Answer:
Step-by-step explanation:
Let x represent Dan's age
3x be James'age
Paul 2(3x+x)=6x+2x
Suming all ages
x+3x+6x+2x=120
Solving for x
12x=120
x=10 (Dan's age)
3×=30 (James'age)
6×+2×=80(Paul's age)
Answer:
There are 2.22 grams of clay are in each pot.
Step-by-step explanation:
Given:
Dakota has 4/10 kg of clay. He divides the clay to make 888 equal-sized pots.
Now, to find the number of grams of clay are in each pot.
Dakota has clay =
So, by using conversion factor we convert it into grams:
Quantity of clay he has = 400 grams.
Number of equal-sized pots to make = 888.
Now, to get the quantity of grams of clay are in each pot we divide number of equal-sized pots to make by quantity of clay he has:
Therefore, there are 2.22 grams of clay are in each pot.
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
