Question

A positive real number is 8 more than another. If the sum of the squares of the two numbers is 80, find the numbers

100

likes
502 views

Answer to a math question A positive real number is 8 more than another. If the sum of the squares of the two numbers is 80, find the numbers

Expert avatar
Darrell
4.5
61 Answers
Absolutely, let's solve this problem. Here's how to find the numbers: **1. Set up the equations:** * Let 'x' be the first number. * The second number is 'x + 8' (since it's 8 more than the first). * The sum of their squares is 80: x² + (x + 8)² = 80 **2. Solve the equation:** * Expand the equation: x² + x² + 16x + 64 = 80 * Combine like terms: 2x² + 16x - 16 = 0 * Divide by 2 for simplicity: x² + 8x - 8 = 0 * Factor the quadratic equation: (x + 4)(x - 2) = 0 * Solve for possible values of x: * x + 4 = 0 => x = -4 (We discard this since we need a positive real number) * x - 2 = 0 => x = 2 **3. Find the second number:** * Since x = 2, the second number is x + 8 = 2 + 8 = 10 **Answer:** The two numbers are 2 and 10.

Frequently asked questions (FAQs)
What is the derivative of the function f(x) = (10^x)/(e^x)?
+
Question: For the cosine function f(x) = cos x, what is the value of f(π/3)?
+
What is the maximum or minimum value of a quadratic function with vertex (2, -3)?
+
New questions in Mathematics
Use the digits of 1,9,2,3 to come up with all the numbers 98 and 95
³√12 x ⁶√96
2x-y=5 x-y=4
Suppose that a device has been created that launches objects at ground level and that its operation is modeled by the function h(x) = -4ײ + 256x, with h being the height (in meters) and x being the distance (in meters) What is the maximum height that the object reaches?
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.
In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?
A recurring sequence is one where elements repeat after completing one standard. If the sequence AB8C14D96AB8C1... is recurring its twentieth term is equal to: (A) B. (B) 8. (C) A. (D) 6. (E) D.
Engineers want to design seats in commercial aircraft so that they are wide enough to fit ​95% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.2 in. Find P95. That​ is, find the hip breadth for men that separates the smallest ​95% from the largest 5​%.
The simple average of 15 , 30 , 40 , and 45 is
4+168×10³×d1+36×10³×d2=-12 -10+36×10³×d1+72×10³×d2=0
X~N(2.6,1.44). find the P(X<3.1)
Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never made, how many recipes does the cookbook contain?
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
find missing measure for triangle area = 48 m square base = 10m heaighy = ? m
How to factorise 5y^2 -7y -52
2 - 6x = -16x + 28
calculate the product of 4 and 1/8
9n + 7(-8 + 4k) use k=2 and n=3
(3.1x10^3g^2)/(4.56x10^2g)