what is the quotient of 6x^3+2x-x/x where x≠0

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.

Given that,

GH ≅ JH

FH ≅ HI

And,

∠GHF = ∠JHI

Therefore,

ΔGHF ≅ ΔJHI (SAS Congruency)

∴ FG = IJ (CPCT theorem)

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

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Yes, isosceles triangles have three congruent angles.

An isosceles triangle is a triangle with at least two congruent sides and two congruent angles. The two congruent sides and two congruent angles form an isosceles triangle. The two congruent angles are known as the base angles, and they are opposite to the two congruent sides. The third angle in an isosceles triangle must also be congruent to the two base angles in order for the triangle to be true. This is because the angles of a triangle must always sum up to 180 degrees. Therefore, isosceles triangles have three congruent angles. These angles are all equal in measure and have the same shape. The angles of each isosceles triangle can be different from other isosceles triangles, but the angles are still congruent to each other. Therefore, isosceles triangles have three congruent angles.

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The triangle in the figure can be proved by ASA, SAS, and AAS

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.

Alternate angles in the figure are also equal

According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.

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Answer:

absolute deviation means distance between each data value and the mean of the data set.

Step-by-step explanation:

(MAD)

or

(Average)

Answer:

Step-by-step explanation:

Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:

Case 1 --> 8x + 5y = 220 ----------(1)

Case 2 --> 5x + y = 112 ----------(2)

Multiplying equation (2) by 5:

8x + 5y = 220

25x + 5y = 560 ------(3)

Subtracting equation (1) from equation (3) we get :

17x = 340

x = 20

Putting x in (2):

5 x 20 + y = 112

y = 12

therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees

Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.

Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones

Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones

Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones

Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones

So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.

It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.

Step-by-step explanation:

Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The number of different types of ice creams can be obtained as follows,

10% - Mint.

= (10/100)×300.

= 30.

25% - Strawberry.

= (25/100)×300.

= 75.

15% - Chocolate chip.

= (15/100)×300.

= 45.

50% - Vanilla.

= (50/100)×300.

= 150.

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Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

Mai uses 10 ounces of cheese to make 4 pizzas, so she uses 10/4 = <<10/4=2.5>>2.5 ounces of cheese per pizza.

To make 15 pizzas, she will need 152.5 = <<152.5=37.5>>37.5 ounces of cheese.

x+5 is the way we can write 5 more than a number.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.

Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".

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Answer:

[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]

1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.

Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.

To find the winning combination we use the following formula

n !/ r!( n – r ) !

Where n = total number of to be drawn

r = the number which are drawn

In this question, n = 13, and r = 5

from the formula

13 !/5!( 13 – 5 ) !

= 13! / 5! 8!

= 13*12*11*10*9*8! / 5*4*3*2*1*8!

= 154,440 / 120

= 1287

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The length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

What is perimeter?

The total length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given:

A rectangle has a perimeter of 36 cm and an area of 72 cm^2.

Let the length of the rectangle's shorter side is 'a' and

the length of the rectangle's longer side 'b'.

As the perimeter is 36 cm.

⇒ Perimeter = 2(a + b)

               36 = 2(a + b)

                18 = a+ b

                 a = 18 - b

Now the area of rectangle is 72cm^2.

⇒                   Area = ab

                         72 = (18 - b)*b

                         72 = 18b - b^2

      b^2 - 18b + 72 = 0

b^2 - 12b - 6x + 72 = 0

b(b - 12) - 6(b - 12) = 0

         (b - 12)(b - 6) = 0

(b - 12) = 0,    (b - 6) = 0

b = 12,   b = 6

When  b = 12   ⇒  a = 18 - 12 = 6

When  b = 6   ⇒  a = 18 - 6 = 12

Hence, the length of the rectangle's shorter side is 6cm and the of the rectangle's longer side is 12cm.

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Answer:

To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.

So you need to work for 224 / 56 = <<224/56=4>>4 minutes.

Step-by-step explanation:

Answer:

girl I have the same question

In response to the question, we may say that As a result, the orangutan's expression mass in kilogrammes is roughly 64.55 kg.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To convert pounds to kilogrammes, divide the pound weight by the conversion ratio of 2.2.

Hence, to calculate the orangutan's mass in kilos, do the following:

Divide the orangutan's weight in pounds by the conversion ratio of 2.2:

142 pounds divided by 2.2 is 64.54545... kilos (rounded to the nearest hundredth)

As a result, the orangutan's mass in kilogrammes is roughly 64.55 kg.

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Answer: ummm B

Step-by-step explanation:

Answer: B

Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.

The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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There are 60 different ways of choosing a meal for this wedding.

There were five distinct main courses available for selection.

There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.

A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.

60 distinct main dishes might be purchased since.

There are 60 different ways of choosing a meal for this wedding

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Answer:

Acc.to question,

A+B=90° (since,they are complementary angles)

or,A+ A/2=90°(since,A is. twice the measure of B)

or,3A/2=90°

or,A=(90°×2)/3

:.A=60°

Also,

B=A/2=60/2=30°

Answer: 0.8333

Step-by-step explanation:

Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction.

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

Answer:

Mary bought the most flour

Step-by-step explanation:

Ana bought 12 3/6 kg of flour

12 3/6 = 75/6 = 12.5 kg of flour

Mary has brought 14 2/8 kg of flour

14 2/8 = 114/8 = 14.25 kg of flour

Kristina bought 11 8/12 kg of flour.

11 8/12 = 140/12 = 11.66 kg of flour

So, Mary bought the most flour.

The rule for the given set of data is y = 3x - 1.

The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.

A function rule can be defined as the procedure that transforms an input value into an output in plain English.

Lets put two of the points in slope formula

y - y₁ = m(x - x₁)

29 - (-13) = m(10 - ( -4))

42 = m14

m = 42/14

m = 3

Now lets make the equation

y - 29 = m(x - 10)

y = 3x - 30 + 29

y = 3x - 1

Thus, the rule for the given set of data is y = 3x - 1.

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Therefore, the players are 6.84 meters apart from each other.

An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.

The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:

tan(40°) = 3.5/x

tan(50°) = 3.5/(x+1)

We can solve for x in both equations, and set them equal to each other, we get x= 6.84m

Therefore, the players are 6.84 meters apart from each other.

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16 full days will be covered by the 785.7 pounds of food.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

We are able to locate the missing value using the unitary technique.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

According to our question-

1 pound of food will last = 1/48.5 day

Pounds equal 785.7*(1/48.5) = 785.7

= 785.7/48.5

= 16.2

Only full days will be counted, therefore

We'll only count up to 16.

So, the 785.

16 days will pass after 7 days.

The 785.7 pounds of food will therefore be plenty for 16 full days.

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Answer: 7

Step-by-step explanation:

The value of x in 2(5x)=14 is 1 2/5.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

When converting a mixed fraction to an improper fraction, the denominator and the whole number are multiplied, the product is added to the numerator, and the sum is written as the numerator and denominator.

2(5x) = 14

10x = 14

x = 14/10

Simplify the fraction, by turning it into a mixed number.

x = 1 4/10

Simplify the equation by dividing it by 2, so that it is in simplest form.

x = 1 2/5

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The solution to the system of equations is x = 4 and y = 5.

3x + 2y = 7

y = 3x - 11

Substitute 3x - 11 for y in the first equation:

3x + 2(3x - 11) = 7

Simplify:

3x + 6x - 22 = 7

Combine like terms:

9x - 22 = 7

Add 22 to both sides:

9x = 29

Divide both sides by 9:

x = 29/9

x = 4

Change x in the second equation to 4:

y = 3(4) - 11

Simplify:

y = 12 - 11

y = 1

The solution to the system of equations is x = 4 and y = 1.

The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.

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1) Number of 200 notes = 17,923,275

Number of 100 notes = 35,846,550

Number of 50 notes = 71,693,100

Number of 20 notes = 179,232,750

2) Number of 200 notes = 428,800

Number of 100 notes = 857,600

Number of 50 notes = 1,715,200

Number of 20 notes = 4,288,000

3) Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Ghana credits 200,100,50 and 20 notes.

Now,

Since, Ghana credits 200,100,50 and 20 notes.

1) Hence, To credit the amount 3584655000,

Number of 200 notes = 3584655000/200 = 17,923,275

Number of 100 notes =3584655000/100 = 35,846,550

Number of 50 notes =3584655000/50 = 71,693,100

Number of 20 notes = 3584655000/20 = 179,232,750

2) To credit the amount 85760000;

Number of 200 notes = 85760000/200 = 428,800

Number of 100 notes = 85760000/100 = 857,600

Number of 50 notes = 85760000/50 = 1,715,200

Number of 20 notes = 85760000/20 = 4,288,000

3) To credit the amount 146737000;

Number of 200 notes = 733,685

Number of 100 notes = 1,467,370

Number of 50 notes = 2,934,740

Number of 20 notes = 7,336,850

4) To credit the amount 5555627000;

Number of 200 notes = 27,778,135

Number of 100 notes = 55,556,270

Number of 50 notes = 111,112,540

Number of 20 notes = 277,781,350

5) To credit the amount 7777000;

Number of 200 notes = 38,885

Number of 100 notes = 77,770

Number of 50 notes = 155,540

Number of 20 notes = 388,850

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Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

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