In rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
The area of a rectangle is the product of its length and its width.
In the question, we are given two rectangles:-
Rectangle P:
length = 40 cm,
width = x cm,
Thus, the area = length * width = 40x.
Rectangle Q:
length = 25% more than the length of P = 40 + 25% of 40 = 40 + 0.25*40 = 40 + 10 = 50 cm.
width = y cm,
Thus, the area = length * width = 50y.
Now, we are given that, the area of rectangle Q is 10% less than the area of rectangle P.
Thus, we can write that,
Area of rectangle Q = Area of rectangle P - 10% of the area of rectangle P,
or, 50y = 40x - 10% of 40x,
or, 50y = 40x - 0.10*40x,
or, 50y = 40x - 4x,
or, 50y = 36x,
or, y = 36x/50.
We are asked to find the ratio of x:y = x/y.
Substituting y = 36x/50, we get,
x/y = x/(36x/50) = 50x/36x = 25/18.
Thus, the ratio x:y = 25:18.
Thus, in rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
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Write a paragraph proof to determine whether quadrilateral PQRS is a parallelogram.
Based on the vertices of quadrilateral PQRS, we can infer that quadrilateral PQRS is NOT a parallelogram.
Why is quadrilateral PQRS not a parallelogram?Quadrilateral PQRS would be a parallelogram if the sides have the same slope as this would prove that they are parallel.
The slope of PQ is:
= (6 - 5) / (6 - 4)
= 1/2
The slope of RS is:
= (2 - 4) / (7 - 9)
= -2 / -2
= 1
The slopes are not the same so quadrilateral PQRS is NOT a parallelogram.
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Answer: The quadrilateral is not a parallelogram.
Step-by-step explanation:
I am given that the vertices of quadrilateral PQRS are P(4,5), Q(6,6), R(9,4) and S(7,2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides:
slope of PQ= 1/2
slope of QR= -2/3
slope of RS= 1
slope of SP= -1
Since each side has a different slope, none of the sides are parallel. So quadrilateral PQRS is not a parallelogram.
A running track in the shape of an oval is shown. The ends of the track form semicircles.
A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 46 m and length of one straight edge 150 m.
What is the perimeter of the inside of the track?
The perimeter of the inside of the track is 444.44m
How to calculate the perimeter?Based on the information given, the length will be 150m and the width is 46m.
The circumference will be:
=2πr
= (2 × 3.14 × 46/2)
= 144.44
The length will be:
= 2 × 150
= 300
The perimeter of the oval will be:
= 300 + 144.44
= 444.44m
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Part of the graph of the function f(x) = (x + 4) (x - 6) is shown below. A 2 Which statements about the function are truc? Select two options.
The true options include the following:
The vertex of the function is at (1,–25).The graph is negative on the entire interval –4 < x < 6.What is a Graph?This is defined as a pictorial representation of data or variables in an organized manner.
Function f(x) = (x + 4)(x – 6)
Graph intersects the x-axis at points (-4,0) and (6,0).
x-coordinate of vertex = -4+6/2 = 1
y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25
The vertex is at the point (1,-25).
The graph is positive for all x< -4 or x>6.
The graph is negative for –4 < x < 6.
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Suppose cotangent (theta) = startfraction 5 over 12 endfraction, where pi less-than theta less-than startfraction 3 pi over 2 endfraction. what is sin(θ)?
sin(Q) = -(12/13)
What are trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively. It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.
cot(Q) = 5/12
sin(Q) = 1/cosec(Q)
[tex]sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}\\[/tex]
sin(Q) = ±12/13
Because, π < Q < (3/2)π
Therefore, sin(Q) = -12/13
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Answer:
A- -12/13
Step-by-step explanation:
PLEASE show me a fifth-degree polynomial with three terms in standard form
Answer:
a. 6x^5- 3x^3+ 21
b. (6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)= 2x^5+ x^4+10
Step-by-step explanation:
The degree of the polynomial is the highest power of the terms of the polynomial .e.g
x³+ 2ax+ b² is a polynomial of 3rd degree because the highest power of the terms given is 3.
As we need a polynomial of 5th degree the highest power will be
5.6x^5+ 4x^4+ 3x^3+ 5x^2+ x+21
But this polynomial has 5 terms. We need a 5th degree polynomial with three terms so it can be any one of the following
6x^5- 3x^3+ 21
6x^5+ 4x^4+21
6x^5+ 5x^2+21
6x^5 + x+21
All of the above polynomials are in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.
Part B:
Suppose we have 2 polynomials
6x^5+ 4x^4+21 and 4x^5+ 3x^4+11
When the closure property of subtraction is applied
(6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)
= 6x^5+ 4x^4+21 - 4x^5- 3x^4-11 → coefficients are changed b/e of subtraction
= 2x^5+ x^4+10
the coefficients are changed because of subtraction.
In Polynomials the sign is changed due to subtraction and same degree terms ( like terms) are subtracted to get the answer.
A ferry traveling along the river at a constant rate covers of the distance between two ports in of
an hour. At this rate, what fraction of the distance between the two ports can the ferry travel in one
hour?
(A) 3/24 (B) 1/3 (C) 7/18 (D) 25/42
The formula speed = distance ÷ time can be rearranged, just like any other equation. The formula can be rearranged in three ways: speed = distance ÷ time , distance = speed × time.
Speed tells us how slow or fast an object moves. Distance refers to extent of space between two events. Time refers to an interval separating two events.
ASSUME a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports in 3.5 hours.
Distance that the ferry would be able to trave in 1 hour can be found out by :
unit rate=distance / time
=1/7÷3/5
Reciprocal:
=1/7×5/3
=5/21th of distance per hour
The distance that the ferry would be able to travel in 3.5 hours:
= (5/21 ) ×3.5
=(5/21)×(7/2)
Further solving:
=(5/3)×(1/2)
5/6th of the distance between two ports.
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Disclaimer:
Your question was incomplete. Please check below the full content.
Complete question could be a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports in 3.5 hours.
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You have 4/6 cup of cornmeal in your cupboard. A recipe for 2/5 muffins calls for
cup of cornmeal. How much cornmeal would you have left if you made the
muffins?
A teacher is decorating their classroom by placing posters in a row on one wall. The
teacher has 12 posters, of which 4 are colored and 8 are black & white.
a) If the teacher decides to only use 6 posters, determine how many arrangements
can be made? Describe 2 different ways to get an answer to this problem.
b) If the teacher uses all 12 posters, but wants to have a black & white poster at each
end, how many arrangements can be made? Justify your answer.
c) If the teacher uses all 12 posters, but wants all the colored posters to be side-by-
side, how many arrangements can be made? Justify your answer.
The permutation illustrates that when the teacher decides to only use 6 posters, the number of arrangements that can be made will be 665280 ways.
How to calculate the values?When the teacher decides to only use 6 posters, the number of arrangements will be:
= 12P6
= 12!/(12 - 6)!
= 12!/6!
= 665280 ways.
The fundamental principle will be:
= 12 × 11 × 10 × 9 × 8 × 7
= 665280 ways
When the teacher uses all 12 posters, but wants to have a black & white poster at each end, the number of arrangements will be 203212800 ways.
When the teacher uses all 12 posters, but wants all the colored posters to be side-by-side, the number of arrangements will be:
= 4!8!
= 4 × 3 × 2 × 1 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 967680 ways.
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35/6 divided by 5/4 in ait simplest form
The simplest form of 35/6 ÷ 5/4 is 14/3
Given,
35/6 ÷ 5/4
hence it is written as= 35/6 ×4/5
= 7×2/3×1
= 14/3
The simplest form of fractions are determined by following the given steps:
List the denominator's and numerator's factors.Find the common factors between the denominator and numerator.The fraction obtained is in the reduced form when the numerator and denominator are divided by the common factors until they have no common factor but 1.This number can't be further subdivided. Hence we get the the simplest form of 35/6 ÷ 5/4 as 14/3.
If we get numbers which share common highest common factor then divide the number by both numerator and denominator to bring the simplest form of number.
Therefore we get the simplest form of number as 14/3.
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What is 16% of 750?
Answer:
120
Step-by-step explanation:
For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120
Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown below. Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4. Casey: The rule is (x + 2, y + 4) because the image is (2, 4). Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites. Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4. Which student is correct?
Answer:
Raheem
Step-by-step explanation:
The figure shows a circle circumscribed around a triangle.
Triangle U T V is inscribed within a circle. A point is at the center of the triangle. Lines are drawn from the points of the triangle to the point in the middle. Lines are drawn from the point in the middle to the sides of the triangle to form right angles.
What is constructed first when creating the circle?
perpendicular segments to the vertices of the triangle
perpendicular bisectors of the sides of the triangle
angle bisectors of each angle of the triangle
the incenter of the triangle
Option B is right perpendicular bisectors of the sides of the triangle
What circumcircle?If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.
One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.
When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.
When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C
In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC
Therefore Option B is right perpendicular bisectors of the sides of the triangle.
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more math i need help in
Answer:
It is B
Step-by-step explanation:
I need answer quickly
Answer:
b = 4.5
Step-by-step explanation:
a = 4
c = 6
c² = a² + b²
6² = 4² + b²
36 = 16 + b²
b² = 36 - 16
b² = 20
[tex]b = \sqrt{20} [/tex]
b = 4.5
In the given figure CB ǁ QR, CA ǁ PR, AQ = 12cm, CB = CQ =15cm. Calculate PC and BR .
By applying basic proportionality theorem (BPT), the length of side PC and BR are 25 cm and 9 cm respectively.
How to calculate the length of side PC and BR?In order to determine the length of side PC and BR, we would apply basic proportionality theorem (BPT) as follows:
PC/CQ = AR/AQ
PC/15 = 20/12
Cross-multiplying, we have:
12PC = 20 × 15
PC = 300/12
PC = 25 cm.
For the length of side BR, we have:
PC/CQ = PB/BR
PC/15 = 15/BR
25/15 = 15/BR
25BR = 225
BR = 225/25
BR = 9 cm.
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IJ=
Measure of IJ
Help me thanks
Answer: 11
Step-by-step explanation:
By the secant-secant theorem,
[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]
There are five different points on a line. how many segments are there on the line?
There are 10 line segments on a line with five different points on it.
What are a line and a line segment?Line:
A line is formed with infinite points and it is extended infinitely along a straight path in both directions.
Line segment:
The part of the line that lies between two distinct points on the line. This is also called the shortest distance between two points on the line.
How many segments are there on the line with five different points?Consider a line with five points on it as A, B, C, D, and E.
So, the possible line segments are
AB, AC, AD, AE, BC, BD, BE, CD, CE, DE
So, there are 10 line segments are formed on line with five different points.
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A
B
Value: 10
AB=
12√2
BC=
45°
Find the missing side lengths. (Enter your answer
without units.)
C
Answer:
12
Step-by-step explanation:
This is a special triangle with angle measure 45-45-90
The side lengths for this special right triangle is as follows:
The side length that sees angle measure 90 is represented by a[tex]\sqrt{2}[/tex]
The side lengths that see angle measures 45 is represented by a
We can see from the image hypotenuse (the side that sees angle 90)
is given as 12[tex]\sqrt{2}[/tex] that means a = 12
So the missing side lengths (both see angle measure 45) = 12
Alone LiZ can complete a project in 12 hours and Julia could do it alone in 24 hours. Liz worked on the project alone 2 hours before Julia joined her. How many hours did they work together to finish ?
Answer:
Julia and Liz worked 10 hours to finish the project.
Step-by-step explanation:
I don't know if I am 100% right, but I believe this is the answer.
If you take the 24 hours it will take Julia to finish the project on her own and subtract the time it would take Liz you would have 12 hours left then take the 2 hours Liz has already been working on the project you would have 10 hours for both of them to finish the project together.
24 -12 = 12
12 - 2 = 10
HELP HELP HELP
Just 5 quick algebra 1 questions for 50 points!
1. x = a
2. y = b
3. It has an undefined slope.
4. You can either use, rise/run or change in y / change in x.
5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.
What is the Equation of a Line?Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.
1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.
Vertical line equation is: x = a.
2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.
3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.
4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.
5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:
y - 3 = 6x - 24
y = 6x - 24 + 3
y = 6x - 21
The y-intercept, b, is: -21.
Therefore, the coordinate of the y-intercept would be: (0, -21).
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4. Mr.X is thinking of two numbers. -The sum of the numbers is 212. -The difference between them is 88. Solve a system of equations to determine the value of each number.
Answer:
62 and 150
Step-by-step explanation:
let the 2 numbers be x and y , x > y , then
x + y = 212 → (1)
x - y = 88 → (2)
add the 2 equations term by term to eliminate y
2x + 0 = 300
2x = 300 ( divide both sides by 2 )
x = 150
substitute x = 150 into (1)
150 + y = 212 ( subtract 150 from both sides )
y = 62
the 2 numbers are 62 and 150
A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3
The work required to pump the water out of the spout is 5000ft⋅lb
Given
The volume V=12(4ft)(5ft)(6ft)=60ft3,
Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.
Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.
Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.
In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.
We have to lift that slice 4ft−y, so work is
w = [tex]\int\limits^4_0[/tex] (62.5)(4 − y) (7.5y)
dy = (62.5)[15y2−2.5y3]40 = 5000ft⋅lb
The work required to pump the water out of the spout is 5000ft-lb
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144 = -12(x+5)
I need help with solving this problem it’s very difficult too solve
[<Answer>] (3):
Hello! I'm Avery. And I would love to help you :)
---------------------------------------------------------------------------------------------------------
[<The Explanation>}:
Step one: Distribute
[tex]144 = -12(x + 5)[/tex]
[tex]144 = -12x - 60[/tex]
Step two: Add 60 to both sides
[tex]144 = -12x - 60\\144 + 60 = -12 - 60 + 60[/tex]
Step three: Simplify
Adding..Adding..(Done!): [tex]204 = -12x[/tex]
Step four: Divide both sides by the same factor
[tex]204 = -12x\\\frac{204}{-12} = \frac{-12x}{-12}[/tex]
Last and not least..Step five:
Divide then, Cancel the terms, Move the Variable to the left...
And.. x = -17 is the answer :D
----------------------------------------------------------------------------------------------------------
[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! >:D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
Simplify the expression by combining like
terms:
4x² + 6x + 5x²-x
Enter the number that belongs in the green box.
[?]x² + [ ]x
Answer:
9x² + 5x
Step-by-step explanation:
4x² + 6x + 5x²-x
Combine like terms:-
4x² + 5x² = 9x²
6x - x = 5x
9x² + 5x
-----------------------------
Please help ASAP
Please help ASAP
Please help ASAP
Answer:
Step-by-step explanation:
Answer:
9% only a guess.May not be correct..
In this circle, the area of sector COD is 50.24 square units.
The radius of the circle is ____ units, and mAB is ____ units.
Answer:
Radius = 8 units
Length of arc AB = 8.37758 units
Step-by-step explanation:
The sector COD is 1/4 the size of the circle.
the vertex angle is 90° and a circle has 360° at the center.
So the area of sector COD/area of Circle = 90/360 = 1/4
This means the area of the circle is 4 * 50.24 = 200.96 square units
Area of circle = πr² where r is the radius
πr² = 200.96
r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units
The circumference of the circle is 2πr = 16π units
arc AB has a vertex angle of 30°.
30°/360° = 1/6
So the length of the arc is 1/6th the circumference of the circle =
(1/6) * 16π = 2.67π units or 8.37758 units
Jackson conducted a survey at his school about its students' favorite
sport. He chose a name at random from a list of all the students in the
school, and chose every 10th student after that for the sample.. Was this
a random sample, and if so, which sampling method did Jackson use?
OA) Yes, simple random sample.
O B) Yes, systematic random sample.
OC) Yes, stratified random sample.
OD) No, it was not a random sample.
Answer:
OB
Step-by-step explanation:
it's not a beacuasenhes not doing everyone
and we have no info on whether anyone serveylayed a sport so the only possible option is 2
Help!
What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values.
The graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
How to determine the regression equation?From the table of values, we can see that:
As the time increases, the distance increases
However, the increment in the distance is not a linear increment.
This means that:
The graph cannot be (a) and (d); these graphs show scattered pointsThe graph cannot be (c); it shows that distance decreases, as time increasesThe graph (b) represents an exponential model.
When the points on the table are entered in a graphing calculator, we have the regression equation to be
y = 1.030 * 3.709^x
Hence, the graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
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i need help with this question guys i’ll give you brainly
Answer:
C
Step-by-step explanation:
C is most relevant to the question
Please helpppppppppp
Answer:
1 4/5
Step-by-step explanation:
On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 [tex]\frac{4}{5}[/tex].