Answer: x=7.21
Step-by-step explanation: This is a right triangle- remember the Pythagorean theorem: a² + b² = c². To find leg a, you'd use a = √(c² - b²) **leg a would be the side that is labeled with 12. To find leg b, you'd use b = √(c² - a²) *this is the equation we need. To find the hypotenuse, or <em>c</em>, you'd use c = √(a² + b²). This equation works for right triangles only.
Hope this helps :)
Answer:
Hope this helps!
Step-by-step explanation:
2L + 3S = 83
4L + 8S = 197
Multiplies the top equation by -2.
-4L + -6S = -166
4l + 8S = 197
Adding them together...
2S = 31
S = 31/2 = 15.5
Plugging into the first equation:
2L + 3S = 83
2L + 3(15.5) = 83
2L + 46.5 = 83
2L = 83 - 46.5
2L = 36.5
L = 36.5/2 = 18.25
check:
2L + 3S = 2(18.25) + 3(15.5) = 36.5 + 46.5 = 83
4L + 8S = 4(18.25) + 8(15.5) = 73 + 124 = 197
The Large box weighs 18.25
The small box weighs 15.5
Hello!
Since we are given that the speed of sound in the air travels about 343 meters per second, we can multiply 343 meters per second by 5, and then we convert the meters to kilometers.
343 · 5 = 1715 meters per 5 seconds.
1000 meters are equal to 1 kilometer. So, we can divide 1715 by 1000 to convert meters to kilometers.
1715 / 1000 = 1.715
Therefore, the speed of sound in air is about 1.715 kilometers per 5 seconds.
Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:
m = (5 - 1)/(5 - 0) = 4/5 = 0.8.
Hence the equation that gives the approximate height after x weeks is:
y = 0.8x + 1.
After 8 weeks, the expected height is:
y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.
More can be learned about linear functions at brainly.com/question/24808124
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