true?(1 point)
Responses
49
49
9
9
25
25
16
11 answers
To solve the equation \(2\sqrt{x} + 13 = 27\), we first isolate the square root.
Subtract 13 from both sides: \[ 2\sqrt{x} = 27 - 13 \] \[ 2\sqrt{x} = 14 \]
Next, divide by 2: \[ \sqrt{x} = \frac{14}{2} \] \[ \sqrt{x} = 7 \]
Finally, square both sides to solve for \(x\): \[ x = 7^2 \] \[ x = 49 \]
The value of \(x\) that makes the equation true is \(\boxed{49}\).
To solve the equation \(7 + 2k^2 = 25\), we first isolate the term involving \(k^2\).
Subtract 7 from both sides: \[ 2k^2 = 25 - 7 \] \[ 2k^2 = 18 \]
Divide both sides by 2: \[ k^2 = \frac{18}{2} \] \[ k^2 = 9 \]
Take the square root of both sides: \[ k = \pm3 \]
Thus, the solution set for \(k\) is \({ -3, 3 }\).
The correct option is \({ -3, 3 }\).
To solve the inequality \(k + 1 < -3\), we start by isolating \(k\).
The set that expresses the solution to the inequality is \({k: k < -4}\).
So the correct option is \({k:k < -4}\).
To determine how many solutions the equation \(4h + 6 = 14 - \frac{1}{2}(16 - 8h)\) has, we first simplify both sides.
Start with the equation: \[ 4h + 6 = 14 - \frac{1}{2}(16 - 8h) \]
Distribute \(-\frac{1}{2}\) on the right side: \[ -\frac{1}{2}(16) + \frac{1}{2}(8h) = -8 + 4h \] So, the equation now looks like: \[ 4h + 6 = 14 - 8 + 4h \] \[ 4h + 6 = 6 + 4h \]
Next, subtract \(4h\) from both sides: \[ 6 = 6 \]
Since this results in a true statement that is always true, it indicates that the equation holds for any value of \(h\).
Thus, there are infinite/many solutions.
The correct option is infinite/many solutions.
Let's represent the ages of the four individuals. If we let \( a \) be the age of Chen (the youngest), then the ages of the others can be represented as follows:
Now, we can set up the equation for the sum of their ages: \[ a + (a + 1) + (a + 2) + (a + 3) = 74 \]
Simplifying the left side: \[ a + a + 1 + a + 2 + a + 3 = 74 \] \[ 4a + 6 = 74 \]
So, the equation that can be used to determine the age of Chen, \( a \), is: \[ 4a + 6 = 74 \]
The correct option is 4a + 6 = 74.
To solve the problem, we first need to determine how fast Sharice's car is traveling, then we can find out how fast Maluma's car is traveling based on the relationship provided.
Convert the time Sharice took to hours:
Calculate Sharice's speed: Using the formula \( d = s \times t \): \[ d = 93 \text{ miles}; \quad t = 1.5 \text{ hours} \] \[ s = \frac{d}{t} = \frac{93}{1.5} = 62 \text{ miles per hour} \] So Sharice is driving at a speed of 62 miles per hour.
Determine Maluma's speed: Let \( m \) be the speed of Maluma's car in miles per hour. According to the problem, Sharice's speed is \( 10 \) miles per hour slower than twice the speed of Maluma's car: \[ s = 2m - 10 \] We already found that Sharice's speed \( s \) is \( 62 \): \[ 62 = 2m - 10 \]
Solve for \( m \): Add \( 10 \) to both sides: \[ 72 = 2m \] Divide both sides by \( 2 \): \[ m = 36 \]
Therefore, Maluma is driving at a speed of 36 miles per hour.
