Use long division to rewrite the following rational expression.

Answer:

B. Reflexive Property

Step-by-step explanation:

The statement is that BC ~= BC. That is, that BC is congruent to itself. The reason is that all numbers are equal to themself. Angle measures are equal to themself. Segments are equal to themself.

Like looking at a reflection in a mirror. The word "reflection" can help you memorize the reason why something is equal to itself:

Reflexive Property

The distance of the student from the light pole is 21.4 feet.

A student sees a bird on top of a 15 foot high light pole. The angle of elevation to the top of the light pole is 35 degrees.  

The distance of the student from the pole can be calculated as follows:

The situation forms a right angle triangle.

using trigonometric ratios,

tan 35  = opposite / adjacent

tan 35 = 15 / x

cross multiply

x tan 35 = 15

divide both sides by tan 35

x = 15 / tan 35

x = 15 / 0.70020753821

x = 21.4222201012

x = 21.4 feet

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Answer: The original fraction is 8/15

Step-by-step explanation:

The part about the 7 more than the numerator is not needed. All you have to do is add 3 to the numerator and 3 to the denominator.

5+3=8

&

12+3=15

So

8/15

I hope this helps!

On solving the provided question, we got that the number of months is proportional to the number of years

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.

We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

12/1 = 12

24/2 = 12

36/3 = 12

48/4 = 12

So, They are proportional to each other.

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The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

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

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

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The required value of N when t = 200 is given as 10,000.

Given that,
The Bateria in culture increases according to the law ds/dt = N/4

if intially N = 200, then what is the value of N when t = 200 is to be determined.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
ds/dt = N/4 = 200/4 = 50
Now,
N = 50t
N = 50[200]
N = 10,000

Thus, the required value of N when t = 200 is given as 10,000.

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The simplified expression of √136 is 2√34

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

√136

Expand the expression

So, we have the following representation

√136 = √68 * 2

Further, expand the expression

So, we have the following representation

√136 = √34 * 2 * 2

So, we have

√136 = √34 * 4

Take the square root

√136 = 2√34

The expression cannot be further simplified

Hence, the solution is 2√34

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The cost of the bench is $ 375 and the Cost of the garden table is $ 446.

We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.

Here we have

A garden table and a bench cost $ 821 combined

Let x, and y be the cost of the garden table and bench

Given that

The garden table costs $71 more than the bench.  

=> x = y + $ 71 ---- (1)  

It is also given that

The total cost of the garden table and a bench = $ 821  

=>  x + y = 821  

=>  y + 71 + y =  821

=>  2y = 821 - 71

=>  2y = 750

=>  y = 375

=> Cost of bench, y = $ 375

=> The cost of the garden table, x = $ 375 + $ 71 = $ 446

Therefore,

The cost of the bench is $ 375 and the Cost of the garden table is $ 446.  

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Answer:

Step-by-step explanation:

100%-10%=90%

90/100=0.9%

3000*0.9^10 years= 1046.04

Step-by-step explanation:

For annually,

3000×(1.10)^10= 7781.23

For quarterly,

3000×(1.10)^40= 135777.77

For montly,

3000×(1.10)^120=278127206.5

Procedimiento:

Empezamos separando el problema por partes. En este caso, a "un número" le daremos el nombre "x", y al "otro número distinto" le daremos el nombre "y".

1. Entonces, "el triple de un número" significa que es el triple de "x". En otras palabras, es 3 veces "x", osea:

3x

2.Como dice "la suma", entonces sabemos que nuestro 3x se va a sumar con otro término, entonces nuestro enunciado está quedando así:

3x+

3.El segundo término de la suma es "el doble de otro número distinto al cuadrado". Si el "otro número distinto" es "y", tenemos que "el doble" de "y" es 2 veces "y", osea, "2y".

Finalmente, se explica que este término está al cuadrado, lo cual daría que nuestro segundo término sea (2y)^2.

4.Entonces, la expresión completa es:

3x+(2y)^2

Answer:

y = (2/3)x - 4

Step-by-step explanation:

To find the equation of the line in slope-intercept form given a table of values, you will need to calculate the slope of the line and the y-intercept. The slope of a line is a measure of its steepness, and it is calculated as the rise (change in y-values) divided by the run (change in x-values) between two points on the line. The y-intercept is the point at which the line crosses the y-axis.

Given the table x: 9, 3, -3, -9 and y: 2, -2, -6, -10, you can use any two points to calculate the slope. For example, you could use the points (9, 2) and (3, -2) to calculate the slope:

slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4 / -6 = 2/3

To find the y-intercept, you can use the slope and one of the points from the table to substitute into the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Using the slope and the point (9, 2), you can solve for b:

y = mx + b

2 = (2/3) * 9 + b

2 = 6 + b

b = -4

Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 4.

To answer the other questions, you can use this equation to determine the y-value for a given x-value or the x-value for a given y-value. You can also use the equation to graph the line on the coordinate plane.

From the given expressions the equivalent expression is,  

8x + 4y = 4(2x + y).

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider, the given expression

8x + 4y  and 4(2x + 1)

Consider, 4(2x + 1)

Simplifying this,

4(2x + 1) = 8x + 4

8x + 4 is different from 8x + 4y.

Hence, 8x + 4y is not equivalent to 8x + 4.

Now consider, 8x + 4y = 6x(4y + 2x)

Simplifying this

8x + 4y = 24xy + 12x^2

⇒ 8x + 4y = 6x(4y + 2x) is not equivalent.

Now consider, 8x + 4y = 8(x + 4y)

(8x + 4y) = 8x + 32y

⇒ 8x + 4y = 8(x + 4y is not equivalent.

Now consider,  8x + 4y = 4(2x + y)

8x + 4y = 8x + 4y

⇒ 8x + 4y = 4(2x + y) is equivalent.

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The equation has no solution if the blank is filled with 5y, so option c is correct.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given equation:

5y + 9 = _

Use the hit and trial method and put the value zero,

5y + 9 = 0

y = -9 / 5

So the equation has a solution,

Again put

5y + 9 = 5y

9 = 0, which is not possible

Therefore, the equation has no solution if we fill the blank with 5y.

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a) An exponential function to model the population of foxes in t years after 2000 is given by P(t) = 21,100 x 1.09^t.

b) From the exponential function from part (a), the estimated fox population in the year 2008 is 42,052.

An exponential function is a mathematical expression written in the form of y = ab^x.

Exponential functions can be used to model growth factors, especially the population of animals and bacteria increasing at a constant rate.

The continuous growth rate in the fox population = 9%

Estimated population of foxes in the year 2000 = 21,100

A function to model the population in t years after 2000: P(t) = 21,100 x 1.09^t

In 2008, the population function:

P(t) = 21,100 x 1.09^8

= 21,100 x 1.993

= 42,052

Thus, we can conclude that using the exponential function, the fox population growing at 9% per year reached 42,052 in 2008 from its 21,100 number in the year 2000.

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The value of distance between points A and B is 54.4 feet.

What is the law of cosine?

The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known as the law of cosines states: c²=a²+b²−2ab cos C .

Solution:

Using the law of cosines we get:

(AB)²=(AC)²+(BC)²-2AC×BC×cos(C)

(AB)²= (45)²+(69)²-2(45)(69)cos(52°)

(AB)² = 2025 + 4761 - 3823.2577

∴ AB = 54.4 feet

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The degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.

What is the quotient?

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

To find the quotient and remainder when dividing 8x³ +16x² + 12x+13 by 2x+2, we can use polynomial long division.

First, we divide the leading coefficient of the dividend (8x³) by the leading coefficient of the divisor (2x). This gives us a quotient of 4x². We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the first term of the remainder:

8x³ +16x² + 12x + 13

(2x+2)(4x²)

8x³ - 8x³ -8x² -8x² +12x+13

This leaves us with 12x+13 as the first term of the remainder.

Next, we bring down the next term of the dividend (16x²) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 8x. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the next term of the remainder:

12x+13

(2x+2)(8x)

12x+13 - 16x² - 16x

-4x² -4x

This leaves us with -4x² -4x as the next term of the remainder.

Finally, we bring down the last term of the dividend (12x) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 6. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the final term of the remainder:

-4x² -4x

(2x+2)(6)

-4x² -4x -12x -12

-16x² -16x

This leaves us with -16x² -16x as the final term of the remainder.

Hence, the degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.

We can write the result of the division as:

(8x³ + 16x² + 12x + 13) ÷ (2x+2) = (4x² + 8x + 6) + (-16x² -16x)/(2x+2)

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"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.

Relation:

In math relation means the relationship between sets of values of ordered pairs.

Given,

Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.

As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.

Here we have to identify the type of relation between a an b.

Here we have given that the relation a uniquely determines the value in b.

So, this type primarily refers the dependency of the relation.

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Answer:

[tex]x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]

Step-by-step explanation:

[tex](x+7)^2=11 \\ \\ (x+7)=\pm \sqrt{11} \\ \\ x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]

Answer:

  -1/2

Step-by-step explanation:

You want the slope of the line through points (8, -3) and (-6, 4) using the slope formula.

The formula for the slope of the line through points (x1, y1) and (x2, y2) is ...

  m = (y2 -y1)/(x2 -x1)

For the two given points, the slope is ...

  m = (4 -(-3))/(-6 -8) = 7/-14 = -1/2

The slope of the line is -1/2.

a) The synthetic division table is given by the image shown at the end of the answer.

b) The result of the division is given as follows:

-x³ + 4x² + 4x - 8 + 0/x + 2.

In this problem, the dividend is given as follows:

-x^4 + 2x³ + 12x² - 16.

Hence the coefficients are given, respectively, by:

-1, 2, 12, 0 and -16.

The divisor is of:

x + 2.

Hence the term on the left box is of:

x + 2 = 0 -> x = -2.

Then the procedure goes as follows:

From the coefficients of the bottom box, we have that:

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Answer:

Andre walks more steps

Step-by-step explanation:

Step-by-step explanation:

dawn step rate=8400/60=140step/he

dawn step=140×240=33600 steps

teddl step=142 ×240 =34080

Answer:

4√2

Step-by-step explanation:

hypotenuse = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} =\sqrt{2*16} = 4\sqrt{2}[/tex]

The expression for the exact number of inches in 1 centimeter is 2.54/2.54 cm = 1/2.54 in and the number of inches is 0.39

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

1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.

To calculate the number of inches expression, we make use of the following equation

1 inch = 2.54 centimeters

Divide both sides of the equation by 2.54

So, we have the following representation

1/2.54 inch = 2.54/2.54 centimeters

Rewrite the expression as

2.54/2.54 centimeters = 1/2.54 inch

So, we have

2.54/2.54 cm = 1/2.54 in

So, the expression is 2.54/2.54 cm = 1/2.54 in

In (a), we have'

Expression: 2.54/2.54 cm = 1/2.54 in

This implies that

2.54/2.54 cm = 1/2.54 in

Evaluate the quotients

1 cm = 0.39 in

Hence, the value is 0.39 inches

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Using the given information, the distance from point A to point B is 568ft

You should know that Distance is defined as the numerical or occasionally qualitative measurement of how far apart  points are from each other.

The distance between A and B can be measured using the Trigonometric ratio of angles.

The drawing formed a right angled triangle.

Using the tangent function

Tan∅=[tex]\frac{opposite}{adjacent}[/tex]

Tan11⁰=x/126

x=126tan11⁰

Also, in the second angle of depression,

Using the tangent ratio as stated above,

y=126tan78⁰

The distance between A and B is given thus:

AB =126tan78⁰-126tan11⁰

AB =126*4.7046-126*0.1944

AB =592.78-24.4944

AB =568.28553

AB =568ft

In conclusion, the distance from point A to point B is 568ft

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Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex].  On adding he would be getting  [tex]1\frac{1}{2}[/tex]

What is number line?

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

It is given that Evan added [tex]-2\frac{1}{2}[/tex] and 4 but got [tex]6\frac{1}{2}[/tex]

The mistake that Evan did was instead of adding, he substracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex]. This is because

4 -  [tex]-2\frac{1}{2}[/tex]

= 4 + [tex]2\frac{1}{2}[/tex]

=  [tex]6\frac{1}{2}[/tex]

This is wrong as he was asked to add and not to subtract.

Therefore, on adding  [tex]-2\frac{1}{2}[/tex] and 4, we get,

= 4 [tex]-2\frac{1}{2}[/tex]

= [tex]1\frac{1}{2}[/tex]

Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got          [tex]6\frac{1}{2}[/tex].  On adding he would be getting  [tex]1\frac{1}{2}[/tex]

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The total area of the given figure is 68.56 units².

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil.

It has two dimensions.

The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

So, the total area of the given figure:
We can divide the figure into separate rectangles and circles:

Area of rectangle: l*b

14*4

56 units²

Area of circle: πr² (D = 4, R = 4/2 = 2)

πr²

3.14(2)²

3.14*4

12.56 units²

The total area of the figure:

56 units² + 12.56 units² = 68.56 units²

Therefore, the total area of the given figure is 68.56 units².

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The inequality that shows how long the temperature in Round Rock  will remain colder than that in Austin is 72 - 3t > 65 - 2t and the time is less than 13 hours

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

Austin

Initial temperature = 65 degrees Fahrenheit

Rate of decrement = 2 degrees Fahrenheit

Round Rock

Initial temperature = 72 degrees Fahrenheit

Rate of decrement = 3 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

So, we have

Austin: A(t) = 65 - 2t

Round Rock: B(t) = 72 - 3t

When Round Rock is colder than Austin, we have

B(t) > A(t)

Substitute the known values in the above equation, so, we have the following representation

72 - 3t > 65 - 2t

Evaluate the like terms

-t > -13

Divide both sides by -1

t < 13

Hence, the interval is less than 13 hours

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Answer:

Rotation

Step-by-step explanation:

The function  [tex]f(x)=mx+b[/tex] , is the equation of a line given in slope-intercept form. Where m is the slope of the line and b is the y-intercept of the line. If you were to change the value of m, while keeping the value of b the same, that would result in a rotation. If you were to change the value of b, while keeping the value of m the same, that would result in a translation (specifically a vertical translation).