The factors of equation, x²- 9x + 18 = 0 are (x- 3)(x- 6), where x is variable.
Factorization is a mathematical process that is applied to split a number, an expression, matrix etc. into the product of factors such that when we multiplied these factors again we get the original one. We have, an equation is x² - 9x + 18 = 0 --(*) and we have to factorize it. Steps to factorize the quadratic equation, ax² + bx + c = 0, are :
Splitting the middle term, b such that the product of splitting terms is ac and sum or difference is b. grouping the terms factors of each groupNow, comparing the equation (*) with standard equation we get, a = 1 , b = -9 , c = 18.
So, Split the number 9, into 6 and 3
=> x² - 9x + 18
=> x² - 6x - 3x + 18
=> (x² - 6x) - (3x - 18) [ grouping]
=> x( x - 6) - 3( x-6) [ factors of group ]
=> (x- 3)(x- 6)
so, x² - 9x + 18 = (x- 3)(x- 6) = 0 helps to get the solution of it (x- 3)(x- 6) = 0 => x = 6,3
Hence, the required factors are (x- 3)(x- 6).
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Complete question:
What is the factor of x² - 9x + 18 = 0?.
What is the simplest way of remembering the first three trigonometric ratios?.
You may quickly determine the fundamental trigonometric numbers of the most typical angles by utilizing a trigonometry table or the SOHCAHTOA approach.
Make a new table for trigonometry. Create a table with six rows and six columns. Put the trigonometric ratios in the first column (sine, cosine, tangent, cosecant, secant, and cotangent). Write the usual trigonometric angles (0°, 30°, 45°, 60°, and 90°) in the first column. Leave all of the other table entries blank.
the three basic trig ratios that are used to solve for missing sides and angles in a right triangle. It is defined as follows: SOH: Opposite / Hypotenuse = Sin().
Fill the sine, cosine, and tan values in the appropriate columns.
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Therefore , light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.
Equation: What is it?In a mathematical formula, the equal symbol (=) is used to denote that the statements are equivalent. It is demonstrated that many quantitative variables are comparable using mathematical equations, which are statements of reality. The equal sign, for instance, separates the numbers 12 and b + 6 into 2 halves within the equation y + 6 = 12. It is possible to calculate how many expression words each edge of a symbol represents. The meaning of a symbol usually contradicts itself.
Here,
It is important to understand that the function Corey wrote is:
=>y = (x + 8)(x - 2) (x - 2)
=> y = x² - 2x + 8x - 16
=> y = x² + 6x - 16
Kimberly spelled out y = x + 6x - 16
Joshua spelled out (x + 3)² - 25.
=> (x + 3)(x + 3) - 25
=> x² + 3x + 3x + 9 - 25
=> x² + 6x - 16
In light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.
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*Convert the following statements into equations.*
(a) 3 added to a number is 11
b
(b) 2 subtracted from a number is equal to 15.
(c) 3 times a number decreased by 2 is 4. (d) 2 times the sum of the number x and 7 is 13.
Answer:
Step-by-step explanation:
Answer:
(a) x + 3 = 11
(b) x - 2 = 15
(c) 3x -2 = 4
(d) 2(x-7) = 13
Step-by-step explanation:
Given:(a) 3 added to a number is 11
(b) 2 subtracted from a number is equal to 15.
(c) 3 times a number decreased by 2 is 4.
(d) 2 times the sum of the number x and 7 is 13.
Solve:(a) 3 added to a number is 11
Answer : x + 3 = 11
Base on the given it states that 3 added to a number is 11. A number is identified as x. Hence, a number added 3 equal 11.
Hence, x + 3 = 11 is the equation.
(b) 2 subtracted from a number is equal to 15.
Answer : x - 2 = 15
Base on the given 2 subtracted from a number is equal to 15. As known, a number is identified as x. Equal to 15 = Total. Hence, x - 2 = 15.
(c) 3 times a number decreased by 2 is 4.
Answer : 3x - 2 = 4
Base on the given 3 times a number decreased by 2 is 4. As known, a number is identified as x. 3 times is identified as times 3. And decreased is identified as subtract. Hence, 3x-2 = 4 is the equation.
(d) 2 times the sum of the number x and 7 is 13.
Answer : 2( x + 7 ) = 13.
Base on the given 2 times the sum of the number x and 7 is 13. As known, a number is identified as x. 13 is the total. 2 times equals multiply 2. Sum of the number x and 7 meaning is Addition. Sum = Addition. Hence, 2(x+7)=13 is the equation.
RevyBreeze
How do you write 149600000000 in standard form?.
To write 149600000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point. 149600000000 in standard form would be written as 1.496 x 10^11.
To arrive at this form, we move the decimal point 11 places to the left (since there are 11 zeros in 149600000000) and add the power of 10 notation, indicating that we moved the decimal point 11 places to the left. The number 1.496 is the coefficient and 11 is the exponent. This way, we get 1.496 x 10^11 which is the standard form of 149600000000.
Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10
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10007 in the expanded form.
Answer:
10,007
Ten thousand seven
Step-by-step explanation:
Akio draws a graph to record the distance he rides on a long bike ride. What is the slope of the line for the first two hours? What is the slope of the line for all five hours? What does the slope mean in this situation?
Answer:
Below
Step-by-step explanation:
To find the slope of a line, we use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
In this case, if Akio recorded the distance he rode on his bike ride in hours, the slope of the line for the first two hours would be the change in the y-coordinates (distance) divided by the change in the x-coordinates (time) between those two points.
To find the slope of the line for all five hours, we will need to know the specific coordinates of all five points, otherwise, it's impossible to calculate the slope.
The slope of a line represents the rate of change in the y-coordinates (distance) per unit of change in the x-coordinates (time). In this situation, the slope represents Akio's speed, since the change in distance is divided by the change in time. A positive slope indicates an increase in distance over time, which means Akio is getting faster, whereas a negative slope indicates a decrease in distance over time, which means Akio is getting slower.
It's worth noting that a slope of zero would mean that there is no change in distance over time, which would mean that Akio isn't moving.
What does a square have in common with a rectangle?
Each squares and rectangles are a form of quadrilateral, with four inner angles that are both 90 degrees, and opposite sides that are parallel to one another.
Are a square and a rectangle usually similar?
As a result, every square is a rectangle since it is a quadrilateral with right angles at each of its four corners. But not all rectangles are squares; for a shape to be a square, all of its sides must be the same length.
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
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Are 1 4 and 2 8 equivalent fractions?.
Yes, 1/4 and 2/8 equivalent fractions.
Mathematical fractions that have the same denominator but different numerators are called equivalent fractions. As an illustration, since 2/4 and 3/6 both equal 1, they are both comparable fractions. The total is divided into fractions. When referring to identical components of the total, equivalent fractions are utilized.
By multiplying the numerator and denominator by the same integer, it is possible to determine the equivalent fraction of each fraction. In spite of differences in appearance, equivalent fractions signify the same value. For instance, if you take one piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.
= 1/4 = 2/8
= 1/4 = 1/4
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Correct Question:
Are 1/4 and 2/8 equivalent fractions?.
What i the total cot of 1. 8 cubic yard of oil if it ell for $17 per cubic yard ?
The total cost of 1.8 cubic yards of oil at $17 per cubic yard would be $30.6.
Cost of Oil CalculationThis can be calculated by multiplying the number of cubic yards (1.8) by the cost per cubic yard ($17).
1.8 × 17 = $30.6
The calculation I provided is a basic mathematical concept of multiplying a quantity (1.8 cubic yards) by a unit price ($17 per cubic yard) to find the total cost. This is a fundamental concept in mathematics, specifically in the field of arithmetic, which deals with the manipulation of numbers and basic mathematical operations such as addition, subtraction, multiplication, and division.
Arithmetic is a branch of mathematics that deals with the manipulation of numbers and basic mathematical operations such as addition, subtraction, multiplication, and division. The formula 1.8 cubic yards x $17 per cubic yard = $30.6 is an example of multiplying a quantity by a unit price which is an arithmetic operation. This operation is used to find the total cost of a specific quantity of a product or material that is sold by volume.
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Paulo's pizzeria sells personal pizzas that start at $7 for plain cheese. The pizzeria also offers a variety of toppings, all priced at $1 each. Write an equation that shows how the price of a personal pizza, y, depends on the number of toppings, x.
The equation that shows how the price of a personal pizza y depends on the number of toppings x is y = 7 + x.
The equation of a straight line is an equation that comes in the form of an algebraic equation. It is also referred to as Slope - Intercept form. It can be represented using the equation below:
Equation : y = mx + c
where:
m = Gradient
c = Slope of the line
The equation that shows how the price of a personal pizza y, depends on the number of toppings x is y = 7 + x
This question can be solved and represented using the equation of a straight line.
Let's represent
y = price of a personal pizza
x = number of toppings
The price for a plain cheese pizza = $7
The price for each of the toppings = $1
Therefore, the equation that shows how the price of a personal pizza y, depends on the number of toppings x is written as:
y = $7 + $1 × x
y = 7 + x
Therefore, y = 7 + x is the equation represents the relationship between the price of a personal pizza and the amount of toppings.
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How will a graphing calculator help a student understand mathematics better?.
The study comes to the additional conclusion that both interventions—traditional methods of instruction and the use of graphing calculators—improve students' abilities to compute mathematically.
Typically, graphing calculators are used by high school students or students in higher classes. In addition, if you are enrolled in one of these levels, you are already familiar with the higher-levelJust by looking at a few numerical characters, mathematical puzzles can become complex, and not all books have the answers to all of those puzzles. However, using a graphing calculator will allow you to avoid this circumstance. When taking a math test, one problem we frequently experience is not knowing whether the response is right or wrong. because even a small mistake can change the entire result. For that to be known, the data and graphical lines must match precisely.To learn more about graphing calculators here
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Compare the following sets of data for June 2006 and June 2005.
Canadian Housing Prices by City ($)
June 2006
June 2005
Canadian City
Vancouver
Victoria
Calgary
Edmonton
Regina
Saskatoon
Ottawa
Toronto
Montreal
Fredericton
Saint John
Halifax
Sources: MLS and Remax
Mean:
1. Find the measures of central tendency for each. State any conclusions found.
Median:
Mode:
508 435
538 913
367 033
254 240
137 022
160 548
260 458
358 035
222 879
136 371
127 586
201 316
Conclusions:
June 2006
June 2006
422 843
469 588
245 803
199 409
132 054
139 728
254 725
345 065
210 740
134 334
125 455
184 853
June 2006
June 2005
June 2005
June 2005
The Mean for June 2006 and 2005 is $345,909 and $335,977 respectively. The median for June 2006 and 2005 is $254,000 and $139,000 respectively, there's no mode in this question.
Explain mean, median, mode briefly?In statistics, the mean, mode, and median are three measures of central tendency that describe a set of numerical data.
The mean is the average of a set of numbers, calculated by adding up all the values and dividing by the number of values. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the mean is (1 + 2 + 3 + 4 + 5) / 5 = 3.
The mode is the value that appears most frequently in a set of data. For example, if a set of data contains the values {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4, because it appears three times, which is more than any other value.
The median is the middle value in a set of data when it is ordered in ascending or descending order. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the median is 3, because it is the middle value. If there is an even number of values, then the median is the average of the two middle values.
It is important to note that different sets of data may have different measures of central tendency, and sometimes none of these measures may be appropriate.
Measures of central tendency are used to summarize and describe a set of data. The most common measures of central tendency are the mean, median, and mode.
1. Mean:
• Mean for June 2006: (508+435+538+913+367+033+254+240+137+022+160+548+260+458+358+035+222+879+136+371+127+586+201+316)/22 = $345,909
• Mean for June 2005: (422+843+469+588+245+803+199+409+132+054+139+728+254+725+345+065+210+740+134+334+125+455+184+853)/22 = $335,977
2. Median:
• Median for June 2006: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $254,000
• Median for June 2005: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $139,000
3. Mode:
• Mode for June 2006: There is no mode, because no value is repeated.
• Mode for June 2005: There is no mode, because no value is repeated.
Conclusions:
• The mean housing price in June 2006 is higher than the mean housing price in June
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To rent a certain meeting room, a college charges a reservation fee of $41 and an additional fee of $7.30 per hour. The history club wants to spend less than $92.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use for the number of hours the meeting room is rented, and solve your inequality for .
Answer:
Step-by-step explanation:
first we subtract 92.1 from 41 which gives us 51.1 now we want to see how many hours we can keep the room for while staying under 91.1 so we divide the value of 51.1(as we have to first pay the fee of $41) by 7.3 as that is the amount they are charging per hour(51.1/7.3) which gives us 7 so we can rent the roof for 7 hours max or just for 1,2,3,4,5 or 6 hours
to the nearest tenth
[tex] \sqrt{50} [/tex]
The rounded number to the nearest tenth is 7.1
How to round to the nearest tenth?
Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. The tenth place value should remain unchanged if it is less than 5, but all subsequent numbers should be eliminated.
√50 = 7.071
hundredth number is 7 greater than 5
Add one to the tenth value if the number is more than 5
all subsequent numbers should be eliminated.
Thus, the rounded number to the nearest tenth is 7.1
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How many symmetrical lines do they have? (a).[ (b) (c)
To the nearest whole degree, what is the measure of Q?
O 44°
O 49⁰
O 54⁰
O 59⁰
Answer: believe it's 49 degrees
Step-by-step explanation:
Is 4 a real number?.
Yes. 4 is a real number. Real numbers includes both rational number and irrational numbers.
Every Real numbers can be expressed as an infinite decimal expansion. It include integers, natural numbers. Real numbers can be of positive and can be of negative numbers. Real numbers can be both a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. Irrational numbers are the type of real numbers. The real numbers has the closure property, commutative property, the associative property and the distributive property. This explains the properties of Real numbers.
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Calculate the average speed of a train that travels 500km in 4 hours
Answer:
125 km per hour
Step-by-step explanation:
divide 500 by 4 to find the averge
Answer:
[tex] \sf \: 125km/hr[/tex]
Step-by-step explanation:
Average speed = [tex] \sf \: \frac{distance \: travelled}{time \: taken} [/tex]
Ave. speed = [tex] \sf \frac{500km}{4hr} = 125kmhr {}^{ - 1} [/tex]
Hence, the average spred is 125km/h respectively.
In ΔABC, c = 75 cm, mm∠B=154° and mm∠C=13°. Find the length of a, to the nearest 10th of a centimeter.
The length of a, to the nearest 10th of a centimeter is 18.6 cm.
Give a short note on triangle?A triangle is a three-sided polygon that is defined by three points in a plane, called its vertices. The three sides of a triangle are also called edges, and are connected by three angles. The sum of the angles in a triangle is always 180 degrees. There are different types of triangles, including:
Right triangle: has one angle of 90 degrees.Acute triangle: all three angles are less than 90 degrees.Obtuse triangle: has one angle greater than 90 degrees.Isosceles triangle: has two sides of the same length.Equilateral triangle: has three sides of the same length.Triangles are fundamental in mathematics and are used in many areas such as geometry, trigonometry, and engineering.
In a triangle, the measure of an angle is related to the lengths of the sides opposite and adjacent to it by the formula:
c = a/sin C
Given that c = 75 cm and mm∠C = 13°, we can use this formula to find the length of a:
a = c*sin C
where C is in radians.
a = 75 * sin(13°) = 75 * 0.2225 = 16.7 cm
Also, we know that the sum of the angles in a triangle is always 180°, so we can use that information to find the measure of angle A.
mm∠A = 180 - (mm∠B + mm∠C) = 180 - (154 + 13) = 180 - 167 = 13°
Therefore, using the Law of Sines, we can find the value of a.
[tex]\frac{a}{sin A}[/tex] = [tex]\frac{b}{sin B}[/tex] = [tex]\frac{c}{sin C}[/tex]
a = [tex]\frac{c*sin A}{sin C}[/tex]
a = [tex]\frac{75*sin(13^{0}) }{sin(154^{0}) }[/tex]
Now, you can use a calculator or a table of trigonometric values to find sin(13°) and sin(154°) and substitute them in the above equation to find the length of a. To the nearest tenth of a centimeter, a is approximately 18.6 cm.
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Is a triangle 180 or 360?.
Answer:
180° are triangles 360° are circles
Step-by-step explanation:
How to graph piecewise functions
Step by step
Please help, been stuck on thus question for 2 days
Answer:
see attached
Step-by-step explanation:
You want to graph the piecewise defined function ...
f(x) = 2x+9 for x < -3; 2x-2 for x > 4
GraphYou normally graph a line by finding (at least) two points on the line and drawing a line through them to make the graph. Often, it is convenient to start with the y-intercept. Here, it is convenient to start with the end point of the domain on which the line is defined. Additional points can be found by making use of the slope: rise 2 for each run of 1 to the right.
For x < -3, the value of y at x=-3 is ...
y = 2(-3) +9 = 3
So, the point (-3, 3) will appear on the graph. This point is not actually in the domain, which is x < -3, so will be graphed as an open circle. The line goes down and to the left from there with a slope of 2.
For x > 4, the value of y at x=4 is ...
y = 2(4) -2 = 6
So, the point (4, 6) will appear on the graph as an open circle, because x=4 is not actually in the domain of the function. The line will go up to the right from there with a slope of 2.
See the attachment for a finished graph.
How do you explain division to a 7 year old?.
Answer:
Step-by-step explanation:
Give them a fixed number of beads, and tell them to divide them equally between a certain number of tins. Start with showing the child how to divide the beads into two tins, using different numbers of beads each time, then gradually move to dividing by different numbers.
Rachel jut old her home and paid $18,427 in cloing cot. Her brokerage fee, which i included in that figure, wa 6%. She netted $230,063. What were her non-brokerage fee-related cloing cot? Round to the nearet dollar
Rachel's non-brokerage fee-related closing costs can be calculated by subtracting the brokerage fee from her total closing costs.
Since the brokerage fee was 6%, the fee comes out to be $1,105.20. To calculate the non-brokerage-related closing costs, subtract $1,105.20 from the total closing costs of $18,427, which yields a total of $17,321.80.
18427-1105.20=17321.80
This is the amount of non-brokerage fee-related closing costs that Rachel paid for her home. Rachel's net gain from the sale of her home was $230,063, which is the difference between the sale price of her home and the total closing costs, including the brokerage fee.
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STOP GIVING ME FALSE ANSWER , AND PLEASE HURRY! THIS IS A TEST!
Help Please, Also give steps.
The altitude of the right triangle is as follows:
BD = √330 units
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
ΔABC is a right angle triangle with altitude BD drawn to the hypotenuse AC. Therefore,
AD = 15 units
DC = 22 units
The length of BD in the simplest form can be found as follows:
Using similar triangle,
Hence,
let
BD = x
15 / x = x / 22
cross multiply
x² = 22 × 15
x² = 330
x = √330
Therefore,
BD = √330 units
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what the square root of 25
Answer:
Step-by-step explanation:
It's obvious 5x5=25
Therefore, the square root of 25 is 5.
A long year-end status report for work is 125 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.66 each.
Answer:
$18.30
Step-by-step explanation:
125 x 18 = 2250
2250/500 = 4.5 (round up to 5)
5 x 3.66 = $18.30
What is a triangle with 3 60 degree angles called?.
Answer: acute triangle
Step-by-step explanation: acute triangle are also known as equilateral triangle, meaning all sides are equal. This also makes it equiangular (angle measurement are 60 degrees). Remember triangle ALWAYS add up to 180 degrees.
How do you satisfy an equation?.
To satisfied the solution of an equation after substituting the value of the variable left hand side value should equals to right hand side value.
As given in the question,
To satisfied the solution of the given equation we need to follow the following steps :
After simplifying the equation get the value of variable.Now. substitute the value of the variable in the left hand side .The value of the left hand side after calculation should be equal to right hand side.If left hand side equals to right hand side the solution satisfied the given equation.Therefore, to satisfied the solution of the given equation left hand side value should be equal to right hand side.
The above question is incomplete , the complete question is :
How do you satisfy the solution of an equation?
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Is the inverse of a square root function a quadratic function?.
The inverse of a square root function looks like a half parabola which resembles the shape same as that of a quadratic function graph but we can not be certain about it.
Square root function graphs are usually curved. The curve above is, in reality, half of a parabola that is laying on its side. It represents half of the parabola that would result from graphing the equation y² = x.
f(x) = ax² + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
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