What do you call the well-defined collection of objects?

Answer:

3.88 : 3.25   ≈   13 : 11

Step-by-step explanation:

I don't know what are you in, geometry or algebra? I'll post my way of solution. It may need some calculator calculation that I can't give detail of steps here. I just like to explore something, wish it help.

suppose D is the origin, DA = 4 and AB = 5

A (0,4)    B(5,4)    C(5,0)    D(0,0)

AE/AC = 3/4   (i.e. AE/EC = 3/1)

parallel of EF with DC and EG with BC

CF/BC = CE/AC = 1/4

CF = BC x 1/4 = 4 x 1/4 = 1

DG/DC = AE/AC = 3/4  

DG = DC x 1/4 = 5 x 3/4 = 15/4

coordinator of E (3.75 , 1)

length of DE = √3.75² + 1² = 3.88

length of BE = √1.25² + 3² = 3.25

DE : BE = 3.88 : 3.25 ≈ 13: 11     (3.88/13 ≈ 0.29,  3.25/11 ≈ 0.29)

Answer:

[tex]consider \: {1}^{st} and \: {3}^{rd} columns\\ slope = \frac{(96 - 32)}{(12 - 4)} \\ = \frac{64}{8} \\ slope = 8[/tex]

Indicating the solution to an inequality such as \displaystyle x\ge 4x≥4 can be achieved in several ways.

We can use a number line as shown in Figure 2. The blue ray begins at \displaystyle x=4x=4 and, as indicated by the arrowhead, continues to infinity, which illustrates that the solution set includes all real numbers greater than or equal to 4.

A number line starting at zero with the last tick mark being labeled 11. There is a dot at the number 4 and an arrow extends toward the right.

Figure 2

We can use set-builder notation: \displaystyle \{x|x\ge 4\}{x∣x≥4}, which translates to “all real numbers x such that x is greater than or equal to 4.” Notice that braces are used to indicate a set.

The third method is interval notation, in which solution sets are indicated with parentheses or brackets. The solutions to \displaystyle x\ge 4x≥4 are represented as \displaystyle \left[4,\infty \right)[4,∞). This is perhaps the most useful method, as it applies to concepts studied later in this course and to other higher-level math courses.

The main concept to remember is that parentheses represent solutions greater or less than the number, and brackets represent solutions that are greater than or equal to or less than or equal to the number. Use parentheses to represent infinity or negative infinity, since positive and negative infinity are not numbers in the usual sense of the word and, therefore, cannot be “equaled.” A few examples of an interval, or a set of numbers in which a solution falls, are \displaystyle \left[-2,6\right)[−2,6), or all numbers between \displaystyle -2−2 and \displaystyle 66, including \displaystyle -2−2, but not including \displaystyle 66; \displaystyle \left(-1,0\right)(−1,0), all real numbers between, but not including \displaystyle -1−1 and \displaystyle 00; and \displaystyle \left(-\infty ,1\right](−∞,1], all real numbers less than and including \displaystyle 11. The table below outlines the possibilities.

I hope I will help

Answer:

11700 mm²

Step-by-step explanation:

A rectangle is a quadrilateral with two equal, opposite and parallel sides. Each of the angles in a rectangle is 90°.

The horizontal distance of the rectangle = r + r + r + r = 4r

The vertical distance = r + h + r = 2r + h

Where h is the distance between the midpoint of the 2 up circles and the midpoint of the down circle.

Using Pythagoras:

 (2r)² = h² + r²

h² + r² = 4r²

h² = 3r²

h = √3r²

h = r√3

Vertical distance = 2r + h = 2r + r√3

Area of rectangle = vertical distance * horizontal distance

Area = 4r * (2r + r√3) = 8r² + 4r²√3 = 4r²(2 + √3)

Substituting:

Area = 4r²(2 + √3) = 4(28²)(2 + √3) = 11703.711 mm²

Area = 11700 mm² to 3 s.f

Answer:

88

Step-by-step explanation:

it meets the mean

Answer:

88%

Step-by-step explanation:

:)

Answer:

Inequality equation:

0.03125x + 0.015625y ≤ 50 pounds

Step-by-step explanation:

We convert the ounces to pounds

1 ounce = 0.0625 pound

For the gold coin = 0.5 ounce

1 ounce = 0.0625 pounds

0.5 ounce = x

x = 0.5 × 0.00625 pounds

x = 0.03125 pounds

For the Silver coin = 0.25 ounce

1 ounce = 0.0625 pounds

0.25 ounce = x

x = 0.25 × 0.00625 pounds

x = 0.015625 pounds

The basket holds no more than 50 pounds of material.

Let the number of gold coins = x

The number of silver coins = y

Hence: our inequality equation:

0.03125x + 0.015625y ≤ 50 pounds

Answer:

220 student and 241 adults

Step-by-step explanation:

x+y=461

3x+4y=1624

y=-x+461-----> 3x+4(-x+461)=1624

                              -x+1844=1624

                             +x  -1624

                                   x=220

3(220)+4y=1624

660+4y=1624

4y=964

y=241

There are 241 adult tickets and 220 student tickets did Sara sell.

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

Given that;

Sara sold 461 tickets for a school play.

And, Student tickets cost $3 and adult tickets cost $4. Sara’s sales totaled $1624.

Let number of adult tickets = x

And, Number of student tickets = y

Hence, We get;

⇒ x + y = 461  .. (i)

And, 4x + 3y = 1624 .. (i)

Multiply by 3 in (i);

⇒ 3x + 3y = 1383  .. (iii)

Subtract form (ii);

⇒ x = 241

And, From (i);

⇒ x + y = 461

⇒ 241 + y = 461

⇒ y = 461 - 241

⇒ y = 220

Thus, There are 241 adult tickets and 220 student tickets did Sara sell.

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9514 1404 393

Answer:

  (b)  sin⁻¹

Step-by-step explanation:

The relevant trig function relating angles to sides is ...

  Sin = Opposite/Hypotenuse

Here, we have ...

  sin(A) = 4/12 = 1/3

  A = arcsin(1/30 = sin⁻¹(1/3)

The inverse sine function can be used to find the angle.

Answer:

(f*g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4)  or = 2x³ + 6x² - 4x -12

Step-by-step explanation:

F(x) = x +3

G(x) = 2x^2 -4

(f*g)(x) = f(x) * g(x)

(f*g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4)  or = 2x³ + 6x² - 4x -12

The function (f x g)(x) is equal to 2x³ + 6x² - 4x -12.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

The function (f x g)(x) is calculated as,

F(x)  = x +3

G(x) = 2x² -4

(f x g)(x) = f(x)  x  g(x)

(f x g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4)  

(f x g)(x)  = 2x³ + 6x² - 4x -12

Therefore, the function (f x g)(x) is equal to 2x³ + 6x² - 4x -12.

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Answer:

x = 80, y = 100

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7 , then

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

y + 135 + 140 + 150 + 120 + 135 + 120 = 900, that is

y + 800 = 900 ( subtract 800 from both sides )

y = 100

x and y are adjacent angles and are supplementary, that is sum to 180°

x + y = 180

x + 100 = 180 ( subtract 100 from both sides )

x = 80

Thus x = 80 and y = 100

Answer:

x=4

Step-by-step explanation:

21x+6=90(alternate angles)

21x=90-6

x=94/21

Therefore, x=4

Answer:

x=4

Step-by-step explanation:

21x+6=90

-6. -6

21x=84

/21. /21

x=4

Step-by-step explanation:

When n = 2,

(2)²a + (2)b = 8.

=> 4a + 2b = 8.

When n = 5,

(5)²a + (5)b = 65.

=> 25a + 5b = 65.

4a + 2b = 8. => 10a + 5b = 20

25a + 5b = 65

- (10a + 5b = 20)

=> 15a = 45, a = 3.

Therefore 4(3) + 2b = 8, 2b = -4, b = -2.

We have a = 3 and b = -2.

Hence when n = 10,

an² + bn

= (10)²(3) + (10)(-2)

= 300 - 20

= 280.

The 10th term of the sequence is 280.

Answer:

The 10th term of the sequence is 280

Step-by-step explanation:

When n = 2,

(2)²a + (2)b = 8.

=> 4a + 2b = 8.

When n = 5,

(5)²a + (5)b = 65.

=> 25a + 5b = 65.

4a + 2b = 8. => 10a + 5b = 20

25a + 5b = 65

- (10a + 5b = 20)

=> 15a = 45, a = 3.

Therefore 4(3) + 2b = 8, 2b = -4, b = -2.

We have a = 3 and b = -2.

Hence when n = 10,

an² + bn

= (10)²(3) + (10)(-2)

= 300 - 20

= 280.

Answer:

The value of (f о h) (2) is 2

Step-by-step explanation:

Let us solve the question

In the composite function (f о h) (x) we substitute x in f(x) by h(x)

∵ f(x) = 2x² - 9x + 2

∵ h(x) = x² - 4

∵ We need to find (f о h) (2)

→ That means use x = 2

∴ x = 2

We will find at first h(2), then substitute x in f by the answer of h(2)

∵ x = 2

∵ h(2) = (2)² - 4

∴ h(2) = 4 - 4

∴ h(2) = 0

Now substitute x in f by 0

∵ x = 0

∵ f(0) = 2(0)² - 9(0) + 2

∴ f(0) = 0 - 0 + 2

∴ f(0) = 2

∴ (f о h) (2) = 2

Answer:

AD∥BC,BD is the transversal line

⟹∠ADB=∠DBC (∵alternate angles)

⟹z=30

Step-by-step explanation:

Answer:

R=-3

Step-by-step explanation:

-11=r+4+4r

-11=5r+4

-4 both sides

-15=5r

Divide 5 both sides

r=-3

Answer:

r=-3

Step-by-step explanation:

Answer:

9-24=4(3)

-15=4×3

-15=12

Answer:

9-24= 4(3)

Multiply first

9-24=12

Then subtract the other digits in the side

-15=12

Step-by-step explanation:

Follow the PEMDAS rule which it to do which ever one of these first before furthering the math.

(Parentheses, exponents, multiply, division, addition and subtraction)

BUT hopefully there wasn’t a missing letter variable in the equation so you could get a single answer

Answer:

do we need to explain in words or numbers

Step-by-step explanation:

Answer:

[tex]a:b = -17:1[/tex]

Step-by-step explanation:

Given

[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]

Required

Find a:b

[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]

Cross Multiply

[tex]3(a-3b) = 4(a+2b)[/tex]

Open brackets

[tex]3a - 9b = 4a + 8b[/tex]

Collect Like Terms

[tex]3a - 4a = 8b+9b[/tex]

[tex]-a = 17b[/tex]

Divide through by -b

[tex]\frac{-a}{-b} = \frac{17b}{-b}[/tex]

[tex]\frac{a}{b} = \frac{17}{-1}[/tex]

[tex]\frac{a}{b} = \frac{-17}{1}[/tex]

Represent as a ratio

[tex]a:b = -17:1[/tex]

Answer:

hey long time no see!

9514 1404 393

Answer:

  x = 7 1/3

Step-by-step explanation:

The smaller triangle is 6/9 = 2/3 the size of the larger triangle, so the left side is ...

  (x -2) = (2/3)(8)

  3(x -2) = 16 . . . . . multiply by 3 to clear fractions

  3x -6 = 16 . . . . . . eliminate parentheses

  3x = 22 . . . . . . . . add 6; next divide by 3*

  x = 22/3 = 7 1/3 . . . . . feet

_____

* Note that we multiplied by 3, then divided by 3. If you're comfortable working with fractions and/or mixed numbers, these steps are unnecessary. The answer is simply x = 2 + 16/3 = 22/3.

Answer:

15x+60<240     is x<12

Step-by-step explanation:

Let's solve your inequality step-by-step.

15x+60<240

Step 1: Subtract 60 from both sides.

15x+60−60<240−60

15x<180

Step 2: Divide both sides by 15.

15x

15

<

180

15

x<12

Answer:

x<12

Step-by-step explanation:

Answer:

∠ A = 50°

Step-by-step explanation:

In a parallelogram, consecutive angles are supplementary, sum to 180°

∠ A + 130° = 180° ( subtract 130° from both sides )

∠ A = 50°

Answer: 480 children's tickets

Step-by-step explanation:

On the Friday, 720 adult tickets were sold.

This number was 9 times the number of children's tickets sold. Number of adult tickets sold was therefore:

= 720/9

= 80 children's tickets.

On the Saturday, 6 times the above amount was sold:

= 6 * 80

= 480 children's tickets

Answer:

y÷8

Step-by-step explanation:

The quotient is the result of division between two numbers.

SOOO its y÷8 because a quotient is a division problem and y and 8 are the variables in the equation!