Add or subtract. Simplify where possible. 5 / y+3 + 15 / y-3

Answer:

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.

Step-by-step explanation:

in easy language it's Transformations. Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

Answer:

x = 7

Step-by-step explanation:

➟ x² = 49

in order to find the value of x will have to take square root of both side

➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]

Calculate

➟ [tex] \sf \: x = 7[/tex]

The least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).

According to the given question.

We have two polynomials 9(x + 2)(2x - 1) and 3(x + 2).

Since, we have to find the least common multiple of 9(x + 2)(2x -1) and 3(x+2).

As we know that, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

From the definition of least common multiple, we can say that the least common multiple of 9 and 3 is 3 and (x +2)(2x -1) and (x + 2) is (x + 2).

Thereofrore, the least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).

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The slope of the equation is 5 for the coordinates (-3,5) and (4,5).

Locate two points along the chosen line and find their coordinates.

Find the y-coordinate difference between these two sites (rise).

Find the x-coordinate difference between these two sites (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope calculation formula is -

m = y2 - y1 / x2 - x1

Given points are -

(-3,5) and (4,5)

Now, putting the values in equation,

m = 5-5 / 4+3

m = o

As slope is 0, this implies,

the equation of line is y = 5

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[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-16} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(-1)}~~~~ ,~~~~ -16-\cfrac{ (-6)^2}{4(-1)}\right) \implies \left( - \cfrac{ -6 }{ -2 }~~,~~-16 - \cfrac{ 36 }{ -4 } \right) \\\\\\ (-3~~,~~-16+9)\implies (-3~~,~~-7)[/tex]

Part (a)

The horizontal part of the rectangle goes from m = -1 to n = 4. This is a distance of 5 units because |m-n| = |-1-4| = 5

The height is some unknown variable h

It must multiply with the base (5) to get an area of 1

base*height = area

5h = 1

h = 1/5

h = 0.2

========================================================

Part (b)

x = dismissal time minutes after class

Something like x = 2 means he dismisses class 2 minutes after the bell, while x = -1 is him dismissing class 1 minute early before the bell.

The phrasing "within 1 minute" means that x is between p = -1 and q = 1. So we can say [tex]-1 \le x \le 1[/tex]

This is a span of 2 units because |p-q| = |-1-1| = 2. Divide this over the entire horizontal span: 2/5 = 0.4

Exactly 40% of the time the teacher lets his class out within one minute of the scheduled end time.

Answer:

The Answer is y=-6

an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

See the pattern

-32-(-20) = -12

-20-(-8) = -12

-8-4 = -12

By this the explicit and a recursive formula for each sequence is  an=a1+d(n−1).

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The required value of constant of variation, k does not exist for which x and y vary directly..

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is  y + 3 = -3 x

y = -3 x - 3

y = -3(x + 1)

Comparing with equation 1, we get that y does not vary directly for any value of k.

Hence, the required value of constant of variation is does not exist.

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The function is neither an even function nor an odd function

The function is given as

g(x) = x + x^2

Calculate g(-x)

So, we have

g(-x) = -x + (-x)^2

Evaluate

g(-x) = -x + x^2

Calculate -g(x)

So, we have

-g(x) = -x - x^2

In the above computations;

g(x) does not equal g(-x) and -g(x)

Hence, the function is neither an even function nor an odd function

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13 litres of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher.

Concept: In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items. It is an operation used for equal grouping and equal sharing in math.

Quantity of 1 glass of water= 0.8 liters

Quantity to be filled completely = 10.4 liters

No . of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher = 10.8/0.4 = 13

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Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.

The sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ be 2.407.

The equation be Sn = a(1 - rⁿ)/(1 - r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the series be Σ⁴ n=1 (2/3)ⁿ⁻¹

Σ⁴ n=1 (2/3)ⁿ⁻¹ = (2/3)¹⁻¹ + (2/3)²⁻¹ + (2/3)³⁻¹ + (2/3)⁴⁻¹

= 1 + (2/3) + (2/3)² + (2/3)³

= 1 + (2/3) +(4/9) +(8/27)

Where, the first term is a = 1

common ratio be r = 2/3

n th term be n = 4

Let the equation be Sn = a(1 - rⁿ)/(1 - r)

substitute the values in the above equation, we get

S4 = 1(1 - (2/3)⁴)/(1 - (2/3))

S4 = 1(1 - (16/81)⁴)/(1/3)

S4 = (65/81) × 3

S4 = (65/27) = 2.407

Therefore, the sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ is 2.407.

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Answer:

1) 140°

2) 40°

3) 140°

4) 40°

5) 140°

6) 40°

7) 140°

Step-by-step explanation:

1) Angles on a straight line = 180°

180° - 40° = 140°

2) Angle 3 is Vertically opposite to Angle 1

So they are the same Angle

3) Angle 4 is Vertically opposite to Angle 2

So they are the same Angle

4) Angle 5 is corresponding to Angle 1

So they are the same angle

5) Angle 6 is corresponding to Angle 2

So they are the same angle

6) Angle 7 is corresponding to Angle 3

So they are the same angle

7) Angle 7 is corresponding to Angle 4

So they are the same angle

The value of 5•10⁷ µs​ quantity in second is 50 .

We know that 10⁶μs is equal to 1 second .

Using unitary method , we get

 1 μs have = 10⁻⁶ second

 5•10⁷ µs​ have = 5 × 10⁷ × 10⁻⁶

                        = 50 second

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The statement "∠1 and ∠7 are alternate exterior angles" is true

Given,

The statement "∠1 and ∠7 are alternate exterior angles"
Here,

∠1 and ∠7 are lie on opposite sides of the transversal and both are nonadjacent exterior angles

So, ∠1 and ∠7 are alternate exterior angles.

Hence, the statement  "∠1 and ∠7 are alternate exterior angles" is true

The complete question is:

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

Angles 1 and 7 are alternate exterior angles.

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Step-by-step explanation:

least value is q

greatest value is n-q

close to zero is q-n

The fraction converted to an improper fraction is 11/3

An improper fraction can be defined as a type of fraction whose numerator is equal to or is greater than its denominator.

Examples of improper fractions are;

5/ 3, 8/2 , 11/ 7, 20/ 5, 4/ 1, 2/ 2, 5/ 3

Given the fraction;

3 2/3; this is a mixed fraction

To convert to improper fraction, we take the steps

Multiply the whole number by the denominator;

= 3 × 3 = 9

Add the value to the numerator

= 9 + 2 = 11

Divide by the denominator

= 11/ 3

Thus, the fraction 3 2/3 converted to an improper fraction is 11/3

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Answer:

Distance: 4√41

Midpoint: (2, 3)

Step-by-step explanation:

A: (-6, 13) B: (10, -7)

    (x₁, y₁)       (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(10 - (-6))² + (-7 - 13)²

d = √(16)² + (-20)²

d = √256 + 400

d = √656

d = √16 × 41

d = 4√41

midpoint:

(x₁ + x₂)    (y₁ + y₂)

---------- , ------------

    2            2

(-6 + 10)   (13 + (-7))

---------- , ------------

    2            2

   4             6

---------- , ------------

    2            2

Midpoint = (2, 3)

I hope this helps!

The compound inequality in this problem is represented by:

y > -(x + 2)² + 6.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (-2,6), hence:

h = -2, k = 6.

y = a(x + 2)² + 6.

When x = 0, y = 2, hence we use it to find a as follows:

2 = 4a + 6

a = -1.

Hence:

y = -(x + 2)² + 6.

The inequality is the interior of the parabola, hence values greater, and the parabola is dashed, hence it is an open interval and the inequality is given by:

y > -(x + 2)² + 6.

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    The Volume of the requested pyramid is 68.5 in³.

  The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.

   We must determine the scale factor with the data of the inclined heights of each of the pyramids:

  If the scale factor is a/b, the reason of the volume will be:;

(a/b)³ = 1/8

1/8 = V/540

V = 1/8 x 540

V = 68.5

V = 68.5in³

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Tanya - Iams ProActive Lamb & Rice

Eddie - Ultimate Pet Nutrition Nutra Complete

Answer: 1.6,1.8,2.5,6.7,6.9,7.5

Step-by-step explanation:

Step-by-step explanation:

1.6 1.8 2.5 6.7 6.9 7.5

was that really all ? I don't see any trap in these numbers, so this is straight forward.

The numerical length of BD is 20.

We have a Line Segment BD and a point C on it.

We have to determine the numerical length of BD.

A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

According to question, we have -

BD = 5x

BC = 4x

CD = 4

Now,

BD = BC + CD

5x = 4x + 4

x = 4

Therefore - BD = 5x = 5 x 4 = 20

Hence, the numerical length of BD is 40.

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Answer:

k = -10

Step-by-step explanation:

1) Because of the division of the left side of the equation by 2, multiply both sides of the equation by 2, which means you now have :

-8 - 3k = 22

2) Now, add eight to both sides. Your equation now looks like this:

-8 + 8 - 3k = 22 + 8

3) Simplify.

-3k = 30

4) You now have k = -10

Answer:69999

Step-by-step explanation:your gay

Your answer would be the second one.

We know that adding [tex]\frac{1}{2}[/tex] to x gives us 4, as that's provided by the question.

So [tex]4=x+\frac{1}{2}[/tex]. Now, to find x, simply subtract [tex]\frac{1}{2}[/tex] from 4 to give us x, which gives us [tex]3\frac{1}{2}[/tex].

Answer:

Step-by-step explanation:

80¢ is your answer because Derek paid $3.20 for a pack of 4 Gatorade so you would have to divide $3.20 by 4 which will be 80¢

So your answer would be 80¢ per bottle.

We can conclude that triangle ΔPQR ≇ ΔXYZ.

So,

Given: P(-3,-3), Q(-5,1), R(-2,6), X(2,-6), Y(3,3), Z(5,-1)

To find if ΔPQR ≅ ΔXYZ

So, ΔPQR ≇ ΔXYZ.

Therefore, ΔPQR ≇ ΔXYZ.

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The ratio of pencils to all the item on the desk is 1 : 10

According to Gary,

    Number of pencils on the desk = 4

    Number of markers on the desk = 12

   Number of crayons on the desk = 24

Total number of item son the desk = 4 + 12+ 24

                                                             = 40

The ratio of pencils to all the item is given as = (number of pencils)/(total number of items)

                                                                                = 4/40

                                                                                = 1/10

                       Which in ratio can be written as 1 : 10

Thus the ratio of pencils to all the item is 1 : 10  

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