Answer: 70x²= 1 30x ALSO= 1 60x⁸= 1 again
Step-by-step explanation: To find the Greatest Common Factor of these three terms you must first factor each term separately:
A researcher found that for the years 2010 to 2018, the equation, y=-0.2(x-5)²+35, models the average gas mileage of new vehicles sold in Switzerland, where x is the number of years since 2010 and y is the average gas mileage, in miles per gallon (mpg).
During what year was the average gas mileage for new vehicles sold in Switzerland the greatest?
Please help me, I need help I didn't understand this!!!
The average gas mileage for new vehicles sold in Switzerland was the greatest in the year 2013.
How did we arrive at the answer?The equation models the average gas mileage of new vehicles sold in Switzerland as a parabolic function, y=-0.2(x-5)²+35.
To find the year in which the average gas mileage was the greatest, we need to find the vertex of this parabolic function.
The x-coordinate of the vertex is given by x = 5 + (-b/2a) = 5 - (-0.2/2(-0.2)) = 5 - (0.2/0.4) = 5 - 0.5 = 4.5 years since 2010, or the year 2013. The y-coordinate of the vertex can be found by substituting x = 4.5 years into the equation, y = -0.2(4.5-5)² + 35 = -0.2(0.5)² + 35 = 0.2 * 0.25 + 35 = 0.05 + 35 = 35.05 mpg.
So the average gas mileage for new vehicles sold in Switzerland was greatest in the year 2013, with a value of 35.05 mpg.
learn more about equation model: https://brainly.com/question/25976025
#SPJ1
PLEASE HELP 10 Points
Answer:
last option
number of students in class plus new students
decide truth values of the following statements, assuming that x; y; z are real numbers. justify your answers. then write the negation of each statement. a. 8x 8y 8z; (z < 0 ^ x < y) ) yz > xz
The statement 8x 8y 8z; (z < 0 ^ x < y) ) yz > xz is true, since the statement x < y and z < 0 both hold true, and thus yz > xz must also be true. The negation of this statement would be 8x 8y 8z; (z ≥ 0 ∨ x ≥ y) ) yz ≤ xz.
The first-order language of (directed) graphs is L = {r}, where r is a binary relation symbol. The only terms are the variables x , y, z. Atomic formulas have the form (x, y, z). These formulas represent relationships between the terms, such as x being adjacent to y and z.
These relationships can be used to model different types of graphs. For example, to model a directed graph, the binary relation x->y can be used to represent a directed edge from x to y. These formulas can be combined and manipulated to express more complex formulas, such as the perpendicularity relation between two lines or the perpendicular bisector theorem. These formulas allow for solving problems related to geometry and algebra in graphs.
Learn more about mathematics:
https://brainly.com/question/30399396
#SPJ4
The two bars are made of polystyrene, which has the stress-strain diagram shown. If the cross sectional area of bar AB is 2.3in^2 and BC is 4in^2, determine the largest force P that can be supported before any member ruptures. Assume that buckling does not occur. ???Does anybody know how to solve the problem completely or show an example with different numbers on how to get the answer?
The largest force that can be supported before any member ruptures is 8, the maximum force that bar BC can support.
To solve this problem, we need to find the maximum force (stress) that each bar can withstand before rupturing.
This can be found using the stress-strain diagram.
For bar AB with a cross sectional area of 2.3 in^2, the maximum stress that it can withstand is given by the maximum slope of the stress-strain diagram, which is approximately 1.
For bar BC with a cross sectional area of 4 in^2, the maximum stress that it can withstand is given by the maximum slope of the stress-strain diagram, which is approximately 2.
Since the force (stress) is equal to the stress times the cross sectional area, the largest force that bar AB can support is given by 1 * 2.3 = 2.3 and the largest force that bar BC can support is given by 2 * 4 = 8.
For more questions on stress-strain
https://brainly.com/question/19102812
#SPJ4
How do you find the sample standard deviation when given the population standard deviation? What formula do you use? If you can make up an example that would be great.
The estimate of the population standard deviation will be the estimated sample standard deviation
You must use sample data when you don't have access to population data. Consider the following hypothetical research question: What is the standard deviation of student heights in Azerbaijan? All of the residents are Azerbaijani students. To gather data on every student in Azerbaijan might be impossible or expensive.
As a result, you measure the heights of 100 pupils who were chosen at random. You next figure out the sample standard deviation. Keep in mind that the lack of population statistics prevents you from calculating the population standard deviation.
In this case, your best estimate of the population standard deviation will be the estimated sample standard deviation.
Know more about standard deviation
https://brainly.com/question/475676
#SPJ4
||
2. Complete the steps for factoring 2x3 - 36x² + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x=
(x2-18x+81)
_2x [x²-2(____)x+ (__________)²]
=
11
(x-.
_)(x-____
_2=(x-_9_) ²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
The complete factorization of the given expression is 2x³ - 36x² + 162x = 2x (x - 9)².
What is factorization?An algebraic expression is factorised when it is written as the product of its factors. These variables, factors, or algebraic expressions could be present. The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
The steps to factorize the given expression is:
2x³ - 36x² + 162x
= 2x (x² - 18x + 81) Factor out 2x.
= 2x (x² - 2(9)(x) + (9)²) Rewrite the trinomial.
= 2x (x - 9) (x - 9) Use the whole square formula.
= 2x (x - 9)² simplify.
Hence, the complete factorization of 2x³ - 36x² + 162x = 2x (x - 9)².
Learn more about factors here:
https://brainly.com/question/26923098
#SPJ1
x=2y in evryday words mean
In everyday words x = 2y means that twice of y makes x
What is multiplication by two?The general rule for solving all multiplication by two problems is to multiply the integer by two by adding the number to itself.
The order of your numbers doesn't matter while solving multiplication issues.
In the problem, x = 2y represents that twice of y is x
the inverse of this is half of x is y
Learn more about equations at:
https://brainly.com/question/22688504
#SPJ1
43. a system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system
Yes, that is correct. A system of linear equations with fewer equations than unknowns is often referred to as an underdetermined system.
In this type of system, there are infinitely many solutions or no solutions, and it is not possible to determine a unique solution for the variables.
Because free variables will give infinitely many solutions by just keeping on changing the values of free variable. We can do it because it is a free variable, it can take any value.When a system of equations has more variables than the equation, therefore, it has fewer rules to curb the variables, giving the variables more freedom to take up values from their respective domain(Usually it is a set of real numbers), in such a condition the system of equations has infinite solutions. This kind of system is known as an underdetermined system.
Hence, the system of equations doesn't have a unique solution.
For more such questions on underdetermined system
https://brainly.com/question/14696452
#SPJ4
4(2y-6) and 8y-24 why are they equivalent
Because in the first expression 4 was factored out to make it 4(2y-6). Before 4 was factored out the expressions were the same.
Write the ratio 12 :30 in the form 1: n
Answer: 1:2.5
Step-by-step explanation:
Step by step explanation:
12:30
÷ by 12
= 1:2.5
In each of the following cases, either find an example that contradicts the statement showing that it is false, or explain why the statement is always true. (a) If {u, 12, 13} is a spanning set for R", then {uj, 12, 13, 14} is also a spanning set for R". What are all possible values of n for which three vectors un, U2, U3 can span Rn? (b) If {u, uy, us} is a spanning set for R", then {u, u, + u2, u, -u3} also spans RM (c) If u, uz, uz are linearly independent, then u,, uy, us, , are also linearly independent. (d) If ui, uy, us are linearly independent, then u, u, + uy, u, -u3 are also linearly independent. (e) If u, u, uz do not span R", then there is a plane P in R that contain all of them. (Bonus: how can we find this plane? Does the plane go through the origin?)
The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
(a) In order for three vectors un, U2, U3 to span Rn, all possible values of n must be 3 or greater. This is because three vectors can only span a 3-dimensional space or higher. Therefore, any n greater than or equal to 3 will work.
(b) Since {u, uy, u3} is a spanning set for Rn, then {u, u, + u2, u, -u3} is also a spanning set for Rn. This is because adding or subtracting any of the vectors in the original set will still form a set of three vectors that span Rn.
(c) This statement is always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(d) This statement is also always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(e) This statement is false. It is possible for three vectors ui, uy, u3 to not span Rn but still lie on the same plane. For example, the three vectors (1,1,1), (2,2,2), and (3,3,3) do not span R3, but they all lie on the same plane that passes through the origin (x+y+z=0).
The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
Learn more about linear combination here:
https://brainly.com/question/26584782
#SPJ4
select all the rates that are unit rates 2/4/5 3/4/1 3:4 9/1 10:1
Note that the rates that are unit rates are given as follows:
Note that a unit rate is a rate in which the second term equals 1. It represents a comparison of a quantity to 1.
Since:
Therefore, it is right or correct to state that 2/4, 9/1, and 10:1 are unit rates.
Learn more about Unit Rate:
https://brainly.com/question/29169781
#SPJ1
I need help with this problem plsss
thanks! :)
Answer:
9.5
Step-by-step explanation:
[tex]1. \ \frac{AB}{PQ} =\frac{BM}{QN} ; = >[/tex]
[tex]2. \ \ \frac{11}{4.4} =\frac{BM}{3.8} ; \ = > \ BM=\frac{11*3.8}{4.4} =9.5.[/tex]
Objective: 1. To apply programming using while loops 2. To determine roots of functions using the bisection method Problem 1 Write a function taylorcosi ne that takes two arguments: the first argument is the angle in radians, and the second argument the relative percentage error, and has two return values: first return value is the Taylor approximation for the cosine of the angle entered and the second is the number of terms required in the Taylor series to reach this level of error. You must use while loops. The Taylor expansion of
f(x)=cosx
about
x=0
is given by
cosx=1− 2!
x 2
+ 4!
x 4
− 6!
x 6
+⋯
Suppose we want to find the approximate value of the function at
x= 3
π
with an error tolerance of
0.1%
. We should be able to call the function as follows:
{
val, nsteps
]=
taylorcosine
( 3
π
,1e−3)
. Note relative error is defined a: To find percentage relative error, multiply by 100. Write a function myBi section that takes three arguments: the first argument is a function handie, the second argument is an array containing the lower and upper limits of the starting interval, and the third argument is the maximum allowable relative error. The return value of the function is the estimate of the root. Error here is defined is the absolute value of the ratio of the difference between the old and the new estimates of the root and the new estimate of the root. i.e. error
=
x new
x nnw
−x eld
Test this function on examples we have done in class. For example,
f(x)=x 2
−3x+2
with an initial bracket of
[1.33.0]
and an error tolerance of
1%
The Taylor expansion of cos(x) around x=0 is [tex]cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) +[/tex]......
We would use this expansion to calculate the cosine of a given angle with an error tolerance of 0.1%.
To do this, we must first write a function taylorcosine() which takes two arguments: the angle (in radians) and the relative percentage error. The function should then return two values: the Taylor approximation for the cosine of the angle, and the number of terms required in the Taylor series to reach this level of error.
For example, if we want to find the approximate value of cos(3π) with an error tolerance of 0.1%, we would call the function as follows:
[tex]val, nsteps = taylorcosine(3π, 1e-3)[/tex]
To find the percentage relative error, we must multiply the relative error by 100.
We can also use the bisection method to determine the roots of a function. To do this, we must write a function myBisection() which takes
three arguments: the function handle, an array containing the lower and upper limits of the starting interval, and the maximum allowable relative error. The return value of the function is the estimate of the root.
For example, if we want to find the root of f(x) = x^2 - 3x + 2, with an initial bracket of [1.3, 0] and an error tolerance of 1%, we would call the function as follows:
root = [tex]myBisection(f, [1.3, 0], 1%)[/tex]
The error is defined as the absolute value of the ratio of the difference between the old and the new estimates of the root and the new estimate of the root.
Error = [tex]|x_new/x_new - x_old|/x_new[/tex]
By writing the taylorcosine() and myBisection() functions, we can calculate the cosine of an angle with a given error tolerance, and determine the roots of a function with a given error tolerance, respectively.
Learn more about Taylor expansion here:
https://brainly.com/question/17442571
#SPJ4
what is the sum that I'm supposed to do?
Answer:
a: 1/8 and 1/4. b: 1/2 1/4. c: 1/1 and 5/12. d: 1 1/2 and 3/4
Step-by-step explanation:
You had to find 2 fractions that add up to a number between the two numbers listed.
10. A skateboarding company produced
10,200 longboards last month and
found that some were defective.
a. The company plans to make 125,000
longboards this year. Predict
approximately how many longboards
will be defective.
1 Month
1 Year
Number of
Longboards Produced
10,200
125,000
Number of Defective
Longboards
204
?
b. Another skateboarding company produced 11,500 longboards last month and found that
225 were defective. If they also plan on making 125,000 longboards this year, predict how many
will be defective. Then determine if this company will produce a product with fewer defects.
The number of longboards that will be defective based on the defective longboards in the month can be predicted to be 2, 500 longboards.
The number of longboards that would be defective for the other skateboarding company is 2, 446 longboards.
How to find the defective items ?To find the defective longboards, first find the percentage of the longboards that were produced in the month. Then multiply this result with the number of longboards to be produced :
= 204 / 10, 200 x 125, 000
= 2 % x 125, 000
= 2, 500 longboards
The same procedure can be used for the other skateboarding company to find the defective products to be:
= 225 / 11, 500 x 125, 000
= 2, 446 longboards
The product for the second company therefore has fewer defects.
Find out more on defects at https://brainly.com/question/2896071
#SPJ1
If the denominator is a friendly number, you can Up or down, or use a
If the denominator is a friendly number, you can easily multiply it with another integer.
What is a Friendly Number in math?In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself.
Friendly numbers are numbers that are easy to work with. For example, multiples of 10 are “friendly” because they are easy to work with when we add or subtract.
Read more about friendly numbers here:
https://brainly.com/question/27595278
#SPJ1
you buy a bond with a fixed coupon rate of 5%. a year later, similar bonds that are issued have a coupon rate of 3%. which of the following is true?O The price of Juan’s bond will increase
O The interest rate of Juan’s bond will increase to reflect the current market
O The price of Juan’s bond will decrease
The correct option is : The price of Juan’s bond will decrease. Because similar bonds are offered a year later with a 3% coupon rate.
Explain about the coupon rate?A fixed-income security's nominal yield is expressed as a coupon rate.The coupon holder would yield less than the current market conditions when the market improves, as the bond won't pay more because its value was predetermined at issuance.When a bond is bought just on secondary market, the yield to maturity is the difference between the bond's interest costs, that could be higher or less than the coupon rate at the time the bond was issued.For the stated question:
You invest in a bond with a 5% fixed coupon rate. Similar bonds are offered a year later with a 3% coupon rate.Then, the price of Juan’s bond will decrease.
To know more about the coupon rate, here
https://brainly.com/question/15205106
#SPJ4
3(w-2) ≥10 3w 212 w24
Answer:
Step-by-step explanation:
3 (w - 2) ≥ 10
3w - 6 ≥ 10
3w ≥ 16
w ≥ 16/3
Cynthia Besch wants to buy a rug for a room that is 25ft wide and 34ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 360 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug are: width is 15 feet length is 21 feet.
Let's call the width of the strip of floor around the rug "x". Then the width of the rug would be 25 - 2x, and the length of the rug would be 34 - 2x.
The total area of the rug should not exceed 360 square feet, so we can set up an equation to represent this:
(25 - 2x)(34 - 2x) = 360
Expanding and simplifying the left-hand side:
25 × 34 - 2 × 25 × x - 2 × 34 × x + 4 × x² = 360
850 - 118x + 4x² = 360
4x² - 118x+ 490 =0
Now we have a quadratic equation that we can solve using the quadratic formula or by factoring. Either way, we find that x = 24.5 or x = 5. Since x represents the width of the strip of flooring, x must be positive. Therefore, x = 5 is the solution.
So the width of the strip of flooring is 5 feet, and the dimensions of the rug are:
width: 25 - 2 × 5 = 15 feet
length: 34 - 2 × 5 = 21 feet
Learn more about the equation here:
brainly.com/question/13947055
#SPJ1
consider the following table. age group frequency 18-29 9831 30-39 7845 40-49 6869 50-59 6323 60-69 5410 70 and over 5279 if you created the probability distribution for these data, what would be the probability of 30-39?
The probability of 30-39 age group is 18.83%. The probability of a given age group is the frequency of that group divided by the total frequency.
To find the probability of the age group 30-39, divide the frequency of this group (7845) by the total frequency (9831 + 7845 + 6869 + 6323 + 5410 + 5279 = 41,478). So the probability of 30-39 is 7845/41478 = 0.19.
In probability distributions, probabilities are calculated as the ratio of the number of occurrences of an event to the total number of possible events. To find the probability of an event in a specific age group, we need to calculate the ratio of the frequency of that age group to the total frequency of all age groups.
In this case, the frequency of the age group 30-39 is 7845. The total frequency of all age groups is 9831 + 7845 + 6869 + 6323 + 5410 + 5279 = 41,657.
So, the probability of the age group 30-39 is 7845/41657 = 0.1883 or 18.83%.
To learn more about frequency please click on below link.
https://brainly.com/question/29739263
#SPJ4
the following pair of triangles are similar. find the value of x 10 x x+2 x+14
The numerical value of x in the similar pair of triangle is 10.
What is the numerical value of x?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
From the diagram,
Side A of the small triangle = 10
Side B of the small triangle = x + 2
Side A of the Big triangle = 10 + x
Side B of the big triangle = x + 14
Hence;
Ratio of Side A to Side B of the small triangle = 10 / x + 2
Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14
Since the triangle area similar, equate the two ratio and solve for x.
10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )
Cross multiply
10( x + 14 ) = ( 10 + x )( x + 2 )
Expand using FOIL method
10x + 140 = 10x + 20 + x² + 2x
10x + 140 = x² + 12x + 20
x² + 12x + 20 = 10x + 140
x² + 12x + 20 - 10x - 140 = 0
x² + 2x - 120 = 0
Factor the left side of the equation
( x - 10 )( x + 12 ) = 0
Hence;
x - 10 = 0 and x + 12 = 0
x = 10 and x = -12
Since the dimension of the triangle cannot be negative,
x = 10
Therefore, the value of x is 10.
Learn more about FOIL Method here: brainly.com/question/28527940
#SPJ1
The diameter of a cone's circular base measures 10 inches, and the slant height of the cone is 8 inches.
What is the approximate surface area of the cone?
Responses
146.3 in²
204.1 in²
314.2 in²
565.2 in²
The surface area of Cone is 204.1 inch².
What is Surface area of Cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr
where r is the radius and l is the slant height
Given:
Radius= 5 inches
Slant height= 8 inches
So, the Surface area of Cone
= πr (l +r)
= 3.14 x 5 ( 8 + 5)
= 15.7 x 3
= 204.1 inch²
Learn more about Surface area of Cone here:
https://brainly.com/question/23877107
#SPJ1
(FoF) (0) f(x) = 3x-2
The solution is (FoF) (0) = -8, when f(x) = 3x-2.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
f(x) = 3x-2
i.e. fof(x)
=3(3x-2)-2
=9x-8
so. fof(0)
=9*0-8
= -8
Hence, The solution is (FoF) (0) = -8, when f(x) = 3x-2.
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
please calculate the probability that a particle in a one-dimensional box of length a is found between 0 and a/2
The probability of finding a particle in a one-dimensional box of length a between 0 and a/2 is[tex](2/a)^3/3[/tex].
The probability of finding a particle in a one-dimensional box of length a between 0 and a/2 can be calculated using the equation [tex]P = (1/h)^3 * (∫0^a/2Ψ^2dx)[/tex]. The equation is derived from the equation of probability density of finding a particle in a given state which is given as [tex]P = (1/h)^3 * ∫Ψ^2dx[/tex]. In this equation, h is the Planck's constant, and Ψ is the wave function of the particle.
For a particle in a one-dimensional box of length a, the wavefunction can be written as [tex]Ψ(x) = (2/a)^1/2 * sin (nπx/a)[/tex]. Substituting this in the equation for probability density, the probability of finding a particle between 0 and a/2 is [tex]P = (1/h)^3 * (2/a)^3 * (1/3 - 0)[/tex]. Therefore, the probability of finding a particle in a one-dimensional box of length a between 0 and a/2 is [tex](2/a)^3/3[/tex].
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
how many kilometers is 2528.5 cm? calculate and type your answer with correct significant numbers (show your work for full credit).
2528.5 centimeters is approximately 0.0253 kilometers.
To convert centimeters to kilometers, we first need to convert centimeters to meters, then meters to kilometers.
1 kilometer = 1000 meters
1 meter = 100 centimeters
So, to convert 2528.5 centimeters to meters, we divide by 100:
2528.5 cm / 100 = 25.285 meters
And to convert meters to kilometers, we divide by 1000:
25.285 m / 1000 = 0.025285 km
Therefore, 2528.5 centimeters is approximately 0.0253 kilometers.
The answer can be rounded to 4 significant figures, which is the number of significant figures in the original measurement of 2528.5 centimeters:
0.0253 km (rounded to 4 significant figures)
To learn more about kilometers, refer:-
https://brainly.com/question/9135515
#SPJ4
on a circle of radius 9 feet, give the degree measure of the angle that would subtend an arc of length 6 feet. round your answer to the nearest hundredth, or two decimal places.
The circumference of the circle is 2 * pi * 9 = 56.5 feet. So, the degree measure is (6/56.5) x 360 = 51.1 degrees. Rounded to two decimal places, the degree measure is 51.1 degrees.
To find the degree measure of an angle that subtends an arc of length 6 feet on a circle of radius 9 feet, use the formula: degree measure = (arc length / circumference) x 360 degrees.
The degree measure of the angle that would subtend an arc of length 6 feet on a circle of radius 9 feet can be found by using the formula:
degree measure = (arc length / circumference) * 360
The circumference of the circle is 2 * pi * 9 = 18 * pi
So, degree measure = (6 / (18 * pi)) * 360 = (6 / 18) * (360 / pi) = 60 / pi
To convert this to degrees, we can use an approximation of pi as 3.14, so
degree measure = 60 / 3.14 = 19.11
Rounding to two decimal places, the degree measure is 19.11, which can be rounded to 19.11 degrees.
To learn more about circumference please click on below link.
https://brainly.com/question/4268218
#SPJ4
(5x + 1) (12x - 8) =
The multiplication of the expression given is 60x² - 28x - 8.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (5x + 1) (12x - 8).
We have to multiply the expressions and simplify.
For any numbers or algebraic expressions, a, b, c and d,
(a + b) (c + d) = ac + ad + bc + bd
(5x + 1) (12x - 8) = (5x × 12x) + (1 × 12x) + (5x × -8) + (1 × -8)
= 60x² + 12x - 40x - 8
= 60x² - 28x - 8
Hence the multiplication of the given expression gives 60x² - 28x - 8.
To learn more about Expressions, click on the link :
https://brainly.com/question/13947055
#SPJ1
P(-3,-1), Q(-1,-1), R (1, 1) are three of the four vertices of a parallelogram PQRS and S is the opposite vertex of Q. Plot these vertices in graph paper and find: (i) the coordinates of the vertex S. (ii) the coordinates of the point of intersection of the diagonals PR and QS.
(i) the coordinates of the vertex S = Q + QS = (-1, -1) + (2, 2) = (1, 1).
(ii) the coordinates of the point of intersection of the diagonals PR and QQS is point (-1, 0).
How did we get the value?(i) The coordinates of the vertex S can be found by shifting the vector PQ to QS. The vector PQ is given by Q - P = (-1 - (-3), -1 - (-1)) = (2, 0). The vector QS can be found by shifting PQ by 2 units vertically, so QS = (2, 2). To find the coordinates of S, we add the vector QS to the point Q: S = Q + QS = (-1, -1) + (2, 2) = (1, 1).
(ii) The point of intersection of the diagonals PR and QS can be found by finding the midpoint of each diagonal and checking if they are equal. The midpoint of PR is given by ( (1 + -3)/2 , (1 + -1)/2 ) = (-1, 0). The midpoint of QS is given by ( (1 + -1)/2 , (1 + 1)/2 ) = (0, 1). Since the midpoints are equal, the diagonals PR and QS intersect at the point (-1, 0).
learn more about parallelogram vertex: https://brainly.com/question/3050890
#SPJ1
The length, width, and height of a rectangular pyramid are multiplied by 1/2. Which of the following describes the effect on the volume?
A.) The volume is multiplied by 1/8.
B.) The volume is multiplied by 3/2.
C.) The volume is multiplied by 2.
D.) The volume is multiplied by 1/6.
Answer:
Option A) The volume is multiplied by 1/8.
Step-by-step explanation:
For the first volume problem involving the rectangular pyramid, the normal volume formula is V = 1/3 (l)(w)(h). Since all 3 dimensions are being multiplied by 1/2, this involves multiplying the original formula by (1/2)(1/2)(1/2) which, put together, is multiplying by 1/8, so the volume will be 1/8 of what it was with the original dimensions.
The volume of the rectangular pyramid is multiplied by ( 1/8 )
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the length of the rectangle be L
Let the width of the rectangle be W
Let the height of the rectangle be H
Now , the volume of rectangle be V = L x W x H
And , when the length , width and height are multiplied by ( 1/2 ) , we get
L' = L/2
W' = W/2
H' = H/2
So , the volume V' = ( L' x W' x H' )
The volume of rectangular pyramid V' = ( 1/8 ) V
Hence , the volume is multiplied by ( 1/8 )
To learn more about volume of rectangle click :
https://brainly.com/question/25422723
#SPJ2