The page is in landscape mode with a width : height is 3: 2
Given that,
The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.
x = length of the horizontal side of the printable area
y = length of the vertical side of the printable area
XY = 42 inch²
y = 42/x
page height = y + 1 + 1
page width = x + 1 + 2
A = area of an entire sheet of paper
= (x+3)(y+2)
= (x+3)(42/x+2)
= x(42/x+2)+3(42/x+2)
= 42+2x+126/x+6
A = 2x+126/x+48
Extremes occur when A' = 0:
A' = 0 = 2 – 126/x²
1 = 63/x²
x² = 9*7
x = 3√(7), x has to be positive
y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)
What should the dimensions of the page be so that the least amount of paper is used?
page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)
page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)
So, the page is in landscape mode with width: height is 3: 2.
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Which of the ordered pairs below is a solution to the system of inequalities?
The ordered pair which is a solution to the system of inequalities is: (-1, 0).
How to determine the solution?In order to determine which ordered pairs are true solutions based on the given system of inequalities, we would have to test each of the ordered pairs by substituting their values into the system of inequalities as follows;
For ordered pair (4, 3), we have:
-7x + 3y > -1
-7(4) + 3(3) > -1
-28 + 9 > -1
-19 > -1 (False).
For ordered pair (2, 8), we have:
-7x + 3y > -1
-7(2) + 3(8) > -1
-14 + 24 > -1
10 > -1 (True).
5x - 9y > -6
5(2) - 9(8) > -6
10 - 72 > -6
-62 > -6 (False).
For ordered pair (-1, 0), we have:
-7x + 3y > -1
-7(-1) + 3(0) > -1
7 + 0 > -1
7 > -1 (True).
5x - 9y > -6
5(-1) - 9(0) > -6
-5 - 0 > -6
-5 > -6 (True).
For ordered pair (-2, 2), we have:
-7x + 3y > -1
-7(-2) + 3(2) > -1
14 + 6 > -1
20 > -1 (True).
5x - 9y > -6
5(-2) - 9(2) > -6
-10 - 18 > -6
-28 > -6 (False).
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Show that
tan15°=2−√3
It is proved that tan15°=2−√3 by using the identity of tan(A-B)
What are the 3 trignometric identities?
The right-triangle theorem, also known as Pythagoras theorem, is the foundation for the three Pythagorean trigonometric identities.
[tex]sin^{2}a+cos^{2}a=1[/tex]
[tex]1+tan^{2}a=sec^{2}a[/tex]
[tex]cosec^{2}a=1+cot^{2}a[/tex]
The reciprocal trigonometric identities are:
Sin θ = 1/Cosec θ or Cosec θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
tan 15 = tan(45 - 30)
As tan(A - B) = (tanA - tanB)/(1 + tanAtanB)
tan15 = tan(45 - 30) = (tan45 - tan30)/(1 + tan30tan45)
= [tex]\frac{1 - \sqrt{3} }{1+\sqrt{3} }[/tex]
= [tex]\frac{1-\sqrt{3} }{1+\sqrt{3} }[/tex] × [tex]\frac{1 - \sqrt{3} }{1-\sqrt{3} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-\sqrt{3} ^{2} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-3}[/tex]
= [tex]\frac{(1-\sqrt{3} )^{2} }{-2}[/tex]
= [tex]\frac{1+3-2\sqrt{3} }{-2}[/tex]
= [tex]\frac{4-2\sqrt{3} }{-2}[/tex]
= 2-[tex]\sqrt{3}[/tex]
Hence it is proved that tan15°=2−√3
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A student solves the problem 354 divided by 24. The student finds an answer of 13 R40. Explain how you can tell that the answer is incorrect just by looking at the remainder.
Answer:
Step-by-step explanation:
When dividing, you always have to make sure that your remainder
(40) is ALWAYS less than your divisor (24)
24<40, so the students' answer is incorrect.
1. The measures of the angles in a triangle are in the extended ratio of 1:4:7. Find the measures of the angles.
i need help with my homework
Answer:
1 : 4 : 7
15 : 60 : 105
Step-by-step explanation:
1 + 4 + 7 = 12
180⁰ ÷ 12units = 15⁰
1 unit = 15⁰
4 units = 15⁰ × 4 = 60⁰
7 units = 15⁰ × 7 = 105⁰
help help help me please
Someone help pleaseeee !
The value of x and y which is on midsegment of the triangle is 1 and 11.
What is midsegment?
A triangle's midsegment is the section of the triangle's shape that connects the midpoints of its two sides. a section of a line connecting the midpoints of two triangle's sides. There are three possible midsegments in a triangle. The section of a line between the midpoints of two triangle sides is known as a midsegment. Due to the fact that triangles have three sides, they also have three midsegments. A line drawn by joining the midpoints of any two of a triangle's sides is known as the midsegment.
let us assume triangle as ABC and DE is the midsegment .
Where DE=2x+1 and BC = 8x-2 .
According to the midsegment theorem ,
=> DE = 1/2 BC
=> 2x+1 = 1/2(8x-2)
=> 2x+1=4x-1
=> 2x=2
=> x=1
Now AB divided intp AD=3z and DB=z+22
Then, AD=DB
=> 3z = z+22
=> 2z = 22
=> z = 11.
Hence the value of x=1 and z= 11.
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Write equivalent fractions for 11/12 and 5/6 using least common denominator.
Type the fractions using a slash ( / ) to separate the numerator and denominator.
11/12 =
5/6 =
A circle has a circumference of 3.143.143, point, 14 units.
What is the diameter of the circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
The diameter of the circle is 4.45 units.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.
A line segment having both the endpoints on the circle and is the largest chord of the circle is called diameter.
Given,
the circumference of circle = 14 units
circumference = πd
14 = 3.14(d)
14/3.14 = d
d = 4.45
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You're shopping for a new shirt and find one that's on sale for $16.25. The sign says it is a 35% discount. What was the original price of the shirt BEFORE the discount?
The original price of the shirt before the discount will be $25.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
You're looking for another shirt and find one that is discounted to $16.25. According to the sign, it is a 35% markdown.
Then the original price of the shirt before the discount will be given as,
⇒ $16.25 / (1 - 0.35)
⇒ $16.25 / 0.65
⇒ $25
The original price of the shirt before the discount will be $25.
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what Is the inequality shown?
The inequality shown is -4 ≤ x ≤ 3.
We are given a diagram of the number line. The diagram shows the range of the inequality. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. Let the variable "x" represent all the values contained in the inequality. The minimum value contained in the inequality is -4. The maximum value contained in the inequality is 3. All the values between the minimum and maximum limits are included in the inequality. Hence, we can write the following inequalities :
-4 ≤ x
x ≤ 3
We can combine these into a single inequality.
-4 ≤ x ≤ 3
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Which expression equals 9/10 ?
O 5√10+4√10
O5 10+4 10
O 5√10+43/10
O 5 10+4 10
Answer:
The second answer:
5cubrt10 + 4cubrt10
Step-by-step explanation:
In order to get a cubrt10 answer you have to add cubrt10's.
The first answer has squareroots, so that's a no.
The last two have cubrt + sqrt, which cannot be simplified.
5cubrt10 + 4cubrt10 = 9cubrt10
Help me plss!!!
Solve for x.
Question 6 options:
1)
32
2)
6
3)
63
4)
3
The value of angle with x, given the equation on the circle, is 4) 3.
How to find the value of x?The angle is given by the expression:
31x + 3
The same angle is shown to be a right angle with the line EF being straight and therefore a right angle. Right angles have a total measure of 90 degrees.
The value of x can therefore be found by equating the expression to 90 degrees:
31x + 3 = 90
31 x = 90 - 3
x = 87 / 31
x = 2.8
x = 3
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A local hamburger shop sold a combined total of 680 hamburgers and cheeseburgers on Friday. There were 70 fewer cheeseburgers sold than hamburgers. How
many hamburgers were sold on Friday?
hamburgers
Answer:
375
Step-by-step explanation:
h + c = 680
c = h - 70
h + h - 70 = 680
2h = 680 + 70
2h = 750
2/2 h = 750/2
h = 375
a new shopping mall is gaining in popularity. every day since it opened, the number of shoppers is 5% more than the number of shoppers the day before. about how many total shoppers would be expected after 10 days, if there were 100 shoppers on the first day?
After 10 days, the expected number of shoppers at the shopping mall is 163.
It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.
As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.
The formula of compound increase is
Amount = Base X (1 + r/n)ⁿˣ
where,
Base = original amount
r = rate of change
n = no. of times the change occurs in the time period
t = time
Here,
Base = 100
r = 5/100
n = 1, since it changes once every day
x = 10
Therefore we get
100 X (1 + 5/100)¹⁰
= 100 X 1.05¹⁰
162.88
Since the number of people cannot be in decimal,
the expected number of people is 163
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Williams and Co. is spliting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million. What is their Total pre-split Market Capitalization?
Total pre-split Market Capitalization is $1,08,125,000.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
Williams and Co. is splitting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million.
Total Value of Shares = $43.25 Share Price × 2.5 × 10⁶ Shares
Total Value of Shares = $1,08,125,000
Let’s say the company’s board decides to approve a 3-for-1 split.
Total Shares = 2.5 × 10⁶ × 3 = 75,00,000
Share Price = $43.25 ÷ 3 = $14.416
Total Value of Shares = $14.416 Share Price × 75,00,000 Shares
Apply the multiplication operation,
Total Value of Shares = $1,08,120,000
Thus, the total pre-split Market Capitalization is $1,08,125,000.
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Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then, interest rates have increased to 12.75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11.10 monthly per thousand on her loan. (You can ignore the small amount of principal paid during the 3 years.)
The old monthly payment is $
.
The new monthly payment is $
.
The percent increase in her monthly payment (to the nearest tenth) is
%.
The old monthly payment was = 9.27 x 50 = 463.5
The new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
Given,
Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan
According to the question:
So, per thousand value of $65000 is 50000/1000 =50
Now, the old monthly payment was = 9.27 x 50 = 463.5
She decides to renew and will now pay $11.10 monthly per thousand on his loan.
So, the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100
19.7411 % and to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 x 50 = 463.5
the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
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Ms. Nettleton wants to create an outdoor space for her dogs. The distance between the furthest corners is 4 feet. The width of the area is 2 feet. How long is the length of the area?
(please help)
The length of the area is 8 feet.
What is the shape of outdoor space?
We know that Square has equal length, Rectangle has opposites sides of equal length.By the given length we found that it is Rectangular outdoor space.Step-by-step explanation:
Given :
Distance between the furthest corners(Length)= 4 feet
Width(breadth) = 2 feet
Area of rectangle = Length * Breadth
= 4 * 2
=8 feet
Hence, The length of the area is 8 feet.
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help
If T=5n+2, which term will have a value of 52?
Answer:
T = 52
Step-by-step explanation:
greta is opening a savings account. she starts with 100$ and plans to add 50$ each week. write an equation she can use to calculate the amount of money she will have after any number of weeks. how much money will she have after 1 year?
Money she will have after 52 weeks = rs.2,700
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Unit rate of change here is =
⇒ Unit rate of change here is =
⇒ Unit rate of change here is = 50%
Part B
Equation to calculate the amount of money Greta will have after any number of weeks = ?
Money after 'x' number of weeks =
⇒ Money after 'x' number of weeks =
Part C
Money Greta will have after 1 year= ?
In a year there are 52 weeks
So, putting x = 52 in the solution of Part B
⇒ Money after 52 weeks =
⇒ Money after 52 weeks =
⇒ Money after 52 weeks = 2,700
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 82°
Step-by-step explanation:
The three angles of the triangle add up to 180°
x + 40° + 58° = 180°
x + 98° = 180°
subtract 98°
x = 82°
Answer:
x = 82°
Step-by-step explanation:
The sum of the internal angles of a triangle = 180°
58° + 40° + x° = 180°
98° + x° = 180°
x° = 180° - 98°
x° = 82°
the physical examination records of the freshmen class of 1935 at university of toronto were examined in 1980 to see whether the freshman's record of bmi at the time of admission to the university were related to their chance of developing coronary heart disease in 1980. this is an example of:
A prospective research of men and women looked at body mass index, waist circumference, and the risk of coronary heart disease.
What is body mass index?Body Mass Index (BMI) is calculated by dividing a person's weight in kilograms (or pounds) by their height in meters squared (or feet). High body fatness may be indicated by a high BMI.BMI does not make a body fat or health diagnosis for a person, but it does screen for weight categories that may cause health issues.Calculate Adult BMI Using This WidgetBy including this widget on your website, anyone can determine their BMI. For the majority of persons, BMI is an accurate indication of body fatness. It is used to check for weight ranges that could cause health issues. The BMI and accompanying weight category are provided by this calculator. Adults who are at least 20 years old should use this calculator.Child and Teen BMI Calculator Widget from the CDCInclude this widget on your webpage. The CDC BMI-for-age growth chart is used to calculate BMI and the related BMI-for-age percentile. From the age of two to nineteen, kids and teenagers can use this calculator.For Schools: The Children's BMI ToolThis spreadsheet can be used by educators, daycare operators, and other experts to calculate BMI forLearn more about bmi here:
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The perimeter of an equilateral triangle is 63 inches. If the length of each side is (3x-9), find the value of x.
Answer:
x=
Step-by-step explanation:
There are 2 ways to do this.
4(3x-9)=63; 12x-36=63; 12x=99; x=8. Or: (3x-9)+(3x-9)+(3x-9)+(3x-9)=63; 12x-36=63; 12x=99; x=
Put these numbers in order from greatest to least.
-24/40
0.5
66 6/15
66.2
-0.4
Answer:
First simplify the ones that need dividing
Step-by-step explanation:
So i got
-0.4, -0.6, 0.5, 4.44, 66.2
Hope this helps!
i need help also i don't know what to do with x. 3(4x-12) = 84
Answer:
x=10
Step-by-step explanation:
3(4x-12)=84
12x-36=84
+36. +36
12x=120
/12. /12
x=10
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Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four. Skip to navigation
If ∠4 ≅ ∠14, then the lines that must be parallel are a and b and so we can say that; a∥b, Converse of the Alternate Interior Angles Theorem
What are Interior Angles?Interior angles are basically the pair of angles created on the inner side of the parallel lines and right on the opposite sides of the transversal when two parallel lines are intersected by a transversal .
We are told that ∠4 ≅ ∠14, which lines,
If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposite angles are equivalent.
Thus, angle 4 is congruent to angle 14.
Therefore, we can deduce the following;
Angle 15 is a corresponding angle to angle 3 and so we can write that;
∠15 ≅ ∠3
Angle 15 is a vertically opposite angle to angle 13 and so we can write that; ∠15 ≅ ∠13
By transitive property of equality, we can say that;
∠3 ≅ ∠13 [Alternate interior angles]
Thus, we have ∠4 ≅ ∠14
Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.
Hence, the correct answer would be an option (B).
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Geometry pls help me
The radius of the given circle is 7.5 units.
What is the radius?A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."The diameter of a circle cuts through the center while the radius extends from the center to the edges of the circle. The diameter of a circle effectively divides the shape in half.So, use the Pythagorean theorem:
Where, c² = a² + b².We know that, AB² = AC² + CB².Now, calculate as follows:
AB² = AC² + CB²AB² = 12² + 9²AB² = 144 + 81AB² = 225AB = √225AB = 15
So, the diameter is 15 units.
Then the radius is:
15/2 = 7.5 unitsTherefore, the radius of the given circle is 7.5 units.
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what is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function?
(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.
As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.
Domain of the tangent function be, R - {(2n+1)π/2}
Range of the tangent function be, R
Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.
So, the restricted domain be (-π/2 , π/2).
In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.
So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.
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If there are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?
The ratio Illustrated shows that the number of vanilla marshmallow is 121.
What is a ratio?A ratio shows how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. It should be noted tjat.A/B will be the formula if one is comparing one data point (A) to another data point (B).
Let the vanilla marshmallow be represented be x.
Since the ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11, the vanilla will be:
= 11 / (5 + 11) × 176
= 11/16 × 176
= 11 × 11
= 121
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Complete question
The ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11. There are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?
professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
Given that;
In his principles of microeconomics subject, Professor Elderman has utilized the same multiple-choice final exam for many years. He looks over the last ten years' worth of statistics and discovers that the scores have a mean of 76 and a standard deviation of 12.
µ = 76 , σ = 12 , n = 36
Using Normal Distribution;
For x = 70
z = (x - µ) / (σ/√n) = (70-76)/(12/√36) = -3.00
P( average greater than 70 ) = P(X>70)
= 1 - P(X<70)
= 1 - P(Z<-3.00)
= 1 - 0.0013
= 0.9987
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
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If $3000 is invested at tan interest rate if 4.8%, compounded hourly for two years what is the ending balance?
The final balance is $97,920.
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Given this, The principal is $3000.
Interest rate = 4.8%
Time = 2 years We must find the final balance.
The end balance formula is
C = P[ 〖(1+r)〗^n – 1]
C = 3000[ 〖(1+4.8)〗^2 – 1]
C = 3000 [ 〖(5.8)〗^2 – 1]
C = 3000 [ 33.64 – 1]
C = 3000 ( 32.64)
C = 97,920
Therefore the ending balance is $97,920
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