The distance from the top of the tree of height 30 tall to the end of the shadow is 50.
What is distance?Distance is the length between two point.
To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.
Note: The tree and the shadow form a right angle.
Formula:
a = √(b²+c²)................. Equation 1Where:
a = Distance of from the top of the tree to the end of the shadowb = Height of the treec = Length of the shadowFrom the question,
Given:
b = 30 c = 40Susbtitute these values into equation 1
a = √(30²+40²)a = √(900+1600)a = √2500a = 50Hence, the distance from the top of the tree to the end of the shadow is 50.
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for values of x f(x) = 2x-3 and g(x)= x^2+1 find gf(x)
Answer:
g(f(x)) = 4x² - 12x + 10
Step-by-step explanation:
to find g(f(x)) substitute x = f(x) ino g(x)
g(f(x))
= g(2x - 3)
= (2x - 3)² + 1 ← expand parenthesis using FOIL
= 4x² - 6x - 6x + 9 + 1
= 4x² - 12x + 10
Mr. Jensen purchased a condo several years ago at a selling price of $295,420. Recently it
was appraised at a value 36.4% lower than that. What is the value of the condo now?
Roun
Answer:
The value of the condo was appraised at 36.4% lower than the selling price, which means it is now worth 100% - 36.4% = 63.6% of the selling price.
The selling price of the condo was $295,420, so the value of the condo now is $295,420 * 63.6% = $<<295420*0.636=188382.72>>188,382.72.
Therefore, the value of the condo now is $188,382.72.
Step-by-step explanation:
The equations of three lines are given below.
Line 1: y= 3x +8
Line 2: y=3x-3
Line 3: 6x - 2y= -8
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
they are all parallel
they all have the same slope of three
least common number
( sorry i forgot what its called )
of 598 and 45
The least common multiple of 598 and 45 is 26, 910
How to find the least common multiple ?To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.
This gives:
598 prime factorization :
2 x 13 x 23 = 598
45 prime factorization :
3 x 3 x 5 = 45
The least common multiple is;
= 2 x 13 x 23 x 3 x 3 x 5
= 26, 910
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When you sign up for dance class you have a startup fee of $75 and then a monthly fee of $54.
The dance company uses the expression 75 + 54m to find out how much it will cost to attend classes.
How much would it cost to take classes for 10 month?
Work Shown:
75+54m
75+54*10
75+540
615
Two car dealerships pay their employees a monthly salary plus a commission on cars that they sell.
The person who is right on the dealership that pays a higher commission, is Tyson because Dealership A pays the higher commission.
How to find the commission paid ?The commission paid on Dealership A cars can be found by the formula :
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 850 - 1, 900 ) / ( 4 - 1 )
= $ 650
The commission paid on Dealership B cars would be:
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 500 - 2, 000 ) / ( 4 - 1 )
= 1, 500 / 3
= $ 500
Dealership A pays the higher commission.
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is 0.2/2.6 0.3/3.6 proportional or not proportional
Answer:
not proportional
Step-by-step explanation:
0.2/2.6 is 1:13
0.3/3.6 is 1:12
the total cost for 5 adult tickets and 18 student tickets at a local theater is $98. The total cost was 98. The total cost for 4 adult tickets and 22 student tickets at the theater is $105. What’s the cost for one adult ticket and one student ticket? PLEASEE BRO
The cost of one adult ticket is 3.6 and cost of one student ticket is 4.3
Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than 14 on x student tickets and 1 adult ticket, what is one possible value of x?Either 4 or is the appropriate response.
Chris spends a total of 2 x + 3 dollars on x student tickets and a total of x adult tickets because each student ticket costs $ 2 and each adult ticket costs $ 3.
Because Chris spends at least $ 11 but no more than $ 14 on the tickets, the entire inequality 2 x + 3 1 can be written.
x = 4 and x = 5.5 are obtained by subtracting 3 from each side of both inequalities and then dividing each side of both inequalities by 2.
A number higher than or equal to 4 and less than or equal to 5.5 must both be integers in order for x to have a value.
Therefore, either x = 4 or x = 5.
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What is the greatest common factor for 27 and 51
Answer:
27:-3×9
51:-3×17
In 27 and 51 the common one is 3 and hence it is the greatest common factor.✓✓
if you want smallest or lowest common factor then you have to take the common 3 as one and multiply like this:-3×9×17=459 is the Lowest common factor.
*mark me brainliest
2. What number is a common multiple of
5 and 9?
. Describe the transformation that changes AABC to AA'B'C'.
Analysing the given figures of the triangles ABC and A'B'C' , the required transformation for changing the traingle ABC to A'B'C' is the translation.
How can a translation transformation be represented in a 2D space?In a two-dimensional space, a translation transformation can be represented by a matrix of the form [1 0 Tx], [0 1 Ty], where Tx and Ty are the horizontal and vertical translation values, respectively. The matrix shows the movement of an object in the x and y directions, with Tx representing the horizontal shift and Ty representing the vertical shift.
What are the effects of a translation transformation on an object?A translation transformation moves an object from one position to another without changing its size or orientation. The shape and size of the object remain the same, but its position changes. The object is moved along a specific direction by a certain distance, and the position of the object within a coordinate system is changed. The effect of a translation can be visualized as sliding an object along a surface, while keeping its orientation and size unchanged.
As we can see from the given graph that the traingle ABC has moved straight downward without any changes in the orientation and the size of the traingle while being transformed to traingle A'B'C', Hence the transformation is translation transformation.
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Given that f(x)=√x, describe the function of g(x)
shown on the graph.
The function is represented by the equation
g(x)=√x +
The function g(x) has a domain x²
The function g(x) has a range y ≥
Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.
Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.
And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.
I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.
Step-by-step explanation:
(5x3)+(nx4)=5(3+4) write each missing number.
Answer:
5
Step-by-step explanation:
5 x 3 = 15
n x 4 = 4n
3 + 4 = 7
(5 x 3) + (n x 4) = 5(3 + 4)
15 + 4n = 5*7
15 + 4n = 35
4n = 35 - 15
4n = 20
n = 20/4
n = 5
Hence, the value of missing number (n) is 5.
Statement of stockholders' equity
The revenues and expenses of Paradise Travel Service for the year ended May 31, 206, follow:
Fees earned
$900,000
Office expense
300,000
Miscellaneous expense
15,000
Wages expense
450,000
Everett McCauley invested an additional $40,000 in the business in exchange for common stock, and $10,000 of dividends were paid during the year. Common June 1, 205.
Prepare a statement of stockholders' equity for the year ended May 31, 206.
Paradise Travel Service
Statement of Stockholders' Equity
For the Year Ended May 31, 206
Common Stock Retained Earnings
Balances, June 1, 20Y5
60.000
300,000 V
Issued common stock
40,000
1♥
Net income
I x
Total
$ 360.000
V
40.000
V
Dividends
0
10,000
10.000
When all liabilities have been paid for a business, what is left over are referred to as the stockholders' equity.
What is the formula for stockholders equity?After all liabilities have been paid, a company's residual assets are referred to as its stockholders' equity. This amount is computed by deducting total liabilities from total assets, or alternatively, by adding share capital and retained earnings and deducting treasury stock.
Total Assets - Total Liabilities = Shareholders' Equity
The aforementioned equation is known as the fundamental accounting equation and is fairly simple to apply. The value of all obligations is subtracted from the total amount of assets on the balance sheet.
SE is therefore the owners' remaining claim to the assets after all debts have been paid. Total assets less total liabilities gives a company's shareholder equity. Shareholder equity includes retained earnings as well as any invested capital.
The complete question is:
Statement of stockholders' equity
The revenues and expenses of Paradise Travel Service for the year ended May 31, 20Y6, follow:
Fees earned $900,000
Office expense 300,000
Miscellaneous expense 15,000
Wages expense 450,000
Everett McCauley invested an additional $40,000 in the business in exchange for common stock, and $10,000 of dividends were paid during the year. Common stock had a balance of $60,000 and retained earnings had a balance of $300,000 as of June 1, 20Y5.
Prepare a statement of stockholders' equity for the year ended May 31, 20Y6.
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When all liabilities have been paid for a business, what is left over are referred to as the stockholders' equity.
What is the formula for stockholders equity?After all liabilities have been paid, a company's residual assets are referred to as its stockholders' equity. This amount is computed by deducting total liabilities from total assets, or alternatively, by adding share capital and retained earnings and deducting treasury stock.
Total Assets - Total Liabilities = Shareholders' Equity
The aforementioned equation is known as the fundamental accounting equation and is fairly simple to apply. The value of all obligations is subtracted from the total amount of assets on the balance sheet.
SE is therefore the owners' remaining claim to the assets after all debts have been paid. Total assets less total liabilities gives a company's shareholder equity. Shareholder equity includes retained earnings as well as any invested capital.
The complete question is:
Statement of stockholders' equity
The revenues and expenses of Paradise Travel Service for the year ended May 31, 20Y6, follow:
Fees earned $900,000
Office expense 300,000
Miscellaneous expense 15,000
Wages expense 450,000
Everett McCauley invested an additional $40,000 in the business in exchange for common stock, and $10,000 of dividends were paid during the year. Common stock had a balance of $60,000 and retained earnings had a balance of $300,000 as of June 1, 20Y5.
Prepare a statement of stockholders' equity for the year ended May 31, 20Y6.
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A fitness center is interested in the average amount of time a client exercises in the center each week.
Match the vocabulary word with its corresponding example.
The average amount of exercise time for the 45 clients from the fitness center who
participated in the study
The average amount of time that all clients from the fitness center exercise
All 45 exercise times there were recorded from the participants in the study
All clients at the fitness center
The amount of time that any given client from the fitness center exercises
b The 45 clients from the fitness center who participated in the study
d
a
c
a. Data
b. Sample
c. Population
d. Variable
e. Statistic
f. Parameter
Textbook Pages
Study data: The 45 exercise sessions from study participants were all recorded.
What is meant by data of study?Study Data includes all information created, obtained, or acquired during the conduct of the Study, including Samples 1 through 3 including databases, documents, reports, and other material.
Any information that has been gathered, noticed, produced, or made specifically to support initial study conclusions is referred to as research data. Research data can also be found in non-digital media like diary and lab notebooks, despite being mostly digital.
A. Study data: The 45 exercise sessions from study participants were all recorded.
B. Study parameter: The average weekly exercise time for all participants.
C. Study variable: The length of time that each individual fitness facility patron exercises.
D. Study participants: all patrons of the fitness club.
E. The 45 gym patrons who took part in the survey made up the study's sample.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
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what is the correct factorization of 33^3x39x4^11
The correct factorization of 33³ × 39 × 4¹¹ = 2²² × 3⁴ × 11³ × 13
What is factorization?Factorization is the collecting together of the common terms of an expression so as to have it in simpler form.
How to find the correct factorization of the expression 33³ × 39 × 4¹¹?To find the correct factorization of 33³ × 39 × 4¹¹, we write out each term in terms of its common factors.
so, we have that the factorization of the first term is 33³ = (3 × 11)³ = 3³ × 11³
Also, we have that the factorization of the second term is 39 = 3 × 13
Finally, we have that the factorization of the last term is 4¹¹ = (2²)¹¹ = 2²²
So, we have that 33³ × 39 × 4¹¹ = 3³ × 11³ × 3 × 13 × 2²²
= 3³ × 3 × 13 × 11³ × 2²²
= 2²² × 3⁴ × 11³ × 13
So, the correct factorization is 2²² × 3⁴ × 11³ × 13
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find the value of x !!
thanks :)
According to question as both side are equal so it is an isosceles triangle and the value of X is 18.
What are the properties of Isosceles Triangle?An isosceles triangle is a triangle with two sides of equal length. Some properties of an isosceles triangle include:
The two equal sides are called the legs of the triangle and the remaining side is called the base.The angle between the legs is always equal to the angle between the base and one of the legs.The altitude (perpendicular line segment from a vertex to the opposite side) bisects the base of the triangle.The median (line segment from a vertex to the midpoint of the opposite side) and the altitude from the same vertex to the opposite side are also congruent.The circumcenter (center of the circle that passes through all three vertices) of an isosceles triangle is always located at the midpoint of the line connecting the two vertices of the congruent sides.The line that is bisecting the angle between the congruent sides (also known as the angle bisector) also bisects the side opposite to that angle.so In this triangle ,
The mid point on horizontal side is given and 5m line cut the mid point of both the sides.
both side are equal as it is an isosceles triangle.
and given in the question,
side/2 =9
and one side is equal to x.
and both sides are equal,
therefore
side = 9*2 = 18
so the value of x = 18.
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i’ll mark whoever brain list for the best answer
As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.
what is area ?An object's surface area is a measurement of the total volume of space that it occupies. The entire region surrounding a three-dimensional shape is referred to as its surface area. Its surface area is the total area of a three-dimensional shape. By adding the surfaces of each of a cuboid's six rectangular sides, one may determine the cuboid's surface area. The box's dimensions could also be named using the following formula: Surface (SA) = 2lw + 2lh + 2hw. A three-dimensional shape's surface area is a measurement of the total area it occupies (a three-dimensional shape is a shape that has height, width, and depth).
given
here,
Length = 3x + 3
Width = 6
Area of the rectangle = y, = length × width
y = [3x - 3 ] × [6]
y = 18x - 18 = 18[x -1]
Perimeter of the rectangle = 2[length + width]
z = 2 [3x + 3]
z = 6[x + 1]
As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.
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The correct question is :- Write a linear equation that represents the area and a linear equation that represents the perimeter of the rectangle (3x-3) cm and 6 cm .
I need c15 and c16 doing please with working out thank you
Therefore , the solution to the given problem of circle comes out to be area = 25.1 sq cm and perimeter=12.5 cm.
What is the circle?Every position in a circle's plane is equally spaced from the centre and is considered to be a closed, double object. A line of reflected symmetry is created as a result of each line traversing the circle. Each angle also has an axis of symmetry that circles its center.
Here,
Given : Diameter = 8
Radius = 8/2 = 4cm
To find the semi circle area
=>semi circle area = πr²
=> 22/7 * 4² *1/2
=> 25.1 sq cm
To find the perimeter of semi circle :
=> 2πr /2
=> πr
=> 22/7*4
=>12.5 cm
Therefore , the solution to the given problem of circle comes out to be area = 25.1 sq cm and perimeter=12.5 cm.
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Select all the correct answers. The manufacturer of a popular brand of markers is planning to release a new color. To determine which color to add, it mailed out surveys to 5,000 of its customers regarding the general color family they prefer. The returned results are shown in this pie chart. A Pie Chart with four sections representing the color preferences Blues, Greens, Yellows, and Pinks Based on the results, one member of the management team says they should choose the new color from the blue family of colors since a majority of people prefer those colors. Another member doesn’t agree and thinks they should do more research. Which statements would support her request? The difference among the percentages is not statistically significant enough to make the claim of majority. A majority of the management team prefers the yellow family of colors. Not all color families were represented in the survey, which could cause a nonresponse bias. The mail-in survey may have resulted in an undercoverage bias. Since only existing customers were surveyed, the results were not random.
The statements that would support her request include:
The difference among the percentages is not statistically significant enough to make the claim of majority.Not all color families were represented in the survey, which could cause a nonresponse bias.The mail-in survey may have resulted in an undercoverage bias.Since only existing customers were surveyed, the results were not random.How to illustrate the information?A well-known marker brand's manufacturer intends to introduce a new shade. It mailed surveys to 5,000 of its customers asking them which general color family they preferred in order to decide which color to add.
The percentage difference is not statistically significant enough to support the majority claim. The survey did not include families of every color, which might have led to nonresponse bias.
It's possible that the mail-in survey had an undercoverage bias. Also, the results were not random because only current clients were polled.
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Answer: the other guy is correct except for the "since only existing customers...".
Step-by-step explanation:
Just took the test, the others he mentioned were right
If m∠ABJ = 28, ∠ABC ≅ ∠DBJ, find m∠JBC.
Answer:
Step-by-step explanation:
If m∠ABJ = 28 and ∠ABC ≅ ∠DBJ, then we can set up the following equation:
m∠ABC = m∠DBJ
Since angles ∠ABC and ∠DBJ are congruent, they have the same measure, so the equation above is true.
Since we are trying to find m∠JBC, we can use the fact that the measure of an angle is equal to the sum of the measures of the other two angles in the triangle to set up another equation:
m∠JBC = m∠ABC + m∠ABJ
Substituting the value for m∠ABC from the first equation into the second equation, we get:
m∠JBC = m∠DBJ + m∠ABJ
Substituting the given value of m∠ABJ into this equation, we get:
m∠JBC = m∠DBJ + 28
Since m∠ABJ = m∠DBJ, we can substitute m∠ABJ in for m∠DBJ:
m∠JBC = m∠ABJ + 28
Substituting the given value of m∠ABJ into this equation, we get:
m∠JBC = 28 + 28
Solving this equation, we find that m∠JBC = 56.
Therefore, the measure of angle ∠JBC is 56 degrees.
Anyone know about this thanks :)
The height of the rock ledge is 20 meters and height of the tree is 59 meters.
What are heights and distances?Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.
From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.
a) Let the height of the rock ledge be x.
Now, tan12°=x/96
0.2125=x/96
x=20.4 meters
x≈20 meters
b) Let the height of the tree be y
Here, part of the tree is y-20
Now, tan22°=(y-20)/96
0.404=(y-20)/96
y-20=38.784
y=58.784
y≈59 meters
Therefore, the height of the rock ledge is 20 meters and height of the tree is 59 meters.
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Evaluate -3x³-4x for x = -1.
A)-1
B)7
C)1
Answer:
B) 7
Step-by-step explanation:
-3x³-4x =
-3(-1)³-4(-1) =
-3(-1)+4=
3+4 =7
Greatest common factor
Step-by-step explanation:
To find the GCD or GCF of two numbers , you should:
List the prime factors of each one of them(the 2 numbers)choose the common number+least exponent multiply themWhich of the following best describes X on the scatter plot below?
The option that best describes X on the scatterplot is;
C: Outlier
How to Interpret a scatterplot?Let us first define the terms in the given options before we analyze the scatterplot.
1) Negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
2) A nonlinear relationship is also referred to as nonlinear association, and it exists when a constant change in the independent variable does not result in a constant change in the dependent variable.
3) An outlier is defined as a data point that differs significantly from other observations.
4) Clusters are small populations that a wider population is divided into.
Now, from the scatter plot, we see that X is isolated from the plotted points which tells us that it differs greatly from the other points and as such it fits the definition of an outlier.
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The missing options are;
A. negative correlation
B. nonlinear association
C. outlier
D. cluster
Iliana rotated trapezoid WXYZ 180° about the origin.
What is the correct set of image points for trapezoid WX'Y'Z'?
The correct set of image points for trapezoid WX'Y'Z' is the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).
What is trapezoid?A trapezoid is a quadrilateral in American and Canadian English that has at least one set of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The parallel sides are referred to as the trapezoid's bases.The bases of a trapezoid (the top and bottom) are parallel to one another. A trapezoid's opposite sides are equal in length (isosceles). Angles close together add up to 180° Both bases and the median run parallel.A parallelogram has two pairs of parallel sides, whereas a trapezoid has one pair of parallel sides. A parallelogram is a trapezoid, therefore.Given data :
From the given figure, it is clear that the vertices of the trapezoid are W(-4,2), X(-3,4), Y(-1,4), Z(0,2).
If a figure is rotated 180 degrees about the origin, then
( x, y ) → ( -x, -y )
Using this rule, we get
W (-4, 2 ) → W' ( 4, -2 )
X ( -3, 4 ) → X' ( 3, -4 )
Y ( -1, 1 ) → Y' ( 1, -4 )
Z ( 0,2 ) → Z' ( 0, -2 )
Therefore, the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).
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please answer this with work
Answer:
Step-by-step explanation:
-38 + -12x < -200
Answer:
-38 - 12x > -200
x = 13.5 min
Step-by-step explanation:
let x = minutes of the dive
-38 ft - 12 ft/min(x) > -200 ft
-12 ft/min(x) < -162 ft
x > -162/-12 **flip the inequality when you divide by a (-) number
x > 13.5 min
Starting at -38 ft, he has to dive longer than 13.5 minutes to go deeper than -200 ft at a rate of -12 ft/min
Find the slope of the line through each pair of points.
(4, 18), (4, -11)
Answer:
undefined
Step-by-step explanation:
slope formula:
m =y2-y1 / x2-x1
m= -11-18 / 4-4= -29/0
you cannot divide by zero so the slope is undefined
I need help completing the square
The formula needed to transform a quadratic polynomial or equation into a perfect square with an additional constant is known as the square formula. It is expressed as, [tex]ax^2 + bx + c = a(x + m)^2 + n[/tex], where, m and n are real numbers.
What does math's "completing the square" mean?When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. A good example is [tex]x^2 + 6x + 7[/tex] . First, let's note that [tex](x + 3)^2 = (x + 3)(x + 3) = x^2 + 6x + 9. x[/tex] because this is two more than our expression.
Quadratic Equation: What Is It?The polynomial equations of degree two in one variable of type[tex]f(x) = ax^2 + bx + c = 0[/tex] and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).
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When you are solving a compound inequality, how can you express the solution?
Please give your rationale.
Answer:
When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.
Using a union:
A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."
Using an intersection:
An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."
Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.
When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).
A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.
When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.
Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.
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