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Blababa [14]
3 years ago
11

Which coordinate (g, z) lies in the solution set for the following system of inequalities?

Mathematics
1 answer:
geniusboy [140]3 years ago
7 0

Answer:

B. (6, 1)

Step-by-step explanation:

A graph of the solution space shows that the point (6, 1) is the only one that satisfies both inequalities.

___

<em>Verification</em>

3(6) +4(1) = 18 +4 = 22 < 24

3(6) -4(1) = 18 -4 = 14 > 12

_____

<em>Notes on the Solution</em>

The graphing calculator used here only recognizes variables x and y. Since g is the first variable in the ordered pair (g, z) we use x to represent g in the equations that are graphed. Similarly, y is used to represent z in the graphed equations.

You graph an inequality by graphing it as though it were an equation, then choosing the appropriate half-plane (one side of the line or the other) to shade as the solution space. Where the shadings from the two inequalities overlap, both are satisfied by points in that area.

In the first inequality, x and y values that are less than those on the line will satisfy the inequality, so the shading is below the line.

In the second inequality, x values greater than those on the line will satisfy the inequality, so the shading is to the right of the line.

In both cases, the line is graphed as a dashed line. This is because the points on the line do not satisfy the < or > conditions, so are not part of the solution set. (If one or both conditions were ≤ or ≥, then the corresponding line would be solid, and the points on the line would be part of the solution.)

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Which relation does not represent a function? A) a vertical line B) y = 5 9 x - 3 C) a horizontal line D) {(1, 7), (3,7), (5, 7)
Alisiya [41]

Answer:

A) a vertical line does not represent a function.

Step-by-step explanation:

For a relation to be a function for each value of x there must be only one value of y. In other words a function is one in which each value in the domain set corresponds to only one value in the range set.

Let us check for this condition in the give choices:

A) a vertical line

A vertical line is given as x=a which meas it is parallel to y-axis and has infinite number of y values for a single x value.

So, its Not a function

B) y=\frac{5}{9}x-3

For the given equation, on plugging in some x value will give a single y value.

So, its a Function

C) a horizontal line

A horizontal line is given as y=a which meas it is parallel to x-axis and has infinite number of x values giving a single y value.

So, its a Function

D) {(1, 7), (3,7), (5, 7), (7,7)}

For the given set for different x valuesthere is only one y value.

So, its a Function

4 0
3 years ago
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Solve y=f(x) for x . f(x)=23x+4 x= Question 2 Find the input when the output is 2. The input is .
Fantom [35]

Let's find f(x) = 2, which is essentially what the problem is asking, what x corresponds to an output of 2.


Let's solve below:

f(x) = 2

  • Setting up what we know

23x + 4 = 2

  • Substituting in 23x + 4 for f(x) (I'm not sure if this is the correct expression for f(x) due to formatting issues)

23x = -2

  • Subtract 4 from both sides to make a step to isolate x (what we are trying to find)

x = - \frac{2}{23}

  • Divide both sides of the equation by 23 to isolate x

Thus the input is \boxed{x = - \frac{2}{23}}.

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3 years ago
Matrices C and D are shown below.
yKpoI14uk [10]

Answer:

it's b

Step-by-step explanation:

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Nancy and Kevin collect coins. Nancy has x coins. Kevin has 9 coins fewer than five times the number of coins Nancy has. Write a
Alexus [3.1K]

Answer:

x + (5x-9)

Step-by-step explanation:

x stands for the number of coins Nancy has

Kevin has 9 less than 5 times what Nancy has, so his part of the expression is 5x-9

To find the total number of coins they have, you have to add Nancy's number of coins x plus Kevin's number of coins 5x-9

x + (5x-9)

But you have to put parentheses around Kevin's 5x-9 so that part of the expression is calculated first, as per order of operations

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2 years ago
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Elodia [21]

Answer:

- 6

Step-by-step explanation:

Step 1:

x ÷ 3 - 5 = - 7   Equation

Step 2:

x ÷ 3 = - 2   Add 5 on both sides

Answer:

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Hope This Helps :)

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