8 * 3 + 2 * 6 __ 60 ÷ 5 * 3
Which operator can be inserted to make the statement true?
(1 point)
>
=
11 answers
Let's first simplify both sides of the inequality.
On the left side, we calculate: 8 * 3 + 2 * 6 = 24 + 12 = 36
Now, for the right side: 60 ÷ 5 * 3 = 12 * 3 = 36
Now we can compare the two sides: Left side: 36 Right side: 36
Thus, we can conclude that the statement is: 36 __ 36
The appropriate operator to make the statement true is "=".
So, the answer is "=".
Let's solve the equation \( 7 + 2k^2 = 25 \).
Start by isolating the term with \( k^2 \): \[ 2k^2 = 25 - 7 \] \[ 2k^2 = 18 \]
Next, divide both sides by 2: \[ k^2 = \frac{18}{2} \] \[ k^2 = 9 \]
Now, take the square root of both sides: \[ k = \pm 3 \]
This gives us the solutions: \( k = 3 \) and \( k = -3 \).
Thus, the solution set is \({-3, 3}\).
The correct option is \({-3, 3}\).
To solve the inequality \( k + 1 < -3 \), we can isolate \( k \):
Thus, the solution set is:
\[ {k : k < -4} \]
Therefore, the correct option is \({k : k < -4}\).
To find out how fast Maluma is driving, let's first analyze the problem step by step.
Convert time: Sharice covers 93 miles in 1 hour and 30 minutes. We can convert 1 hour and 30 minutes to hours: \[ 1 \text{ hour } + 30 \text{ minutes} = 1 + \frac{30}{60} = 1.5 \text{ hours} \]
Calculate Sharice's speed: We can use the formula \( s = \frac{d}{t} \) to find Sharice's speed: \[ s_{\text{Sharice}} = \frac{d}{t} = \frac{93 \text{ miles}}{1.5 \text{ hours}} = 62 \text{ miles per hour} \]
Express Sharice's speed in terms of Maluma's speed: According to the problem, Sharice's speed is 10 miles per hour slower than twice the speed of Maluma's car. Let \( s_{\text{Maluma}} \) be Maluma's speed. Then we have: \[ s_{\text{Sharice}} = 2s_{\text{Maluma}} - 10 \]
Set up the equation: Substituting Sharice's speed into the equation: \[ 62 = 2s_{\text{Maluma}} - 10 \]
Solve for Maluma's speed:
Thus, Maluma is driving at 36 miles per hour.
The correct answer is 36 miles per hour.
To solve the absolute value equation \( 4|7 - x| + 1 = -1 \), we first isolate the absolute value term:
Subtract 1 from both sides: \[ 4|7 - x| = -1 - 1 \] \[ 4|7 - x| = -2 \]
Now, divide both sides by 4: \[ |7 - x| = -\frac{1}{2} \]
Since the absolute value of any expression is always non-negative (i.e., \(\geq 0\)), there are no values of \(x\) that can satisfy the equation \( |7 - x| = -\frac{1}{2} \).
Thus, the equation has no solution.
To find a line that is perpendicular to the line \( y = \frac{3}{5}x + 6 \) and passes through the point \((-3, 6)\), we need to determine the slope of the perpendicular line.
Determine the slope of the given line: The given line has a slope of \( \frac{3}{5} \).
Find the slope of the perpendicular line: The slope of a line that is perpendicular to another line is the negative reciprocal of the other line's slope. Therefore, if the slope of the given line is \( \frac{3}{5} \), the slope of the perpendicular line \( m \) is: \[ m = -\frac{1}{\left(\frac{3}{5}\right)} = -\frac{5}{3} \]
Use the point-slope form of a line to find the equation of the perpendicular line: The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope.
Here, we use the point \((-3, 6)\), so \(x_1 = -3\) and \(y_1 = 6\): \[ y - 6 = -\frac{5}{3}(x + 3) \]
Now, simplify the equation: \[ y - 6 = -\frac{5}{3}x - 5 \] \[ y = -\frac{5}{3}x + 1 \]
Thus, the equation of the line that is perpendicular to \( y = \frac{3}{5}x + 6 \) and passes through the point \((-3, 6)\) is: \[ y = -\frac{5}{3}x + 1 \]
So the correct option is \( y = -\frac{5}{3}x + 1 \).
