Question

Consider the following statement:
8 * 3 + 2 * 6 __ 60 ÷ 5 * 3
Which operator can be inserted to make the statement true?
(1 point)
>
=

Answer 1

Which option contains the solution set for the value of k in the equation 7 + 2k^2 = 25?
{-9,9}
{-3,3}

Answer 2

Which option is the set that expresses the solution to the inequality k + 1 < -3?

{k : k < -4}
{k : k > -4}

Answer 3

The speed of a body is the distance it travels per unit of time and is represented by the formula d = sxt where d is distance, s is speed, and t is time.
Sharice's car is traveling 10 miles per hour slower than twice the speed of Maluma's car. Sharice covers 93 miles in 1 hour and 30 minutes.
How fast is Maluma driving?
(1 point)
36 miles per hour
29 miles per hour

Answer 4

Solve the absolute value equation 4|7 - x| + 1 = -1
x = 7
no solution

Answer 5

Which line is perpendicular to the line y = 3/5 * x + 6 and goes through the point (- 3, 6)?
y = 3/5 * x + 6
y = - 5/3 * x + 1

Answer 6

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 "=".

Answer 7

Let's solve the equation \( 7 + 2k^2 = 25 \).

1. Start by isolating the term with \( k^2 \):
\[
2k^2 = 25 - 7
\]
\[
2k^2 = 18
\]

2. Next, divide both sides by 2:
\[
k^2 = \frac{18}{2}
\]
\[
k^2 = 9
\]

3. 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 \(\{-3, 3\}\).

Answer 8

To solve the inequality \( k + 1 < -3 \), we can isolate \( k \):

1. Subtract 1 from both sides:
\[
k < -3 - 1
\]
\[
k < -4
\]

Thus, the solution set is:

\[
\{k : k < -4\}
\]

Therefore, the correct option is \(\{k : k < -4\}\).

Answer 9

To find out how fast Maluma is driving, let's first analyze the problem step by step.

1. **Convert time:** Sharice covers 93 miles in 1 hour and 30 minutes. We can convert 1 hour and 30 minutes to hours:
\[
1 \text{ hour } + 30 \text{ minutes} = 1 + \frac{30}{60} = 1.5 \text{ hours}
\]

2. **Calculate Sharice's speed:** We can use the formula \( s = \frac{d}{t} \) to find Sharice's speed:
\[
s_{\text{Sharice}} = \frac{d}{t} = \frac{93 \text{ miles}}{1.5 \text{ hours}} = 62 \text{ miles per hour}
\]

3. **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:
\[
s_{\text{Sharice}} = 2s_{\text{Maluma}} - 10
\]

4. **Set up the equation:** Substituting Sharice's speed into the equation:
\[
62 = 2s_{\text{Maluma}} - 10
\]

5. **Solve for Maluma's speed:**
- Add 10 to both sides:
\[
62 + 10 = 2s_{\text{Maluma}}
\]
\[
72 = 2s_{\text{Maluma}}
\]
- Divide by 2:
\[
s_{\text{Maluma}} = \frac{72}{2} = 36 \text{ miles per hour}
\]

Thus, Maluma is driving at **36 miles per hour**.

The correct answer is **36 miles per hour**.

Answer 10

To solve the absolute value equation \( 4|7 - x| + 1 = -1 \), we first isolate the absolute value term:

1. Subtract 1 from both sides:
\[
4|7 - x| = -1 - 1
\]
\[
4|7 - x| = -2
\]

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**.

Answer 11

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.

1. **Determine the slope of the given line:** The given line has a slope of \( \frac{3}{5} \).

2. **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:
\[
m = -\frac{1}{\left(\frac{3}{5}\right)} = -\frac{5}{3}
\]

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 \(y_1 = 6\):
\[
y - 6 = -\frac{5}{3}(x + 3)
\]

4. **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 \( y = -\frac{5}{3}x + 1 \).**