Solve the following and list any extraneous solutions
1. √30- x = x
2. x = √42 - x
3. √12-r=r
4. m = √56 - m
5. r = √-1-2r
6. √4n+8 = n +3
7. -n+√6n + 19 = 2
8. 4+√-3m + 10 = m
9. x-5=√x+1
10. n-7= √√3n - 21

The point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

As a line has length but no width, it is a one-dimensional figure in geometry. A line is constructed from a collection of points that can be stretched indefinitely in opposite directions. In a two-dimensional plane, it is determined by two points. In a two-dimensional coordinate plane, there are various ways to express line equations. The general or standard form of the equation of a line, the slope-intercept form, and the point-slope form are the three most often used ways. The point-slope form, as its name implies, combines a line's point with the straight-line slope. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line.

The point slope equation with the point (x1, y1) is given by the formula:

(y - y1) = m (x - x1)

Here, (x1, y1) are the coordinates of the point on the graph.

m is the slope of the line.

Hence, the point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

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The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

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The linear function that models this problem is y = 25x + 25 and the cost for 6 hours is $175

To solve this problem, we have to find the slope and y-intercept of the line.

m = y2 - y1 / x2 - x1

Taking two points from the line;

A = (2, 75)

B = (5, 150)

Substituting the values into the formula;

m = 150 - 75 / 5 - 2

m = 25

Using the slope;

y = mx + c

150 = 25(5) + c

150 = 125 + c

c = 150 - 125

c = 25

The equation of line is ;

y = 25x + 25

The cost for 6 hours will be

y = 25(6) + 25

y = 175

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The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

Let 'a' is the leading coefficient and 'b' is the factor.

The exponent is given as,

y = a(b)ˣ

Some points regarding the exponent function:

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

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Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Quadrilateral RSTV is dilated with the origin as the center of dilation using the rule (x, y) = (3/2x, 3/2y) to create quadrilateral R'S'T'V'.

Here, All the coordinates of vertex of Quadrilateral RSTV are,

R = (- 3, - 2)

S = (- 2, 3)

T = (2, 2)

V = (3, - 1)

Hence, By applying rule we get;

All the coordinates of vertex of Quadrilateral R'S'T'V' are,

R' = (- 3 × 3/2, - 2× 3/2) = (- 9/2. - 3)

S' = (- 2 × 3/2, 3 × 3/2) = (- 3, 9/2)

T' = (2 × 3/2, 2× 3/2) = (3, 3)

V' = (3 × 3/2, - 1 × 3/2) = ( 9/2. - 3/2)

Now, Distance between R and S;

RS = √ (- 3- (- 2))² + (- 2 - 3)²

     = √1 + 25

     = √26

And, Distance between R' and S';

R'S' = √ (- 3- (- 9/2))² + (- 3 - 9/2)²

     = √(3/2)² + (15/2)²

     = √9/4 + 225/4

    = √234/4

Hence, The scale factor is,

⇒ RS / R'S' = √26 / (√234/4)

                  = 2√26/ √234

                  = 2/3

                  = 0.67 < 1

Thus, Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

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Answer:The volume would be 8,341,984

Step-by-step explanation:

Inputting the values provided yields:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

A + B = 5 - sqrt (34)after simplifying and solving for a + b. 

As a result, we have established that a + b=  0.27.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.

Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:

[tex]CH^2 = CB^2 - BH^2[/tex]

Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:

[tex]CH^2 = AC^2 - x^2[/tex]

We can also use the given values of x and h to find AC:

[tex]AC^2 = x^2 + h^2[/tex]

Substituting this into the equation for [tex]CH^2[/tex], we get:

[tex]CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2[/tex]

Taking the square root of both sides, we get:

CH = h = 4

Therefore, we have found that CH = 4.

Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:

Area = (1/2) * CH * AB

Area = (1/2) * AC * BC

Setting these two expressions equal to each other and substituting the given values, we get:

(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5

Simplifying and solving for y, we get:

2x + 8 = 15 - 5/2 * y

2x + 13/2 = 5/2 * y

y = 2x + 13/5

Using the given value of x, we can find y:

y = 2(3) + 13/5 = 6.6

Therefore, we have found that y + h = 6.6 + 4 = 10.6.

Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:

[tex]AC^2 + BC^2 = AB^2[/tex]

Substituting the given values, we get:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

Simplifying and solving for a + b, we get:

a + b = 5 - sqrt(34)

Therefore, we have found that a + b ≈ 0.27.

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Answer:

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

Step-by-step explanation:

Let R be the number of roses and D be the number of daisies.

Now we can set the following equations to represent the cost and the total number of flowers,

Cost equation=3.50R + 1.25D

                       = 300

Number of flowers equation= R + D

                                              = 150

We need to find the number of roses and daisies that we can purchase, as according to question the total number of flowers is 150. To find R, we can put value of  the number of flowers in the equation for R in terms of D, and also put this expression for R in the cost equation,

R = 150 - D

3.50R + 1.25D

= 300

3.50(150 - D) + 1.25D

= 300

525 - 3.50D + 1.25D

= 300

-2.25D = -225

D = 100

Therefore, we can buy 100 daisies and the remaining 50 flowers must be roses.

The cost of 100 daisies is 100 × 1.25

= $125

The cost of 50 roses is 50 × 3.50

= $175.

Therefore, the total cost is $125 + $175

= $300.

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

The key features of this rational function include the following:

Domain: (-∞, 1) ∪ (1, ∞)

Range: (-∞, 3) ∪ (3, ∞)

Y-intercept: -5.

X-intercept: 5/3.

Vertical asymptote: x = 1.

Horizontal asymptote​: y = -3.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

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This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

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Answer:

7.25

Step-by-step explanation:

Divide 8.99 by 1.24

The data collected at the beginning of the process, after a problem has been identified, are known as baseline data.

Baseline data is used as a reference point for measuring the performance of a process before any changes or improvements are made. This allows for a comparison to be made between the initial performance and the performance after changes have been implemented, in order to assess the effectiveness of the changes.

In summary, baseline data is important for evaluating the success of a process improvement initiative and for making informed decisions about further changes.

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Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

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Answer:

fraction:26/100

decimal:0.26

Using the graph of the line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

What is meant by inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given that the boundary line of equality has points (4,5) and (1,-1) on it.

So we can write the equation of the line.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = -1-5 / 1-4 = 2

Equation of the line:

y - y1 = m (x-x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

y + 2x = -3

Point (−3, −5) makes the inequality false.

Substituting,

-5 + 2 * -3 = -5 - 6 = -11

y + 2x should not be -11

When graphing the line it should not include the point (−3, −5).

This point is present on the lower portion of the line.

So the upper portion of the line should be the inequality including the line itself.

Therefore using the graph of line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

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Answer: f=756

Step-by-step explanation:

f/28=7

multiply both sides of the equation by 28

28 x f/28=28 x 27

cancel out the greatest common factor 28

f=28 x 27

multiply 28 x 27

f=756

Answer:

Using the ratio given, we know that for every 5 colored pencils, there are 2 markers in each box.

Therefore:

The first blank represents the number of colored pencils in the box. Since the ratio of colored pencils to markers is 5 to 2, we can calculate that there are 5 colored pencils for every 2 markers. This means that for each box, there are 5/7 of the total number of items are colored pencils. So the missing value in the first row is 35.

The second row indicates that there are 20 items in the box. We know that the first row (colored pencils) has 35 items, and since the total number of items in the box is 20, the missing value in the second row (markers) is 20 - 35/7 = 15.

The third row represents the total number of colored pencils and markers in each box. We know that there are 35 colored pencils and 15 markers in each box, so the total number of items in each box is 50.

Therefore, the completed table would be:

Boxes for sale

||||||||||||||||||||||||||||||||||||||||||

Number of Colored | 35 | 20 | 35 |

Pencils | | | |

||||||||||||||||||||||||||||||||||||||||||

Number of Markers | 6 | 15 | 6 |

| | | |

Total Number of ||||||||||||||||||||||||||||||||||||||||||||

Colored Pencils and | 41 | 35 | 50 |

Markers in the Box |||||||||||||||||||||||||||||||||||||||||||||​

Trigonometric functions have some interesting symmetry properties

If tan x= -2.5, then tan (-x)= 2.5 and If sin x= 0.4 then sin (-x)= -0.4

If cos x = 0.9 then cos (-x)= 0.9  If tan x = 1.5 then tan (pi+x)= -1.5

Trigonometric functions are mathematical functions that are widely used in various fields, including mathematics, physics, and engineering. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Trigonometric functions have some interesting symmetry properties. For example, the sine and tangent functions are odd functions, which means that sin(-x) = -sin(x) and tan(-x) = -tan(x). On the other hand, the cosine function is an even function, which means that cos(-x) = cos(x).

These symmetry properties have important implications in many applications of trigonometric functions. For example, if we know the value of sin(x), we can immediately determine the value of sin(-x) by using the odd symmetry property. Similarly, if we know the value of cos(x), we can determine the value of cos(-x) by using the even symmetry property.

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Answer: The value of a=29/23 and b=124/23

Step-by-step explanation:

Given equations are,

2b-3a=7       _(1)

3b+7a=25     _(2)

Multiplying (1) by 7

14b-21a=49

Multiplying (2) by 3

9b+21a=75

solving the above equations,

14b-21a=49

9b+21a=75

23b      =124

b=124/23

Substituting the value of b in eq. (1)

a=29/23

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Answer:

x = 10182634

y = - 462847/46

Step-by-step explanation:

Divide both sides of the equation by the coefficient of variable

x =   -1012y

y = - 10182634/ 1012

x =   -1012y(  - 10182634/ 1012)

The correct matching of the fractions

0.1 - 1/10

0.01 - 1/100

100% - 1

A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.

The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.

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Step-by-step explanation:

1/2 cup per 1/4 bag goes to the less than

all the other ones should be in the greater than category

The statement 3/4> 13/16 is false and the statement 6/7> 5/8is true.

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Using the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

The first statement is:

3/4 > 13/16

Take the LCM:

12/16 > 13> 16

Comparing the numerator we see that, 12 > 13 is false. Hence, the statement is false.

The second statement is:

6/7 > 5/8

Take the LCM:

48/56 > 35/56

Comparing the numerator we see that, 48 > 35 is True.

Hence, the statement is True.

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The x and y values are x=5 and y= -2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=4x-22 ----(1)

2x+3y=4------(2)

Substitute (1) into (2)

=> 2x+3(4x-22)=4

=> 2x+12x-66 = 4

=> 14x = 4+66

=> 14x = 70

=> x=70/14 = 5

(1) => y=4*5-22 = 20 - 22 = -2

So, the x and y values are x=5 and y= -2

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The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

An experiment in probability is a process or activity that involves observing or measuring an outcome or event, in order to determine the likelihood or probability of certain outcomes.

In probability, an outcome refers to a possible result that can occur from an experiment or event. It is one of the possible outcomes that can happen, and it may be a single result or a set of results.

In probability, a trial is a single repetition of an experiment or event. It is the process of observing or measuring the outcome of an event or experiment once.

Here we have

At a sports event, a fair coin is flipped to determine which team has possession of the ball.

The coin has two sides, heads, (H), and tails, (T).  

From the given options correct answers are

a. The experiment identifying whether a head or tail is flipped is correct because the experiment is to determine which side of the coin will be facing up after the coin is flipped, either heads (H) or tails (T).

b. The experiment is flipping the coin is correct because the experiment involves physically flipping the coin.

d. A trial is one flip of the coin is correct as a trial is defined as a single performance of an experiment, in this case, flipping the coin once.  

Therefore,

The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

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a. Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Numbers less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. Non-zero coefficients between +1 and -1 are used to show lower degrees of connection. 0 means there is no propensity for the variables to change simultaneously, either positively or negatively.

a. A weak negative linear relationship between hours worked and donations collected in this context means that as Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

b. When we say there is a weak correlation between two variables, we are referring to their level of relationship. The negative correlation in this instance indicates that there is a propensity for the amount of donations collected to decline as the time spent working increases, but the relationship is not very strong, indicating that there is a lot of variability in the data and making firm predictions or conclusions based on this correlation alone is challenging.

c. Tom's boss's claim is wrong as the negative correlation or the decline in donation is a mere coincidence and does not have a relation to Thor's work.

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The possible rational roots of the polynomial are ±1, ±2, ±4, ±5, ±10, ±20.

The correct option is D.

Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.

And the standard form of the cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.

Given:

A cubic polynomial,

x³ + 5x² -8x - 20 = 0.

The possible rational roots are;

p/q = -20/1

= -20

The factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20.

Therefore, the possible roots are ±1, ±2, ±4, ±5, ±10, ±20.

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Answer:

Error refresh.

Step-by-step explanatithanksforfreepointlolon:

Answer:

a. The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of b.

b. Approximately 8.

b. Enter the approximate slope of the estimated line of best fit in the second box. slope=24 (Enter your estimate to the nearest tenth.)

Approximately 2.4.