The algebraic expression for √(4+x)(10-x), which is 121.
To find the value of √(4+x)(10-x) algebraically, we start by simplifying the given equation:
√(4+x) + √(10-x) = 6
To eliminate the square roots, we can square both sides of the equation:
(√(4+x) + √(10-x)[tex])^2 = 6^2[/tex]
Expanding the left side using the binomial formula, we get:
(4+x) + 2√[(4+x)(10-x)] + (10-x) = 36
Simplifying further:
14 + 2√[(4+x)(10-x)] = 36
Subtracting 14 from both sides:
2√[(4+x)(10-x)] = 22
Dividing both sides by 2:
√[(4+x)(10-x)] = 11
Now we can square both sides again to get rid of the square root:
[(4+x)(10-x)] = [tex]11^2[/tex]
Simplifying further:
(4+x)(10-x) = 121
For more questions on algebraic expressions
https://brainly.com/question/4344214
#SPJ8
A house on the market was valued at 432,000. After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answer:
$393,120
Step-by-step explanation:
To find the decrease in the house's value in dollars, we need to calculate 9% of the initial value:
Decrease in value = (Initial value) * (Percentage decrease) = $432,000 * 9%
Converting the percentage to a decimal:
Decrease in value = $432,000 * 0.09 = $38,880
The house's value decreased by $38,880.
Now, to find the current value of the house, we need to subtract the decrease in value from the initial value:
Current value = Initial value - Decrease in value = $432,000 - $38,880 = $393,120
The current value of the house is $393,120.
Hope this helps!