Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.
What exactly is a math graph?
A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.
This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.
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What is the point-slope form of a line with slope that contains the point (-2, 1)?
Answer:
Below
Step-by-step explanation:
The point-slope form of a line is:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point on the line.
Given that the line contains the point (-2, 1) we know that this point is on the line, so we can use it as (x1, y1) in the point-slope form.
By using the point (-2,1) we can write the point-slope form of the line as:
y - 1 = m(x + 2)
This means that the point-slope form of a line with slope that contains the point (-2, 1) is y - 1 = m(x + 2) where m is the slope of the line.
Carrie’ head i full of curler. There are 16 in all. One-fourth of the curler are pink. There are twice a many green curler a pink one. The ret are oda can. How many can are on Carrie’ head?
Carrie average has a head full of 16 curlers, with 4 of them being pink, 8 of them being green, and the remaining 12 being can curlers.
1. There are 16 total curlers on Carrie's head
2. One-fourth of the curlers are pink, so that is 16 ÷ 4 = 4 pink curlers
3. There are twice as many green curlers as pink ones, so that is 4 x 2 = 8 green curlers
4. The remaining 12 curlers are can curlers, so there are 12 can curlers on Carrie's head
Carrie has a head full of 16 curlers in total. One-fourth of the curlers are pink, so we can divide 16 by 4 to get 4 pink curlers. There are twice as many green curlers as pink ones, so we can multiply 4 by 2 to get 8 green curlers. This leaves 12 curlers, which must be can curlers. Therefore, there are 12 can curlers on Carrie's head. We can use basic mathematics to break down the problem into smaller pieces and calculate the number of each type of curler on her head.
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x¹10x² +9=0
Step 1. Identify the quadratic form
Let t=
We now have:
t²-10t+9=0
Step 2. Factor
Factor this and solve for t to get t
and
Step 3. Solve for
We have solved for t now we need to use this value for t
to help us solve for x. Revisit step 1 to remind you of
the relationship between t and x. Type your answers
from smallest to largest.
and +/-
x = +/-
Answer:
x = -3, -1, 1, 3.
Step-by-step explanation:
x^4 - 10x^2 + 9 = 0
Step 1
Let t = x^2
So , we have the quadratic
t^2 - 10t + 9 = 0
Step 2
Factorise:
(t - 1)(t - 9) = 0
Step 3
So, t - 1 = 0 or t - 9 = 0
t = 1, 9.
But t = x^2
So, we have x^2 = 1 or x^2 = 9
So, x = ±1, ±3.
x = -3, -1, 1, 3.
Is f x )= 2x 3 a one-to-one function?.
Yes, the function f(x)=2x-3 is a one-to-one function.
The Inverse of a Function:
The inverse of a function can be computed if the function can be proven to be one-to-one. Take the one-to-one function and compute its inverse by interchanging x and y in the expression and solving for y.
Graphically, then, the graphs of the function and its inverse are the reflections of each other about the line y=x.
Use the definition to test the one-to-one of f.
Let x and x be the elements in the domain off and assume f(x₁)=f(x₂)
2x₁-3=2x₂-3
2x₁=2x₂
x₁=x₂
since f(x₁)=f(x₂) implied x the function f is one-to-one.
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f. Starting around the year 2000, there was a dramatic increase in the price of carpeting since it was a petroleum-based product. As a result, selling by the yard made it look expensive. Some stores started selling carpet by the square foot. How much would a square yard of carpet selling for $8.95 per square foot cost?
A square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.
What is the conversion factor?
A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equals 1 foot.
A square yard of carpet is equivalent to 9 square feet because 1 yard = 3 feet and 1 square foot = 1 foot x 1 foot.
So, to find the cost of a square yard of carpet that is selling for $8.95 per square foot, we need to multiply the price per square foot by the conversion factor of 9 square feet per square yard.
$8.95/square foot * 9 square feet/square yard = $80.55/square yard
Hence, a square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.
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Tom’ cell phone plan ha a monthly fee of $105, which include unlimited free text meage and phone call and 4GB of data. Each extra gigabyte of data, or part thereof, cot $12. A. Find the cot of a month in which Tom ued 7. 1GB of data b. If x repreent the number of gigabyte ued, expre the monthly charge c(x) of thi plan a a piecewie function
Total charge that Tom has to pay is $142.2, and the express function for the monthly charge is c(x) = 105 + (x -4) * 12
How to determine the monthly charge function and total charge for Tom on that month?
As per data given, monthly value given is $105 = free text + free call + 4gb and extra gigabyte x $12. Tom that use 7.1 of data will be charge as follow:
Tom charge = normal use + extra use
To charge = 105 + extra gigabyte x12
Extra gigabyte = tom use - normal use
Extra gigabyte = 7.1 - 4
Extra gigabyte = 3.1
Tom charge = 105 + 3.1 x 12
Tom charge = 105 + 37.2
Tom charge = 142.2
The expression of monthly charge, since we have already define that value is $105 = free text + free call + 4gb and extra gigabyte x $12. We can see that text is not charge and call is not charge. So the formula will be:
Monthly charge = 105 + (extra gigabyte - 4) x 12
As per question said the variable for extra gigabyte is x and monthly charge is c(x) then
c(x) = 105 + (x - 4) * 12
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What is the distance between the pair of points (- 5 7 and (- 1 3?.
The distance between the pair of points (- 5, 7) and (- 1, 3) is 5.7 units.
We know that the distance formula.
The distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given a pair of points (- 5, 7) and (- 1, 3)
Let us assume that (x₁, y₁) = (-5, 7)
and (x₂, y₂) = (-1, 3)
Using above distance formula,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]} \\\\ d = \sqrt{[(-1 - (-5))^2 + (3 - 7)^2]}\\\\d = \sqrt{[(-1+5)^2 + (-4)^2]}\\\\d = \sqrt{[(4)^2 + (-4)^2]}\\\\d = \sqrt{(16+16)}\\\\d = \sqrt{32}\\\\d = 5.7~ units[/tex]
So, the distance is 5.7 units.
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The complete question is:
What is the distance between the pair of points (- 5, 7) and (- 1, 3)?.
Is 64 a root number?.
Yes, the square root of 64 is a rational number.
and Square root of 64 is 8
Now, According to the question:
Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then n2 is the square of n.
What are the examples of square numbers?
The examples for square numbers are:
[tex]6^2[/tex] = 36
[tex]10^2[/tex] = 10 x 10 = 100
[tex]15^2[/tex] = 15 x 15 = 225
[tex]12^2[/tex] = 12 x 12 = 144
Hence, Yes, the square root of 64 is a rational number. As we know that √64 = 8, a rational number.
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Express the following ratio in it's simplest form: 60cm:1,2m
Answer:30:1
Step-by-step explanation:
60÷2
=30/1
=30:1
Do you want to go to the movie a ticket for a movie cot $10. 90 there’ a tudent dicount for 20% off the tax rate charged i 5. 75% what i the ale price?
Yes, I would like to purchase a ticket for the movie. The discounted sale price would be $8.37 after factoring in the 20percentage student discount and the 5.75% tax rate.
Original Price: $10.90
Student Discount: 20% of 10.90 = 2.18
Subtotal: 10.90 - 2.18 = 8.72
Tax Rate: 5.75% of 8.72 = 0.50
Final Sale Price: 8.72 + 0.50 = 8.37
Yes, I would like to purchase a ticket for the movie. The original price of the ticket is $10.90. As a student, I am eligible for a 20% discount, which when applied to the original price brings it down to $8.72. To calculate the final sale price, I then need to factor in the 5.75% tax rate. This is done by multiplying the subtotal of $8.72 by 0.0575, which gives me a tax amount of $0.50. When this amount is added to the subtotal, the final sale price becomes $8.37.
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In the diagram below, DE ¯¯¯¯¯¯¯∥ BC¯¯¯¯¯. Elena thinks length BC¯¯¯¯¯ is 16.5 units. Lin thinks the length of BC ¯¯¯¯¯¯is 17.1 units. Who do you agree with? Why? (2 points)
Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.
Whose are agree this ?The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,
[tex]$\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$[/tex]
[tex]$\mathrm{BC}^ 2=196-36=160$[/tex]
[tex]$\mathrm{BC}=12.649$[/tex] or [tex]$12.65$[/tex]
Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .
A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.
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Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ When I entered the last answer, it was incorrect.
The sum of the roots of the equation is
97/9
What are the roots of the equation?Generally, The roots of equation 3x^2 + 4x + 12 = 0 can be found by factoring or by using the quadratic formula.
By factoring: 3x^2 + 4x + 12 = 0 \Rightarrow (3x + 4)(x + 3) = 0$
Thus, the roots are
r = [tex]-\frac{4}{3}[/tex][tex]-\frac{4}{3}[/tex]
s = -3.
By using the quadratic formula:
[tex]r,s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\ = \frac{-4 \pm \sqrt{4^2 - 4(3)(12)}}{2(3)} \\\\= \frac{-4 \pm \sqrt{-48}}{6}\\\\ = -\frac{2}{3} \pm \frac{\sqrt{-3}}{3}i[/tex]
The sum of squares of roots is
r^2+s^2 =[tex](-\frac{4}{3})^2 + (-3)^2[/tex]
[tex]= \frac{16}{9} + 9\\\\ = \frac{16+81}{9}[/tex]
= [tex]\boxed{\frac{97}{9}}[/tex]
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What is the y value of the solution to the system of equations 3x 5y 17x 4y − 13?.
The y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.
In the given question, we have to solve the y-value of the solution to the system of equations.
3x + 5y = 1..................(1)
7x + 4y = -13...............(2)
Multiply equation 1 by 4 and equation 2 by 5, we get
12x + 20y = 4................(3)
35x + 20y = -65................(4)
Subtract equation 4 by 3, we get
23x = -69
Divide by 23 on both side, we get
x = -3
Now putting the value of x in the equation 1, we get
3(-3) + 5y = 1
-9 + 5y = 1
Add 9 on both side, we get
5y = 10
Divide by 5 on both side, we get
y = 2
Hence, the y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.
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The complete question is:
What is the y-value of the solution to the system of equations?
3x + 5y = 1; 7x + 4y = - 13
How do you write an absolute value equation to describe a graph?.
The general form for the absolute value equation to describe a graph is written as f(x) = a|x - h| + k .
The Absolute Value Function is defined as a function in algebra where the variable is inside the absolute value bars.
The general form for absolute value function is f(x) = a |x - h| + k and commonly used form of this function is f(x) = |x| .
Plot the graph of function f(x) = |x| whose formula can also be expressed as f(x) = x, if x ≥ 0 and -x, if x < 0.
Consider different points for x = -1 , y is 1 ,
for x = 1 , y is 1 .
On plotting we get the graph as shown below .
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(HELP QUICKLY PLEASE) Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $97.50. Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. Determine the price of each bag of popcorn and the price of each drink.
Each bag of popcorn costs $____
and each drink costs $_____
Answer:
Each bag of popcorn is $5.50Each bag of popcorn is $5.50 and the drink is $6.Step-by-step explanation:
Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:
9p + 8d = 97.50
Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:
5p + 4d = 51.50
where P = popcorn
d = drink
The equations will be:
9p + 8d = 97.50
5p + 4d = 51.50
Multiply equation i by 5
Multiply equation ii by 9
45p + 40d = 487.50
45p + 36d = 463.50
Subtract
4d = 24
Divide.
d = 24/4
d = 6
Drink = $6Since 9p + 8d = 97.50
9p + 8(6) = 97.50
9p + 48 = 97.50
9p = 97.50 - 48
p = $5.50
Popcorn cost $5.50.hope it helps<3where P = popcorn and d = drink
The equations will be:9p + 8d = 97.50 (multiply by 5)9 x 5 = 45p8 x 5 = 40d97.50 × 5 = 487.505p + 4d = 51.50 (multiply by 9)5 x 9 = 45p4 x 9 = 36d51.50 x 9 = 463.50THEN SUBTRACT45p + 40d = 487.5045p + 36d = 463.5045p - 45p = X40d - 36d = 4d487.50 - 463.50 = 244d = 24 ÷ 44 ÷ 4 = 1/d24 ÷ 4 = 6DRINK = $6Since 9p + 8d = 97.509p + 8(6) = 97.509p + 48 = 97.509p = 97.50 - 48.00POPCORN = $5.50The cost of the drink is $6 and each bag of popcorn is $5.50.
What are the 2 types of solution *?.
In mathematics, particularly in algebra, there are mainly two types of solutions for an equation: real and complex solutions.
Real solutions: These are type of solutions that are real numbers, which can be found by solving the equation algebraically. For example, if the equation is x² + 2x - 3 = 0, the real solutions are x = -1 and x = 3.
Complex solutions: These are solutions that are complex numbers, which can be found by solving the equation algebraically. Complex numbers are numbers that have both real and imaginary parts, represented by a + bi, where a and b are real numbers and i is the imaginary unit (i² = -1). For example, if the equation is x² + 1 = 0, the complex solutions are x = i and x = -i.
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If Jenny had one apple and she added another apple to the basket how many apples would she have
Answer:
2 apples
Step-by-step explanation:
It is because she had 1 apple then she added another which made it 2.
prove that:sinA/1-cosA-1=1/cosA
Answer:
Step-by-step explanation:
To prove that sinA/(1-cosA) = 1/cosA, we will start with the left-hand side and simplify it using trigonometric identities.
sinA/(1-cosA) = sinA/(1-cosA) * (sin^2A + cos^2A) / (sin^2A + cos^2A)
= (sinAsin^2A + sinAcos^2A) / (sin^2A + cos^2A - sin^2AcosA - cos^2AcosA)
= (sinAsinAcosA + sinAcosAcosA) / (sinAcosA - cosAcosA)
= sinA/cosA / (sinA/cosA - 1)
= 1/cosA
Therefore, sinA/(1-cosA) = 1/cosA, which is true.
If the top of a hill is 532 ft. above the bottom of a hill, and it is 7 miles
between the highest and lowest points, what is the gradient between them?
(round answer to the nearest tenth)
The answer will be 76, using a gradient.
What is the gradient of the slope?
A physical feature, landform, or manmade line's grade, also known as its slope, incline, gradient, rainfall, pitch, or rise, is the tangent of that surface's angle with respect to the horizontal.Since zero denotes horizontality, it is a specific case of the slope. Increased or steeper "tilt" is indicated by a greater number.The slope is frequently determined as a ratio of "rise" to "run" or as a fraction ("rise over run"), where the run is the horizontal distance (not the slope's length), and the rise is the vertical distance.To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.
The vertical distance is 532The horizontal distance is 7miles.532/7=76
Hence the answer is 76
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If you wanted to buy a 75 inch tv for your living room and the width is 43.25 inches, what is the height
The height of the TV would be 61.27 inches.
What is Pythagoras theorem?
The hypotenuse's square length is equal to the sum of the squares of the lengths of the other two sides of the right-angled triangle, according to the Pythagorean theorem, commonly known as the Pythagoras theorem.
Here, The 75 inches represents the length of diagonal of the TV because the length of TV is always measured diagonally. So, the diagonal's length is 75 inches.
We've width as 43.25 inches.
Since TV is of the shape of rectangle, we can calculate the height by applying Pythagoras theorem.
So, we've hypotenuse² = (side 1)² + (side 2)²
It can be written as,
diagonal² = height² + width²
(75)² = height² + (43.25)²
height² = (75)² - (43.25)²
= 5625 - 1870.5625
= 3754.4375
height = √3754.4375 = 61.27 inches.
Hence, height will be 61.27 inches.
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A quantity with an initial value of 1800 grows continuously at a rate of 0.7% per hour. What is the value of the quantity after 327 minutes, to the nearest hundredth?
the answers 1870
The value of exponential growth after 327 minutes is 1870.
What is exponential growth?Exponential growth is the process by which quantity increases over time. It occurs when a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself.
An exponential function depicts the relationship between an input and an output by using repeated multiplication on an initial value to obtain the output for any given input.
We are aware that
The exponential growth equation is equal to
y = a(1 + r)ˣ
where
an is the starting point.
r denotes the growth rate.
x represents the time in hours.
y is the quantity's value.
We now have
a = 1800
r = 0.7%
= 0.7/100
= 0.007
By substituting,
y = 1800(1 + 0.007)ˣ
x = 5.45 hr
y = 1800(1.007)^5.45
y = 1869.748182
y = 1870
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How do you spell sum in maths?.
Sum in math the sum of the series is computed using the summation formulas.
The sum of the series is computed using the summation formulas. There are many different kinds of sequences, including arithmetic and geometric sequences, and consequently, there are many different kinds of summing formulas for those different kinds of sequences.
There are also summation formulas that determine the sum of natural numbers, sum of natural number squares, sum of natural number cubes, sum of natural number evens, sum of natural number odds, etc. The list of summation formulas is provided here. Each of these formulas will be covered in detail in the section that follows.
a₁ + a₂ + a₃ +.......aₙ = Σ a
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Ytem of linear equation ha no olution. One of the equation of the ytem i hown. Y = 2 x − 1 y=2x−1 Which equation could be the other equation of the ytem?
The other equation of the system of linear equation that has no solution is y = 2x - 2.
If a system of linear equations has no solution, it means that the equations are inconsistent, which means that the two lines represented by the equations will not intersect. Therefore, the lines are parallel with each other.
One way to find the equation of the other line that would make the system inconsistent is to find the equation of a line that is parallel to the given equation but has a different y-intercept.
The given equation is in slope-intercept form, y = mx + b, where m is the slope (in this case, m = 2) and b is the y-intercept (in this case, b = -1).
A line that is parallel to the given line will have the same slope (m = 2), but a different y-intercept. For example, a line with y-intercept of -2: y = 2x - 2.
So, one equation that could be the other equation of the system and make it inconsistent is y = 2x - 2.
The problem seems incomplete, it must have been...
"A system of linear equation has no solution. One of the equations of the system is shown. y = 2x − 1 Which equation could be the other equation of the system?"
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PLEASE PLEASE PLEASE HELP ~ URGENT WILL MARK BRAINLIEST
Can someone please help me find my y - intercept for this scatter plot?
THANM YOU SO MUCH!!
Answer:
11,000 or to be more specific $11,000
Step-by-step explanation:
Well there is no equation provided so one has to go by the graph
The y-intercept is where the line intersects the y-axis
Looking at the graph we see this is at y ≅ 11,000
Of course it all depends on your best fit line that you have drawn though it looks OK
Basically the y-intercept for this graph is $11,000 which is the cost of the Prius in 2004
Angel check out 12 library book and Inola check out 1/3 le than that. How many doe Inola check out?
Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.
What is algebraic equation ?
An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.
Let x be the number of books that Inola check out
We know that:
Angel checks out 12 books
Inola checks out 1/3 less than Angel
We can set up the equation:
x = 12 - (1/3*12)
x = 12 - 4
x = 8
So, Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.
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Angel checks out 12 books
Inola checks out 1/3 less than Angel
We can set up the equation:
x = 12 - (1/3*12)
x = 12 - 4
x = 8
What is the relationship of the degree of a quadratic equation to the number of its solution?.
The relationship of the degree x - [[- b+v(b2 - 4ac)V2a] = 0 describes the relationship between a quadratic equation's factors and its solutions. A quadratic equation's general equation is f(x) = ax*+ bx +. function:
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and respectively.
expression: Terms (constants and variables) are separated by mathematical operators to form a mathematical expression. equation: Two expressions are equated using a mathematical equation. The quadratic equation f(x) = axe + bx + c is given.
The quadratic equation (ax2 + bx + c= 0) can be expressed as a product of its linear factors as (x - k)(x - h), where h, k are the quadratic equation's roots. This process is known as factoring a quadratic equation.
We may write [h] =- b + v(b2 - 4ac)y2a [K]=(-b- V(b2 - 4ac))/2a using the quadratic formula. The link between the elements of a quadratic equation and its solutions can be expressed as - x- [[-b+v(b- 4ac)y2a] =0
X=[(b' - 4AC)y2A] = 0.
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A rectangle has an area of 209 square yards and a height of 19 yards. What is the length of the base?
The length of the base of the rectangle is B = 11 yards
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the value of A is
Let the base of the rectangle be represented as B
Area of rectangle A = 209 yards²
The length of the rectangle L = 19 yards
And , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = 19 x B
209 = 19 B
Divide by 19 on both sides of the equation , we get
B = 209 / 19
B = 11 yards
Hence , the length of the base of rectangle is 11 yards
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How do you determine whether a number is rational or irrational?.
If the number can be expressed in the form of the fraction [tex]\frac{p}{q}[/tex] , then the number is called as Rational Number otherwise it is called as irrational number .
The Rational Numbers are the type of numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where p and q both are integers , and the denominator q should not be equal to 0 .
For Example : the numbers 5 , 2/3 , 6 are rational numbers .
The Irrational Numbers are defined as the type of real numbers which cannot be represented as simple fractions. The Irrational number cannot be expressed as a ratio .
For Example : [tex]\sqrt{2}[/tex] , [tex]\sqrt{5}[/tex] cannot be expressed as a fraction of integers , so they are irrational .
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What is a solution set in math?.
The set of values that satisfy a given set of equations or inequalities is known as a solution set in mathematics.
The solution set, for instance, is the subset of a set of polynomials over a ring on which all of the polynomials formal disappear (evaluate to 0).
How is a solution set obtained?Plug in each value from the replacement set and evaluate both sides of the equation to determine the solution set from the replacement set. The value is a solution to the equation if the two sides are equal. One example: From the replacement set, choose the set with the solution 11 - 5w = 1.
What is a set of kids' solutions?The set of values that satisfy a given inequality is called a solution set. This indicates that the inequality will be satisfied by every value in the solution set and by no other value. Example: 2x + 3 7, where x is a natural number, is the solution.
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5x² + 10x + 2 in the form p(x +q)² + r,
5([tex]x^{2}[/tex] + 10/2[tex]x[/tex]) + 2
The number in the brackets is b/2a.
So:
5(x + 10/2(5))^2
5(x + 10/10)^2
5(x + 1)^2
Expand the double brackets for (x + 1)^2:
[tex]x^{2}[/tex] + [tex]x[/tex] + [tex]x[/tex] + 1
This simplifies to:
[tex]x^2[/tex] + 2[tex]x[/tex] + 1
5([tex]x^2[/tex] + 2[tex]x[/tex] + 1)
5x^2 + 10x + 5
2 - 5 = -3
5(x + 1)^2 - 3
Answer:
5(x + 1)^2 - 3
