if you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the equation?

Answers

Answer 1

Answer: You gave no choices. / / / This may surprise you . . . An EQUATION says that the two sides are EQUAL. So anything you do with either side produces the same result as doing the same thing to the other side. (We always use this important law when we SOLVE equations!)

Answer 2

Answer:

The correct answer is:

The solution will be the intersection point of the lines formed by each side of the equation.

Explanation:

Treating each side of an equation as a separate line and graphing it is treating it as a system of equations. In a system of equations, the solution is the set of coordinates that work for both equations. This will be true here as well; the solution to the equation will be the value that works for both sides of the equation. This will be represented by the intersection point.

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Which best describes the solution set for the compound inequality below? (pick the best answer)2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
A. no solution
B. x = 1
C. all real numbers except x = 1
D. all real numbers

Answers

2(x + 7) - 1 > 15 3(x + 2) < 2x + 7
2x + 14 - 1 > 15 3x + 6 < 2x + 7
2x + 13 > 15 3x - 2x < 7 - 6
2x > 15 - 13 x < 1
2x > 2
x > 2/2
x > 1

so, x > 1 OR x < 1.....all real numbers except 1

Answer:

C is your answer

Step-by-step explanation:

A gaming console that is $300 plus 8% tax. What is the final cost of the console? (Round to the nearest cent)

Answers

Answer: $324.00

Step-by-step explanation:

Convert 8% to decimals. You can do this by dividing by 100

$(8)/(100)=0.08$

Calculate 8% of 300 (0.08*300) and add 300 (+300)

$0.08(300)+300\n24+300\n324$

Marjorie consumed 1.5 gallons of water in one day. How many milliliters are equal to 1.5 gallons, if 1 liter = 1,000 milliliters and 1 gallon = 3.785 liters

Answers

Answer:

Step-by-step explanation: 1.5 gallons X 3.785 liters = 5.6775 liters X 1,000 = 5,677.5 milliliters is the answer.

Kendra has a bowl containing 10 blue marbles, 15 yellow marbles, 5 green marbles, and red marbles of the same size. She will randomly put out a marble, keep it outside the bowl, then pull out another marble.What is the probability she will draw a red marble and then a yellow marble?

1/14
5/72
1/18
3/20

Answers

The answer is 1/14.

There are in total 36 marbles:
10 blue + 15 yellow + 5 green + 6 red.

The probability to put out a red marble in the first draw is 6 out of 36 marbles because there are 6 red marbles of total 36:
P(r) = 6/36 = 1/6.

After that 1 red marble is outside the bowl, there are now 35 marbles in total.
The probability to put out a yellow marble in the second draw is 15 out of 35 because there are 15 yellow marbles of total 35 marbles:
P(y) = 15/35 = 3/7.

If we want both these events to occur (1. to draw the red marble and 2. to draw the yellow marble), we will use a multiplication rule. The multiplication rule calculates the probability that both of two events will occur:
P(r) × P(y) = 1/6 × 3/7 = 3/42 = 1/14.

Therefore, the probability Kendra will draw a red marble and then a yellow marble is 1/14.

a 5ft ladder is leaning against a 4 ft wall. how far must the bottom of the ladder be from the wall so that the top of the ladder rests on the top of the wall?

Answers

The ladder leaning against the wall forms a right angled triangle with the gound and the wall. So we can use the formula:

a² + b² = c²

The ladder is the hypotenuse c²

The vertical leg is b²

The base or horizontal leg is a²

We need to find the length of the base a², so:

a² = c² - b²

a² = 5² - 4²

a² = 25 - 16

a² = 9

a = √9

a = 3

Therefore the bottom of the ladder must be 3 feet from the wall.

"The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?

Answers

G(x)=x²
The graph has moved to the right 4 units, therefore the new graph will be:
H(x)=(x-4)²

It has also move 4 units up, therefore the new graph will be:
F(x)=(x-4)²+4

Answer:
F(x)=(x-4)²+4

y = (x - 4)² + 4

or y = x² - 8x + 20

Further explanation

Transformation of a graph is changing the shape and location of a graph.

There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).

In this case, the transformation is shifting horizontally or vertically.
Translation (or shifting): moving a graph on an analytic plane without changing its shape.
Vertical shift: moving a graph upwards or downwards without changing its shape.
Horizontal shift: moving a graph to the left or right downwards without changing its shape.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Hence, the combination of vertical and horizontal shifts is as follows:

$\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right

Given: $\boxed{ \ g(x) = x^2 \ becomes \ f(x) = ? \ }$

In the graph, notice the shifting of the vertex from (0, 0) to (4, 4).

From this, we can describe that from g(x) to f(x) there has been a shift to the right 4 units and upward 4 units.

Let us construct f(x) from g(x).

$\boxed{ \ g(x) = y = x^2 \ } \rightarrow \boxed{ \ f(x) = y = (x + h)^2 + v \ }$

We set h = -4 and v = +4 and we get the equation f(x) as

$\boxed{\boxed{ \ f(x) = (x - 4)^2 + 4 \ }}$

Let's expand it if we want to represent a standard form of a quadratic function, like this:

$\boxed{ \ f(x) = x^2 - 8x + 16 + 4 \ }$

$\boxed{\boxed{ \ f(x) = x^2 - 8x + 20 \ }}$

Conclusion

The graph of f(x) is drawn by the combination of shifting the graph of g(x) to the right 4 units and upward 4 units.

Learn more

Transformations that change the graph of (f)x to the graph of g(x) brainly.com/question/2415963
The similar problem brainly.com/question/1369568
Determine the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: transformations, the graph of f(x), resembles, g(x) = x², f(x) = (x - 4)² + 4, y = x² - 8x + 20, translation, shifting, right, upward, horizontal, vertical

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