Learn more about functions at:

#LearnwithBrainly

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Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle is translated 4 units down and 3 units left. Which rule r

crimeas [40]

Option C: $(x, y) \rightarrow(x-3, y-4) ; (5,-1)$ is the coordinates of C after translation.

Explanation:

The triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3).

Also, given that the triangle is translated 4 units down and 3 units left.

We need to determine the coordinates of the vertex C after translation.

The triangle is shifted 4 units down means subtracting 4 units from the y - coordinate of the graph.

Thus, it can be written as $y-4$

Also, the triangle is shifted 3 units left means subtracting 3 units from the x - coordinate of the graph.

Thus, it can be written as $x-3$

Thus, the translation is given by

$(x, y) \rightarrow(x-3, y-4)$

The vertices of C after translation can be determined by

$(8, 3) \rightarrow(8-3, 3-4)\implies (5,-1)$

Thus, $(x, y) \rightarrow(x-3, y-4) ; (5,-1)$ is the coordinates of C after translation.

Hence, Option C is the correct answer.

3 0

3 years ago

Read 2 more answers

NO SPACES AND NO DECIMALS

KonstantinChe [14]

Answer:

Happy paws

y = 20 + 4x

Woof watchers

y = 9 + 5x

x = 11 hours

Step-by-step explanation:

Let

Number of hours = x

Total cost = y

Total cost = fixed cost + variable cost

The equations are:

Happy paws

y = 20 + 4x

Woof watchers

y = 9 + 5x

solve the equation to find for how many hours the total cost of the services is equal.

Equate total cost of both services

20 + 4x = 9 + 5x

Collect like terms

20 - 9 = 5x - 4x

11 = x

x = 11 hours

Check:

Happy paws

y = 20 + 4x

= 20 + 4(11)

= 20 + 44

= 64

Woof watchers

y = 9 + 5x

= 9 + 5(11)

= 9 + 55

= 64

6 0

3 years ago

If m angle ECD is six less than five times m angle BCE, and mangle BCD = 162º. find each

Usimov [2.4K]

Answer:

see explanation

Step-by-step explanation:

let ∠BCE = x then ∠ECD = 5x - 6 and

∠BCE + ∠ECD = ∠BCD, substitute values

x + 5x - 6 = 162, that is

6x - 6 = 162 ( add 6 to both sides )

6x = 168 ( divide both sides by 6 )

x = 28

Hence

∠BCE = x = 28°

∠ECD = 5x - 6 = (5 × 28) - 6 = 140 - 6 = 134°

5 0

3 years ago

Read 2 more answers

What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE

maks197457 [2]

Given:

The equation of a line is:

$2y+3x=10$

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

$2y+3x=10$

For $x=0$ ,

$2y+3(0)=10$

$2y+0=10$

$y=\dfrac{10}{2}$

$y=5$

For $x=2$ ,

$2y+3(2)=10$

$2y+6=10$

$2y=10-6$

$2y=4$

Divide both sides by 2.

$y=\dfrac{4}{2}$

$y=2$

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(0,5)\to A'(3(0),3(5))$

$A(0,5)\to A'(0,15)$

Similarly,

$B(2,2)\to B'(3(2),3(2))$

$B(2,2)\to B'(6,6)$

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\dfrac{6-15}{6-0}(x-0)$

$y-15=\dfrac{-9}{6}(x)$

$y-15=\dfrac{-3}{2}x$

Multiply both sides by 2.

$2(y-15)=-3x$

$2y-30=-3x$

$2y+3x=30$

Therefore, the equation of the line after the dilation is $2y+3x=30$ .

3 0

3 years ago

A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Le

kumpel [21]

(x•19)4=752

x would be multiplied by 19 then after it’s getting multiplied by 4.

3 0

3 years ago