If the measure of angle A is doubled and then decreased by 10 while the complement of angle A is decreased by one-third of itself, then these two anlges formed are still complementary. Find the supplement of angle A.
Please explain so i could understand. thank you !
Isn't this statement the same as
(2*A - 10) + (2/3)(90-A)=90
Then you want the supplement of A after you solve for A.
check my thinking.
whats ur email address..im jane
Ok, what do we know about supplements and complements? Suppose we're given angle A (in degrees). Let's denote it's supplement by A" and it's complement by A'. Then we know
A + A" = 180 and A + A' = 90.
The problem you have states:
"If the measure of angle A is doubled and then decreased by 10 while the complement of angle A is decreased by one-third of itself, then these two anlges formed are still complementary. Find the supplement of angle A."
We need to convert the words into algebraic equations we can solve. This is probabaly the most difficult part of the problem in my opinion.
We're told A is doubled and decreased by 10. This means we have
(1) 2A-10
while A' decreased by 1/3. Thus
(2) A' - (1/3)A'=(2/3)A' We're then told that if we add (1) and (2)
2A-10 + (2/3)A' = 90 (they're still complimentary)
We now have a system of equations:
A + A' =90
2A-10 + (2/3)A' = 90
Do you know how to solve a system of equations? If not, or you're stuck, I'll provide more help, but I need you to show some work too.
After you find angle A there should be no trouble finding the complement.
I need help in solving a graphing equation. this is the problem x+3y<6
and x>-4 and y(is greater or equal to) 2x-5
Sure! I'd be happy to help you with the graphing equation problem.
First, let's simplify the inequality x + 3y < 6. We can solve this inequality by treating it like an equation and graphing the corresponding line. To graph the line x + 3y = 6, we can rewrite it in slope-intercept form as y = -(1/3)x + 2.
Next, let's graph the line x = -4. Since x is always equal to -4, the graph will be a vertical line passing through the point (-4,0).
Now, let's graph the inequality y ≥ 2x - 5. We can start by graphing the line y = 2x - 5. This line has a slope of 2 and a y-intercept of -5.
To represent the inequality y ≥ 2x - 5, we can shade the region above the line, including the line itself.
Finally, we can find the solution by identifying the region that satisfies both inequalities. This is the area where the shaded region and the line representing x = -4 overlap.
I hope this helps! Let me know if you have any more questions or need further assistance.
To solve this system of inequalities, we will graph the individual inequalities on a coordinate plane to find the solution region.
First, let's graph the inequality x + 3y < 6. To do this, we need to find two points on the line formed by x + 3y = 6 by assuming x = 0 and y = 0 respectively.
When x = 0, we have 0 + 3y = 6, which gives us y = 2. So, one point we found is (0, 2).
When y = 0, we have x + 3(0) = 6, which gives us x = 6. So, another point we found is (6, 0).
Plot these two points and draw a dotted line passing through them. This line represents the boundary of the inequality x + 3y < 6.
Next, let's graph the inequality x > -4. This is a vertical line passing through x = -4. Since x is greater than -4, we need to draw a dashed line to represent the boundary.
Lastly, let's graph the inequality y ≥ 2x - 5. To graph this line, we need to find two points on the line formed by y = 2x - 5.
When x = 0, we have y = 2(0) - 5, which gives us y = -5. So, one point we found is (0, -5).
When x = 1, we have y = 2(1) - 5, which gives us y = -3. So, another point we found is (1, -3).
Plot these two points and draw a solid line passing through them. This line represents the boundary of the inequality y ≥ 2x - 5.
Now, shade the region that satisfies all the given inequalities. Since x + 3y < 6, we shade the region below the dotted line. Since x > -4, we shade the region to the right of the dashed line. Lastly, since y ≥ 2x - 5, we shade the region above the solid line.
The solution to the system of inequalities is the overlapping shaded region.
I hope this helps! Let me know if you have any further questions.
To solve the system of inequalities:
1. x + 3y < 6
2. x > -4
3. y ≥ 2x - 5
We can start by graphing each inequality on a coordinate plane.
1. Graphing x + 3y < 6:
Rewriting the inequality in slope-intercept form, we have:
3y < -x + 6
y < -(1/3)x + 2
Graph the line y = -(1/3)x + 2 as a dashed line, and shade the region below the line to represent the solution to the inequality.
2. Graphing x > -4:
This is a vertical line passing through x = -4. Since x is greater than -4, we shade the region to the right of the line.
3. Graphing y ≥ 2x - 5:
Rewriting the inequality in slope-intercept form, we have:
y ≥ 2x - 5
Graph the line y = 2x - 5 as a solid line, and shade the region above the line to represent the solution to the inequality.
The solution to the system of inequalities is the overlapping shaded region that satisfies all three inequalities. The region where the shades overlap is the set of points that satisfies all the given conditions.
If you have trouble graphing or determining the solution from the graph, let me know and I can assist you further.