==========================================================
Explanation:
L = x = length of the rectangleW = 2x-9 = width of the rectangle, since its 9 less than twice the lengtharea of rectangle = L*W = 129
L*W = 129
x*(2x-9) = 129
2x^2-9x = 129
2x^2-9x-129 = 0
Apply the quadratic formula. We'll use a = 2, b = -9, c = -129.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-129)}}{2(2)}\\\\x = \frac{9\pm\sqrt{1113}}{4}\\\\x \approx \frac{9\pm33.36165464}{4}\\\\x \approx \frac{9+33.36165464}{4}\ \text{ or } \ x \approx \frac{9-33.36165464}{4}\\\\x \approx \frac{42.36165464}{4}\ \text{ or } \ x \approx \frac{-24.36165462}{4}\\\\x \approx 10.59041366\ \text{ or } \ x \approx -6.09041364\\\\[/tex]
We ignore the negative solution because a negative length makes no sense.
The length is approximately L = 10.5904 cm.
The width is 2L-9 = 2*10.5904-9 = 12.1808 cm approximately.
As a quick check,
L*W = 10.5904*12.1808 = 128.99954432
which isn't too far off from 129. We have rounding error which is why we don't perfectly land on the target area value. If you wanted to get closer to the value 129, then use more decimal digits in the approximations of L and W.
----------------------------
If you draw a diagonal in the rectangle, then you form two identical or congruent right triangles.
Focusing on one of those triangles, we have
a = 10.5904b = 12.1808c = unknown hypotenuse = diagonal lengthApply the pythagorean theorem
a^2+b^2 = c^2
c = sqrt( a^2 + b^2 )
c = sqrt( (10.5904)^2 + (12.1808)^2 )
c = 16.1408940520653
c = 16.14
The diagonal is roughly 16.14 cm long.
what is the measure of m?
The required value of m for the given triangle is given as m = 12.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
Applying Pythagoras' theorem,
n² = m² - 6² - - - - (1)
m ² + base² = 24²
base² = 24² - m² - - - - (2)
n² + 18² = base²
From equation 1 and 2
m² - 6² + 18² = 24² - m²
2m² = 24² + 6² - 18²
m = 12
Thus, the required value of m for the given triangle is given as m = 12.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
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The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 7 to 5. If there were 4115 no votes, what was the total number of votes?
Answer:
9876
Step-by-step explanation:
7:5
x:4115
To find x mulitply 7 by 823 (because this is what we multiplied 5 by in order to get 4115)
7*823= 5761
Take the sum to find the total number of votes
4115+5761= 9876
Solve for x. WILL GIVE BRAINIEST
Answer:
x≤16
Step-by-step explanation:
1/2x - 3 ≤5
Add 3 to each side
1/2x -3+3 ≤5+3
1/2x≤8
Multiply each side by 2
1/2x*2 ≤8*2
x≤16
Complete the square to form a true equation;
x^2-3/4x+__ = (x-__)^2
Answer: x² - (3/4)x + 9/64 = (x + 3/8)²
Step-by-step explanation:
Concept:
Here, we need to know the idea of completing the square.
Completing the square is a technique for converting a quadratic polynomial of the form ax²+bx+c to the form (x-h)²for some values of h.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
If we expand (x - h)² = x² - 2 · x · h + h²
Given equation:
x² - (3/4)x +___ = (x - __)²Since [x² - (3/4)x +___] is the expanded form of (x - h)², then (-3/4)x must be equal to 2 · x · h. Thus, we would be able to find the value of h.
(-3/4) x = 2 · x · h ⇔ Given-3/4 = 2 · h ⇔ Eliminate xh = -3/8 ⇔ Divide 2 on both sidesFinally, we plug the final value back to the equation.
x² - 2 · x · h + h² = (x - h)²x² - (3/4)x + (-3/8)² = (x + 3/8)²x² - (3/4)x + 9/64 = (x + 3/8)²Hope this helps!! :)
Please let me know if you have any questions
Suppose you just received a shipment of seven televisions. Four of the televisions are defective. If two televisions are randomly selected, compute the probability
that both televisions work. What is the probability at least oone of the two televisions does not work?
The probability that both televisions work is
(Round to three decimal places as needed.).
The probability that at least one of the two televisions does not work is
(Round to three decimal places as needed.)
e
Answer:
- What is the probability at least one of the two televisions does not work?
The probability at least one of the two televisions does not work is 0.8163
- The probability that both televisions work is?
The probability that both televisions work is 0.1837
Step-by-step explanation:
Total televisions are 7
Faulty televisions are 4
Number of televisions selected is 2
Jul
attachments.office.net
6
7
A car journey is in two stages.
Stage 1 The car travels 110 miles in 2 hours.
Stage 2 The car travels 44 miles at the same average speed as Stage 1
Work out the time for Stage 2
Give your answer in minutes.
[3 m
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Answer:
48 minutes
Step-by-step explanation:
Since the speed is the same for Stage 2, the time is proportional to the distance.
t2/(44 mi) = (120 min)/(110 mi)
t2 = (44/110)(120 min) = 48 min . . . . . . multiply by 44 mi
The time for Stage 2 was 48 minutes.
Find dy/dx given that y = sin x / 1 + cos x
Answer:
[tex] \frac{1}{1 + \cos(x) } [/tex]
Step-by-step explanation:
[tex]y = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
differentiating numerator wrt x :-
(sinx)' = cos x
differentiating denominator wrt x :-
(1 + cos x)' = (cosx)' = - sinx
Let's say the denominator was "v" and the numerator was "u"[tex] (\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} } [/tex]
here,
since u is the numerator u= sinx and u = cos x v(denominator) = 1 + cos x; v' = - sinx[tex] = \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} } [/tex]
[tex] = \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} } [/tex]
since cos²x + sin²x = 1
[tex] = \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} } [/tex]
diving numerator and denominator by 1 + cos x
[tex] = \frac{1}{1 + \cos(x) } [/tex]
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
This is the Written equation.
x+6x=56
Solve the equation.
Interpret the results and write the answer in words.
The smaller piece is x = _ in.
The longer piece is _x = _ ( ) = _ in.
The lengths of the two pieces are _ in
and _ in.
Part 1 of 2
_ in
Part 2 of 2
_ in
Answer:
8 inches
48 inches
total 56 inches
Step-by-step explanation:
x+6x = 56
7x = 56
Divide by 7
7x/7 = 56/7
x = 8
The smaller piece is x inches or 8 inches
The larger piece is 6x inches or 6*8 =48 inches
8+48 = 56 inches
The total length is 56 inches
Answer:
8 inches, and 48 inches
Step-by-step explanation:
x+6x=56
Solve the equation.
7x=56
x=8
Interpret the results and write the answer in words.
The smaller piece is x = 8 in.
The longer piece is 6x = 6 (8) = 48 in.
The lengths of the two pieces are 8 in
and 48 in.
The sum of a number and twice its square is 105. Find the number.
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years.
Answer:
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.
This means that [tex]n = 2322, \pi = \frac{408}{2322} = 0.1757[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 - 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1627[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 + 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1887[/tex]
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
Is there a difference in the number of people who have an Annual pass to Disney World comparing people who live in Florida to those who do not?
Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
People who live in Florida and also have annual pass to Disney world is 221, sample size selected for group 1 is 350.
People who do not live in Florida and have annual pass to Disney world is 365, sample size selected for Group 2 is 650.
Group 1 sample proportion is : 221 / 350 = 0.6314
Group 2 sample proportion is 365 / 650 = 0.5615
Test statistics is 0.8317
Since test stats value is greater than the sample proportion significance level, we fail to reject the null hypothesis.
Help?? Please “Use a benchmark to compare 4/7 and 2/10”
Answer:
4/7 > 2/10
Step-by-step explanation:
4/7 is close to 1/2
2/10 is close to 0
4/7 > 2/10
14 ft
3 ft
6 ft
O 87
1313
252ft
0 262
52.31
Answer:
35
Step-by-step explanation:
the legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
Write your answer in SIMPLIFIED SQUARE ROOT FORM
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 + 10^2 = c^2[/tex]
2.[tex]125 = c^2[/tex]
3. [tex]c=5\sqrt{5}[/tex]
plssss
How much fat is in a mixture created
with x pints of 8% butterfat and y pints
of 15% butterfat?
Answer:
0.08x + 0.15y
Step-by-step explanation:
multiply the amount of pints with the given percent of fat
Answer:
Hence total fat in mixture is 8x+15y100 pints
Jessy pastes stamps for 160 envelopes in 2 hours. If she pastes the stamps at the same rate, for how many envelopes can she paste stamps in 30 minutes ?
2 hours=160
1 hours=160÷2=80
30 minutes=80÷2=40
Answer:She can paste 40 stamps in 30 minutes
Hank has a bottle of diluted syrup that is 60% maple syrup and a bottle of pure syrup that is 100% maple syrup in his restaurant. How many ounces of pure syrup should he mix with the diluted syrup in order to make 100 ounces of 85% maple syrup? Express your answer as a decimal rounded to the nearest hundredth if necessary.
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Answer:
62.5 oz of 100%
Step-by-step explanation:
Let p represent the number of ounces of pure syrup. Then (100-p) is the number of ounces of 60% syrup. The amount of maple syrup in the desired mix is ...
p +0.60(100 -p) = 0.85(100)
0.40p +60 = 85 . . . . . . . . . . . simplify
0.40p = 25 . . . . . . . . . . subtract 60
p = 62.5 . . . . . . . . . divide by 0.4
62.5 ounces of pure syrup should be mixed with the diluted syrup to make 100 ounces of 85% maple syrup.
_____
The other 37.5 ounces will be 60% syrup.
2. (03.05)
A cell phone plan has a monthly cost that is shown in the table below. What is the correct statement regarding the average rate of change during the 40-minute time of talk?
X Total min of talk time
0
10
20
30
40
Y Monthly cost of cell phone in $
14.95
15.95
16.95
17.95
18.95
Answer:
The average change rate increases by a dollar for every 10 minutes you speak.
Step-by-step explanation:
If you do not speak at all you pay the standard price.
After that, If you add 10 minutes to your talk time, you add a dollar to your payment
hope it helps c:
The number of animals at a shelter from day to day has a mean of 37.6, with a standard deviation of 6.1 animals. The distribution of number of animals is not assumed to be symmetric. Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days
Answer:
Between 19.3 and 55.9 animals.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean of 37.6, standard deviation of 6.1.
Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days?
Within 3 standard deviations of the mean, so:
37.6 - 3*6.1 = 19.3
37.6 + 3*6.1 = 55.9
Between 19.3 and 55.9 animals.
Can someone help me out please
HELP PLS DUE IN 6 MINUTES
6TH GRADE MATH
Answer:
C
Step-by-step explanation:
trust me its easy
Answer:
C: None of the above
Step-by-step explanation:
when 3a^2-2a+5 is subtracted from a^2+a-1 the result is
Please help, will give brainliest!!!!!
Answer:
third option
Step-by-step explanation:
Brainliest please~
What are the equations of the asymptotes for the functiony=tan2pix where 0
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Answer:
(b) x = 0.25, 0.75, 1.25, 1.75
Step-by-step explanation:
The asymptotes of tan(α) are found at ...
α = π/2 +nπ
We want to find x such that ...
2πx = α = π/2 +nπ
Dividing by 2π gives ...
x = 1/4 +n/2 . . . . . . . for integers n
In the desired range, the values of x are ...
x = 0.25, 0.75, 1.25, 1.75
Which of the relations given by the following sets of ordered pairs is a function?
C_{(1,2), (2, 3), (3, 4), (5,6), (2, 1)}
C {( - 2,5), (7,5), ( – 4,0), (3,0), (1, - 6)}
Ċ {(2, – 8), (1, – 4), (0,0), (1, 4), (2,8)}
{(3, – 3), (3,
1), (3, 1), (3, 3), (3,5)}
Submit
Pass
elp
Don't know
answer
14
tv
va
The first or second one because a function can't have the x value repeating
A wire is to be cut into two pieces. One piece will be bent into an equilateral triangle, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 64 m2, what is the minimum length of wire that can be used? What is the maximum length of wire that can be used?
(Use decimal notation. Give your answer to one decimal place.)
⠀⠀⠀⠀⠀⠀⠀⠀⠀Stolen from GoogIe :p
The minimum length of wire needed is approximately 22.5 meters and the maximum length of wire needed is also approximately 22.5 meters.
How to get the Length?Let's assume the length of the wire is "L" meters. We need to find the minimum and maximum values of L that satisfy the given conditions.
To find the minimum length of wire needed, we should minimize the combined area of the equilateral triangle and the circle. The minimum occurs when the wire is distributed in a way that maximizes the area of the circle while minimizing the area of the equilateral triangle.
Minimum length (L_min):
Let "x" be the length of the wire used to form the equilateral triangle, and "y" be the length used to form the circle.
The area of an equilateral triangle is given by (√(3)/4) * side², where the side is the length of one of the triangle's equal sides.
The area of a circle is given by π * radius².
Since the perimeter of an equilateral triangle is three times the length of one of its sides, and the circumference of a circle is given by 2 * π * radius, we have:
x + y = L ...(1) (The total wire length remains constant)
x = 3 * side ...(2) (Equilateral triangle perimeter)
y = 2 * π * r ...(3) (Circle circumference)
The area enclosed by the two pieces is given by:
Area = (√(3)/4) * side² + π * r²
We want to minimize this area subject to the constraint x + y = L.
To find the minimum, we can use the method of Lagrange multipliers.
By solving this optimization problem, we find that the minimum value of the combined area is approximately 64 m² when x ≈ 7.5 m and y ≈ 15 m. Thus, the minimum length of wire needed (L_min) is approximately 7.5 + 15 = 22.5 meters.
Maximum length (L_max):
To find the maximum length of wire needed, we should maximize the combined area of the equilateral triangle and the circle. The maximum occurs when the wire is distributed in a way that minimizes the area of the circle while maximizing the area of the equilateral triangle.
By solving this optimization problem, we find that the maximum value of the combined area is approximately 64 m² when x ≈ 15 m and y ≈ 7.5 m. Thus, the maximum length of wire needed (L_max) is approximately 15 + 7.5 = 22.5 meters.
So, the minimum length of wire needed is approximately 22.5 meters, and the maximum length of wire needed is also approximately 22.5 meters.
Learn more about maximum length here: https://brainly.com/question/32886114
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What value of x makes the equation 3x+7=22 true?
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
Given [tex]3x+7=22[/tex], our goal is to isolate [tex]x[/tex] such that will have an equation that tell us [tex]x[/tex] is equal to something.
Start by subtracting 7 from both sides:
[tex]3x+7-7=22-7,\\3x=15[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3},\\x=\frac{15}{3}=\boxed{5}[/tex]
Therefore, the value of [tex]x=5[/tex] makes the equation [tex]3x+7=22[/tex] true.
Answer:
x = 5
Step-by-step explanation:
Subtract 7 from both sides: 3x + 7- 7 = 22 - 7
Simplify: 3x = 15
Divide both sides by 3
Simplify: x = 5
Hope this helps:)
You are installing new carpeting in a family room. The room is rectangular with dimensions 20 1/2 feet × 13 1/8 feet. You intend to install baseboards around the entire perimeter of the room except for a 3 1/2-foot opening into the kitchen. How many linear feet of board must you purchase?
Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
A fruit company delivers its fruit in 2 types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 79 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 199 kilograms. How much does each type of box weight?
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Answer:
large: 15.5 kgsmall 6.5 kgStep-by-step explanation:
Let x and y represent the weights of the large and small boxes, respectively. Then the two delivery weights give rise to the equations ...
3x +5y -79 = 0
12x +2y -199 = 0
Using the "cross multiplication method" of solving these equations, we find ...
d1 = (3)(2) -(12)(5) = 6 -60 = -54
d2 = 5(-199) -(2)(-79) = -995 +158 = -837
d3 = -79(12) -(-199)(3) = -948 +597 = -351
1/d1 = x/d2 = y/d3
x = d2/d1 = -837/-54 = 15.5
y = d3/d1 = -351/-54 = 6.5
The large boxes weigh 15.5 kg; the small boxes weigh 6.5 kg.
_____
Additional comment
My preferred quick and easy way to solve equations like this is using a graphing calculator. In addition to that, an algebraic method is shown.
The "cross-multiplication method" shown here is what I consider to be a simplified version of what you would find in videos. It is a variation of Cramer's rule and the Vedic maths methods of solving pairs of linear equations. I find it useful when "elimination" or "substitution" methods would result in annoying numbers. In such cases, it uses fewer arithmetic operations than would be required by other methods.
Short description: writing the coefficients of the general form equations in 4 columns, where the last column is the same as the first, a "cross multiplication" is computed for each of the three pairs of columns. Those computations are of the form ...
[tex]\text{column pair: }\begin{array}{cc}a&b\\c&d\end{array}\ \Rightarrow\ d_n=ad-cb[/tex]
The relationship between the differences d₁, d₂, and d₃ and the variable values is shown above.
Clara made two investments. Investment A has an initial value of $500 and
increases by $45 every year. Investment B has an initial value of $300 and
increases by 10% every year. Clara checks the value of her investments once a
year, at the end of the year. What is the first year in which Clara sees that
Investment B's value has exceeded investment A's value?
Answer:
The first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.
Step-by-step explanation:
Since Clara made two investments, and Investment A has an initial value of $ 500 and increases by $ 45 every year, while Investment B has an initial value of $ 300 and increases by 10% every year, and Clara checks the value of her investments once to year, at the end of the year, to determine what is the first year in which Clara sees that Investment B's value has exceeded investment A's value, the following calculation must be performed:
500 + (45 x X) = A
300 x 1.1 ^ X = B
A = 500 + 45 x 5 = 500 + 225 = 725
B = 300 x 1.1 ^ 5 = 483.15
A = 500 + 45 x 10 = 950
B = 300 x 1.1 ^ 10 = 778.12
A = 500 + 45 x 15 = 1175
B = 300 x 1.1 ^ 15 = 1253.17
A = 500 + 45 x 14 = 1,130
B = 300 x 1.1 ^ 14 = 1,139.25
Therefore, the first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.
