Answer:
<u>23/2 units</u>
Step-by-step explanation:
Points are :- (-21/2, -3) and (1, -3)
Distance = √(y₂ - y₁)² + (x₂ - x₁)²
= √(-3 + 3)² + (1 + 21/2)²
= √(23/2)²
= <u>23/2 units</u>
Answer:
<h2>m∠ABC = 72</h2>
Step-by-step explanation:
![\text{If}\ \overrightarrow{BD}\ \text{bisects}\ \angle ABC,\ \text{then}\ \angle ABD\cong\angle DBC\to m\abgle ABD=m\angle DBC.\\\\\text{We have}\ m\angle ABD=12x+24\ \text{and}\ m\angle DBC=20x+16.\\\\\text{Make the equation:}\\\\12x+24=20x+16\qquad\text{subtract 24 from both sides}\\\\12x=20x-8\qquad\text{subtract}\ 20x\ \text{from both sides}\\\\-8x=-8\qquad\text{divide both sides by (-8)}\\\\x=1\\\\m\angle ABC=m\angle ABD+m\angle DBC=2m\angle ABD](https://tex.z-dn.net/?f=%5Ctext%7BIf%7D%5C%20%5Coverrightarrow%7BBD%7D%5C%20%5Ctext%7Bbisects%7D%5C%20%5Cangle%20ABC%2C%5C%20%5Ctext%7Bthen%7D%5C%20%5Cangle%20ABD%5Ccong%5Cangle%20DBC%5Cto%20m%5Cabgle%20ABD%3Dm%5Cangle%20DBC.%5C%5C%5C%5C%5Ctext%7BWe%20have%7D%5C%20m%5Cangle%20ABD%3D12x%2B24%5C%20%5Ctext%7Band%7D%5C%20m%5Cangle%20DBC%3D20x%2B16.%5C%5C%5C%5C%5Ctext%7BMake%20the%20equation%3A%7D%5C%5C%5C%5C12x%2B24%3D20x%2B16%5Cqquad%5Ctext%7Bsubtract%2024%20from%20both%20sides%7D%5C%5C%5C%5C12x%3D20x-8%5Cqquad%5Ctext%7Bsubtract%7D%5C%2020x%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C-8x%3D-8%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-8%29%7D%5C%5C%5C%5Cx%3D1%5C%5C%5C%5Cm%5Cangle%20ABC%3Dm%5Cangle%20ABD%2Bm%5Cangle%20DBC%3D2m%5Cangle%20ABD)
![m\angle ABD=12x+24\\\\\text{Put}\ x=1\ \text{to the equation:}\\\\m\angle ABD=12(1)+24=12+24=36\\\\m\angle ABC=(2)(36)=72](https://tex.z-dn.net/?f=m%5Cangle%20ABD%3D12x%2B24%5C%5C%5C%5C%5Ctext%7BPut%7D%5C%20x%3D1%5C%20%5Ctext%7Bto%20the%20equation%3A%7D%5C%5C%5C%5Cm%5Cangle%20ABD%3D12%281%29%2B24%3D12%2B24%3D36%5C%5C%5C%5Cm%5Cangle%20ABC%3D%282%29%2836%29%3D72)
Answer:
We know that an isosceles triangle has 2 of its sides being equal
With R, being the midpoint of PS, we can say that
PR=RS
Noting that, with R as midpoint, we can conclude that RT is a straight line which divides angles TPR and TSR into 2 right angle triangles
Step-by-step explanation:
therefore angle at P is 45°. Angle at S also 45°
Therefore PT = TS
This is because T is 45 degrees as well as P which is also 45 degrees
angle in triangle PTS is 180 degrees
R is 90 degrees, P is 45 degrees and the whole of T is also 45 degrees(which has been split into 2)
Answer:
6x+9+2x
Step-by-step explanation:
8x+9
hope it helps uh
Answer:
26 units
Step-by-step explanation:
![\boxed{distance \: between \: 2 \: points = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } }](https://tex.z-dn.net/?f=%5Cboxed%7Bdistance%20%5C%3A%20between%20%5C%3A%202%20%5C%3A%20points%20%3D%20%20%5Csqrt%7B%20%7B%28x1%20-%20x2%29%7D%5E%7B2%7D%20%2B%20%20%7B%28y1%20-%20y2%29%7D%5E%7B2%7D%20%20%7D%20%7D)
Using the formula above,
distance between (-10, 3) and (0, 27)
![= \sqrt{ {( - 10 - 0)}^{2} + {(3 - 27)}^{2} }](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B%20%7B%28%20-%2010%20-%200%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%283%20-%2027%29%7D%5E%7B2%7D%20%7D%20)
![= \sqrt{ {10}^{2} + ( - 24) {}^{2} }](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B%20%7B10%7D%5E%7B2%7D%20%20%2B%20%28%20-%2024%29%20%7B%7D%5E%7B2%7D%20%7D%20)
![= \sqrt{100 + 576}](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B100%20%2B%20576%7D%20)
![= \sqrt{676}](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B676%7D%20)
= 26 units