Solve the inequality and graph on a number line. 7x + 4 ≤ x – 2

Answer:

Volume of each Marble: 0.06 liters

Water required for the marbles and water: 14 Liters

Answer:

He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.

Step-by-step explanation:

He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.

If he needs to make an inference on the whole school he needs to randomly pick people from the school and ask the same question. Then he can make a better inference about the favorite  class of students.

Answer:

His sample group does not represent the entire school body.

Step-by-step explanation:

The side length of the square window with a perimeter of (8x+12) feet is found by dividing the perimeter by 4, resulting in an expression for the side length as 2x + 3 feet.

To find the side length of a square window with a given perimeter, you can use the fact that the perimeter (P) of a square is equal to four times the side length (s). In this case, the perimeter is expressed as (8x+12) feet. Since there are four sides of equal length in a square, you divide the perimeter by 4 to find the length of one side.

The formula for the perimeter of a square is:

P = 4s

Given the perimeter P = (8x+12), we can solve for the side length s by dividing both sides of the equation by 4:

s = (8x+12) ÷ 4

Simplifying the equation, we get:

s = 2x + 3

Therefore, the expression for the side length of the square window in feet is 2x + 3.

The y-value increases by 4 when the x-value increases by 2, so the slope is

... 4/2 = 2

Your equation for the line with slope m through point (h, k) is

... y - k = m(x - h)

and you have m = 2, (h, k) = (-6, 6)

Filling in those values gives

... y - 6 = 2(x - (-6))

The dimension of the square is 1.125 by 1.125 units and the area of the square is 1.265625 square units.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The given expression represents the area of a square is 64r² – 144r + 81.

The dimension of the square will be

Using the formula method, we have

64r² – 144r + 81

Then

[tex]\rm r = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Then we have

a = 64

b = –144

c = 81

Then

[tex]r = \dfrac{-(-144) \pm \sqrt{(-144)^2-4*64*81}}{2*64}\\\\\\r = \dfrac{144 \pm \sqrt{20736- 20736}}{128}\\\\\\r = \dfrac{144}{128}\\\\\\r = 1.125[/tex]

The dimension of the square is 1.125 by 1.125 units and the area of the square is 1.265625 square units.

More about the factorization link is given below.

https://brainly.com/question/6810544

The perimeter of the fountain = 94.2 ft

The area of the fountain = 628 ft²

Given:

Diameter of the semicircle = 20 ft

Therefore, Radius (r) = half of diameter = 10 ft

Radius of the quarter circle = 20 ft

Perimeter of the fountain = ½(2πr) + ½(2πr) + ¼(2πr)

Perimeter of the fountain = ½(2π(10)) + ½(2π(10)) + ¼(2π(20))

Perimeter of the fountain = 94.2 ft

Area of the fountain = 2(½(πr²)) + ¼(πr²)

Area of the fountain = 2(½(π10²)) + ¼(π20²)

Area of the fountain = 628 ft²

Learn more about area of a circle on:

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Consider the ratio written like a fraction:

Count of sandwichescount of people→46

But we need the count of sandwiches for 1 person. So we need to change the 6 people into 1 person. To change 6 into 1 divide it by 6

6÷6=1

For ratios, when multiplying or dividing, what we do to the bottomwe do to the top.

So to change 46 into what we want we apply

4÷66÷6=231← Count of sandwichescount of people

So each person ends up with 23 of a sandwich

Now see where the shortcut comes from 46=23 of a sandwich

Answer:

Cost of 200 gram chess  = $0.88.

Step-by-step explanation:

Given  : If cheese is $4.40 per kilogram.

To find : What should I pay for 200 gram.

Solution : We have given

1 kilogram = 1000 gram.

Cost of 1000 gram chess =  $4.40.

Cost of 1 gram chess = [tex]\frac{4.40}{1000}[/tex].

Cost of 200 gram chess =  [tex]\frac{4.40}{1000}* 200[/tex].

                                        = $0.88.

Therefore, Cost of 200 gram chess  = $0.88.

The proof that 10⁹ + 10⁸ + 10⁷ is divisible by 555; Is true and has been proved below

Let the number N be expressed as;

10⁹ + 10⁸ + 10⁷

We can factor out 10⁷ to get;

⇒ 10⁷(100 + 10 + 1)

⇒ 10⁷(111)

⇒ 10 × 10⁶(111)

We can factorize 10 further to get;

5 × 2 × 10⁶(111)

⇒ 555 × 2 × 10⁶

Since the answer contains 555, then we can say that it is divisible by 555.

Read more on divisibility of numbers at; https://brainly.com/question/14871175

Final answer:

To find the distance the flying squirrel must glide to reach the acorn, the Pythagorean theorem is used. The tree's height (15 feet) and the horizontal distance to the acorn (8 feet) provide the two sides of a right triangle. The squirrel's glide distance is the hypotenuse, calculated to be 17 feet.

Explanation:

To calculate the distance the flying squirrel needs to glide to reach the acorn, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario, the tree height forms one side of a right triangle, the distance from the base of the tree to the acorn forms the second side, and the squirrel's glide path represents the hypotenuse.

Given:

Tree height (side a): 15 feet

Distance from the tree to the acorn (side b): 8 feet

Using the Pythagorean theorem:

c² = a² + b²

c² = 15² + 8²

c² = 225 + 64

c² = 289

c = √289

c = 17 feet

Therefore, the flying squirrel needs to glide 17 feet to reach the acorn.

The solution of the expression are,

⇒ x = 3.5 and x = - 3.5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 12 - x² = 0

Now, We can simplify as;

⇒ 12 - x² = 0

⇒ 12 = x²

⇒ x = √12

⇒ x = ± 3.5

⇒ x = 3.5 and x = - 3.5

Thus, The solution of the expression are,

⇒ x = 3.5 and x = - 3.5

Learn more about the mathematical expression visit:

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