9. Write a rational
expression that is
equal to the following
rational expression
whenx doesn’t =3 or — 5.
-
(x+9)(x+5)/
(x+5)(x-3)

To me, I would rather stick to your cash allowance so as not to be in debt but the choice between using a credit card or cash allowance depends on your individual financial situation and goals. If you are concerned about overspending or managing debt, using a cash allowance might be a better choice.

The Advantages of using cash allowance:

Lastly, No temptation to overspend - When using cash, it's easier to keep track of your spending and avoid overspending compared to using a credit card.

However, if you want to build a positive credit history and take advantage of rewards, a credit card might be a good option for you.

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A conditional equation is neither an identity nor a contradiction. It is a statement that is only true under certain conditions.

A conditional equation is an equation that expresses a condition. It has two parts: a hypothesis (or antecedent) and a conclusion (or consequent). The hypothesis states that a certain condition must be met in order for the conclusion to be true. For example, the equation "if x = 4, then x + 1 = 5" is a conditional equation. If the condition (x = 4) is true, then the conclusion (x + 1 = 5) is also true. However, if the condition is false, then the conclusion is also false. Therefore, a conditional equation is neither an identity nor a contradiction, but rather a statement that is only true under certain conditions.

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1. The victims from Catanduanes and Cagayan receive P 2,500.00.

Mrs. Ramirez donated P 5,000.00 and 50% of it was sent to Catanduanes while another 50% was sent to Cagayan.

So, the victims from Catanduanes received P 5,000.00 x 50/100 = P 2,500.00 and the victims from Cagayan received P 5,000.00 x 50/100 = P 2,500.00.

2. The percentage of the calamansi used for juice is 60%

Mang Juan harvested calamansi and put them in a small basket. 2/5 of the calamansi were ripe, and the rest were unripe. He used all the ripe calamansi and 25% of the unripe calamansi for juice.

So, the number of ripe calamansi used for juice is 2/5 x the total number of calamansi, and the number of unripe calamansi used for juice is 25/100 x (1-2/5) x the total number of calamansi.

The total percentage of the calamansi used for juice is (2/5 + 25/100 x (1-2/5)) x 100%.

So, The percentage of the calamansi used for juice = (2/5 + 1/5) x 100 = (3/5) x 100 = 60%

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The value of x when y = 37.5 if y varies directly as x and y = 5 when x = 0.4 is 3

y = k × x

Where,

k = constant of proportionality

If y = 5 when x = 0.4

y = k × x

5 = k × 0.4

5 = 0.4k

divide both sides by 0.4

k = 5/0.4

k = 12.5

If y = 37.5, find x

y = k × x

37.5 = 12.5 × x

37.5 = 12.5x

divide both sides by 12.5

x = 37.5 / 12.5

x = 3

Therefore, the value of x when y = 37.5 is 3

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The value of x from y is x = 3

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

y varies directly as x and y = 5 when x = 0.4,

The equation of direct variation is

k = y/x

So, we have

k = 5/0.4

Evaluate

k = 12.5

So, we have

y/x = 12.5

When y = 37.5. we have

37.5/x = 12.5

Solve for x

x = 3

Hence, the solution is x  3

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In case of parallel lines, the of the lines are always equal.

And the product of slopes of perpendicular lines is -1.

We know that the parallel lines are the lines in a plane that are always the same distance apart.

Also, the parallel lines never intersect.

The slopes of parallel lines are always equal.

The y-intercept of parallel lines is different.

Whereas, the perpendicular lines are the lines that intersect at a right angle (90 degrees angle).

The product of slopes of perpendicular lines is -1.

All perpendicular lines are always intersecting lines, but all intersecting lines need not be  perpendicular.

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Answer:

1.) x = 7  

3.) m = 1 and m = 5  

5.)  [tex]x=\frac{3}{7}\\[/tex]

7.) n = 4  , [tex]n=-\frac{3}{2}[/tex]

Extra credit) [tex]t=-\frac{1}{9}[/tex]

Step-by-step explanation:

Question 1

Multiply both sides by 5
simplify: x - 1 = 6
Add 1 to both sides

Question 3

Multiply by the Least common multiple (5 = 6m - m^2)

solve 5 = 6m - m^2!

Question 5

Cross multiply

move x to the left side

Divide both sides by 7

Simplify

Question 7

Cross Multiply

Solve

Extra Credit

Multiply by Least Common Denominator

move 2 to the right and t to the left side.

Divide both sides by 18

Simplify

Answer:

To evaluate the expression (-(7)/(10)+0.15)/(-(1)/(8)), we need to simplify it step by step by following the order of operations (PEMDAS)

Parentheses: First we need to simplify the expressions inside the parentheses,

(7)/(10) = -0.7

-(1)/(8) = -1/8

Addition and Subtraction: Next we need to add and subtract the numbers,

-0.7 + 0.15 = -0.55

Division: Next we need to divide the numbers,

(-0.55) / (-1/8) = -0.55 * 8/-1 = 4.4

So the final result is 4.4

Note that the negative signs in the numerator and denominator can be thought as multiplying by -1.

Answer: 25800

Step-by-step explanation: If you want to round to the nearest hundred, then you look at the tens digit. Since the tens digit is 4, you round it down and then you get 25800.

If Over 4 days, Krista deposited $45 into her bank account, transferred $30 to a friend, the mean change per day to Krista's account during that week is $14.

First step is to find the total money in the account

Total money in the account = $45 - $30 + $59 - $18

Total money in the account  = $56

Now let find the mean change per day

Mean change per day  = Total money in the account  /Total number of days

Mean change per day = $56 /4 days

Mean change per day = $14

Therefore the Mean change per day is $14.

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The trigonometric functions sin R and Cos Q will have same Trigonometric ratios as Sin R=24/51 and Cos Q=24/51

What are trigonometric functions?

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions

Now

As Trigonometric ratios for Sin R=Perpendicular/Hypotenuse and Cos Q=Base/Hypotenuse

Hence,

Sin R=24/51 and Cos Q=24/51

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So, Sarah receives $9 as her allowance every week.

Sarah wants to deposit her allowance for 16 weeks straight, so she will have a total of $355 in her account.

We know that she had $211 initially in her account and after 16 weeks, she will have $355.

So the amount she will have to deposit every week as her allowance is:

$355 - $211 = $144

We can divide the total amount of allowance by the number of weeks to find out how much she receives per week:

$144 / 16 = $9

Therefore, Sarah receives $9 as her allowance every week.

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Answer:

Price per topping

Step-by-step explanation:

Because the price changes per number of toppings, the graph shows the price per number of toppings.

Answer:

Pascal's

Step-by-step explanation:

By calculating , the values of angles D and E are 80 , 80 respectively.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees .

Given ,

from the figure ,

In triangle ECD

The sum of three angles = 180

so ,

E+C+D = 180

50+50+D = 180

D = 180-100

D = 80

And in the Quadrilateral AECB,

A+E+C+B = 360

110+70+100 + E = 360

E = 360 - 280

E = 80

Hence, the values of angles D and E are 80 , 80 respectively.

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the width of the bulletin board is -200 in.

Step-by-step explanation:

Let w = the width of the bulletin board

Since the perimeter of the bulletin board is 300 in, we can write the equation:

2w + 2(300 - w) = 300

Simplifying:

2w + 600 - 2w = 300

0 = 300 - 600

-600 = 300

Therefore, the width of the bulletin board is -200 in.

Now that we know the width of the bulletin board, we can express the area A(w) as a function of its width w:

A(w) = w * (-200)

A(w) = -200w

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Answer:

[tex]28a {}^{2} + 47a + 15[/tex]

Step-by-step explanation:

Multiply what's inside the brackets with the outside brackets:

[tex](4a + 5)(7a + 3) = [/tex]

[tex](4a \times 7a) + (4a \times 3) + (5 \times 7a) + (5 \times 3) = [/tex]

[tex]28a {}^{2} + 12a + 35a + 15 = [/tex]

[tex]28a {}^{2} + 47a + 15[/tex]

An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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The exponential function showing relationship between y and t will be y=2600(23/20)^t.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

Initial bacteria cells=2600 (p)

rate of increment = 15% (r)

Number of hours = t

y=Number of bacteria cells at any time

To find the relationship between y and t

we use the formula Quantity = Initial quantity*(1+r/100)^t  

                                                                               --  (A=p*(1+r/100)^t )

therefore,

y=2600(1+15/100)^t

y=2600(23/20)^t

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The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y ≤ - 5/6x + 2/3

Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.

Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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lado Chus machigne Randi ko ban

Step-by-step explanation:

lado Chus bosadike louder you mother father mc mf

The value of angle x in decimal place is 57.8°.

A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.

Draw the altitude of the triangle

We know that

sinθ =  Opposite / Hypotenuse

sin 38° = y/11

y = 11 sin 38°

y = 6.77

sin(x) = y/8

sin(x) = 6.77/8

sin(x) = 0.84625

sin(x) = 57.8°

Thus, the value of angle x in decimal place is 57.8°.

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Out of 100 messages, Trey sent 12 messages, Mary sent 15 messages and Lamar sent 75 messages.

Let the number of messages sent by Trey be x. So, the number of messages sent by Mary will be (x+10). The number of messages by Lamar will be 3×(x+10). Their sum of is 100, so representing the information in equation form.

x + x + 10 + 3(x + 10) = 100

Performing multiplication on Left Hand Side of the equation

x + x + 10 + 3x + 30 = 100

Performing addition

5x + 40 = 100

Rewriting the equation

5x = 100 - 40

Performing subtraction

5x = 60

x = 60/5

Performing division

x = 12

Messages sent by Trey = 12

Messages sent by Mary = 12 + 3

Messages sent by Mary = 15

Messages sent by Lamar = 3(15 + 10)

Messages sent by Lamar = 3×25

Messages sent by Lamar = 75

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The angle bisectors of a triangle bisect at a common point that is equidistant from the all the sides of the triangle, this point of coincidence is called the incenter of the triangle.

Incenter all the time lies inside the triangle, the circle drained with incenter as the center is inscribed in the triangle and it is called incircle.

The use of Angle bisectors in real life are in architecture, for making quilts and in produce cakes.

It is also used in playing several games as well like football, rugby, billiards.

we use the point of concurrency for angle sever of a triangle theorem.

From that theorem, R is equidistant from the three sides of triangle ABC, so XR= YR = ZR

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When it takes 6 hours to travel and 8.7 hours to return home, there is a 45% increase in travel time.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

Time take to arrive at vacation destination=6 hours

Time take to arrive at home=8.7 hours

percent increase=(8.7-6)/6*100

=45%

The percent increase in the time taken to come back to home is 45% when they took 6 hours to reach and 8.7 hours to comeback.

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Complete question:

It took the Phillips family 6 hours to drive to their vacation destination. Due to traffic, it took them 8 hours and 42 minutes to drive home. Percentage for Increase or Decrease!!

The number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.

The question states that there are five different prizes and the top five winners will get them, but no one can get more than one prize. Since there are only two entries received, the number of ways the prizes can be awarded is determined by the number of ways to select two winners from the two entries received

This is a combination problem where we have to select 2 items (winners) out of 2 items (entries) without regard to the order.

The number of ways to select k items out of n items without regard to the order is given by the binomial coefficient (n choose k), which is calculated as:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items selected and ! denotes factorial.

So in this problem, we have to calculate the number of ways to select 2 winners out of 2 entries, the binomial coefficient is:

2C2 = 2! / (2!(2-2)!) = 2*1/1 = 2

Therefore, the number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.

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Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.

Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.

Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.

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Answer:

6x^2 - 5x - 4

Step-by-step explanation:

Here you go. A pic.

Therefore , the solution to the given problem of triangle comes out to be X=16 and Y=5.

The fact that a triangle contains four points or sections qualifies it as a polygon. It is an elementary geometric form. Triangle ABC is the name given to a rectangle with side A, B, or C. Euclidean geometry produces a single surface and square where sides are not collinear. It is a polygon if a triangular has three parts and three corners. The intersection of a triangle's three sides is at its corners. Three triangle angles added together equal 180 degrees.

Here,

Assumed: X=16 Y=5.

Since both sides of an equilateral triangle are the same length, the equation is 18y-41=3x+1=49.

working out x

Considering 3x+1=49

grouping similar terms

3x=49-1=48

units: x=48/3=16

working out y

thinking about 18y-41=49

18y=49+41=90

units of y=90/18=5

As a result, X=16 and Y=5 are the answers to the triangle problem given.

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The order of g is a power of 2, Hence G is abelian.

Everything is in order, with the exception of identification.

2, then  a2=e

where  a∈G

 (including identity this time). So,  a−1=a

  for all  a∈G

Hence  ab=(ab)−1=b−1a−1=ba

 for all  a b∈G

For every x∈G

we have x2=e

where e

represents the identity in.

Then x−1=x

Now, let a,b

be two arbitrary elements in G

We have ab=(ab)−1=b−1a−1=ba

Hence G is abelian.

(First equality is true because  ab

is also an element of  G

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