For each point, add 7 to the x coordinate and take away 1 from the y-coordinate.
<span>I am using a "tick-mark" to show the corresponding point, after "translation" (movement in a straight line). </span>
<span>A(-2, 2) becomes A'(5, 1) </span>
<span>Because all points have been translated in a straight line, in the same direction (the direction [7 -1]) by the same distance, the new figure A'B'C'D' will have the same shape, same size and same orientation as the original image. </span>
<span>It will simply be in a different location on the graph. </span>
<span>If you were to join A with A', B with B', and so on, you would see that all 4 vectors are parallel and are of equal length. </span>
<span>If you were to compare the segment AB (side AB of the original quadrilateral) with the segment A'B' (in the new quadrilateral), you would see that they are parallel (same slope) and have the same length. </span>
<span>Same with the other sides. </span>
<span>Tow figures that are identical (except for their location) are said to be "congruent". </span>
<span>--- </span>
<span>The new rectangle will be far to the right (7 units in x) and a bit below (-1 in y) from the old one. </span>
<span>You should draw the two figures on a graph, and you will see a lot of this very clearly.</span>
Answer:
x° = 37°
Step-by-step explanation:
* Lets revise some facts of a circle
- The secant is a line intersect the circle in two points
- If two secants intersect each other in a point outside the circle,
then the measure of the angle between them is half the difference
of the measures of their intercepted arcs
* Now lets solve the problem
- There is a circle
- Two secants of this circle intersect each other in a point outside
the circle
∴ The measure of the angle between them = 1/2 the difference of the
measures of their intercepted arcs
∵ The measure of the angle between them is x°
∵ The measures of their intercepted arcs are 26° and 100°
- Use the rule above to find x
∴ x° = 1/2 [ measure of the large arc - measure of small arc]
∵ The measure of the large arc is 100°
∵ The measure of the small arc is 26°
∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°
∴ x° = 37°
Pot A volume: 12 ^3 = 1728
Pot B Volume: 3^3 = 27
1728 /27 = 64
ratio should be 64:1
Answer:
(-3,1)
Step-by-step explanation:
9x+8y=-19
7x+9y=-12
I'll assume the question is to find the solution to these equations. The solution will be the point (x,y) where the two lines intersect. The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.
We can either solve matematically of graph to find the intersection. I'll do both, and hope the answers are identical.
<u>Matematically</u>
Rearrange either equation to isolate one of the variables (either x or y). I'll take the second and isolate x:
7x+9y=-12
7x = -9y - 12
x = (-9y - 12)/7
Now use this definition of x in the other equation:
9x+8y=-19
9((-9y - 12)/7) + 8y = -19
(-81y - 108)/7 + 8y = -19
-81y - 108 + 56y = - 133
-25y = -25
<u>y = 1</u>
If y = 1, then:
9x+8y=-19
9x+8(1)=-19
9x = -27
<u>x = -3</u>
<u></u>
<u>The solution is (-3,1)</u>
<u>Graphing</u>
<u></u>
Graph both lines and look for the intersection. The attached graph shows the lines cross at (-3,1).
The solution, bu both approachjes, is (-3,1)
