Answer:
x=50
Step-by-step explanation:
60+70=130
180-130=50
according to vertical angles x equals 50 degrees
The average rate of a body is the total distance travelled divided by the total time.
<em>The cheetah runs at an average rate of 50.91mph, not 55mph</em>
Let
<em />
<em> distance</em>
<em />
<em> average rate</em>
<em />
<em> time</em>
<em />
We have:
![r_1 =70](https://tex.z-dn.net/?f=r_1%20%3D70)
![r_2 = 40](https://tex.z-dn.net/?f=r_2%20%3D%2040)
![d = r_1t_1 = r_2 t_2](https://tex.z-dn.net/?f=d%20%3D%20r_1t_1%20%3D%20r_2%20t_2)
The average rate of the trip is:
![r = \frac{2d}{t}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B2d%7D%7Bt%7D)
Where
<em />
<em> the total distance from A to B and back to A</em>
![2d = r_1t_1 + r_2t_2](https://tex.z-dn.net/?f=2d%20%3D%20r_1t_1%20%2B%20r_2t_2)
and
<em />
<em> total time spent from A to B and back to A</em>
![t =t_1 + t_2](https://tex.z-dn.net/?f=t%20%3Dt_1%20%2B%20t_2)
becomes
![r = \frac{r_1t_1 + r_2t_2}{t_1 + t_2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Br_1t_1%20%2B%20r_2t_2%7D%7Bt_1%20%2B%20t_2%7D)
Recall that:
![d = r_1t_1 = r_2 t_2](https://tex.z-dn.net/?f=d%20%3D%20r_1t_1%20%3D%20r_2%20t_2)
Make
the subject
![t_2 = \frac{r_1t_1}{r_2}](https://tex.z-dn.net/?f=t_2%20%3D%20%5Cfrac%7Br_1t_1%7D%7Br_2%7D)
Substitute
in ![r = \frac{r_1t_1 + r_2t_2}{t_1 + t_2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Br_1t_1%20%2B%20r_2t_2%7D%7Bt_1%20%2B%20t_2%7D)
![r = \frac{r_1t_1 + r_2\times \frac{r_1t_1}{r_2}}{t_1 + \frac{r_1t_1}{r_2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Br_1t_1%20%2B%20r_2%5Ctimes%20%5Cfrac%7Br_1t_1%7D%7Br_2%7D%7D%7Bt_1%20%2B%20%5Cfrac%7Br_1t_1%7D%7Br_2%7D%7D)
Factor out t1
![r = \frac{t_1(r_1 + r_2\times \frac{r_1}{r_2})}{t_1(1 + \frac{r_1}{r_2})}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bt_1%28r_1%20%2B%20r_2%5Ctimes%20%5Cfrac%7Br_1%7D%7Br_2%7D%29%7D%7Bt_1%281%20%2B%20%5Cfrac%7Br_1%7D%7Br_2%7D%29%7D)
![r = \frac{r_1 + r_2\times \frac{r_1}{r_2}}{1 + \frac{r_1}{r_2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Br_1%20%2B%20r_2%5Ctimes%20%5Cfrac%7Br_1%7D%7Br_2%7D%7D%7B1%20%2B%20%20%5Cfrac%7Br_1%7D%7Br_2%7D%7D)
![r = \frac{r_1 + r_1}{1 + \frac{r_1}{r_2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Br_1%20%2B%20r_1%7D%7B1%20%2B%20%20%5Cfrac%7Br_1%7D%7Br_2%7D%7D)
Substitute values for r1 and r2
![r = \frac{70 + 70}{1 + \frac{70}{40}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B70%20%2B%2070%7D%7B1%20%2B%20%20%5Cfrac%7B70%7D%7B40%7D%7D)
![r = \frac{140}{1 + 1.75}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B140%7D%7B1%20%2B%20%201.75%7D)
![r = \frac{140}{2.75}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B140%7D%7B2.75%7D)
![r = 50.91](https://tex.z-dn.net/?f=r%20%3D%2050.91)
Hence
- <em>The equation of the average rate is: </em>
<em>.</em> - <em>The average rate is 50.91mph, not 55mph</em>
<em />
Read more about distance, average rates and time at:
brainly.com/question/16769277
Answer:
its tb=tc g
Step-by-step explanation:
Answer:
166
Step-by-step explanation:
463-297=166
Step-by-step explanation:
f(x) = x² + x + 3/4
in general, such a quadratic function is defined as
f(x) = a×x² + b×x + c
the solution for finding the values of x where a quadratic function value is 0 (there are as many solutions as the highest exponent of x, so 2 here in our case)
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 1
c = 3/4
x = (-1 ± sqrt(1² - 4×1×3/4))/(2×1) =
= (-1 ± sqrt(1 - 3))/2 = (-1 ± sqrt(-2))/2 =
= (-1 ± sqrt(2)i)/2
x1 = (-1 + sqrt(2)i) / 2
x2 = (-1 - sqrt(2)i) / 2
remember, i = sqrt(-1)
f(x) has no 0 results for x = real numbers.
for the solution we need to use imaginary numbers.