Estimate 1.9 times 4.4

The graph of g(x) is the graph of f(x)=x+6 reflected across the x-axis. Which equation describes the function g?

nika2105 [10]

ANSWER

The correct answer is $g(x)=-x-6$

EXPLANATION

The mapping for reflection across the x-axis is given by $(x,-y)$

Given $f(x)=x+6$ . We can let $y=x+6$

we can write the ordered pair $(x,y)$ or $(x,x+6)$ as the ordered pair of the preimage of $f$ .

The image function will have the ordered pair $(x,-y)$

or

$(x,-x-6)$ .

That is, we negate all the y-coordinates.

Therefore

$g(x)=-x-6$ .

4 0

2 years ago

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PLEASE HELP! Robin bought a four-scoop ice cream cone having a scoop each of vanilla, chocolate, strawberry, and cherry. In how

soldi70 [24.7K]

There are 3 choices for the bottom scoop. Then there are only 3 choices for the scoop above that (since one flavor has already been used), then 2 choices for the next scoop, and 1 choice for the final scoop. This gives a total of 18 possible cones.

Hope this helps.

4 0

2 years ago

Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist

Lera25 [3.4K]

Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

7 0

2 years ago

CL 6-131. Solve each system using the method of your choice.

shepuryov [24]

System 1: The solution is (x, y) = (-4, 5)

System 2: The solution is $(x, y) = (\frac{11}{3}, -3)$

Solution:

Given system of equations are:

2x + 3y = 7 ------ eqn 1

-3x - 5y = -13 --------- eqn 2

We can solve by elimination method

Multiply eqn 1 by 3

6x + 9y = 21 ------ eqn 3

Multiply eqn 2 by 2

-6x - 10y = -26 ------- eqn 4

Add eqn 3 and eqn 4

6x + 9y -6x - 10y = 21 - 26

-y = -5

y = 5

Substitute y = 5 in eqn 1

2x + 3(5) = 7

2x + 15 = 7

2x = -8

x = -4

Thus the solution is (x, y) = (-4, 5)

<h3>Second system of equation is:</h3>

8 - y = 3x ------ eqn 1

2y + 3x = 5 ----- eqn 2

We can solve by susbtitution method

From given,

y = 8 - 3x ----- eqn 3

Substitute eqn 3 in eqn 2

2(8 - 3x) + 3x = 5

16 - 6x + 3x = 5

3x = 16 - 5

3x = 11

$x = \frac{11}{3}$

Substitute the above value of x in eqn 3

y = 8 - 3x

$y = 8 - 3 \times \frac{11}{3}\\\\y = 8 - 11\\\\y = -3$

Thus the solution is $(x, y) = (\frac{11}{3}, -3)$

4 0

2 years ago

For an outdoor track meet to be cancelled, the temperature, t, outside must be colder than 35 degrees. Complete the following in

qwelly [4]

Answer: I'm pretty sure it would be -7º Celcius for it to be cancelled. Hope it helped!

7 0

2 years ago

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