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Which option is the solution to the inequality −12g+18>−5g+53

Responses:

g>−5

g>71/−17

g<−5

g<71/−17

11 answers

To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:

  1. Rearrange the inequality to get all terms involving \(g\) on one side and constants on the other side.

    \(-12g + 18 > -5g + 53\)

    We can add \(12g\) to both sides:

    \(18 > 7g + 53\)

  2. Subtract 53 from both sides:

    \(18 - 53 > 7g\)

    \(-35 > 7g\)

  3. Divide both sides by 7 (note that since we're dividing by a positive number, the direction of the inequality remains the same):

    \(-5 > g\)

    which can also be written as:

    \(g < -5\)

Thus, the solution to the inequality is:

g < -5

So the correct response from the options provided is:

g < -5.

find the solution set of 4x−3>9
and x+6>−2
Responses:

{x|x>−8}

The solution set is null.

{3,−8}

{x|x>3}

To find the solution set for the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will solve each inequality separately.

First Inequality: \(4x - 3 > 9\)

  1. Add 3 to both sides: \[ 4x > 12 \]

  2. Divide by 4: \[ x > 3 \]

Second Inequality: \(x + 6 > -2\)

  1. Subtract 6 from both sides: \[ x > -8 \]

Combine the Solution Sets

Both inequalities \(x > 3\) and \(x > -8\) must be satisfied. However, since \(x > 3\) is more restrictive, the combined solution is simply:

\[ x > 3 \]

Final Answer

The solution set is:

{x | x > 3}

Thus, the correct response from the options provided is:

{x | x > 3}.

What is the undefined value for the equation 14=7x9+4x

Responses:

x≠−94

x≠−49

x≠94

x≠0

To determine the undefined value for the equation \(14 = 7x + 4x\), let's first simplify the equation.

  1. Combine the terms on the right side:

    \[ 14 = 11x \]

  2. Now, solve for \(x\):

    \[ x = \frac{14}{11} \]

This indicates that \(x\) can take the value \(\frac{14}{11}\). However, none of the provided option responses indicate that \(x\) has a defined value, but rather they indicate restrictions on \(x\).

To identify potential undefined values in equations, you typically look for values that could make the equation invalid (e.g., divisions by zero). In this case, there are no divisions present in the simplified equation, so there are no specific undefined values.

Conclusion

Since none of the options given relate directly to any indeterminate or undefined value derived from the equation, we can say that none of the response options correctly address the situation based on the final solution derived from the equation.

If you are looking for a response that categorically provides an undefined value, then it seems there may be a misunderstanding in the equation provided, or the question should be reformulated as it doesn't directly create a scenario where \(x\) is undefined.

which correctly shows the area formula for a trapezoid, A=1/2h(b1+b2) , rearranged for the quantity of interest h?(1 point)
Responses:

h=1/2A(b1+b2)

h=2A/b1+b2

b1=2A/h−b2

h=b1+b2/2A

To rearrange the area formula for a trapezoid \( A = \frac{1}{2}h(b_1 + b_2) \) to solve for the height \( h \), follow these steps:

  1. Start with the original area formula: \[ A = \frac{1}{2}h(b_1 + b_2) \]

  2. Multiply both sides by 2 to eliminate the fraction: \[ 2A = h(b_1 + b_2) \]

  3. Now, divide both sides by \( (b_1 + b_2) \) to isolate \( h \): \[ h = \frac{2A}{b_1 + b_2} \]

Conclusion

The correctly rearranged formula for the height \( h \) is:

\[ h = \frac{2A}{b_1 + b_2} \]

So, the correct response from the options provided is:

h = 2A/(b1 + b2).

Given the formula for time in terms of distance and velocity, t=d/v , what operation would you use to isolate the distance?(1 point)
Responses:

division

addition

subtraction

multiplication

To isolate distance (\(d\)) in the formula for time, given by:

\[ t = \frac{d}{v} \]

you would follow these steps:

  1. Multiply both sides by \(v\) to eliminate the fraction. This gives:

\[ t \cdot v = d \]

So, to isolate distance (\(d\)), you need to perform the operation of multiplication.

Conclusion

The correct response is:

multiplication.

Sebastian needed to buy new tires for his car. The tire shop was running a holiday deal that allowed customers to buy three tires and get the fourth tire for $5. If the total price for all his tires was $237.50, what was the cost of each of the first three tires?

Let's denote the cost of each of the first three tires as \(x\). According to the deal, the total cost can be expressed as follows:

  1. The cost of the first three tires: \(3x\)
  2. The cost of the fourth tire, which is on sale: $5

The total cost for all four tires is given by the equation:

\[ 3x + 5 = 237.50 \]

Now, we can solve for \(x\):

  1. Subtract 5 from both sides: \[ 3x = 237.50 - 5 \] \[ 3x = 232.50 \]

  2. Divide by 3 to find \(x\): \[ x = \frac{232.50}{3} \] \[ x = 77.50 \]

Thus, the cost of each of the first three tires is $77.50.