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The set of rational expressions are closed under subtraction because the subtraction will result to a rational expression

The ratio of two polynomials is a rational expression.

A rational expression can be expressed in the form p/q, where p and q are polynomials,

Closure property of rational expression

According to the closure property, a - b is also a rational number for any pair of two rational numbers, a and b. The outcome is a rational number. Therefore, under subtraction, the rational numbers are closed.

In the polynomial subtraction

= P(x) /q(x) - r(x)/s(x)

= (P(x) * s(x) - r(x) * q(x)) / (q(x) * r(x))) also a rational number

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Answer: The correct interpretations about the graph of r(t) are B, D, and E.

Interpretation B is correct because the graph shows that the average mortgage rate fell to a relative minimum between 2002 and 2003.

Interpretation D is correct because the graph shows that the average mortgage rate was highest between 2006 and 2007, based on the absolute maximum.

Interpretation E is correct because an appropriate domain for this function would be 0≤t≤10, as t represents time and the graph shows data for the period between 2002 and 2010.

Interpretation A is not correct because the graph does not show that the average mortgage rate increased continuously between 2003 and 2005.

Interpretation C is not correct because the y-intercept does not represent the average mortgage rate in 2010. The y-intercept represents the value of the function when t = 0, which does not correspond to any time in the given data.

Step-by-step explanation:

Answer:

4 1/6

Step-by-step explanation:

15 3/4 ÷ 2 5/8 × 5 5/6 ÷ 8 2/5

assuming this order of operations:

(15 3/4 ÷ 2 5/8) × (5 5/6 ÷ 8 2/5)

63/4 x 8/21 = 505/84 = 6

35/6 x 5/42 = 175/252

6 x 175/252 = 1050/252 = 4 42/252 = 4 1/6

Answer:

10 Inches

Step-by-step explanation:

All you gotta do is add the side you are given then subtract (I believe)

Answer:

1. -3, -2

2. 2, -7

3. 1, 2.5

4. infinitely many solutions

Answer:

1. (-3,-2)

2. (1, -7)

3. (1, 2.5)

4. No solution

Step-by-step explanation:

Number 1: Substitution

Plug y in to substitute and get

2x + (2x + 4) = -8

4x + 4 = -8

4x = -12

x = -3

Then plug into the y equation

y = 2(-3) + 4

y = -6 + 4

y = -2

(-3, -2)

Number 2: Elimination

Begin eliminating by crossing out same values

40x + 12y = -44

-2y = 14

Solve for y

-2y = 14

y = -7

Solve for x

40x + 12(-7) = -44

40x - 84 = -44

40x = 40

x = 1

(1, -7)

Number 3: Elimination

Add the two and get:

-3x + 2y = 2

6y = 15

Solve for y:

6y = 15

y = 5/2

Solve for x:

3x + 4(5/2) = 13

3x + 10 = 13

3x = 3

x = 1

(1, 2.5)

Number 4: Substitution

Solving for y to begin with:

4x - y = -3

-y = -3 - 4x

y = 3 + 4x

Then solve for y in the second system

-8x + 2y = 6

2y = 6 + 8x

y = 3 + 4x

Set equal to each other

3 + 4x = 4 + 4x

3 = 4

No solution

Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2

So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.

when reduced it would simplify back to 30/100.

You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.

Step-by-step explanation:

Answer:

2 1/3

Step-by-step explanation:

Seperate equation

(3 1/2) - 1

( 3 - 1 ) + 1/2

2 and 1/3

Answer:

4.8 miles

Step-by-step explanation:

have a good day!

Answer:

4.8 Miles

Step-by-step explanation:

Answer:

Step-by-step explanation: Find the number between 40 and -10.

start at 40 and end at -10.

-40=0

0-10=-10

the tempature changed by 50 degrees.

Answer:

The answer is "0.096".

Step-by-step explanation:

In this question, the X is a number of the students who enroll in a psycholog y course,  follows a Poisson distribution with mean [tex]= \lambda= 105[/tex]  

[tex]\therefore P(X=x)=\frac{e^{-105} 105^{x}}{x!},(x=0,1,2,3.....)\\\\\to p(teach\ two \ sections) = P(X \geq 119)\\\\=1-P(X<119)\\\\=1-\sum_{x=0}^{118}P(X=x)\\\\=1-\sum_{x=0}^{118}\frac{e^{-105} 105^{x}}{x!}\\\\=0.0956747863537\\\\=0.096\\[/tex]

Answer:

1/53 I believe because it says I believe sorry if I am wrong hope you get it right

The measure of ∠ 1 is 68.7°

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given is a figure of angles showing the pair of linear angles.

Therefore, by the definition of linear pair angles,

∠ 1 + 111.3° = 180°

∠ 1 = 180° - 111.3°

∠ 1 = 68.7°

Hence, the measure of ∠ 1 is  68.7°

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Answer: 5%

Step-by-step explanation:

Answer:

answer is 10

Step-by-step explanation:

Answer:

13 is your number

Step-by-step explanation:

23 = -29 x 4x

add 29 to both sides

52 = 4x

divide both sides by 4

13 = x

Answer:

13

Step-by-step explanation:

13 x 4 = 52 - 29 = 23

Answer:

8.5

Step-by-step explanation:

there's a rule to get the distance between 2 points

√((1st x- 2nd x)²+(1st y- 2nd y)²)

√((-6-(-6))²+(5-(-3.5))²)

=√((-6+6))²+(5+3.5))²)

you can just type that on your calculator and you'll get the result

√((-6+6))²+(5+3.5))²)

=√((5+3.5))²)

= √((8.5))²)

the root goes away with the power (exponent)

so it equals 8.5

Answer:

The cost of a manicure set in Nina's store is $12.30.

Step-by-step explanation:

To find the cost of the manicure set in Nina's store, you can use the following formula:

Selling price = Cost + Cost * Markup percentage

Substituting the given values into this formula, you get:

Selling price = $8.36 + $8.36 * 47%

To find the value of the markup percentage, you can convert 47% to a decimal by dividing it by 100: 47/100 = 0.47

Then you can use this value in the formula to find the selling price:

Selling price = $8.36 + $8.36 * 0.47

Answer:

y = 9/4x - 81

Step-by-step explanation:

Given the slope = 9/4

The point (36, 0) ; x1 = 36 ; y1 = 0

Slope intercept relation :

y = mx + c ; c = intercept, m = slope

Using the relation :

y - y1 = m(x - x1)

y - 0 = 9/4(x - 36)

y - 0 = 9/4x - 81

y = 9/4x - 81

Hence, the required equation is : y = 9/4x - 81

9/4 = slope ; - 81 = intercept

Answer:

The answer is 12 (B)

I hope this helped!!!

Step-by-step explanation:

First Quartile Q1 = 14

Second Quartile Q2 = 18

Third Quartile Q3 = 26

Interquartile Range IQR = 12

Median = Q2 x˜ = 18

Minimum Min = 12

Maximum Max = 35

Range R = 23

You can use a calculator for this, just search it up! I can't include the link because then my answer would be reported, but just search up IQR calculator.

Answer:

42.3°

Step-by-step explanation:

Use SOH-CAH-TOA (O=opposite, A=adjacent, H=hypotenuse) we see that they give us the angle missing, x, but we first need to identify what method to use. They give us the opposite side from the angle, and they also give us the adjacent side from the angle, so TOA=tan.

now plug it in, since there is no angle then we plug it in as [tex]tan^{-1}=\frac{10}{11}[/tex]

in the calculator, (be sure to be in degree mode)

x=  42.3°

(does that make sense)

Answer:

53 centimeters

Step-by-step explanation:

Answer: 53 centimeters

Answer:

screenshot plz

Step-by-step explanation:

Answer:

fruit loops

Step-by-step explanation:

because i said FRUIT LOOPSSSSSSSSS

Answer:

0.95meters

Step-by-step explanation:

last year her was 0.45m tall

this past year he is 0.5m

Total = 0.45 + 0.5 = 0.95

Answer: 0.95

Step-by-step explanation: add 0.45+0.5=0.95

Answer:

3 possibilities

Step-by-step explanation:

possibilities

2 brown 1 yellow

1 brown 2 yellow

3 yellow

A combination is denoted by 'C'. The number of ways of selecting 3 marbles out of this bag is 10.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\[/tex]

where,

n is the number of choices available,

r is the choices to be made.

Given the bag contains 2 brown marbles and three yellow marbles, therefore, the number of ways of selecting 3 marbles are,

Number of marbles = ⁵C₃ = 10

Hence, the number of ways of selecting 3 marbles out of this bag is 10.

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As a result, the first term of the answer to the given arithmetic mean problem is 14.

The Arithmetic Mean or Average of the Group is the product of the sum of all the numbers in a group and the amount of items in that list, divided by both. The Geometric progression is also same as this .This average of the numbers 5, 7, and 9 is, for instance, 4, as 5 + 7 + 9 is 21, and 21 split by 3 [there really are three numbers] equals 7.

Here,

In this case, t(n) = (a + ((n — 1) * d)),

The value of the nth term is t(n),

The first term of the AS is a.

The position of a value in the A.S. is represented by the positive whole integer n, and

The constant common difference among A.S. words is d.

In light of the question, we can say:

11 = (5 + ((4 — 1) * d)),

Take 5 away from both sides.

11 — 5 = (5 + ((4 — 1) * d)) — 5,

On the RHS, the fives cancel one another out.

6 = 3d,

d = 2.

In summary, the common distinction is: 2.

=> 20 = a + 3d

=> 20 - 6

=> a =14

As a result, the first term of the answer to the given arithmetic mean problem is 14.

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The correct set of image points for trapezoid WX'Y'Z' is the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).

Given data :

From the given figure, it is clear that the vertices of the trapezoid are W(-4,2), X(-3,4), Y(-1,4), Z(0,2).

If a figure is rotated 180 degrees about the origin, then

( x, y )  → ( -x, -y )

Using this rule, we get

W (-4, 2 ) → W' ( 4, -2 )

X ( -3, 4 ) → X' ( 3, -4 )

Y ( -1, 1 ) → Y' ( 1, -4 )

Z ( 0,2 ) → Z' ( 0, -2 )

Therefore, the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).

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Answer:

157[tex]ft^{3}[/tex]

Step-by-step explanation:

Volume =  the area of the base times the height.

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

a = [tex]\pi[/tex][tex](5^{2})[/tex]   I am going to use 3.14 for [tex]\pi[/tex]

a = 3.14(25)

a = 15.7

Volume = 15.7 x 10 = 157

Answer:

785 ft२

Step-by-step explanation:

volume =3.13*5२*10

=3.14*25*10

=785 ft२

The system of equations will have no solutions if the two lines are parallel, then one example can be:

5x - 2y = 1

15x - 6y = 0

Here we have the following system of equations:

5x - 2y = 1

a*x - 6y = b

The system will have no solutions only if the two equations are parallel. You can see that the coefficient of y on the second equation is 3 times the coefficient on the first equation.

Then a should also be 3 times the coefficient of x on the first equation:

a = 3*5

a = 15

And b should be any number but 3 times the constant on the other equation:

b ≠ 3*1

So we can take b = 0, for example.

So the system with no solutions will be:

5x - 2y = 1

15x - 6y = 0

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