The product of the sum and difference of two terms can be found using the distributive property and the FOIL (First, Outer, Inner, Last) method.If you have two terms, A and B, the sum and the difference of these terms can be represented as:
Sum: A + B Difference: A - B
To find the product of the sum and difference, you can multiply the sum and the difference together:
(A + B)(A - B)
Using the distributive property, we can expand the product:
AA - AB + AB - BB
Which is equal to:
A^2 - B^2
This is the difference of squares of the terms.
It's worth noting that this is a very common pattern in algebra, and it's called the difference of squares. It is the product of the sum and difference of two terms. The distributive property and FOIL method can be used to expand the product of two binomials, but it's important to recognize patterns, like this one to solve the problem in a faster way.
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Given a polynomial and one of its factors, find the remaining factors of the polynomial.
x^3-9x^2+27x-27; x-3
Answer:
(x-3)^3
Step-by-step explanation:
[tex]= x^3-9x^2+27x-27 \\ =(x − 3) (x² + 3x + 9) − 9x (x - 3) \\ =(x − 3) · (x² + 3x + 9 − 9x) \\ =(x-3)·(x²-6x+9) \\ =(x − 3) · (x − 3)^2 \\ = {(x - 3)}^{3} [/tex]
Or Apply cube of difference rule
[tex]{x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} [/tex]
Answer:
[tex](x-3)^3[/tex]
Step-by-step explanation:
Given polynomial:
[tex]x^3-9x^2+27x-27[/tex]
Given (x - 3) is a factor of the polynomial, divide the polynomial by the factor using long division to find the other factor:
[tex]\large \begin{array}{r}x^2-6x+9\phantom{)}\\x-3{\overline{\smash{\big)}\,x^3-9x^2+27x-27\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-3x^2)\phantom{-b0000000)}}\\-6x^2+27x-27\phantom{)}\\-~\phantom{()}\underline{(-6x^2+18x)\phantom{0000.}}\\9x-27\phantom{)}\\-~\phantom{()}\underline{(9x-27)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore:
[tex]x^3-9x^2+27x-27=(x-3)(x^2-6x+9)[/tex]
Factor (x² - 6x + 9):
[tex]\implies x^2-6x+9[/tex]
[tex]\implies x^2-3x-3x+9[/tex]
[tex]\implies x(x-3)-3(x-3)[/tex]
[tex]\implies (x-3)(x-3)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies x^3-9x^2+27x-27=(x-3)(x-3)(x-3)[/tex]
[tex]\implies x^3-9x^2+27x-27=(x-3)^3[/tex]
Which number line shows |x - 21| < 3
The line showing this inequality is B.
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality, |x - 21| < 3
Solving, the inequality,
|x - 21| < 3
x-21 < 3 and x-21 > -3
x < 24 and x > 18
Since, we get 18 < x < 24,
Hence, the line showing this inequality is B.
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(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and
(
−
6
,
−
3
)
(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions on either side of an equals sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates, we get m = (7 - (-3))/(-9 - (-6)) = 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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Complete Question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is the equation?A mathematical statement that expresses the equivalence of two expressions is known as an equation. It typically consists of two expressions on either side of an equal sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7), and (-6,-3)(−6,−3) can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y₂ - y₁)/(x₂ - x₁). Plugging in the coordinates, we get
m = (7 - (-3))/(-9 - (-6))
= 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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The complete question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
How do you find the height of a 45 45 90 triangle?.
The height of a right triangle can be calculated, given the length of the base, and the height of a right triangle formula can be calculated using the Pythagoras theorem as, (Hypotenuse)² = (Height)² + (Base)².
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Find the missing length.
ADEF~AVUT
D
140
37
50
U
E
60
168
T
F
DELL
Is a triangle always 360 degrees?.
A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.
No, a triangle is not always 360 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.
This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.
For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).
Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.
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Adam is traveling from NY to Washington, a distance of 450 miles. If his car averages 15 miles per gallon, what is the cost of his trip from NY to Washington and back if gasoline costs 50 cents per
gallon?
Step-by-step explanation:
15 miles consume 1 gallon
450 miles consume 450÷15 = 30 gallon per a way
For round trip, it will consume 30*2=60 galloon
1 gallon costs 50 cents
30 galloon costs 30*50=1500 cents per a way
For round trip, 1500*2=3000 cents
Nate has $50 to go spend at the grocery store. He feels shopping cart with items total and $46. I’ll check out he will have to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart?
Nate have enough money to buy everything in his cart because his total expenses is lees than 50 dollars.
How to check if his money is enough to buy the grocery using the sales tax?Nate has $50 to go spend at the grocery store. He fills his shopping cart with items total and $46. He will have to pay a sales tax of 6% on al items on the cart.
Therefore, let's check if Nate have enough money to buy the groceries.
Hence,
sales tax amount = 6% of 46
sales tax amount = 6 / 100 × 46
sales tax amount = 276 / 100
sales tax amount = 2.76 dollars
Therefore,
the amount in total of the grocery = 46 + 2.76 = 48.76 dollars
Therefore, he has enough money to pay for his groceries.
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What is meant by a substitution reaction give an example with equation of the substitution reaction of an alkene?.
A substitution reaction is one in which one (or more) hydrogen atoms from a hydrocarbon are swapped out for another atom (like chlorine).
Example: Substitution reaction of methane with chlorine:
Methane reacts with chlorine in the presence of sunlight to form chloromethane and hydrogen chloride.
[tex]CH_{4} + Cl_{2}[/tex] ---------> [tex]CH_{3} Cl + HCl[/tex]
When one functional group in a chemical molecule is replaced by another functional group, the chemical reaction is known as a substitution reaction. In organic chemistry, substitution reactions are of utmost significance.
An alkene is a hydrocarbon with a carbon-carbon double bond in organic chemistry. Alkene, which refers to any hydrocarbon with one or more double bonds, is frequently used as a synonym for olefin.
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Workout the maximum number of hiker who could have walked between 6 mile and 17 mile
The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 and the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
The minimum number refers to the smallest value that is possible, allowed, or required based on the given interval. The maximum number refers to the largest value that is possible, allowed, or required based on given interval. The provided table provides intervals for the number of miles x the number of hikers can walk and the corresponding number of hikers.
In order to determine the minimum and maximum number of hikers that could walk between 6 miles and 17 miles, we look at the intervals which include the range between 6 miles and 17 miles.
a) The minimum value is determined by considering the common interval 10 ≤ x < 15 (5 ≤ x < 10 and 15 ≤ x < 20 are not considered as it includes values outside the range). Hence the corresponding number of hikers is 9.
b) The maximum value is determined by considering all the intervals which include the range between 6 miles and 17 miles, i.e. 5 ≤ x < 10, 10 ≤ x < 15, 15 ≤ x < 20. Hence, the maximum number of hikers is 2 + 9 + 8 = 19.
Note: The question is incomplete. The complete question probably is: The table below shows information about the distance walked by some hikers. a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.
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Solve x2 + 2 = 6 by graphing the related function.
A) 2
B) there are two solutions +v8
C) no real number solutions
D) +2
The solutions of the given equation are 2 or -2
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x²+2 = 6
x²+2 = 6
Solving we get,
x²+2 = 6
x² = 6-2
x² = 4
x = ±2
Hence, there are two solutions of the equation 2 or -2
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Which equation goes through the point (-6,2) and is perpendicular to y=3x-8
A. Y - 2 = 1/3 (x+6)
B. Y = 3x - 5
C. Y - 2 = -1/3 (x + 6)
D. Y = -3x + 6
Correct option is C, the correct equation is Y - 2 = -1/3 (x + 6).
Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation. Y = m x + b y=mx+b y=mx+by, equals, m, x, plus, b, where m is the slope and b is the y-intercept, is the slope intercept form.
Given points are (-6,2)
The required line should be perpendicular to y=3x-8.
When two lines are perpendicular,
their slopes are such that,
m1 = - 1/m2 [1]
⇒ slope of line 2 =
⇒ -1/3 [using (1) relationship ]
Now substituting the points are slope in the equation of line -
y - y₀ = m (x - x₀)
⇒ y - 2 = -1/3 (x + 6)
⇒ 3y - 6 = -x - 6
⇒ 3y + x = 0
⇒ x = -3y
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What is the difference between a frequency histogram and a relative frequency histogram?
The vertical axis of a relative frequency histogram employs relative or proportional frequency rather than plain frequency, which is the only difference between it and a frequency histogram.
Explain the difference between frequency and relative frequency?Frequency can be expressed most simply in absolute terms. The number of times a specific value for a variable (data item) has been seen to occur in relation to the overall number of values for that variable is referred to as the relative frequency.Histogram is a term from the quality glossary. The frequency distribution of a collection of data reveals how frequently each unique value appears. The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.Relative frequencies, on the other hand, do not employ raw counts. Instead, they use percentages, proportions, or fractions to compare the count for one type of event to the entire number of events. The word "relative" refers to a specific tally in relation to the overall number, which is where it is used.Learn more about frequency histogram refer to :
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Assignment Simplity [8q² -2 [q²-2 (3q²-3q+5)
The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5) is 18q² −12q + 20.
What is simplified from?Reduce a fraction to its simplest form to simplify it. A fraction is said to be in its simplest form if both its numerator and denominator only contain the number one. As we attempt to solve fractional problems, the process of simplifying difficulties is crucial. Even after we simplify them, the fraction's value will not change. This shows that the true fraction and the simplified fraction are two equivalent fractions.
Lets Simplify
= [8q² -2 [q²-2 (3q²-3q+5)
= [8q² -2(q²−6q² +6q−10)
= 8q² + 10q² −12q + 20
= 18q² −12q + 20
Thus, The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5) is 18q² −12q + 20.
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A giant balloon i dropped from a plane landing on tahir and zach at point w(42,-15) and ending two friend flying off an equal ditance in oppoite direction. Of tahir end up at coordinate t(-18,36) where would we expect to find zack
Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
What is coordinate ?
A coordinate is a set of numerical values that are used to identify the position of a point in a specific space, such as a two-dimensional plane or a three-dimensional space. In two-dimensional space, coordinates are commonly represented by an ordered pair (x, y) or (x, y, z) in three-dimensional space.
The problem states that the balloon lands at point W(42,-15) and Tahir ends up at point T(-18,36). We know that Tahir and Zack are flying off in opposite directions from point W at equal distances. To find the point where Zack is expected to land, we can use the midpoint formula which states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates.
We can find the midpoint of line segment WT by taking the average of the x-coordinates and y-coordinates:
x_midpoint = (x1 + x2) / 2 = (42 + -18) / 2 = 12
y_midpoint = (y1 + y2) / 2 = (-15 + 36) / 2 = 10.5
So the midpoint of line segment WT is (12,10.5). Since Zack is flying off in the opposite direction from Tahir at the same distance, we can expect Zack to end up at the point which is the reflection of point T over the midpoint of line segment WT.
This point would be (-12,-10.5)
Therefore , Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
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Select the number below that is irrational.
O 5462.263
O √19
O 13/24
O 3.33333
The number that is irrational is √19.
An irrational number is a number that cannot be expressed as a ratio of two integers (a fraction) and it cannot be represented as a repeating or terminating decimal. The square root of 19 is an irrational number because it cannot be expressed as a ratio of two integers. It is non-repeating, non-terminating decimal that goes on forever, so it cannot be represented as a decimal.
The marked price of a car i $49500 a peron can pay a depoit of 30% and imple interet at 12% per annum i charged on the outtanding balance. The total amount payable i to be paid in 2 1/2 year. Calculate the amount of each intallment
Each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.
given simple interest is 30%
Installments every month
a. Recurring payment
30 months in 2 1/2 years
First move
Payment due: [49,500 * (1-.30)] / 30 months
Amount due = (49,500 *.70) / 30 months
$34,650 payments over 30 months
Amount due: $1,155
Second action
Monthly payment equals [$1,155* (1+0.12)]
Monthly payment equals $1,155 * 1.12
The monthly payment is $1,293.6
The monthly payment equals $1,294 (Approximately)
Hire-purchase (b)
Hire purchase equals $1,155 * .12 over 30 months
=> 1155 * 0.12* 30
$4,158 for a hire buy
As a result, each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.
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Jona i given a tet quetion aking him to how that the um of two odd integer i alway an even integer. Which choice i the bet proof of hi conjecture?
B. Let (2a + 1) and (2b + 1) are different odd numbers. sum of these odd number is 2(a+ b +1) is a multiple of 2.
Whole numbers in mathematics can be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.
Let (2a + 1) and (2b + 1) are different odd numbers. the sum of these odd numbers is 2(a+b+1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the summation of two odd numbers is always even.
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The complete question is:
Jona is given a test question asking him how that the um of two odd integers is always an even integer. Which choice is the best proof of his conjecture?
A) Every time you add two odd numbers, the sum is an even number.
B) Let a and b both represent odd numbers and a+b be an even number. Therefore, a+b=b+a which shows that the sum of two odd numbers is even.
C) Look at these different examples: 5+3=8, 15+7=22, 21+13=34. So the sum of two odd numbers must be even.
D) Let (2a+1) be one odd number and let (2b+1) be the other odd number. (2a+1)+ (2b+1) = 2a+2b+2 = 2(a+b+1). Because 2(a+b+1) is a multiple of 2,it is an even number.
I round two number to the nearet 1000000 and then add them together to get a total of 7000000. If both number were rounded up and one number wa le than 3000000 to tart with, what are the greatet number each could have been before being rounded?
The larger number could have been before rounding is 4000001.
We know that both numbers were rounded up to the nearest million and added together to get 7000000.
Since one number was less than 3000000 to start with and both numbers were rounded up, the greatest that the smaller number could have been before rounding is 2999999.
We can use the equation:
(x + y) = 7000000
Where x is the smaller number and y is the larger number before rounding.
We know that x < 3000000 and x = 2999999
So we can substitute these values into the equation:
(2999999 + y) = 7000000
Solving for y:
y = 7000000 - 2999999
y = 4000001
So the greatest that the larger number could have been before rounding is 4000001.
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NEED HELP ASAP!!
Which ratio is equal to the ratios plotted on the graph?
A- 4/2
B- 2/3
C- 1/2
D- 10/14
Answer:
Hi i found the answer 3/2 could you please check your options?
if you apply the slope formula here,
12-6/8-4 gives you the value 6/4 which is 3/2
good luck!
What is the value sin 45?.
The Sin 45 value is 1/√2.For the purpose of determining the Sin 45 value, let's use the ABC right angle triangle.
The ratio of a triangle's opposing side's length to its hypotenuse is known as the Sin of an angle.
Sin ϴ = Opposite side or perpendicular / Hypotenuse
Sin ϴ = AC/AB
Sin ϴ = B/C
Calculation of the Value of Sin 45 Degree in Fraction
Sin 45 = √2/
= 1 / √2
Consider a right triangle with angle X= 45°,then it is obvious that third will also be 45°.hence the side length of triangle are L, L, √2L .then apply
sin 45°= L/√2L
Sin 45°= 1/√2
Sin 45°=0.7071
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What are the symbols used in graphing linear inequalities?.
The symbols used in graphing linear inequalities are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways.
Not equal ≠ Less than (<) Greater than (>) Less than or equal to (≤) Greater than or equal to (≥)Learn more about Linear inequalities:
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Doug etimate that hi occer team will win 7 game thi year. The team actually win 10 game. What i the percent error of Doug' etimate? Round the anwer to the nearet tenth percent if neceary
Doug's estimate was incorrect by 30% because probability his team won 10 games instead of the 7 he predicted.
Doug estimated 7 wins
Actual number of wins was 10
Error = (Actual - Estimate) / Estimate x 100
Error = (10 - 7) / 7 x 100
Error = 3 / 7 x 100
Error = 30%
Doug estimated that his soccer team would win 7 games this year. However, the team ended up winning 10 games in total. This means that Doug's estimate was incorrect by 30%. To calculate this percent error, we used the following formula: Error = (Actual - Estimate) / Estimate x 100. In this case, the actual number of wins was 10 and the estimate was 7. Plugging these numbers into the formula, we got that the error was 3/7 x 100, which is equal to 30%. This means that Doug's estimate was off by 30%. This is a significant overestimate since the team ended up winning 3 more games than what Doug had predicted.
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I need help on this asap!
Receives some cash from his mother for his journey. He has already put aside a total of $\$ 220$ for the trip. There is a 55-gallon gas purchase cap .
What is the greatest number of gallons ?[tex]$$\begin{aligned}& 3.25 \mathrm{~g}+40 \leq 220 \\& -403.25 \mathrm{~g} \\& \frac{3.25}{3.25} \leq \frac{180}{3.25} g \leq 55.38 \approx 55\end{aligned}$$[/tex]
Chang-to has a gas purchase limit of 55 gallons.
[tex]$$\begin{aligned}& 3.25 g+40 > 92 \\& \frac{-40}{\frac{3.25 g}{3.25} > \frac{-40}{32}} \\& \mathrm{~g} > 16\end{aligned}$$[/tex]
More than 16 gallons of gas could have been purchased by him .
[tex]$$\begin{aligned}& 3.259+40 \leq 170 \\& \frac{3.2 / 59}{3.2^{\prime} 5} \leq \frac{130}{3.25} \\& g \leqslant 40\end{aligned}$$[/tex]
He only allowed to purchase 40 gallons of gas during the journey.
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what’s a geometry concept you’ve learned or found really helpful
Hey there!
There are various concepts that are used in the world of Geometry, however there are some simple concepts that may be easier to work with.
Simple Concepts in GeometryPoints - In geometry, a point is a location represented often by a dot on a x-y graph. The point does not have any length, width, shape or size, it only has a position.Lines - In geometry, a line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.Segments - In geometry, a line segment is a piece or part of a line having two endpoints. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units such as feet or inches.Rays - In geometry, a ray is usually taken as a half-infinite line (also referred to as a 'half line') with one or the two points and taken to be at infinity._____________________________________________________
So, in summary to all of this, it really depends on what concepts in geometry you are currently learning and which concept(s) you personally find the most useful and helpful.
how do i do 4/2 + 8?
Answer:
If that means division then here
Step-by-step explanation:
4/2=2
then,
2+8=10
Write the ratio 1.8 : 4.2 inches Simplest for
The most simplified form of the given ratio 1.8: 4.2, which is a ratio of lengths in inches is 3/7.
What is meant by ratios?
In mathematics, a ratio shows how frequently one number appears in another. When expressed as a:b, a fraction has the form of a ratio. A ratio is a comparison or compressed version of two identical values. Like fractions, ratios can be entirely simplified. Divide all of the numbers in a ratio by the same number to make it simpler. Divide each integer in a ratio by their largest common factor to fully simplify the ratio. The ratio's numbers must always be whole numbers.
Given the ratio, 1.8: 4.2
The ratio can be simplified by dividing both the terms in the ratio by the highest common factor.
The highest common factor of 1.8 and 4.2 is 0.6.
So we divide both terms by 0.6.
1.8: 4.2 = 1.8/0.6 : 4.2/0.6 = 3:7
Therefore the simplified form of the given ratio, 1.8: 4.2 is 3:7.
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Find the length of the third side. If necessary, round to the nearest tenth. 24 10
The length of the third side will be equal to 21.81 units.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that the bigger side of the triangle is 24 and one of the legs is 10 units. The length of the third side will be calculated as,
Use the Pythagorean theorem,
B² = H² - P²
B² = (24)² - (10)²
B² = 576 - 100
B = √476
B = 21.81 units
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NEED HELP ASAP! CMON
Answer:
A: x < 3
Step-by-step explanation:
Answer: x < 3
Step-by-step explanation:
We start by subtracting 6 from both sides -
x + 6 - 6 < 9 - 6
Then, we get this -
x < 3
Which is the answer
2. Use function notation to represent each statement.
a. Six hours after it started raining, the amount of rain was 37 millimeters.
b. The amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining
a. Let t represent the time in hours when it started raining. We can use function notation to represent the amount of rain r at any time t with r(t) = 37 millimeters. This is because after 6 hours, the amount of rain was 37 millimeters. Therefore, we can use the equation r(t) = 37 millimeters to represent this statement.
b. We can use function notation to represent the amount of rain at any time t with r(t) = r(t-1.5). This is because the amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining. Therefore, we can use the equation r(t) = r(t-1.5) to represent this statement.
This type of function notation is useful for representing relationships between different values related to the same property or phenomenon. It allows us to quickly and easily analyse and compare data, as well as make predictions about future values. It is also useful for describing how certain parameters are changing over time.
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