simplify the expression and find domain that will make it equivalent to previous expression.

[tex]\frac{1}{a^{2}+ab } +\frac{1}{ab+b^{2} }[/tex]

Answer:

B. 50

Step-by-step explanation:

Let x be the number of coupons sent to existing members.

The number of coupons sent to potential members is 4 times the number of coupons sent to existing members, or 4x.

The total number of coupons sent is the sum of the number of coupons sent to existing members and the number of coupons sent to potential members, or x + 4x = 5x.

The club sent out 250 coupons, so 5x = 250.

Dividing both sides of the equation by 5, you get x = 250 / 5 = 50.

Therefore, the club sent 50 coupons to existing members.

A function is a relation where each conceivable input value results in exactly one potential output value. The phrase "the output is a function of the input" frequently used.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

   3 ,-3 is an input value of the function

   0 is an output value of the function in this graph

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The estimate of the quotient expression using compatible numbers is 100

From the question, we have the following parameters that can be used in our computation:

7 | 497

This quotient expression from the question can be expressed as

497 ÷ 7

From the question, we are to make use of compatible numbers

This means that we have the following approximation

497 = 500

7 = 5

Next, we estimate the quotient using approximated values

So, we have

497 ÷ 7 = 500 ÷ 5

Evaluate the quotient

497 ÷ 7 = 100

Hence, the estimate is 100

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Answer:

He picked a total of 52

Step-by-step explanation:

You would add 16 (red apples), then divide 1/2 from the 16 red apples, +28 green apples which would equal 52.

However, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other. There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event.

Causal relationships between variables may consist of direct and indirect effects. Direct causal effects are effects that go directly from one variable to another. Indirect effects occur when the relationship between two variables is mediated by one or more variables.

Direct and indirect effects may make up causal connections between variables. Effects that flow directly from one variable to another are referred to as direct causal effects. When one or more factors mediate the link between two variables, indirect effects result.

What are examples of causal relationships?

Causal relationships: A causal generalization, e.g., that smoking causes lung cancer, is not about an particular smoker but states a special relationship exists between the property of smoking and the property of getting lung cancer.

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do your work buddy and dont cheat

Step-by-step explanation:

dont cheat and actually study

Answer:

As a fraction: 7988004000/7

As a decimal: 1141143428.571429

Step-by-step explanation:

Multiply (1998)(1999)=3994002

Multiply (3994002)(2000)=7988004000

As a fraction it will be 7988004000/7

Turn it into a decimal!

Just divide 7988004000 by 7 or 7988004000/7

This should be: 1141143428.571429

Answer:

EE.

Step-by-step explanation:

x+1>x+8. 1+8. ∅

Answer: x= -8

Step-by-step explanation:

A vertical asymptote is a line cut in the middle of both graphs!

It can't be x= 0 or y= 0  because it is not the middle of both graphs!

It can't be y= -8 because it is not cut in the middle.

So x=-8 is the right answer!

(0,-3) is the best approximation for the relative minimum of the polynomial function graphed below.

A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.

The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.

From the graph it is shown that,

In the x axis the value is between 0 and 1 , and the y-axis is in between 0 to -3 then the answer is: (0,-3)

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The complete question is as follows:

Answer:

∠ a & ∠ d

∠ b & ∠

Answer:

∠ A and ∠ D

∠ B and ∠ E

Step-by-step explanation:

Step-by-step explanation:

Here, not sure if it got the answer you were looking.

Therefore , We have proved AE ≅ CF in the given quadrilateral .

Two figures or objects are said to be congruent in geometry if they are the same size and shape, or if one is the mirror image of the other.

Here,

Statement                                                  

1)AB≅CD , AB║CD ,BF⊥AC and                    

DE⊥AC

2)ABCD  is a parallelogram                  

3)  AD≅BE , AD║BE

4)ΔDAE≅ ΔBCF

5)ΔDAE≅ ΔBCF are right  Δ's

6)  ΔDEA≅ ΔBFC

7)  ΔADE≅ ΔCBF

8)AE ≅ CF

Reasoning

1)Given

2)if a quadrilateral has 1 pair of opposite side both side ≅, ║, then it is a parallelogram

3)In a  parallelogram opposite side are ≅, ║          

4)Alternate interior angles   Δ's are congruent.

5)⊥ segments forms right Δ's.

6)right Δ's. are  ≅.

7)AAS congruency theorem

8)Cpetc

Therefore , We have proved AE ≅ CF in the given quadrilateral .

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There are 7776 different outcomes possible when 5 dice of different colors are rolled.

The ratio of favorable outcomes to the total number of outcomes of an event is said to be the probability of that event.

P(E) = n(E)/n(S)

It is given that, there are 5 dice with different colors.

There are 6 outcomes for each die rolling. That is the number coming up on each die when it is rolled (1, 2, 3, 4, 5, 6).

So, for five dice when rolled, the number of possible outcomes is

n = 6 × 6 × 6 × 6 × 6

⇒ n = 7776

Therefore, 7776 different outcomes are possible.

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The slope intercept form of the given situation is y=3x+10.

y = mx + b is the slope-intercept form, where m is the slope and b is the y-intercept.

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.

Let x= $3 per game

and we have to add $10 for rental shoes. So slope form will ne

y= 3x+10.

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Students do not likes to fly, can drive is 0.13. Therefore, the completed  relative frequency table is given below.

Given that, on a recent survey, students were asked if they like to fly and if they can drive.

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

From the table

Likes to fly

Row totals = Can drive + Cannot drive

0.32+Cannot drive =0.70

Cannot drive =0.38

Can drive:

Column totals=Likes to fly + Do not likes to fly

0.32 + Do not likes to fly=0.45

Do not likes to fly=0.13

Cannot drive:

Column totals=Likes to fly + Do not likes to fly

0.38 + Do not likes to fly=0.55

Do not likes to fly=0.55-0.38

= 0.17

Row totals = 0.13 + 0.17

= 30

Students do not likes to fly, can drive is 0.13. Therefore, the completed  relative frequency table is given below.

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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83

What is compounded?

to combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.

Given that, principal=$3620, rate of interest=6.5% and time period=9 months.

Here, principal compounded quarterly

Thus, Amount
[tex]\$ 3,620 \times 6.5 \% \times \frac{1}{4}=\$ 58.83[/tex]

The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).

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Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded is $58.83

What is compounded?
To combine into a single unit; combine: to mix medications to create a new medication. to create something by putting pieces, things, etc. together; construct: to combine elements of various previous plans to create a new one.The interest on a loan or deposit calculated based on the initial principal, and the collective interest from previous periods is called compound interest. It is basically 'interest earned on money that was previously earned as interest'.

Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount
$3,620x6.5%x1/4=$58.83
The first period interest is product of the principal, the annual interest rate and the interest period (expressed in years).

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Answer:

ANS:- No solution

Step-by-step explanation:

-7x + 7 + 12x = 5x + 7

5x + 7 = 5x + 7

0 = 0

Answer:

The lie is #2

Step-by-step explanation:

Just like how dividing powers with the same bases is like subtracting exponents, multiplying them is like adding exponents.

If you substitute 4 as x in #1, you get [tex]13^2*13^4=13^6[/tex]. This is the same as saying [tex]13^2^+^4=13^6[/tex], which is true.

If you substitute 4 as x, 6 as y, and 8 as z in #2, you get [tex]m^6*m^8=m^4[/tex]. This is the same as saying [tex]m^6^+^8=m^4[/tex], which is not true.

If you substitute 6 as y in #3, you get [tex]5^6*5^6=5^1^2[/tex]. This is the same as saying [tex]5^6^+^6=5^1^2[/tex], which is true.

The x = 5-y line passes through (0,5) and (5,0).

The y = 2x -4 line passes through (0,4) and (2,0).

What is a linear equation?

The graphs of all first-degree equations in two variables will be straight lines. This fact will be used here even though it will be much later in mathematics before you can prove this statement. Such first-degree equations are called linear equations.

Here, we have

Given inequalities

x - y < 5

y ≥ 2x - 4

We have to describe the graph of the system of inequalities.

For, x < 5+y

x = 5-y

We put y = 0, we get

x = 5

We put x =0, and we get

y = 5

Hence, the x = 5-y line passes through (0,5) and (5,0).

For, y ≥ 2x - 4

y = 2x -4

We put x = 0, and we get

y = 4

We put y = 0, we get

x = 2

Hence, the y = 2x -4 line passes through (0,4) and (2,0).

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The amount of time Jim spent on the bicycle is 6.5 hours.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

Total distance, d = 255 miles,

Total time, t = 7 hours,

The speed of walking, s = 3 miles / hour,

The speed of riding bicycle, S = 39 miles/hour,

Calculate the time spent on the bicycle as shown below,

Total time = Time on bicycle + Time walking

7 = Distance on bicycle/speed + Distance of walking / speed

7 = b / 39 + w / 3

Here w is the distance by walking and b is the distance covered by bicycle,

b + w = 255 (As given)

Solve both equations,

w = 1.5 miles and b = 255 - 1.5 = 253.5 miles

Calculate the time spent on a bicycle as shown below,

The time spent on the bicycle = b / 39

The time spent on the bicycle = 253.5 / 39 = 6.5 hours

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In  a right angled triangle, the opposite and adjacent sides are the sides proportional to the two acute angles of the triangle.

In every triangle, the sum of angles is 180⁰.  In a right angled triangle, one of the angles is = 90⁰.

The side facing the right angle is called the hypothenuse side.

The sum of the other two angles is 90⁰. That each of the angles is acute angle.

The sides proportional to the acute angles are the opposite and adjacent.  

If an angle is given in one of the angle, the side proportional to the given angle is called the opposite while the other one is called the adjacent.

if the angle is changed to the other angle, the side proportional to the given angle becomes the opposite while the other is the adjacent.

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Answer:

Let the odd numbers be 2n + 1 and 2n + 3 where n is any positive integer. Therefore, the numbers are 19 and 21.

In the given Isosceles trapezoid, the value of x and y is 12 and 5 respectively.

An isosceles trapezoid, or isosceles trapezium in British English, is a convex quadrilateral in Euclidean geometry that has a line of symmetry cutting through one pair of opposite sides.

It is an uncommon instance of a trapezoid.

Alternately, it can be described as a trapezoid with equal amounts of both the base angles and the legs.

Note that the second requirement, or the fact that it lacks a line of symmetry, prevents a non-rectangular parallelogram from being an isosceles trapezoid.

Two opposite sides (the bases) of each isosceles trapezoid are parallel, while the remaining two sides (the legs) are each the same length (properties shared with the parallelogram).

So, solve for x and y:

For x:

4x - 27 = x + 9

3x = 36

x = 36/3

x = 12

For y:

3y + 19 = 11y - 21

8y = 19 + 21

8y = 40

y = 40/8

y = 5

Therefore, in the given Isosceles trapezoid, the value of x and y is 12 and 5 respectively.

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The required transformation of the given figure is given as 4 units right and 2 units down.

Given that,
To determine the trasformation of the given figure.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

here,
As shown in the figure,
The figure is translated as of the former figure to 4 units in the positive x direction and 2 units towards the negative y direction.

Thus, the required transformation of the given figure is given as 4 units right and 2 units down.

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The first step to start the is dividing both sides by 3, so the correct option is the second one.

The linear equation in slope-intercept form is:

y = (1/2)*x + 1

To do that, we need o isolate the variable y in one of the sides of the linear equation:

3*(x + 2) = 6y

We can divide both sides by 3 to get:

x + 2 = (6/3)*y

x + 2 = 2y

Now, we can divide both sides by 2, so we will get:

(x + 2)/2 = y

y = (x + 2)/2

y = (1/2)*x + 1

The equation in the slope-intercept form is:

y = (1/2)*x + 1

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Answer: y= 1/2x + 2

Step-by-step explanation:

The linear equation is y= mx + b

The y-intercept is located at (0,2), so b equal to 2

Let's pick two points ( 0,2) ( 2, 1)

To find the slope, we need to find the rise over run.

Rise decrease by 1, and run increase by 2, so the slope is 1/2

So the equation is y= 1/2x +2

Answer:

113

Step-by-step explanation:

30° + 37° + angle c = 180° (Sum of all angles of a triangle is 180°)

or, 67° + angle c = 180°

or, angle c = 180° - 67°

or, angle c = 113°

The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

The quadrilaterals are LMNP and LKJQ shown.

In quadrilaterals LMNP and LKJQ,

LK = LM = LQ = LP         (Given)

JK = JQ = NM = NP        (Given)

∠KJQ = ∠MNP          (Given)

∠KLQ = ∠MLP           (Given)

∠JKL = ∠NML            (Given)

∠JQL = ∠NPL            (Given)

The ratio of all the corresponding sides and corresponding angles is one. Then the quadrilateral is congruent with each other.

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