Two numbers have a sum of 30 and a product of 209. what is the positive difference between them?
y + x = 30
xy = 209
y = 30 -x
x(30-x) = 209
30x - x^2 = 209
x^2 - 30x + 209 = 0
x = 19
y = 11
the difference is 19-11 = 8
The numbers are 11 and 19.
Given to us,Sum of the two numbers = 30,Product of the two numbers = 209,AssumptionLet's assume that the first number be a and the second is b.
equation 1,a + b = 30
equation 2,ab = 209
Therefore, in equation 1,
[tex]a\times b = 209\\b= \dfrac{209}{a}[/tex]
substitute the value of b in equation 1,
[tex]a+b=30\\\\a+\dfrac{209}{a}=30\\\\\dfrac{a^2+209}{a} =30\\\\a^2 +209 = 30a\\a^2-30a +209 = 0[/tex]
[tex]a^2 -30a+209= 0\\a^2 -19a-11a+209= 0\\a(a-19)-11(a-19)=0\\(a-11)(a-19)=0[/tex]
Substituting the factor against 0,
[tex](a-11) = 0\\a = 11\\\\(a-19)=0\\a = 19[/tex]
Therefore, the numbers are 11 and 19.
Learn more about factorization:
https://brainly.com/question/6810544
At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answer:
21
Step-by-step explanation:
For the function f(x) = –5x, which ordered pair will be a point on the graph of the function?
A.
(–5, 1)
B.
(2, 10)
C.
(15, –3)
D.
(0, 0)
Answer:
0,0 i think.. not sure so dont get mad at me
Step-by-step explanation:
True or false? in order to inscribe a circle in a triangle, the circle's center must be placed at the circumcenter of the triangle
Answer:
False.Step-by-step explanation:
A inscribe circle in a triangle means to draw the biggest circle possible inside such triangle. To do that perfectly, we first have to find the incenter of the circle, which is the intersection of all three internal bisector of the triangle, that point is the center of the inscribed circle.
Therefore, the statement is false.
In addition, a circumcenter allow to perfectly draw a circumscribed circle, which is outside the triangle, which is not the case here.
An image showing the inscribed circle is attached.
Answer:
false
Step-by-step explanation:
The average grade mark received on 4 tests was 94. if he drops his lowest grade of 85, what will his new average be
After dropping his lowest marks of 85 the new average test mark is 97.
Given, average test score of 4 tests is 94.
Average concept:
Average = sum of all the observations / total number of observations.
Average of 4 test marks = 94
94 = Sum of all the marks obtained in 4 tests / 4
Sum of all the marks obtained in 4 tests = 94 × 4
Sum of all the marks obtained in 4 tests = 376
Now the lowest marks of 85 are removed,
Remaining sum of 3 test marks = 376 - 85
Remaining sum of 3 test marks = 291
New average of 3 tests:
Average of 3 test marks = 291/3
Average of 3 test marks = 97
Know more about average,
https://brainly.com/question/2426692
#SPJ5
In the diagram below, line segment bc is an altitude of triangle abd. What is the length of line age meant cd? If necessary, round your answer to two decimal places, PLEASE HELP ME IM REALLY STUCK
On a 10-item test, three students in professor hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. for this distribution of test scores, the standard deviation is equal to the square root of
What is the solution of y − 4x = 0 and 3x + 6y = 9?
(NEED HELP!!!)Which of the following lines is perpendicular to y= 3x + 2?
A. y=3x -1/2
B. y=-1/3x+6
C. y=1/3x+2
D. y=3x+1/2
Answer:
[tex]y=\frac{-1}{3}x+6[/tex]
Step-by-step explanation:
We have to find the equation of the line from the options given which is perpendicular to the line y=3x+2.
In order to do so we must know that , the product of the slope of the two perpendicular lines is always -1
Hence
if the slope of line A is "m" and the line B which is perpendicular to A, will have [tex]-\frac{1}{m}\\[/tex]
Also , in the slope intercept form of any equation the coefficient of x is our slope. Hence the slope of y=3x+2., is 3
Hence the slope of any line perpendicular to this will be [tex]\frac{-1}{3}[/tex]
as the product of two slopes is -1
Hence in the given options only c options has the line whose slope is [tex]\frac{-1}{3}[/tex]
f(x) = Square root of x plus eight.; g(x) = 8x - 12 Find f(g(x))
Final answer:
To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
Explanation:
To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).
f(x) = 2x² + 3; g(x) = −2x² + 4x
Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3
Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3
Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3
What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?
salas little brother is learning to talk. he has a vocabulary of 30 words. each week his vocabulary grows by about 6%. at this rate how many words will he know 5 weeks from now
30 * (1+0.06)^5=
30* 1.338225578 = 40.146
he will know 40 words in 5 weeks
A normal curve is ___________ about the mean. consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean.
what is the value of x to the nearest tenth
Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression. The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is .
To simplify the equation using logarithmic functions, take the natural logarithm of both sides and use properties of logarithms to solve for x and y. Then substitute the values in the simplified expression to evaluate it.
Explanation:To simplify the expression on the left side of the equation using the properties of logarithmic functions, let's work step by step:
Take the natural logarithm (ln) of both sides of the equation. The natural logarithm cancels the exponential function.The natural logarithm of 5.6/16.0 is -1.050.Now, we have the equation ln(x) - ln(2y) = -1.050.Using the property of logarithms, subtracting the logarithms of two numbers is equivalent to dividing the numbers. So we have ln(x/2y) = -1.050.To find the value of x/2y, take the inverse natural logarithm (e^) of both sides.So we have x/2y = e^(-1.050).To solve for x, multiply both sides of the equation by 2y.Therefore, x = 2y * e^(-1.050).Once you have the values for x and y, substitute them into the simplified expression to find its value.Alice wants to buy some paper towels. She has two options. She can either buy a package of four rolls or she can buy one roll now and buy another when she runs out. Which of these options is better? Give reasons for your answer.
Answer:
Correct Answer: Alice should buy the package of four paper towels because buying in bulk means she gets each roll of towels for less money.
Step-by-step explanation:
What is the work done by moving in the force field f~ (x, y) = h2x 3 + 1, 2y 4 i along the parabola y = x 2 from (−1, 1) to (1, 1)?
a.compute directly
b.use the theorem?
You're 35 years old now, and you want to purchase life insurance which will cover your spouse for your lost income in the event of your death. You want this policy to last until what would be your normal retirement age of 65. Based on the given information, what is the best policy to buy?
-8-(3x+6)=4-x
Wow I'm dumb lol
Two way Frequency table question
The original price of a couch is $650. It is on sale for $546. What is the percent change in the price off the couch?
The probability that an american industry will locate in shanghai, china, is 0.7, the probability that it will locate in beijing, china, is 0.4, and the probability that it will locate in either shanghai or beijing or both is 0.8. what is the probability that the industry will locate
The average of six numbers is 4. a seventh number is added and the new average is 5. what is the seventh number?
According to the question, the seventh number is 11.
Use the concept of average defined as:
Average, also known as the mean, is a statistical measure that represents the central value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total count of numbers.
To find the seventh number,
If the average of six numbers is 4, then the total sum of those six numbers would be 6 multiplied by 4, which is 24.
Assume the seventh number is 'x'.
If the new average (after adding the seventh number) is 5, then the total sum of all seven numbers would be 7 multiplied by 5, which is 35.
To find the seventh number 'x',
Subtract the sum of the initial six numbers (24) from the sum of all seven numbers (35).
This gives us 35 - 24 = 11.
Hence,
The seventh number is 11.
To know more about average visit:-
brainly.com/question/24057012
#SPJ5
Sec^-1(-square root 2)
Who can help me with that one please ? Thanks!
The last step in a proof contains the
At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
The speed of the plane with no wind is 451 miles per hour.
Explanation:Let's solve this problem step-by-step:
We are given that the airplane travels 2460 miles against the wind in 6 hours at maximum speed. This means that the speed of the airplane relative to the ground is its maximum speed minus the speed of the wind. So, the equation is: x - y = 2460/6 or x - y = 410 (where x is the maximum speed of the plane and y is the speed of the wind). We are also given that the airplane can travel the same distance with the wind in 5 hours. This means that the speed of the airplane relative to the ground is its maximum speed plus the speed of the wind. So, the equation is: x + y = 2460/5 or x + y = 492. To find the speed of the plane with no wind, we can add the two equations: (x - y) + (x + y) = 410 + 492. This simplifies to: 2x = 902. Dividing both sides by 2, we get: x = 451. Therefore, the speed of the plane with no wind is 451 miles per hour.
Raina makes eight dollars for each hour of work. Write an equation to represent her total pay p after working h hours
angle LMP and angle PMN are complementary. Find the value of x.
A. 22.5
B. 7.5
C. 15
D. 30
a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. Describe what is being measured in this experiment and what variable is being manipulated?