Answer:
x > - 5
x < 10
Step-by-step explanation:
Divide 7x>-35 by 7
Divide - 5x>-50 by - 5
Since we divide by a negative whe change the inequality sign.
3. Look at the picture.
We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:
![x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o](https://tex.z-dn.net/?f=x%5Eo%2B90%5Eo%2B43%5Eo%3D180%5Eo%5C%5C%5C%5Cx%5Eo%2B133%5Eo%3D180%5Eo%5C%20%5C%20%5C%20%7C-133%5Eo%5C%5C%5C%5Cx%5Eo%3D47%5Eo)
![Answer:\ \boxed{47^o}](https://tex.z-dn.net/?f=Answer%3A%5C%20%5Cboxed%7B47%5Eo%7D)
4.
Look at the picture.
Use Pythagorean theorem:
![x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8](https://tex.z-dn.net/?f=x%5E2%2B14%5E2%3D%2810%2Bx%29%5E2%5C%5C%5C%5Cx%5E2%2B196%3D10%5E2%2B2%5Ccdot10%5Ccdot%20x%2Bx%5E2%5C%20%5C%20%5C%20%5C%20%7C-x%5E2%5C%5C%5C%5C196%3D100%2B20x%5C%20%5C%20%5C%20%7C-100%5C%5C%5C%5C20x%3D96%5C%20%5C%20%5C%20%7C%3A20%5C%5C%5C%5Cx%3D4.8)
![Used:\ (a+b)^2=a^2+2ab+b^2](https://tex.z-dn.net/?f=Used%3A%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2)
![Answer:\ \boxed{4.8\ units}](https://tex.z-dn.net/?f=Answer%3A%5C%20%5Cboxed%7B4.8%5C%20units%7D)
5.
TRUE: 1; 2; 4
6.
We find a slope of the line OP:
![m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5CO%282%3B%5C%206%29%5Cto%20x_1%3D2%3B%5C%20y_1%3D6%5C%5C%5C%5CP%284%3B%5C%203%29%5Cto%20x_2%3D4%3B%5C%20y_2%3D3%5C%5C%5C%5Cm%3D%5Cdfrac%7B3-6%7D%7B4-2%7D%3D%5Cdfrac%7B-3%7D%7B2%7D)
We have:
![OP:\ y=-\dfrac{3}{2}x+b](https://tex.z-dn.net/?f=OP%3A%5C%20y%3D-%5Cdfrac%7B3%7D%7B2%7Dx%2Bb)
Now, we must find the slope of the line perpendicular to the line OP.
We know:
![k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1](https://tex.z-dn.net/?f=k%3Ay%3Dm_1x%2Bb%3B%5C%20l%3Ay%3Dm_2x%2Bc%5C%5C%5C%5Ck%5C%20%5Cperp%5C%20l%5Ciff%20m_1m_2%3D-1)
therefore
![-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}](https://tex.z-dn.net/?f=-%5Cdfrac%7B3%7D%7B2%7Dm_2%3D-1%5C%20%5C%20%5C%20%7C%5Ccdot%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%5C%5C%5C%5Cm_2%3D%5Cdfrac%7B2%7D%7B3%7D)
So. We have the answer! :)
Answer:
a)-6(x-2) = 4r-17
B) 10x +307 - 20) = 13-20
6) (18-19) -(4-720) = -73
г)-3(4-5y)+2(3-6y)=-39
Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:
![y =\frac{1}{2}x-5](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B1%7D%7B2%7Dx-5)
Step-by-step explanation:
Given points are:
(x1,y1) = (6,-2)
(x2,y2) = (12,1)
The slope intercept form is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
We have to find the slope first
![m =\frac{y_2-y_1}{x_2-x_1}\\=\frac{1-(-2)}{12-6}\\= \frac{1+2}{6}\\=\frac{3}{6}\\=\frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%3D%5Cfrac%7B1-%28-2%29%7D%7B12-6%7D%5C%5C%3D%20%5Cfrac%7B1%2B2%7D%7B6%7D%5C%5C%3D%5Cfrac%7B3%7D%7B6%7D%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
Putting the value of slope
![y = \frac{1}{2}x+b](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%2Bb)
To find the value of b, putting (12,1) in the equation
![1 = \frac{1}{2}(12)+b\\1 = 6+b\\b = 1-6\\b=-5](https://tex.z-dn.net/?f=1%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2812%29%2Bb%5C%5C1%20%3D%206%2Bb%5C%5Cb%20%3D%201-6%5C%5Cb%3D-5)
Putting the values of m and b
![y =\frac{1}{2}x-5](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B1%7D%7B2%7Dx-5)
Hence,
Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:
![y =\frac{1}{2}x-5](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B1%7D%7B2%7Dx-5)
Keywords: Equation of line, slope-intercept form
Learn more about equation of line at:
#LearnwithBrainly
Answer:
yes
step-by-step explaination