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George tells you that when variables are in the denominator, the equation
2/3+5/x=8/9 becomes unsolvable. George explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to George how the equation is still solvable and explain your reasoning.

The solution of [tex]x^{2} - 3x-4=0[/tex] is x=(4,−1).

What is fraction ?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator. In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions.

Have given ,

[tex]x^{2} - 3x-4=0\\x^{2} -4x +x-4=0\\x(x-4)+1(x-4)=0\\(x-4)(x+1) = 0\\[/tex]

x - 4 = 0                

x = 4

and x + 1 = 0

x = -1

The solution of [tex]x^{2} - 3x-4=0[/tex] is x = (4,−1).

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The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.

An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.

Given: 3x² + 2kx + 27 = 0

Comparing with standard quadratic equation ax² + bx + c = 0

a = 3 b = 2k c = 27

Given that the roots of the equation are real and equal

Thus, D = 0

Discriminant D = b² – 4ac = 0

(2k)² – 4.3.27 = 0

4k² – 324 = 0

4k² = 324

k² = 81 taking square root on both sides

k = 9 or k = – 9

Hence, The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.

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Answer: -6

Step-by-step explanation: To determine the largest integer value of x in the solution of the inequality 2x+6<-4, we first need to isolate x on one side of the inequality. We can do this by subtracting 6 from both sides of the inequality, which gives us 2x<-10. Next, we can divide both sides of the inequality by 2, which gives us x<-5. Since the inequality has a strict inequality symbol, we can conclude that the largest integer value of x that satisfies the inequality is -6.

There are only two factors of the number 31 which are 1 and 31. Then the integer number 31 will be a prime number.

A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.

The prime numbers from 1 to 100 are given below.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

The factor of the 31 will be given as,

31 = 1 x 31

There are only two factors of the number 31 which are 1 and 31.

Thus, the integer number 31 will be a prime number.

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The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.

The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

let

x = number of two-points

y = number of three-points

Hence, using equation

x + y = 43

2x + 3y = 105

Multiply equation(i) by 2

2x + 2y = 86

2x + 3y = 105

subtract equation(i) from equation(ii)

y = 19

Let's find x as follows:

x = 43 - 19

x = 24

Therefore,

number of two points = 24

number of three points = 19

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The remaining angles  ∠B ,∠C and ∠D is 90°,60°,90°.

Given : Angle A = 120°

To find: ∠B ,∠C , ∠D

Solution: In figure, an inscribed angle is the angle formed in the innards of a circle when two heartstrings cross on the circle. It can also be outlined as the angle subtended at a point on the circle by two presented junctures on the circle. Inversely, an incised angle is defined by two heartstrings of the circle sharing an endpoint .

∠A+∠C=180

 ∠C=180-120

 ∠C= 60;

 In triangle ABC :  ∠BAC + ∠ACB+∠ABC=180°

                               60° + 30° + ∠ABC = 180°

                                ∠ABC = 180°-90°

                                ∠ABC = 90° (so B is 90°)

Therefore, ∠B+∠D=180°

                   ∠D=180°-90°

                    ∠D=90°

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Answer:

  178,200

Step-by-step explanation:

You want to know the number of gallons added to a 660,000 gallon pool to raise it from 63% full to 90% full.

The increase from 63% to 90% is an increase of ...

  0.90 -0.63 = 0.27

of the capacity of the pool. That fraction of the capacity is ...

  0.27 × 660,000 gallons = 178,200 gallons

The maintenance company added 178,200 gallons.

{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)} ordered pairs is not a function. A mapping between two sets, which is a relation and can potentially be a function, can be represented by a set of ordered pairs.

Complete question :

Which of the relations given by the following sets of ordered pairs is not a function?

a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}

b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}

c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}

d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}

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The equation is y = 1/3 x + 10/3. The y-intercept is 10/3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the point (5,5) is on a line with slope 1/3. The y-intercept will be calculated as,

y = mx + c

5 = (5/3)) + c

c = ( 15 - 5 ) / 3

c = 10 / 3'

y = 1/3x + 10/3

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Draw a line segment, place the compass point on point A, and draw an arc that intersects the line segment. Next, place the compass point on point B, and draw another arc that intersects the first arc at a point on the line segment. Finally, place the compass on the point where the two arcs intersect without changing the width of the second arc, and draw another arc that intersects the line segment. Finally, connect the point where the second arc intersects the segment to point C.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

Angle measures are helpful not just for academic purposes but also for understanding and using the objects around us. They may aid with spatial knowledge and the link between numbers and measurements.

Follow these steps to draw angle ABC:

The base of the angle should be represented by a section of a line.

With the compass's point on point A, draw an arc that crosses the line segment.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass's point on point B.

Place the compass on the intersection of the two arcs and create another arc that intersects the line segment without adjusting the compass's width.

To finish the angle, join point C to the location where the second arc crosses the line segment.

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The continuity of the piece-wise functions is defined as follows:

1. Not continuous.

2. Not continuous.

3. Not continuous.

A piece-wise function is a function that has multiple definitions, depending on the input.

Then the function is classified as continuous if the lateral limits at the points that the function change the definition are equal, and also equal to the numeric values of the function.

None of the functions in this problem are continuous, as:

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Answer:

x=0, y=-4

Step-by-step explanation:

y=3x-4

2(3x-4)-6x=-8

6x-8-6x=-8

Answer:

carbon dioxide + water sunlight glucose + oxygen

Step-by-step explanation:

glucose on the right because it is a by product of photosynthesis.

The example of composition function f(g(x)) is given by f(x) = 2x + 1   and g(x) = 3x then f(g(x)) = 6x + 1.

As given in the question,

Composition function is written as :

(fog)(x) = f(g(x))

Here substitute the value x in the function f(x) as function g(x) :

Example of the composition function is:

f(x) = 2x + 1

g(x) = 3x

(fog)(x)

= f(g(x))

=f(3x)

= 2(3x) + 1

= 6x + 1

Therefore, the example of the composition function f(g(x)) is given by :

f(x) = 2x + 1   and g(x) = 3x then f(g(x)) = 6x + 1.

The above question is incomplete, the complete question is:

What is an example of the function f (g(x))?

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The triangles are congruent if two sets of comparable angles and the side separating them are known to be congruent. Angle-side-angle is the name of this shortened phrase (ASA). Angle-angle-side (AAS), which takes use of the fact that two sets of angles and the excluded side are known to be congruent, is another shortcut.

ASA is another name for angle side angle. According to the criterion, any two angles and the side that is contained between them in one triangle are equivalent to the corresponding angles and the included side of the other triangle if the two triangles are congruent.

According to the Angle Angle Side (AAS) Postulate, two triangles are congruent if two consecutive angles and a non-included side of one triangle are congruent with the equivalent two consecutive angles and a non-included side of another triangle.

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You can get Universal Credit Loophole for $1,500 through Advance Payment.

While you wait for the first distribution of Universal Credit, advance payments up to the full amount of the first anticipated payment are available if you need money to pay bills and other household needs. In your online account or by contacting your Job-Centre Plus job coach, you can submit an application for an advance payment.

You will require:

The money must be repaid within a year by taking deductions from your Universal Credit installments.

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Answer:

√6

Step-by-step explanation:

the altitude is √a*b

and and b being the base so find their distance then multipky them under the root

subtracdt the x values to find the distance

4-1=3

6-4=2

the root of 2*3 is the root of 6

done

Answer:

  x = 4

Step-by-step explanation:

You want the equation of AD perpendicular to BC, where the point coordinates are A(4, 6), B(1, 2), C(6, 2).

We notice the y-coordinates of point B and C are the same, indicating the line is horizontal. Its equation is y = 2.

The line perpendicular to the horizontal line y = 2 will be a vertical line. Its equation will be of the form ...

  x = c

where c is some constant.

We want this line to go through the point (4, 6), which has an x-coordinate of 4. That means the constant in the equation must be 4:

  x = 4 . . . . . . equation of AD

Answer:

Cos A = adjacent/hypotenuse

Cos A = 15/17

Cos A = 2.143

tan A = opposite/adjacent

tan A = 8/15

tan A = 0.533

sin A = opposite/hypotenuse

sin A = 8/17

sin A = 0.471

Step-by-step explanation:

Answer:

m = -1/4

Step-by-step explanation:

The slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y decrease by 2 and the x increase by 8, so the slope is

-2/8 = -1/4

Answer:

Slope = -1/4

Step-by-step explanation:

Now we have to,

→ find the needed slope.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Then the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (1 - 3)/(-1 -(-9))

→ m = -2/(-1 + 9)

→ m = -2/8

→ [ m = -1/4 ]

Hence, the slope is -1/4.

Answer:

[tex]30ft^{2}[/tex]

Step-by-step explanation:

y-8=6x+10

y=6x+10+8

y=6x + 18

this follow y = mx+x it means it's a linear

y= 5x²+19

it doesn't follow y = mx+x so it's a Non Linear

4y = x

it doesn't follow y = mx+x so it's a Non Linear

y = 2x + 9

this follow y = mx+x it means it's a linear

Step-by-step explanation:

always remember Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

this principle must be always fulfilled, otherwise it is not a right-angled triangle.

when your have a triangle problem (particularly for a right-angled triangle) with only side information, there is a high chance that you need to use Pythagoras.

in our case

(2×sqrt(3))² = x² + (sqrt(3))²

4×3 = x² + 3

12 = x² + 3

x² = 9

x = 3

that's all.

FYI : sqrt(x²) has actually 2 solutions : -x and +x, as both are squared equal to x².

but a negative number does not make any sense for general side lengths and similar things. so, the positive solution here is the only valid one.

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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The standard form of the equation of the line for the function is; y =6x + 18

We know that it is possible to obtain the equation of the line by obtaining the slope of the data points. The slope of the data points can be obtained by the use of the points that have been shown in the table.

Taking any two points on the table we have;

[tex]y_{1}[/tex] = 0

[tex]y_{2}[/tex] = -12

[tex]x_{1}[/tex] = -3

[tex]x_{2}[/tex] = -1

Using;

y - [tex]y_{1}[/tex]  =  [tex]y_{2}[/tex]  - [tex]y_{1}[/tex] /[tex]x_{2}[/tex]  - [tex]x_{1}[/tex]  (x - [tex]x_{1}[/tex] )

We have;

y - 0 = (-12) - 0/(-1) - (-3) ( x - (-3))

y = 12/2 (x + 3)

y =6x + 18

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Answer:

  (i) height: 36.6 m

  (ii) BP = 36.6 m

  (iii) AB = 51.8 m

  (iv) AC = 73.2 m

Step-by-step explanation:

Given angles of elevation of 45° and 30° to the same point A from locations 100 m apart, you want to know the height of A, and distances BP, AB, and AC in the diagram.

The figure is divided into two special triangles. The one on the left is an isosceles right triangle with side lengths in the ratio 1:1:√2. The one on the right is a 30°-60°-90° triangle with side lengths in the ratio 1:√3:2. The common side AP corresponds to one ratio unit in each of these ratios.

BP = AP = 1 ratio unit means BP : PC = 1 : √3, and ...

  BP/BC = 1/(1+√3)

  BP = BC/(1+√3) ≈ (100 m)/2.73205

  BP ≈ 33.6 m

  AP = 33.6 m . . . . . . same as BP

AB is √2 times AP, so is ...

  AB = √2 · 36.6 m

  AB ≈ 51.8 m

AC is 2 times AP, so is ...

  AC = 2·(36.6 m)

  AC = 73.2 m

An asymptote calculator is a tool that can be used to find the asymptotes of a given function.

Generally,  An asymptote is a straight line that a curve approaches, but never touches, as it extends indefinitely in one direction or another. There are three types of asymptotes: horizontal, vertical, and oblique.

To use an asymptote calculator, you would typically enter the equation of the function for which you want to find the asymptotes. The calculator will then analyze the equation and determine the type and location of the asymptotes, if any. Some asymptote calculators may also provide a visual representation of the function and its asymptotes, using a graph.

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With an increase of 79% the growth factor is 1.79.

The rate at which a quantity multiplies itself over time is known as its growth factor.

A quantity's growth rate is the factor by which it grows (or shrinks) over time.

An increase of 79% is the same result as multiplying with 1.79.

We call 1.79 a growth factor.

In other words:

With an increase of 79%,

you will get 100+ 79 = 179%.

The growth factor that corresponds with 179% = 179 : 100 = 1.79.

Written as a formula, it looks like this:

With an increase of p % the growth factor is

g = (100 + p) / 100

Simplifying,

g = 1 + p /100

g = 1 + 79/100

g = 1 + 0.79

g = 1.79.

Therefore, the growth factor is 1.79.

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This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y

x = (y - 1) / 16

In order to find the inverse of a given equation, we need to switch the x and y values and solve for the new x. To do this, we start by subtracting 1 from both sides of the equation to isolate the y variable. Then, we divide both sides of the equation by 16 to find the inverse equation, x = (y - 1) / 16. This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y

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On solving the provided question, we can say that, 16 square units make up the area of a circle with a radius of 4 units.

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. Through the center of the circle, a straight line defines the diameter. Half of the diameter is the radius. End in the circle's center after beginning at one of its points.

Pi times the radius squared equals the area of a circle (A = π r²). Learn how to apply this equation to determine a circle's area given its diameter.

16 square units make up the area of a circle with a radius of 4 units.

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