What is the undefined value for the equation 14= 7x/9+4x

Question

?(1 point)
Responses

x≠94
x does not equal Start Fraction 9 over 4 End Fraction

x≠0
x does not equal 0

x≠−9/4
x does not equal Start Fraction negative 9 over 4 End Fraction

x≠−4/9

Answer 1

To find the undefined value for the equation \( 14 = \frac{7x}{9} + 4x \), we need to solve the equation for \( x \).

1. Start by rewriting the equation:
   \[ 14 = \frac{7x}{9} + 4x \]

2. To combine the terms on the right, express \( 4x \) in terms of a fraction with a denominator of 9:
   \[ 4x = \frac{36x}{9} \]

3. Substitute this back into the equation:
   \[ 14 = \frac{7x}{9} + \frac{36x}{9} \]

4. Combine the fractions:
   \[ 14 = \frac{7x + 36x}{9} \]
   \[ 14 = \frac{43x}{9} \]

5. Multiply both sides by 9 to eliminate the denominator:
   \[ 14 \cdot 9 = 43x \]
   \[ 126 = 43x \]

6. Now, solve for \( x \):
   \[ x = \frac{126}{43} \]

Since \( x \) is defined and there are no restrictions on the values of \( x \) from the equation (like dividing by zero), we can conclude that none of the answer options listed represent values where the equation is undefined.

However, if the question refers to a unique solution or case for \( x \), the options listed do not directly pertain to the equation under normal circumstances. Therefore, the correct answer here is that none of the responses correctly reflect an undefined value related to the equation, as \( x \) can take any real number excluding \( \frac{126}{43} \) as a solution.

If we interpret 'undefined' to mean values that \( x \) is not equal to according to the answers you provided, it doesn't apply directly to this linear equation since it is valid for all real numbers.

Thus, the best conclusion is that:

None of the options correspond to undefined values in given equation context.

Answer 2

tell me which one is closest

Answer 3

Let's analyze the options you provided in the context of the original equation \( 14 = \frac{7x}{9} + 4x \):

1. x ≠ 94
2. x does not equal \(\frac{9}{4}\)
3. x ≠ 0
4. x does not equal \(-\frac{9}{4}\)
5. x ≠ -\(\frac{4}{9}\)

To find the value of \( x \) from the equation, we simplified it to:

\[ x = \frac{126}{43} \]

Evaluating \( \frac{126}{43} \) gives us approximately \( 2.9302 \). So while this does not exactly match any of your options, we can examine them for closeness:

1. 94 (not close)
2. \(\frac{9}{4} \approx 2.25\) (not very close)
3. 0 (not close)
4. \(-\frac{9}{4} \approx -2.25\) (not close)
5. -\(\frac{4}{9} \approx -0.444\) (not close)

Given that none of the values are particularly close to \( \frac{126}{43}\), but the option x does not equal \(\frac{9}{4}\) and x ≠ 0 are the closest relative to the positive solutions, the best fit would be:

x does not equal \(\frac{9}{4}\).

This option, \( \frac{9}{4} \) is still the closest representation compared to the approximate solution of \( 2.9302 \).

Answer 4

Solve for s in the following equation: 11s+3+4=5
.(1 point)
s=

Answer 5

To solve for \( s \) in the equation:

\[ 11s + 3 + 4 = 5 \]

1. First, combine like terms on the left side:

\[ 11s + 7 = 5 \]

2. Next, isolate the variable \( s \) by subtracting 7 from both sides:

\[ 11s = 5 - 7 \] \[ 11s = -2 \]

3. Now, divide both sides by 11:

\[ s = \frac{-2}{11} \]

So, the solution is:

\[ s = -\frac{2}{11} \]

Answer 6

Which correctly shows the area formula for a trapezoid, A=12h(b1+b2)
, rearranged for the quantity of interest h?(1 point)
Responses

h=2Ab1+b2
h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction

b1=2Ah−b2
b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline

h=12A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis

h=b1+b22A

Answer 7

To rearrange the area formula for a trapezoid, which is given by:

\[ A = \frac{1}{2} h (b_1 + b_2) \]

for \( h \), we need to isolate \( h \).

Here are the steps:

1. Multiply both sides by 2 to eliminate the fraction:

\[ 2A = h(b_1 + b_2) \]

2. Then, divide both sides by \( (b_1 + b_2) \) to solve for \( h \):

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

Now, let's compare this with the response options you provided:

1. h = \(\frac{2A}{b_1 + b_2}\) (correct)
2. b1 = \(\frac{2A}{h}\) - b2 (not correct)
3. h = \(\frac{1}{2} A(b_1 + b_2)\) (not correct)
4. h = \(\frac{b_1 + b_2}{2A}\) (not correct)

The correct rearrangement of the formula for \( h \) is:

h = \(\frac{2A}{b_1 + b_2}\)

Answer 8

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

multiplication
multiplication

subtraction
subtraction

division
division

addition

Answer 9

The given formula for time in terms of distance and velocity is:

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

To isolate \( d \) (distance), we need to get rid of the \( v \) in the denominator. The operation we would use is multiplication. Specifically, you would multiply both sides of the equation by \( v \):

\[ t \cdot v = d \]

Thus, the distance \( d \) can be isolated as:

\[ d = t \cdot v \]

So, the correct response regarding the operation you would use to isolate the distance is:

multiplication.

Answer 10

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?(1 point)
Responses

$77.50
$77.50

$59.38
$59.38

$79.17
$79.17

$80.83

Answer 11

Let the cost of each of the first three tires be \( x \). According to the deal, if he buys three tires, he gets the fourth tire for $5.

This means the total cost for the four tires can be expressed as:

\[ 3x + 5 = 237.50 \]

Now, let's solve for \( x \):

1. First, subtract 5 from both sides:

\[ 3x = 237.50 - 5 \] \[ 3x = 232.50 \]

2. Next, divide both sides by 3 to isolate \( x \):

\[ x = \frac{232.50}{3} \] \[ x = 77.50 \]

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

Therefore, the correct answer is:

$77.50.