how many solutions does the graph above show?
a. one
b. none
c. Infinite

Answer:

Step-by-step explanation:

Given that there is a system of equations in two variables. When we have a single variable isolated in one of the two equations in a system, we can use substitution method.

So we substitute this variable in terms of other variable in the second equation so that we get now an equation in one variable.  We can solve this by mathematical operations easily.

Hence correct answer is

C. substitute the expression equal to the solved variable into the other equation.

Final answer:

The missile's change in altitude from the starting point 290 feet below sea level to the final position of height 17800 feet is calculated by subtracting the initial position from the final position, resulting in a change of 18090 feet.

Explanation:

The subject of this question falls under the domain of Mathematics, specifically involving numerical operations. It pertains to the calculation of change in altitude. Here's your step-by-step explanation:

1. The missile's starting point is 290 feet below sea level. We represent below sea level as a negative number, so the starting altitude of the missile is -290 feet.

2. The missile then ascended to a height of 17800 feet, which is above sea level and hence positive.

3. To find the change, we subtract the initial position from the final position: 17800 - (-290) = 17800 + 290 = 18090 feet.

So, the change in altitude of the missile is 18090 feet.

Learn more about Change in Altitude here:

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Final answer:

Betty has $17 and Ann has $43.

Explanation:

This problem is a basic algebraic equation. Let's denote Betty's amount as x. From the problem information, we know that Ann's amount is twice Betty's plus $9, so we can denote it as 2x + $9. It's also told in the problem that together they have $60, so we can form the equation: x (Betty's money) + 2x + $9 (Ann's money) = $60.

Solving this equation, we combine like terms, which gives us 3x + $9 = $60. Subtract $9 from both sides to get 3x = $51. Divide each side by 3, we get x = $17. So, Betty has $17. We substitute x = $17 into the equation 2x + $9 to find Ann's money, which gives us 2*$17 + $9 = $43. So, Ann has $43.

Learn more about Algebra here:

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Answer:

First Option {-2 , 0 , 2}

Step-by-step explanation:

A critical point occurs when the derivative is 0 or undefined.

The function in the question is undefined at x = 2 and at x = -2 because if we put x = 2 or x = -2 the denominator becomes 0 hence anything divided by 0 is undefined, and the derivative equals 0 at x = 0 so the critical points are

{-2 , 0 , 2}

Use the quotient rule to find the derivative of the function then equal it to zero