Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
Answers
The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.
How to determine the maximum possible area of an isosceles trapezoid
Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.
A = 0.5 · (B + b) · h (1)
By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:
B = b + 2 · l · cos θ (2)
h = l · sin θ (3)
Where θ is an internal angle, in degrees.
By (2) and (3) in (1):
A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)
A = (b + l · cos θ) · (l · sin θ)
A = b · l · sin θ + l² · sin θ · cos θ
A = b · l · sin θ + 0.5 · l² · sin 2θ (4)
If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:
A = 24 · sin θ + 8 · sin 2θ (5)
Now we determine the angle associated to the maximum area by graphic approach.
According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. \(\blacksquare\)
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Related Questions
if the lcm of a number is 630 and the HCF is 10 what will be the first number it the second number is 10
Answers
Answer:
1000
Step-by-step explanation:
In a survey of 300 T.V. viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs.
Answers
Answer:
0.05543Step-by-step explanation:
The formula for calculating the margin of error is expressed as;
\(M.E = z * \sqrt{\frac{p*(1-p)}{n} }\) where;
z is the z-score at 95% confidence = 1.96 (This is gotten from z-table)
p is the percentage probability of those that watched network news
p = 40% = 0.4
n is the sample size = 300
Substituting this values into the formula will give;
\(M.E = 1.96*\sqrt{\frac{0.4(1-0.4)}{300} }\\ \\M.E = 1.96*\sqrt{\frac{0.4(0.6)}{300} }\\\\\\M.E = 1.96*\sqrt{\frac{0.24}{300} }\\\\\\M.E = 1.96*\sqrt{0.0008}\\\\\\M.E = 1.96*0.02828\\\\M.E \approx 0.05543\)
Hence, the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs is approximately 0.05543
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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So far, I got 3 out of 5 but I don't know the rest
Answers
The indicated 40% of the people who are female and 10% female who are left-handed indicates;
The percentage of people who are not female who are left handed is 16.8%What is a percentage?A percentage is the representation of a quantity as a fraction with a denominator of 100.
The percentage of females in the town = 40%
The percentage of the females that are left handed = 10%
The percentage of left handed people in the town = 20.8%
Let F represent the females, let L represent the left handed, and let U represent all the people in the town, we get;
The percentage of the people that are both females and left handed is therefore;
P(F ∩ L) = 10% × 40% = 4%
Therefore, in 100 people in the town, 4 are female and left handed, which indicates;
20.8 percent of all people in the town are left handed, therefore, in 100 people, 20.8 are left handed
The number of people that are left handed but not female is therefore;
20.8 - 4 = 16.8
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If a polynomial function has integer coefficients, then every rational zero of the function has the form p/q, where p is a factor of the ? and q is a factor of the ?
Answers
If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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Can some one tell me the slope please and thank yiu
Answers
Answer:
\(-\frac{5}{3}\)
Step-by-step explanation:
The slope between two points can be found by taking the ratio of the change in y-coordinates to the difference in x-coordinates of the two points. This can also be represented by the formula: \(slope=\frac{rise}{run}\).
From left to right, we see that the second point decreases by 5 units from the first point, and is 3 units to the right of the first point.
Thus, slope of line joining the two points
\(=\frac{-5}{3}\)
\(=\bf{-\frac{5}{3} }\)
Note that the change in the y-coordinates is -5 since it is a decrease in the y-axis, and the line segment is sloping downwards.
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Absolute value -1+5 |n|=44 pls show work
Answers
Answer:
n = -9 or 9
Step-by-step explanation:
-1 + 5|n| = 44
~Add 1 to both sides
5|n| = 45
~Divide 5 to both sides
|n| = 9
~Knowing the absolute value rule, the answer can be positive or negative.
Best of Luck!
Answer:
The value of n is 9 or -9.Step-by-step explanation:
-1 + 5|n| = 44=> 5|n| = 44 + 1=> 5|n| = 45=> |n| = 45/5=> |n| = 9 or -9=> n = 9 or -9Hence, the value of n is 9 or -9.
Hoped this helped.
\(BrainiacUser1357\)
Select the system of linear inequalities whose solution is graphed. O y < 3x-2, x + 2y > 4 O y ≤ 3x-2, x + 2y 2 4 O y> 3x-2, x + 2y < 4 O y2 3x-2, x + 2y ≤ 4
Answers
Option D is the correct answer.
From the graph, we can conclude that,
1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.
2. The points on the lines of the shaded region are also included in the solution.
The only option that matches with the above conditions is option D. So, option D is the correct answer.
Let us verify it.
Now, let us consider a point that is inside the shaded region and also on any one line.
Let us take (0, 2).
Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.
Considering the inequalities,
y ≥ 3x - 2
x + 2y ≤ 4
Solving we get,
2 ≥ 3(0) - 2
2 ≥ -2
x + 2y ≤ 4
0 + 2(2) ≤ 4
4 ≤ 4
Here, both inequalities are correct.
So, option D is the correct answer.
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The complete question is =
Which system of linear inequalities is graphed?
A. y < 3x-2
x + 2y ≥ 4
B. y < 3x - 2
x + 2y > 4
C. y > 3x - 2
x + 2y < 4
D. y ≥ 3x - 2
x + 2y ≤ 4
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 9%, interest periods: 4, number of years: 18
After 18 years, the investment compounded periodically will be worth $? more than the investment compounded annually.
(Round to two decimal places as needed.)
Answers
After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.
What is compounded interest?Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.
The period of compounding in a year determines the worth of the future value.
The future value can be ascertained using an online finance calculator as follows:
Interest periods: = 4 times yearly (Quarterly)
Principal = $5,000
Annual interest rate = 9%
Number of years: 18
N (# of periods) = 72 quarters (18 years x 4)
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $24,815.83
Total Interest = $19,815.83
Interest periods: = Annually
N (# of periods) = 18 years
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $23,585.60
Total Interest = $18,585.60
Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)
Thus, an investment compounded periodically earns more than an investment compounded annually.
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Write the fraction below as a sum or difference.
11x + 5
6
Answers
The fraction in form of sum or difference will be;
⇒ 11/6x + 5/6
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ (11x + 5) / 6
Now,
Since, The fraction is,
⇒ (11x + 5) / 6
It can be written as;
⇒ (11x + 5) / 6
⇒ 11x/6 + 5/6
Thus, The fraction is written as;
⇒ 11/6x + 5/6
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Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answers
Applying the sine rule the value of side w is calculated to be 6.2
How to find the size of wThe size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal
the formula is
Sin A / a = Sin B / b = Sin C / c
applying the formula for the problem
Sine W / w = Sine X / x
plugging in the values
Sine 38 / w = Sine 84 / 10
cross multiplying
w = 10 x Sin 38 / Sine 84
x = 6.185
x = 6.2 to the nearest tenth
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A
X
Find the value of x.
D
X+2
x = [?]
B
3
E
2
C
![AXFind the value of x.DX+2x = [?]B3E2C](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/NizqkSoyno5R9ihZJuX6BBJHmDyqL8LN.png)
Answers
Answer:
x = 4
Step-by-step explanation:
if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.
DE is such a line , then
\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\) ( substitute values )
\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )
3x = 2(x + 2)
3x = 2x + 4 ( subtract 2x from both sides )
x = 4
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
I need help on listing the four points that have a distance of 5 from the point B, correct answer I will make brainliest thank you!
Answers
Answer:
(0,5) (-5,0) (-5,10) (-10,5)
Step-by-step explanation:
1st Question:
Solve: 3/x-4>0
X<4
X>-4
X>4
X<-4
2nd Question:
Solve x+2/x-4<0
-4
-2
-2
-4
Answers
Answer:
1) 3/4 = x
Step-by-step explanation:
1) 3/x -4 >0
=3/x -4+4>0 +4
=3/x> 4
switch 4 with x
x = 3/4
so literally the ans is x< 4
sorry but I don't know how to do the second question ☹️☹️
Answer:
first Question answer is x > 4. The second question answer is –2 < x < 4
Step-by-step explanation:
EDGE 2021
(SAT Prep) Find the value of x.
Answers
Answer: 36˚
Step-by-step explanation:
180 - 3x = 2x
180 = 5x
.: x = 36˚
last year lien earned $1,300 more then get husband. together they earned $58,600. how much did each of them earn?
Answers
Husband earned 57,300
Explanation: 58,600-1,300 would give you 58,300 which would be the husbands money.
Answer:
lien earned 29950, husband earned 28650
Step-by-step explanation:
you subtract 1300 from the total then divide by 2 and add the 1300 to liens half.
Hhhhhhhhhhhhhhhhfehhdgdhdhdu
Answers
Answer:
it should be 450 yards
Step-by-step explanation:
A= a+b/ 2
h=27+18/ 2·20= 450
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. The retail price of a particular smartphone and the number of units sold at that price
Answers
Answer:
no correlation
Step-by-step explanation:
The price of the smartphone is fixed beforehand, therefore price does not depend upon the number of units sold.
Hence, there is no correlation between the two given variables.
Hence, no correlation would be the answer.
inverse function of f(x)=x-7/x+4
Answers
Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7
Lashonda purchased a prepaid phone card for $25. Long distance calls cost 8 cents a minute using this card. Las
distance call. If the remaining credit on her card is $23.48, how many minutes did her call last?
Answers
Answer:
About 2 minutes
\(25-(2*.8)= 23.4\)
What is the volume of the cylinder? A about 2414.7 cm³ Babout 6281.6 cm³ about 9076.3 cm³ 3 O about 36,305.0 cm³ 21.5 cm 25 cm
Answers
The volume of the cylinder is 9071.65 cubic centimeters.
We have to find the volume of the cylinder with a height of 25 cm.
The base has a diameter of 21.5 cm.
Radius of cylinder = 21.5/2
=10.75 cm
The formula for Volume =πr²h
Where r is the radius and height is 25 cm.
Plug in the values of radius and height in to the volume formula.
=3.14×10.75²×25
=9071.65 cubic centimeters.
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What is the least common denominator of
Answers
Answer:
Step-by-step explanation:
Least common denominator
x - 1 is not going to be included because x - 1 is included in x^2 - 1
x^2 - 1 factors into (x - 1)(x+1) so you need only 1 x - 1.
You do however, need an x.
The answer is x(x + 1)(x - 1)
Using plane K, name a point that is not on the line.
Answers
Answer:
H
Step-by-step explanation:
Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.
The point in plane K that is not shown on any line is point H.
Refer to the golden ticket parking lottery example (page 296). At the following month's school assembly, the two lucky winners were once again members of the AP Statistics class. This raised suspicions about how the lottery was being conducted. How would you modify the simulation in the
example to estimate the probability of getting two winners from the AP Statistics class in back-to-back
months just by chance?
Answers
Answer: i dont kno man
Step-by-step explanation:
A repair company charges a flat fee of $40 plus $30 for each hour (h) spent making a repair. Which of the following equations could be used to find the charge(c) for any service call?
(1)c=$30h
(2)c=$40h
(3)c=$40+$30h
(4)c=$40h+$30h
(5)c=$30+$40h
Answers
Answer:
(3) c=$40+$30h
Step-by-step explanation:
Answer:
(3) c=$40+$30h
Step-by-step explanation:
Since there is an initial fee for a repair, that is just added. Since the hourly fee depends on how long it takes, it needs a variable with it.
Simplify
4(1 + 9x) thank you
Answers
Answer:
4+36x
Step-by-step explanation:
you multiply the number on the outside of the parentheses with the numbers in the inside of the parentheses.
4 times 1 = 4
4 times 9x = 36x
36x+4
How many cubes would it take to fill the box
Answers
Answer:
27359265815502254
Step-by-step explanation:
52758552
Lin swims 10 laps in the pool in 25 minutes.
How many minutes per lap is that?
I am not good at math (о´∀`о)
Answers
Answer:
The answer is 2.5 minutes per lap.
Step-by-step explanation:
Divide the number of minutes by the amount of laps:
25/10 = 2.5
To check your answer, multiply 2.5 my the amount of laps.
2.5 x 10 = 25
I hope this helped you! If it did, please consider rating, pressing thanks, and/or giving my answer 'Brainliest.' Have a wonderful day. :)
Answer:
40 seconds per lap
Step-by-step explanation:
10 divided by 25 is 0.4
So im pretty sure the anser is 40 secounds
Sorry if im wrong- im not that great at math eaither I just used a calculator.
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s = 17.7 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
Click the picture to view a partial table of critical values.
A.) 99% confidence level requires _____ subjects. (Round up to the nearest subject.)
B.) 95% confidence level requires _____ subjects. (Round up to the nearest subject.)
C. How does the decrease in confidence affect the sample size required?
A. The sample size is the same for all levels or confidence .
B. Decreasing the confidence level decreases the sample size needed*
C. Decreasing the confidence level increases the sample size needed
Answers
a. 99% confidence level requires 452 subjects.
b. 95% confidence level requires 246 subjects.
c. Decreasing the confidence level decreases the sample size needed
How to solve for the sample size nWe are to solve for using the data that is gitten in the question
a. The z value using the 99 percent confidence level is given as (2.576
We have to put the value in the formula
n = (Z * s / E)^2
n = (2.576 * 17.7 / 2)^2
n ≈ 451.24
B For 95 percent, the critical value of Z is given as 1.96
when we out the value in the formula we would have
n = (1.96 * 17.7 / 2)^2
n ≈ 245.24
C. The decrease in the confidence level leads to a fall in the sample size. From the results, the sample size fell from 452 to 246 when the confidence was reduced from 99 to 95 percent
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