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notice the tickmarks, thus TP = PU and TQ = QS, so the PQ segment is then a midsegment of the larger triangle, and thus the angles it makes on the small one, are exactly the same.
Related Questions
Find three positive numbers whose sum is 100 and whose product is a maximum. (enter your answers as a comma-separated list.)
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Let the two positive integers be x and y.
Then x + y = 100, and xy = the product.
Let's eliminate x. Solve x + y = 100 for x: x = 100 - y. Now subst. this last result into P = xy: P = product = (100 - y)(y) = 100y - y^2
Differentiating, dP/dy = 100 - 2y. Set this = to 0 and solve for y: -2y = -100, and y = 50. Since x + y = 100, x is thus also = to 50.
Solution set: (50,50).
Now suppose that three positive integers add up to 100, and that we want to maximize their product.
Then x + y + z = 100. Let's maximize f(x,y,z) = xyz (the product of x, y and z).
Since x + y + z = 100, we can eliminate z by solving x + y + z = 100 for z and subst. the result back into f(x,y,z) = xyz:
We get f(x,y) =xy(100-x-y), a function of two variables instead of three.
I won't go through the entire procedure of maximizing a function in three variables, but will get you started:
Find the 'partial of f with respect to x' and then the 'partial of f with respect to y'. Set each of these partial derivatives = to 0:
f = 0 = (partial of xy(100-x-y) with respect to x
x
= xy(partial of 100-x-y with respect to x) + (100-x-y)(partial of xy with respect to x)
= xy(-1) + (100-x-y)(y)
We must set this partial = to 0: -xy+100y-xy-y^2 = 0
-2xy + 100y - y^2 = 0
or y(-2x + 100 - y) = 0
of which y=0 is one solution and in which -2x + 100 - y = 0
You must now go through the same procedure with respect to the partials with respect to y.
If you'd like to continue this discussion, please respond with questions and comments.
PLZ HURRY!!!
A line passes through the points (6,5) and (2,2) . Select all that describe this line.
1. y − 5 = 3/4 (x − 6)
2. y − 5 = −4/3 (x − 2)
3. y − 2 = −3/4 (x − 6)
4. y − 2 = 3/4 (x − 2)
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The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?
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Answer:
[tex]a_n=5a_{n-1}[/tex]
Step-by-step explanation:
Given fifth term of a geometric sequence is 781.25.
[tex]a_5= 781.25[/tex].
Also, each previous term is 1/5 of the value of the current term.
Therefore, common ratio would be 5.
But we just need to find the recursive formula .
Recursive formula of a geometric sequence is given by
[tex]a_n=ra_{n-1}[/tex]
Plugging value of r in above formula, we get
[tex]a_n=5a_{n-1}[/tex]
Therefore, recursive formula would be [tex]a_n=5a_{n-1}[/tex] represents the situation.Answer: c
Step-by-step explanation:
buddy beneath me is blabbin to much
Solve for 10 - 6x - 9x^2 = -9x10−6x−9x 2 =−9x
Answers
x = (1 ±√41)/6 is the correct answer.
To solve the equation 10 - 6x - 9x^2 = -9x, we'll use the quadratic formula. The solutions for x are (3 + √369)/18 and (3 - √369)/18.
Explanation:To solve the equation 10 - 6x - 9x2 = -9x, we'll start by bringing all the terms to one side of the equation to set it equal to zero. Rearranging the equation, we get 9x2 - 3x - 10 = 0. We can then use factoring, the quadratic formula, or completing the square to solve for x. In this case, let's use the quadratic formula.
The quadratic formula states:
x = (-b ± √(b2 - 4ac))/(2a)
Using the values from our equation, we have:
x = (-(-3) ± √((-3)2 - 4(9)(-10)))/(2(9))
Simplifying further, we have:
x = (3 ± √(9 + 360))/18
x = (3 ± √369)/18
Therefore, the solutions for x are:
x = (3 + √369)/18
x = (3 - √369)/18
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One hundred pounds of co2 is contained in a 10:0-ft3 tank. the safety limit of the tank is 1600 psig.
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Final answer:
To answer the question, we need to convert the mass from pounds to kilograms, use the ideal gas law equation to calculate the pressure in atmospheres, and then convert atmospheres to psig.
Explanation:
In this question, we are given that 100 pounds of CO2 is contained in a 10.0-ft3 tank and the safety limit of the tank is 1600 psig. To convert pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms. So, 100 pounds of CO2 is equal to 45.36 kilograms. Now, we can use the ideal gas law equation PV = nRT to find the pressure in bar. Rearranging the equation, we have P = (nRT) / V. Plugging in the values given, n = mass / molar mass, R = 0.0821 atm L / mol K, T = 273 + degrees Celsius, and V = 10.0 ft3 converted to liters, we can calculate the pressure in atmospheres. Finally, we can convert atmospheres to psig by multiplying by 14.7.
If two parallel lines are cut by a transversal and corresponding angles measure 10x – 1 and 8x + 21, what is the value of x?
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10x -1 = 8x + 21
-8x -8x
2x -1 = 21
+1 +1
2x = 22
x = 11
Hope this helps!
If 300 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters
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[tex]\bf V(x)=x^2\left( \cfrac{300-x^2}{4x} \right)\implies V(x)=x^2\left( \cfrac{75}{x}-\cfrac{x}{4}\right) \\\\\\ V(x)=75x-\cfrac{x^3}{4}\implies \cfrac{dV}{dx}=75-\cfrac{1}{4}\cdot 3x^2\implies \cfrac{dV}{dx}=75-\cfrac{3x^2}{4} \\\\\\ \cfrac{dV}{dx}=\cfrac{300-3x^2}{4}\impliedby \textit{now, let's set the derivative to 0} \\\\\\ 0=\cfrac{300-3x^2}{4}\implies 0=300-3x^2\implies 3x^2=300\implies x^2=100 \\\\\\ x=\pm\sqrt{100}\implies x=\pm 10[/tex]
now, if you do a first-derivative test on +10, say check 9.99 and 10.01 for example, you'll notice you'd get + and - value respectively, meaning is a maximum.
Fraction 4 over 5n = Fraction 2 over 3. n = ___? Fraction 2 over 15 Fraction 5 over 6 1Fraction 1 over 5 1Fraction 7 over 15
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4/5n = 2/3
n = 2/3 x 5/4 . . . . .. if fraction is moved to other side of the equation the numerator and denominator will be swithced
n = 10/12 ......................... divide numerator and denominator by 2
n = 5/6
The answer is Fraction 5 over 6
Answer:
what?
Step-by-step explanation:
What is the third term of the sequence defined by the recursive rule f(1)=2, f(n)=2f(n-1) +1
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20 points! Suppose you find six articles related to the topic of your research paper. In how many ways can you choose four articles to read
a.720
b.30
c.360
d.15
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kelly puts $350 in a savings account. The savings account accrues interest at a flat rate of 1.05% a month. How much will it count be worth in 7 months?
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now, if we nevermind "t" as years and just use it as an interest cycle, then we can say the rate is 1.05% and the period is 7 cycles.
[tex]\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$350\\ r=rate\to 1.05\%\to \frac{1.05}{100}\to &0.0105\\ t=cycles \to 7 \end{cases} \\\\\\ A=350(1+0.0105\cdot 7)[/tex]
The "a" will represent your initial value, the value that you are already given in the problem, in this case, it is $350. The "b" will be your growth/decay factor, in this case is 1.05%. However, it cannot stay a percent, but must be changed into a decimal. For this factor in particular, since there's a decimal already included, you'd move the decimal two places to the left, giving you 0.0105.
Since the factor is more than 1, you'd add the decimal by one, giving you 1.0105. Now, the "x" represents the amount of time. In this case, it would be 7 months. Let's set up the equation:
y = 350(1.0105)^7 = 376.5 (377 if rounded). In 7 months, Kelly will have $376.5.
A superhero recently asked his nemesis how many cats she has. She answered with a riddle:two-thirds of my cats plus two
how many cats does she have
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I need the answer please
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Solving for x
2x+6=x+5
2x-x=5-6
X= -1
In 2015, in Buffalo, New York, there were 8,625 arrests, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffalo is 258,959. What is the ratio of the number of assaults to the number of robberies in simplest form?
Answers
I could be wrong tho
Answer:
The simplest form of the ratio is: [tex]\dfrac{865}{2678}[/tex]
Step-by-step explanation:
We are given information about the buffalo in New york in the year 2015 as:
Number of arrests= 8,625
Number of robberies=2678
Number of assaults= 865
Number of murders= 20
The population of Buffalo is 258,959.
he ratio of the number of assaults to the number of robberies in simplest form is given by:
[tex]\dfrac{865}{2678}[/tex]
As the number in the numerator and the denominator do not have a common factor. hence the simplest form of the ratio is:
[tex]\dfrac{865}{2678}[/tex]
A laptop computer is purchased for $1300. After each year, the resale value decreases by 35%. What will the resale value be after 3 years?
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The distance from Talamunda to Velcratia is 700 miles. The train takes 5 hours to travel the distance. At what unit rate is the train traveling?
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Answer: 140 miles per hour
Step-by-step explanation:
You are planning to buy one of two brands of sofas, which you hope to use over the next twenty years. Brand J costs $975 and lasts for about twenty years. Brand K costs $265 and lasts for about five years, so you will need to buy four Brand K sofas to equal one Brand J sofa. In either case, you plan to pay for your sofa using your credit card, which has an interest rate of 14.55%, compounded monthly. You can pay off a Brand J sofa with eight years of monthly payments, and you can pay off a Brand K sofa with three years of monthly payments. Assuming that you make no other purchases on your credit card, over twenty years, which brand will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.) a. Brand J will be $591.36 cheaper than Brand K. b. Brand J will be $85.00 cheaper than Brand K. c. Brand K will be $1,132.23 cheaper than Brand J. d. Brand K will be $340.32 cheaper than Brand J.
Answers
The loan amount is calculated by amortization and Brand K will be $340.32 cheaper than Brand J
What is Amortization?Loan amortisation is the practise of making recurrent payments over time to completely pay off the principal and interest on a loan.
Mortgage amortisation is a word used in finance to describe the process of paying down your mortgage. The mortgage lender establishes a payment plan for you when you take out a mortgage. This uncomplicated plan, which includes equal payments over the course of your loan if you have a fixed-rate mortgage, is easy to understand.
The amount is calculated using the amortization formula:
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
where:
P is monthly payment
a is credit amount
r is the interest rate
t is the time in years
n is number of times the interest is compounded
Given data ,
Let the total loan amount for the brand J be represented as J
a = $975
r = 14.55% = 0.1455
t = 8 years
n = 12
Now , the amortization formula is
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}
P = $17.24
Total amount paid J = $17.24 × 96 = $1655.04
Let the total loan amount for the brand K be represented as K
a = $265
r = 14.55% = 0.1455
t = 3 years
n = 12
Now , the amortization formula is
P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}
P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}
P = $9.13
Total amount paid K = $9.13 × 12 × 3 × 4 = $1314.72
The difference of amount of sofa j and sofa k = D
D = J - K
D = $1 655.04 - $ 1314.72 = $ 340.32
Hence , Brand K will be cheaper than Brand J by $340.32
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Fred wants to find 48+34 using compensation.He says you can take 2 from 34 and give it to 48 to make 50.What is the sum?Explain why compensation can work to find the sum.
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48 + 34 = borrow 2 from 34 and add to 48
= 50 + 32 50 + 32 is 82
= 82
Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
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Answer:
Isosceles triangle.
Step-by-step explanation:
A triangle has been given in this question with the sides 5 cm, 5 cm, 7 cm.
As per definition of the triangle if two sides are equal then opposite angles of these corresponding sides will be equal.
More than this if two sides of a triangle are equal then the triangle is called as isosceles triangle.
Therefore the given triangle with the equal sides 5 cm, 5 cm will be the isosceles triangle.
find the equation in general form of the circle with center at the origin and radius equal 6.
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Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations mc004-1.jpg and x + 4y = 17. Based on this information, which statement is correct? (–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17. (–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17. (–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17
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Since (-3, 5) is a solution of the system of equations, then (-3, 5) must satisfy both equations.
Answer is choice D.
How to factorise and appear a commun facteur
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the figure below will be translated 4 units up and 3 units to the right. Which of the following represents the coordinates of the transformed figure?
A. A'(6, 9), B'(9, 14), C'(12, 11)
B. A'(8, 10), B'(11, 15), C'(15, 12)
C. A'(9, 9), B'(12, 14), C'(16, 11)
D. A'(9, 10), B'(12, 15), C'(16, 12)
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=> A (5,6) → A' (5 + 3, 6 + 4) = A'(8,10)
=> B(8,11) → B' (8 + 3, 11 + 4) = B'(11,15)
=>C(12,8) → C' (12 + 3, 8 + 4) = C'(15,12)
Answer: B. A'(8, 10), B'(11, 15), C'(15, 12)
A student has three mangos, two papayas, and two kiwi fruits. if the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed
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7! / ( 3! * 2! * 2! ) = 210
There are 210 different ways for the fruits can be consumed.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A student have 3 mangos, 2 papayas, and 2 kiwi fruits.
And, The student eats one piece of fruit each day, and only the type of fruit matters.
Now,
Total number of fruits = 3 + 2 + 2
= 7
And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.
So, Number of ways for the fruits can be consumed, is calculated as;
= 7! / 3! 2! 2!
= 7 x 6 x 5 x 4 x 3! / 3! 2! 2
= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1
= 7 x 6 x 5
= 210
Thus, There are 210 different ways for the fruits can be consumed.
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Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute
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A minute is 6 times as long as 10 seconds, so we expect Karl will ride 6 times as far.
[tex]\dfrac{120\,ft}{10\,s}=\dfrac{120\,ft}{10\,s}\cdot\dfrac{60\,s}{1\,min}=\dfrac{720\,ft}{1\,min}[/tex]
Karl rides 720 ft in 1 minute.
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
write 3.25 x 10^4 as an ordinary number
could you please show your working out it would be helpful
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[tex]3.25\times10^4[/tex] is equivalent to [tex]3.25 \times 10,000[/tex], which translates to taking the decimal point in 3.25 and moving it 4 places to the right, obtaining [tex]32,500[/tex].
Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.
The ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.
What is an ordinary number?Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.
We have,
3.25 x [tex]10^{4}[/tex]
We need to remove the decimal point and the exponents 4.
Let us find in two parts:
3.25 can be written as 325/100 ______(1)
[tex]10^{4}[/tex] can be written as 10 x 10 x 10 x 10 = 10000 ______(2)
Now,
From (1) and (2)
= 3.25 x [tex]10^{4}[/tex]
= (325 / 100) x 10000
= (325/100) x 100 x 100
100 can be canceled.
= 325 x 100
= 32500
Thus the ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.
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"assume that josh throws the discus 36 times. let y denote the sum of the lengths of the 36 throws.
a. what is the expected value of y
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The ice cream Palace received 3 gallons of strawberry ice cream, 5 pints of mocha ice cream, and 1 quart of vanilla ice cream today. How many pints of ice cream did they receive?
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Find the distance the point p(0,0,−4)p(0,0,−4) is to the line through the two points q(−4,1,−2q(−4,1,−2 ), and r(−2,0,−5r(−2,0,−5 ).
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The formula for glue says to add 50ml of hardener to each container of resin. How much hardener should be added to 15 containers of resin?
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If you have 15 containers of resin, Hardener = 15 * 50 = 750.
So you need 750 mL of hardener.
Answer:
0.75
Step-by-step explanation: