Answer:
25 units.
Step-by-step explanation:
The origin is (0,0)
There using distance formula.
![\sqrt{(y2 - y1) { }^{2} + (x2 - x1) {}^{2} }](https://tex.z-dn.net/?f=%20%20%5Csqrt%7B%28y2%20-%20y1%29%20%7B%20%7D%5E%7B2%7D%20%2B%20%28x2%20-%20x1%29%20%7B%7D%5E%7B2%7D%20%20%7D%20)
![\sqrt{0 - ( - 15) {}^{2} + (0 - 20) {}^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%7B0%20-%20%28%20-%2015%29%20%7B%7D%5E%7B2%7D%20%2B%20%280%20-%2020%29%20%7B%7D%5E%7B2%7D%20%20%7D%20)
![\sqrt{15 {}^{2} + 20 {}^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%7B15%20%7B%7D%5E%7B2%7D%20%2B%2020%20%7B%7D%5E%7B2%7D%20%20%7D%20)
![\sqrt{625}](https://tex.z-dn.net/?f=%20%5Csqrt%7B625%7D%20)
Answer is 25 units.
Answer:
No solution.
Step-by-step explanation:
![|2x+1| = -13\\\\\text{No solution for}~ x\in \mathbb{R}~ \text{because absolute value cannot be negative.}](https://tex.z-dn.net/?f=%7C2x%2B1%7C%20%3D%20-13%5C%5C%5C%5C%5Ctext%7BNo%20solution%20%20for%7D~%20x%5Cin%20%5Cmathbb%7BR%7D~%20%5Ctext%7Bbecause%20absolute%20value%20%20cannot%20be%20negative.%7D)
The height the ball rebounds to after its third bounce with the initial height by 10 feet is 6.141 feet.
<h3>What is Algebra?</h3>
Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula
![\rm a_n = 0. 85\ a_{n - 1}](https://tex.z-dn.net/?f=%5Crm%20a_n%20%3D%200.%2085%5C%20a_%7Bn%20-%201%7D)
a₀ = 10 feet
For n = 1, the height will be
![\rm a_1 = 0. 85\ a_{0}\\\\a_1 = 0.85*10\\\\a_1 = 8.5](https://tex.z-dn.net/?f=%5Crm%20a_1%20%3D%200.%2085%5C%20a_%7B0%7D%5C%5C%5C%5Ca_1%20%3D%200.85%2A10%5C%5C%5C%5Ca_1%20%3D%208.5)
For n = 2, the height will be
![\rm a_2 = 0. 85\ a_{1}\\\\a_2 = 0.85*8.5\\\\a_2 = 7.225](https://tex.z-dn.net/?f=%5Crm%20a_2%20%3D%200.%2085%5C%20a_%7B1%7D%5C%5C%5C%5Ca_2%20%3D%200.85%2A8.5%5C%5C%5C%5Ca_2%20%3D%207.225)
For n = 3, the height will be
![\rm a_3 = 0. 85\ a_{0}\\\\a_3 = 0.85*7.225\\\\a_3 = 6.14125 \approx 6.141](https://tex.z-dn.net/?f=%5Crm%20a_3%20%3D%200.%2085%5C%20a_%7B0%7D%5C%5C%5C%5Ca_3%20%3D%200.85%2A7.225%5C%5C%5C%5Ca_3%20%3D%206.14125%20%5Capprox%206.141)
More about the Algebra link is given below.
brainly.com/question/953809
9514 1404 393
Answer:
![f(x)=\left\{\begin{array}{cl}-x^2+11x-28&\text{for $4](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bcl%7D-x%5E2%2B11x-28%26%5Ctext%7Bfor%20%244%3Cx%3C7%24%7D%5C%5Cx%5E2-11x%2B28%26%5Ctext%7Botherwise%7D%5Cend%7Barray%7D%5Cright.)
Step-by-step explanation:
The absolute value function negates its contents when those contents are negative. Here, the quadratic factors as ...
x^2 -11x +28 = (x -4)(x -7)
so will be negative when the factors have different signs. That will be the case for 4 < x < 7.
The piecewise function can be written in 3 parts, one part for x ≤ 4, another part for 4 < x < 7, and the remaining part for 7 ≤ x. The function expressions for x ≤ 4 and 7 ≤ x are identical.
In the answer above, we chose to write it with the part where the quadratic is negated being defined on the appropriate interval, and using "otherwise" for the rest of the function. It is a little unconventional to do it this way, but it is more compact and completely defines the function.
Answer:
3149/999 = 3 152/999
Step-by-step explanation:
I'll assume the bar is over 152 and there is a typo.
Use a step-by-step calculator (I recommend Symbolab) OR:
Let x equal 3.152...
1000x = 3152.152...
1000x-x = 3152.152... - 3.152...
999x =
3152.152...
- 3.152...
3149
Cancel out the .152...
999x = 3149
Divide by 999 on each side
x=3149/999 = 3 152/999