How many degrees is 1/4 of a circle or 1/4 of a full turn? And how many degrees is 1/6 of a circle or 1/6 of a full turn ?

To simplify [tex]\(3x(-11x + 1)\)[/tex], we distribute [tex]\(3x\)[/tex] to both terms inside the parentheses, resulting in [tex]\(-33x^2 + 3x\)[/tex]. Thus, the simplified expression is [tex]\(-33x^2 + 3x\)[/tex]. Therefore, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].

To simplify the expression [tex]\(3x(-11x + 1)\)[/tex], we'll use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].

1. **Apply the distributive property**:

  We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses:

   [tex]\[3x \cdot (-11x) + 3x \cdot (1)\][/tex]

2. **Perform multiplication**:

   [tex]\[= -33x^2 + 3x\][/tex]

Now, let's break down each step in detail:

- **Step 1: Apply the distributive property**:

 We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses: [tex]\(-11x\) and \(1\)[/tex]. This results in two separate terms.

- **Step 2: Perform multiplication**:

 Multiply each term inside the parentheses by [tex]\(3x\)[/tex]. This results in:

 [tex]\[3x \cdot (-11x) = -33x^2\][/tex]

 [tex]\[3x \cdot (1) = 3x\][/tex]

 Combining these two terms, we get [tex]\(-33x^2 + 3x\)[/tex].

Therefore, the simplified form of the expression [tex]\(3x(-11x + 1)\) is \(-33x^2 + 3x\).[/tex]

Hence, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].

Final answer:

The expression for the number of goals Sarah scored, if Christina scored g goals, is 2g, representing that Sarah scored twice as many goals as Christina.

Explanation:

If Christina scored a certain number of goals, g, during a soccer season, and Sarah scored twice as many goals during the same season, we can write an expression for the number of goals Sarah scored as 2g. This expression simply states that Sarah's goals are double the quantity of Christina's goals.

To think about this conceptually, if Christina scored 5 goals, we would substitute g with 5 and calculate Sarah's goals as 2 × 5, which equals 10 goals. This expression is a straightforward representation of the relationship between the number of goals scored by Christina and by Sarah.

Schlitterbahn becomes cheaper than Splashtown after more than 15 rides.

Let's define x as the number of rides:

Cost of Splashtown: $25 + $1 * x
Cost of Schlitterbahn: $40

We need to find the value of x for which the cost of Splashtown becomes greater than the cost of Schlitterbahn.

$25 + $1x > $40

$1x > $40 - $25

x > $15

So, after more than 15 rides, Schlitterbahn would be cheaper than Splashtown.

in order to have the smallest possible number the numbers need to be arranged from smallest to largest

 using 3, 5 & 7 the smallest number would be 357

The distance between the points (−5, −9) and (−5, 13) would be 22. units.

The shortest distance (length of the straight line segment connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

We have been given two points as (−5, −9) and (−5, 13)

Then the distance formula :

D = √[(x-p)² + (y-q)²]  

Now we substitute;

[tex]d = \sqrt{(-5 - (-5)^2 + (13 - (-9)^2}\\d = \sqrt (-5 + 5)^2 + (13 + 9)^2\\d = \sqrt (0^2 + 22^2)\\d = \sqrt (484)\\d = 22[/tex]

Therefore, the distance between the points (−5, −9) and (−5, 13) would be 22. units.

Learn more about the distance between two points here:

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The number of friends who purchased ride passes= 6

It is given that:

A fair charges $7.25 for admission and $5.50 for a ride pass.

Now, if 10 friends visited the fair.

This means that:

Total cost of admission= 7.25×10= $ 72.5

Also, if x friends purchased the ride passes.

Then, the total cost of ride passes= 5.50x

Total cost= 72.5+5.50x

This means that:

72.5+5.50x=105.50

i.e.

5.50x=105.50-72.5

5.50x=33

x=33/5.50

x=6

     Hence, 6 friends purchased ride passes.

The inequality representing the cost of each smoothie is 4x < 16, which simplifies to x < 4, denoting that the cost of each smoothie is less than $4. Sensible values are any positive numbers less than $4.

To represent the cost of each smoothie with an inequality, let's designate the cost of one smoothie as x. Since Lina bought 4 smoothies and the total cost was less than $16, the inequality to represent this situation is:

4x < 16

To solve this inequality, we'll divide both sides by 4:

x < 16 / 4

x < 4

The cost of each smoothie is less than $4.

Values that make sense for this situation would be any positive price per smoothie that is less than $4, as Lina's total purchase for 4 smoothies must not exceed $16. So, x could be any positive real number less than 4.

In linear equation,  4/3  is the scale factor.

given,

The length of the ears on the shadow puppet = 3 inches

The length of the ears on the shadow = 4 inches.

so according to question we apply the formula of scale factor ,

scale factor = length of ears on the shadow/length of ears on the shadow

             scale factor = 4/3

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The estimated value is 50, which is close to the actual value of approximately 49.74.

To estimate the value of 97.5 divided by 1.96, we can round the numbers to make the calculation simpler.

Rounding 97.5 to 100 and 1.96 to 2 gives us an easier division: 100 divided by 2, which equals 50.

This estimation tells us that the actual value will be close to 50.

If we require more accuracy and use a calculator, we would find that 97.5 divided by 1.96.

= 9.75 / 1.96

= 49.74.

Therefore, our rounded estimate of 50 is reasonably close to the actual value.

The deep-sea diver started at 82 feet below the surface and rose in five steps of 15 feet each, which resulted in a new position of -7 feet. This indicates that the diver is still 7 feet underwater, so the integer representing his position is negative.

The diver starts at 82 feet below the surface and rises in five steps of 15 feet each. To find the new position, we start with the initial position and subtract the distance risen in each step:

Initial position: -82 feet (below water is considered negative)

Total rise: 5 steps × 15 feet/step = 75 feet

New position: -82 feet + 75 feet = -7 feet

Therefore, the diver's new position is -7 feet relative to the surface, indicating he is still 7 feet underwater, thus the integer is negative.

To find out how many stamps Scott started with, we can set up an equation. After solving the equation, we find that Scott started with 26 stamps.

To find out how many stamps Scott started with, we can set up an equation using the information given. Let's represent the number of stamps he started with as 'x'. After selling half of them, he would have 'x/2' stamps left. But since he changed his mind and bought sixteen more, he now has 'x/2 + 16' stamps. We know that he currently has 29 stamps, so we can set up the equation: x/2 + 16 = 29. We can solve this equation to find the value of x, which represents the number of stamps Scott started with.

To solve the equation, we can subtract 16 from both sides: x/2 + 16 - 16 = 29 - 16. Simplifying, we get: x/2 = 13. To isolate x, we can multiply both sides of the equation by 2: 2 * (x/2) = 13 * 2. Simplifying, we get: x = 26. Therefore, Scott started with 26 stamps.