Answer:
[15, ∞).
Step-by-step explanation:
–3(6 – 2x) ≥ 4x + 12
-18 + 6x ≥ 4x + 12
6x - 4x ≥ 12 + 18
2x ≥ 30
x ≥ 15
This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).
Hope this helps!
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Ksju [112]
Well, here's one way to do it at least...
<span>For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). </span>
<span>Let P=(4,0) be the projection of B onto the x-axis. </span>
<span>Let Q=(-3,0) be the projection of C onto the x-axis. </span>
<span>Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). </span>
<span>Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). </span>
<span>Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. </span>
<span>||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) </span>
<span>||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) </span>
<span>Using the Law of Cosines... </span>
<span>||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) </span>
<span>||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) </span>
<span>||a||^2 = 86 - 36 </span>
<span>||a||^2 = 50 </span>
<span>||a|| = sqrt(50) </span>
<span>Now apply the Law of Sines to find the other two angles. </span>
<span>||b|| / sin(B) = ||a|| / sin(A) </span>
<span>sqrt(41) / sin(B) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(41) / sqrt(50) = sin(B) </span>
<span>.8222 = sin(B) </span>
<span>asin(.8222) = B </span>
<span>55.305 = B </span>
<span>Two down, one to go... </span>
<span>||c|| / sin(C) = ||a|| / sin(A) </span>
<span>sqrt(45) / sin(C) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(45) / sqrt(50) = sin(C) </span>
<span>.8614 = sin(C) </span>
<span>asin(.8614) = C </span>
<span>59.470 = C </span>
<span>So your three angles are: </span>
<span>A = 65.225 </span>
<span>B = 55.305 </span>
<span>C = 59.470 </span>
Answer:
56 degrees
Step-by-step explanation:
Add 34 and 90 together
34 + 90 = 124
Subtract 180 by 124 = 56
If this answer is correct, please make me Brainliest!
Answer:
Option F
Step-by-step explanation:
F). x + y = 3 -------(1)
x - 3y = -2 --------(2)
Equation (1) minus equation (2)
(x + y) - (x - 3y) = 3 - (-2)
4y = 5
y = 1.25
Hence, y is positive.
G). x + y = 3 --------(1)
x + y = -2 --------(2)
Both the equations represent parallel lines.
There are no solutions of the given equations.
H). x - 3y = -2 -------(1)
x + y = -2 -------(2)
Equation (2) minus equation (1)
(x + y) - (x - 3y) = -2 - (-2)
4y = 0
y = 0
Since, 0 is neither positive nor negative, y will be neither positive nor negative.
J). x + y = 3 -------(1)
x - y = 3 --------(2)
Equation (1) - Equation (2)
(x + y) - (x - y) = 3 - 3
2y = 0
Hence, y is neither negative nor positive.
Therefore, Option F is the answer.
Y = -1/2x - 3
You can find this by first taking the slope of the original two points on the line, which is 2. You then take the opposite, inverse of that to find the new line's slope (perpendicular). So, we use -1/2. You can then find a line that uses that slope and the extra point by using either point-slope form and solving or slope intercept form.