Given same lengths and slopes of the opposite sides and nature of the angle between adjacent sides, we have;
The type of quadrilateral is a parallelogram How can the type of quadrilateral be found?The given points are;
L(-5, 4), M(2, 2), N(0, -3), S(-7, -1)
Lengths of the sides are;
Length of LM = √((2-(-5))²+(2-4)²) ≈ √(53)
Length of MN = √((2-0)²+(2-(-3))²) ≈ √(29)
Length of NS = √((0-(-7))²+((-3)-(-1))²) ≈ √(53)
Length of LS = √(((-7)-(-5))²+((-1)-4)²) ≈ √(29)
Therefore;
The lengths of opposite sides are the same.Slope of LM = (2-4)/(2-(-5)) = -2/7
Slope of MN = (2-(-3))/(0-2) = 5/2
Slope of NS = ((-3)-(-1))/(0-(-7)) = -2/7
Slope of LS = ((-1)-4)/(-7-(-5)) = 5/2
Therefore;
The opposite sides are parallel, and The the adjacent sides are not perpendicularThe quadrilateral created by the points L(-5, 4), M(2, 2), N(0, -3), S(-7, -1) is therefore;
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Can anyone please help me with these 3 math questions? its very urgent ‼️
i don’t understand where to start..
The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.
Brie runs faster.
Unit rateMikayla
2 miles in 12 1/2 minutes
Unit rate = miles / minutes
= 2 ÷ 12 1/2
= 2 ÷ 25/2
= 2 × 2/25
= 4/25
= 0.16 miles per minutes
Brie
5 miles in 22 1/4 minutes
Unit rate = miles / minutes
= 5 ÷ 22 1/4
= 5 ÷ 89/4
= 5 × 4/89
= 20/89
= 0.25 miles per minutes
Brie runs fasterLucy
4 4/5 pounds for $18.50
Unit rate = pounds / price
= 4 4/5 ÷ 18.50
= 24/5 ÷ 18.50
= 24/5 × 1/18.50
= 24/92.50
= $0.26 per pound
Sophie
3 1/2 pounds for $14.75
Unit rate = pounds / price
= 3 1/2 ÷ 14.75
= 7/2 ÷ 14.75
= 7/2 × 1/14.75
= 7/29.5
= $0.24 per pound
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A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173
miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.For this problem, the parameters are given as follows:
a = 94, b = 119, c = 173.
Hence the internal angle C is found as follows:
c² = a² + b² - 2abcos(C)
173² = 94² + 119² - 2 x 94 x 119cos(C)
22327cos(C) = -6932
cos(C) = -6932/22327
C = arccos(-6932/22327)
C = 108º.
The turning angle is the outside angle, which is supplementary with C, hence:
T = 180 - C = 180 - 108 = 72º.
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Which car has "best" car combination of mpg and hp, where mpg and hp must be given equal weight?
The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))
MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.
As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.
The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.
The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.
#sum the scaled values of mpg and hp and add a new column called combination
myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)
#Which car has the best combination of mpg and hp?
print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))
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In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for Independent Practice For See Exercises Example 8-9102113124 Extra Practice Skills Practice p. S5 Application Practice p. S28 the translation that maps the rocket from position I to position 2.
The rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up
How to determine the rule for the translation?The translation is added as an attachment
From the attached figure, we have the following corresponding coordinates:
Figure 1 = (0, 0)
Figure 2 = (4, 4)
The rule of translation is calculated as:
(x, y) = T<Figure 2 - Figure 1>
This gives
(x, y) = T<4 - 0, 4 - 0>
Evaluate
(x, y) = T<4, 4>
Hence, the rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up
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Complete question
In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for the translation that maps the rocket from position I to position 2.
A submarine is descending to examine the seafloor 2,100 feet below the surface. it takes the submarine 2 hours to make this descent. Write an equation to
represent the relationship between the submarine's elevation and time.
Answer:
Step-by-step explanation:
x = time
y = elevation
At x = 0 , y = 0
It takes the submarine 2 hours to make descent of 2100 ft
=> x = 2 , y = - 2100
Slope = ( -2100 - 0)/(2 - 0) = -1050
y - 0 = -1050 ( x -0)
=> y = -1050x
1050x + y = 0
represent the relationship between the submarine's elevation and time.
Rhombus A B C D is shown. All sides are congruent. Lines are drawn from point A to point C and from point D to point B and intersect at point E at the center.
The area of rhombus ABCD is 120 square units.
AE = 12 and BD = x – 2. What is the value of x and the length of segment BD?
x =
BD = units
Answer:
x = 22
BD = 20 units
Step-by-step explanation:
The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.
Area of a rhombusThe formula is ..
A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.
Using the given values, we have ...
120 = 1/2(12)(x-2)
SolutionDividing by 6, we find ...
20 = x -2 = BD
22 = x . . . . . . . . add 2
The value of x is 22.
The length of BD is 20.
Answer:
x=12
BD=10
Step-by-step explanation:
Oltp systems are designed to handle ad hoc analysis and complex queries that deal with many data items.
a. true
b. false
Answer:
b) It is false
What equation can be used to find the sum of 4/10 and 7/100
Answer:
47/100
Step-by-step explanation:
First you have to make the denominators equal.
4/10 * 10/10 = 40/100
40/100 + 7/100 = 47/100
What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Step-by-step explanation:
Circumference = πd
= π × 12
= 37.6991
=38
Answer:38
Step-by-step explanation:
What is the approximate radian measure
of an angle with a degree measure of
59.6°?
Answer:
The approximate radian measure of the angle. So we have 15 nine 0.6 degrees convert degrees to radiance. You have to multiply by pi over 1 80. So if we did that, that'd be 59.6 pi over 1 80. So if we want to know the approximate value, we're going to use the pi button on our calculator to figure out what 59.6 times pi is. That's approximately 187.2389, Divided by 1 80. So now I would divide that number by 180 and that gives me 1.04 radiance, 1.04 radiance is the answer.
7
of the trains are arriving late due to a train strike.
Write down the ratio of on-time trains to late trains.
15
Answer:
15:7
Step-by-step explanation:
you put the numbers in order first the number of on time trains to off time trains
I NEED HELP WITH THIS ASAP! Find x and y
Answer: D
Step-by-step explanation: a^2+b^2=c^2
so use y value for b2 and 6 square root 3 as a and check with it.
A flat of plants contains 12 plants. yoshi wants a garden that has three rows with 10 plants per row. write and solve an equation for the number of flats yos should buy.
Yoshi should buy 3 flats.
What is an equation?The equation is a statement of equality between two expressions that contain variables and/or integers. In essence, equations are questions, and the development of mathematics has been driven by efforts to discover systematic answers to those questions.To find how many flats Yoshi should buy:
First, determine how many plants Yoshi requires in total. Multiply 3 by 10 so the garden will have three rows of ten plants each.3 × 10 = 30 total plantsAfter that, divide this value by the number of plants in a flat.30 / 12 = 2.5 flatsIf Yoshi is unable to purchase half the apartments, this figure must be rounded up to 3 flats.Therefore, Yoshi should buy 3 flats.
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please help I don't understand
Answer:
Each number is increasing by [tex]\frac{1}{4}[/tex]. The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
I am not sure what the question is. I am wondering if they are asking how is the list growing or what would be the next number.
Each number is increasing by 1/4
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex] you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1
Find the next two terms in the sequence. Can you please also tell me how you got the answer?
2, 9, 28, 65
[tex]\begin{array}{cccccccccccc} &&&&&&&&&\downarrow &&\downarrow \\ value&\stackrel{1^3+1}{2}&&\stackrel{2^3+1}{9}&&\stackrel{3^3+1}{28}&&\stackrel{4^3 + 1}{65}&&\stackrel{5^3 + 1}{126}&&\stackrel{6^3 + 1}{217} \\\cline{1-12} term&1&&2&&3&&4&&5&&6 \end{array}[/tex]
Write the following in interval notation
x < 8
Answer:
Yup Yup
Step-by-step explanation:
yessah
Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.
The given inequality x<8 can be written in the interval notation as,
x = (-∞,8)
Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).
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The external and the internal radii of a hollow cylindrical metallic vessel 56 cm long are 10.5 cm and 10.1 cm respectively. Find the cost of the metal contained by the vessel at Rs 2 per cubic cm. Also, find the cost of polishing it's outer surface 20 paisa per square cm.
The total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.
How to estimate the cost of polishing metallic vessel outer surface 20 paisa per square cm.?External radius of the hollow cylinder = 10.5 cm
Internal radius of the hollow cylinder = 10.1 cm
Height of the hollow cylinder = 56 cm
Cost to Polish Outer Surface: 20 paisa/sq. cm.
Surface Area of Hollow Cylinder = Circumference [tex]*[/tex] height
Surface area of hollow cylinder = 2 π r h
= 2 π (10.5 cm) 56 cm
= π (21)(56)
= 3692.64 [tex]cm^2[/tex] (Using π ≈ 3.14 rounding to 2 digits)
Total Cost of metallic cylinder [tex]$= 3692.64 cm^2 * 20 paisa/cm^2[/tex]
= 73,852.8 paisa
= Rs. 738.58
Therefore, the total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.
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Change from rectangular to spherical coordinates. (let ≥ 0, 0 ≤ ≤ 2, and 0 ≤ ≤. ) (a) (5, 5 3 , 10 3 )
The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).
Here, the given rectangular coordinate is (5, 5.3, 10.3).
Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.
We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.
We know, ρ² = (x²+y²+z²)
Therefore, ρ
= √(x²+y²+z²)
= √[(5)²+(5.3)²+(10.3)²]
= √(25+28.09+106.09)
= √(159.18)
= 12.62
Again, tan θ = (y/x)
Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°
Similarly, cos Φ = (z/ρ)
Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°
Here, the spherical coordinate is (ρ, θ, Φ).
Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).
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State what additional information is required in order to know the
triangles are congruent using the theorem or postulate listed.
Answer: line ZX is congruent to line VX (option 4)
Step-by-step explanation:
We already know <X is congruent to <X, we also know that line YX is congruent to line XW. Now all we need is one more line adjacent to X which is going to be ZX ad VX
Situation:
An archaelogist in Turkey discovers a
spear head that contains 57%of its
original amount of C-14.
Find the age of the spear head to the nearest
year.
Enter the correct answer.
Answer:
t = 6162 years
Step-by-step explanation:
This equation takes the form of
We are given everything but the amount of C-14 at time t = 0. But we can figure it out from the info we ARE given. We are told that when the spear head is found it contains 54% of its original amount of C-14. Notice we are dealing in percents. If 54% remains when it is found, it started out with 100% of its amount. That's our N value. Filling in:
Our goal is to get that t down from the exponential position that it is currently in. To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication. So we take the natural log of both sides. On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone. Before that, though, we will simplify by dividing both sides by 54. 100/54 = 1.851851852. So, altogether...
Simplifying by plugging the log of that number into our calculator, we get
.6161861395 = .0001t and
t = 6161.8613
Rounding to the nearest year, t = 6162 years
In a class 4/5 of the students have mathematical instruments 3/4 of these have lost their Protractors if 27 students have lost their protractors how many students are there in class ??
Answer:
4/5 of the students would have protractors.
Step-by-step explanation:
Consider the word pencil. if all of the letters are used, and the first letter can’t be n or l, how many ways can the letters be arranged?
480 Ways can the letters be arranged.
What is the meaning of probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.First letter can't be n or l
= 4! × [tex]5P_{3}[/tex]
= 24 × 5! /3!
= 24 × 5 × 4
= 480
Therefore, 480 ways can the letters be arranged.
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Answer: 480 ways
Step-by-step explanation:
Please please please help
In a lottery, the probability of the jackpot being won in any draw is
a What is the probability that the jackpot prize will be won in each of four consecutive draws? 1/60^4
b How many consecutive draws need to be made for there to be a greater than 98% chance that at least
one jackpot prize will have been won?
The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.
The number of consecutive draws needed will be, n = 233
What is probability?Probability is the likelihood or chance of an event happening or not.
Probability = number of expected outcomes/number of possible outcomes.From the given question, the probability of the jackpot being won in any draw is 1/60.
The probability that the jackpot prize will be won in each of four consecutive draws will be:
1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴
b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:
There is a 100% - 98% chance that that none has been won = 2% that none has been won.
Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60
The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02
Solving for n by taking logarithms of both sides:
n = 233
In conclusion, probability measures chances of an event occurring or not.
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what are these questions i need help
177
3 is a root of f(x) = x2–93987. Find the other roots of f(x).
Write your answer as a list of simplified values separated by commas, if there is more than one value.
The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
What are quadratic equations?Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0
How to determine the other roots of the equation?The equation of the function is given as:
f(x) = x^2 - 93987
The above equation is a quadratic equation
Express the equation as a difference of two squares
f(x) = (x - √93987)(x + √93987)
Set the equation of the function to 0
(x - √93987)(x + √93987) = 0
Split the factors of the above function equation as follows
x - √93987 = 0 and x + √93987 = 0
Solve for x in the above equations
x = √93987 and x = -√93987
Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
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Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e5t2 − 4t dt 4 g'(x) =
The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
According to the statement
we have given that the statement and we have to find the derivative of that term.
So, We know that the
The given equation is
[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]
Now find the derivative of that term
We find the derivative of the given term is with the help of the FTC.
And then
[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]
Then the equation become is
[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]
So, this is the derivative of the given equation.
So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
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really confused about b, how to get the position of w. Hope someone could help me.
Answer + Step-by-step explanation:
(a)
[tex]\overrightarrow{PQ} =a+\frac{3}{5} b[/tex]
(b)
we are given:
[tex]\left\vert \overrightarrow{RQ} \right\vert =\frac{3}{5} \left\vert \overrightarrow{OP} \right\vert[/tex]
Then
[tex]\left\vert \overrightarrow{WR} \right\vert =\frac{3}{5} \left\vert \overrightarrow{WO} \right\vert[/tex]
and we know that :
[tex]\overrightarrow{OW} = \overrightarrow{OR} + \overrightarrow{RW}[/tex]
Then
[tex]\overrightarrow{OW} = a +\frac{3}{5} \overrightarrow{OW}[/tex]
Then
[tex]\frac{2}{5} \overrightarrow{OW} = a[/tex]
Then
[tex]\overrightarrow{OW} = \frac{5}{2} a[/tex]
help help help help me pleaseeeeeeeee
The ticket price which will maximize the student's council is: C. $3.10.
What is price?Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.
Based on the information provided about Valley High School student council, we can logically deduce the following data:
Total number of students = 420 students.Lowest ticket price = $2.00.Increase in ticket price = $0.20.Attendance = 20 fewer students How to determine the ticket price?Mathematically, the equation which model the profit is given by:
Profit = price × number of tickets sold
P(x) = (2 + 0.2x)(420 - 20x)
P(x) = 840 + 84x - 40x - 4x²
P(x) = -4x² + 44x + 840.
For any quadratic equation with a parabolic curve, the axis of symmetry is given by:
Xmax = -b/2a
Xmax = -44/2(-4)
Xmax = -44/-8.
Xmax = 5.5
Ticket price for maximum profit is given by:
Ticket price = 2 + 0.2x
Ticket price = 2 + 0.2(5.5)
Ticket price = $3.10.
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Enter the correct answer in the box. write the expression (x4)8 in simplest form.
The simplest form of the given expression ( x⁴ )⁸ exists x³².
What is an expression?Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.
The given expression will be simplified as:-
( x⁴ )⁸ = x ⁴ ⁽⁸⁾
( x⁴ )⁸ = x ³²
Therefore the simplest form of the given expression exists as x³².
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Ileana received a statement on her certificate of deposit showing that her investment had returned $5,084 over its life. if the certificate of deposit pays a simple interest rate of 4.1% and her initial investment was $15,500, how long had the money been invested? please help me! i'm dying!
Ileana have to invest for 8 years :
What is Simple interest?Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.
How do you calculate simple interest?The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.
Given Data:Principal amount = $15,500
interest = $5,084
Time = ?
Rate = 4.1% simple interest
Solution:to find the simple interest :
I = [tex]\frac{(p*t*r)}{100}[/tex]
Then:
Time = [tex]\frac{I*100}{P*R}[/tex]
= [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]
= [tex]\frac{508400}{63,550}[/tex]
= 8 years
Ileana have to invest for 8 years
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i dont understand the math can pls help
Answer: 46.7 in/3
Step-by-step explanation:
