Y varies jointly with x. Y=16 when x=4 and z=1/2. Find y when x=2 and z=1/4. Enter the value of y in the box. Picture attached,
15 points and I'll give Brainliest! Due in two hours.
1 answer:
Answer:
y = 4
Step-by-step explanation:
Given that y varies jointly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 16 when x = 4 and z = , that is
16 = k × 4 × = 2k ( divide both sides by 2 )
8 = k
y = 8xz ← equation of variation
When x = 2 and z = , then
y = 8 × 2 × = 16 ×
= 4
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Answer:
see attached
Step-by-step explanation:
Dilation is the transformation that changes the size of something. When you choose ×110% on a copy machine, you are making all the dimensions in the copy equal to 1.1 times the dimensions of the original, for example. That is dilation by a factor of 1.1, or 110%.
Here, you're asked to dilate triangle ABC by a factor of 3. That means all of the dimensions on the dilated figure will be 3 times their length on the original.
The center of dilation is point P. That means all the distances from point P are multiplied by 3.
In the attached figure, a gray arrow has been drawn from point P to each of the points A, B, and C. Then two more arrows of the same length are drawn in the same direction. The total distance at the end of the 3 arrows is 3 times the original distance from point P. These are the points A', B', and C' you are asked to draw. Connecting these points gives the dilated triangle A'B'C'.
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You could think of point P (the center of dilation) as having coordinates (0, 0). Then points A, B, and C would have coordinates A(-4, 0), B(0, -3), and C(-4, -3). To dilate these points by a factor of 3, multiply each coordinate value by 3: A'(-12, 0), B'(0, -9), C'(-12, -9). You will see that these are the coordinates of the vertices of the dilated triangle.
