Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD

Answer:

⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]

Step-by-step explanation:

Let average no. of shepherds be x

there are estimated to be 50 dogs

Thus average no. of dogs /  estimated no. of dogs =x/50

Since in sample 1 there are 7 shepherd mix

In sample 2 there are 9 shepherd mix

So total shepherd mix = 9+7=16

Total dogs according to table = 4+7+3+1+2+5+9+5+2+4=42

Thus total shepherd / total dogs = 16/42

A.T.Q

[tex]\frac{16}{42} =\frac{x}{50}[/tex]

⇒[tex]\frac{8}{21} =\frac{x}{50}[/tex]

This proportion  could be used to find the average number of shepherd mixes at the park at any given time

Thus option A is correct

The average number of shepherd mixes at the park at any given time is equal to [tex]\frac{8}{21} =\frac{x}{50}[/tex].

Given the following data:

To determine the average number of shepherd mixes at the park at any given time:

First of all, we would determine the total number of shepherd mixes in sample 1 and sample 2.

Total shepherd mixes = [tex]7 + 9[/tex] = 16 dogs.

For the total dogs:

Total dogs = [tex]4+1+7+3+2+5+9+5+2+4[/tex] = 42 dogs.

The average number of shepherd mixes is given by this mathematical expression:

[tex]\frac{16}{42} =\frac{x}{50}[/tex]

Simplifying further, we have:

[tex]\frac{8}{21} =\frac{x}{50}[/tex]

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72  households in Mike's neighborhood ,begin emphasis, most, end emphasis, likely have a pet.

What is Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

According to question, based on a survey, 3 out of 8 households have a pet. Mike's neighborhood has 192 households.

We have to find how many households in Mike's neighborhood ,begin emphasis, most, end emphasis, likely have a pet.

We get the number of households by following equations:

[tex]\frac{3}{8}[/tex]×[tex]192=72[/tex]

Hence we can conclude that Option C is correct answer.

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Answer:

The correct option is 3.

Step-by-step explanation:

The given expression is

[tex]7\sqrt{28}-5\sqrt{63}[/tex]

It can be written as

[tex]7\sqrt{4\times 7}-5\sqrt{9\times 7}[/tex]

[tex]7\sqrt{2^2\times 7}-5\sqrt{3^2\times 7}[/tex]

Using product property of radical expressions, we get

[tex]7(\sqrt{2^2}\times \sqrt{7})-5(\sqrt{3^2}\times \sqrt{7})[/tex]               [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]

[tex]7(2\times \sqrt{7})-5(3\times \sqrt{7})[/tex]

[tex]14\sqrt{7}-15\sqrt{7}[/tex]

Taking out common factors.

[tex]\sqrt{7}(14-15)[/tex]

[tex]\sqrt{7}(-1)[/tex]

[tex]-\sqrt{7}[/tex]

Therefore the correct option is 3.

This could be answered by using the distributive property.

This is an algebra property which is done to multiply a particular term and two or more terms in a set of parentheses.

So for our problem, 6 (3 + 9):

You first, multiply 6 x 3 = 18

And multiply 6 x 9 = 56

Thus, the answer is 18 + 56 = 72

But following the order of operations, you should add first the number inside the parenthesis and then multiply it to the number outside the parenthesis but it will the same answer still. (6 x 12 = 72)

Answer:

18 + 54

Step-by-step explanation:

Take 6 x 3 = 18

6 x 9 = 54

Answer is 18+54

to check answer 18 + 54 = 72

6(3+9)

6(12)= 72  

Answer:

The correct option is 2. 16 is added to both sides of the equation.

Step-by-step explanation:

The given equation is

[tex]x^2-8x=-10[/tex]

If an expression is defined as [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.

In the given equation b=-8.

[tex](\frac{b}{2})^2=(\frac{-8}{2})^2=(-4)^2=16[/tex]

We need to add 16 on both the sides to solve by completing the square.

Therefore the correct option is 2. 16 is added to both sides of the equation.

Answer with explanation:

It is given that, the difference between one-half of a number and one-sixth of the number is equal to ten more than one-eighth of that number.

Let the number be x.

Writing the statement in terms of equations

 [tex]\frac{x}{2}-\frac{x}{6}=10+\frac{x}{8}[/tex]

This equation can be used to find the number.

Answer:

Option B

Step-by-step explanation:

The given equation function is f(x) =[tex]\sqrt{x-3}[/tex]

Domain of this function will be determined by (x-3) ≥ 0

because square root of negative numbers is not defined.

Option B is the answer.

Answer:

The area is a rational number.

Step-by-step explanation:

Consider the provided information.

A ballroom has a square dance floor. The area of the floor is 400 square feet.

Area of square = (side)²

Substitute the respective value in above formula.

400 = (side)²

√400 = side

20 feet = side

Ignore the negative value as side cannot be a negative number.

Now it is given that the length of each side of the square increased by one foot,

Thus, the new side is 20 + 1 = 21 feet

Now find the area of new square = (side)²

A = 21²

A = 21×21

A = 441 square feet

The number 441 is a rational number.

Hence, the area is a rational number.

We have that If the length of each side of the square increased by one foot,

Yes, Area will be a rational number

From the question we are told that

. The area of the floor is 400 square feet

the length of each side of the square increased by one foot,

Generally the equation for the Area of a square is mathematically given as

a=LxB

a=400

Rational Numbers

This simply means expressible as a ratio of whole numbers.

Therefore

If the length of each side of the square increased by one foot then the value will still be expressible as a ratio of whole numbers.

Hence

Yes, Area will be a rational number

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Answer:

T T → T

Step-by-step explanation:

Boolean table,

p        q        p → q

T         T        T

T         F        F

F         T        T

F         F        T

Given, the conditional statement:

p : True

q : True,

Then by using above table,

p → q  is true,

Hence, the correct answer is,

T T → T

⇒ Third option is correct.

Justin paid $0.49/pound for his 20 pound pumpkin.

This is determined by dividing the total amount paid ($9.80) by the pound total (20lbs).

9.80 / 20= 0.49

The correct mathematical equation representing Michael's total cost at the state fair, considering his base fee and cost per ride, is y=4x+30.

The question centers around linear equations, a subject in mathematics. In this context, Michael's total cost of his trip to the state fair is calculated by his base fee, 30 dollars, plus the number of rides he goes on multiplied by the cost per ride, 4 dollars. The correct equation representing this situation would be y=4x+30, where y is the total cost, x is the number of rides he goes on, and 30 is the flat entry fee.

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Answer: A:<CED is a right angle

B: <CEA is a right angle

D: m<CEB=m<BEA

E: m<DEB=135

Step-by-step explanation

Final answer:

The simplified expression '2x² - y² + 5xy - 2y' contains four terms, of which two are negative.

Explanation:

The expression given is 2x² - y² + 5xy - 2y To determine how many terms are in this simplified expression, we simply count the distinct variables and constant groupings. In this case, there are four terms: 2x², -y², 5xy, and -2y. Among these, two terms have a negative sign in front of them, indicating that they are negative. Thus, there are two negative terms in the simplified expression.

The two expressions 17x−13y+8 and 20x+6y can be rewritten as a difference to be -3x - 19y + 8.

To rewrite the two expressions 17x−13y+8 and 20x+6y as a difference, you can first list them separately and then combine by subtraction.

17x - 13y + 8

and

20x + 6y

. The difference between these two expressions is obtained by performing the subtraction as follows: (17x - 13y + 8) - (20x + 6y). Now, you can simplify this by removing the parentheses and switching the sign of the terms being subtracted, which results in:

17x - 13y + 8 - 20x - 6y

. Finally, you combine like terms, x-terms with x-terms and y-terms with y-terms, ending up with:

-3x - 19y + 8

which is the simplified difference of the two expressions.

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Answer:

The distance of UFO from KA-1212 is 1229.7 km.

Step-by-step explanation:

We are given that,

Distance between the satellites = 900 km

Angle made by the satellite KA-1212 = 60°

Angle made by the satellite SAL-11 = 75°

So, from the figure below,

The third angle is given by = 180° - (60°+75°) = 180° - 135° = 45°

Then, using the law of sines, we have,

[tex]\dfrac{x}{\sin 75}=\dfrac{900}{\sin 45}\\\\x=\dfrac{900\times \sin 75}{\sin 45}\\\\x=\dfrac{900\times 0.966}{0.707}\\\\x=\dfrac{869.4}{0.707}\\\\x=1229.7[/tex]

Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 So, it is 1229.7 km.

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

It is given that

Distance between the satellites  KA-1212 and SAL-11 = 900 km

Angle made by the satellite KA-1212 = 60°

Angle made by the satellite SAL-11 = 75°

So, the third angle is given by

= 180° - (60°+75°)

= 180° - 135°

= 45°

Using the law of sines, we get

x/sin75° = 900/sin 45°

x = 900 × sin75°/ sin 45°

x = 900 × 0.966/ 0.707

x = 1229.7

Thus, the distance of a UFO from KA-1212 is 1229.7 km.

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The rule for the following pattern is to multiply 10 with a constant number 44 everyu sequence.

Explanation;

44; 440; 4,400; 44,000.

44

44*10 = 440

440*10 = 4400

4400*10 =44000 and so on

A series is an ordered listing of numbers or other factors like geometric items, that often comply with a specific pattern or characteristic. Sequences can be both finite and limitless. A series is a listing of numbers in a sure order. each number in a series is known as a term . every time period in a series has a role.

Sequences are useful in a number of mathematical disciplines ... specially, sequences are the idea for series, which might be crucial in differential equations and evaluation. Sequences are also of hobby of their own proper and can be studied as styles or puzzles, including in the look at of prime numbers.

A number series is a fixed of numbers that observe a selected pattern or rule to get from time period to time period. There are foremost kinds of exclusive sequences, they are mathematics sequences, geometric sequences, quadratic sequences and special sequences. It assists with comprehension, specially for narrative texts. series structures assist college students of various abilities organize information and ideas successfully.

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Answer:47.6

Step-by-step explanation: