When you're writing things in scientific notation, the new spot for the decimal number always goes in between the first and second numbers that are not zeroes. For this problem, it'd be 1.4. Then, count how many times the decimal place moves to get to the new spot (#power of ten), which in this case is 4 times. The way I remember this next part is that if it has a negative exponent, the number you get when you solve is really small, so therefore the answer is 1.4×
(10^-4)
We know the slope of this line is 1/3x, which means the slope of the line that is perpendicular to it is -3x
A slope that is perpendicular to another is the negative reciprocal of the other.
The equation of a line that is perpendicular to the line y = 1/3x - 5 is y = -3x - 5
Answer:
The scale factor was used in the dilation is 3
Step-by-step explanation:
Dilation is a kind of transformation that changes the size of figures
Image of a figure by dilation and the figure are similar
If a triangle dilated by a scale factor k then its image is similar to it, and the constant ratio between their corresponding sides is equal to k
∵ Δ ABC is dilated to form Δ DEF
∴ Δs ABC and DEF are similar
- That mean their corresponding sides have constant ratio
equal the scale factor of dilation
∴ 
Size of Δ DEF is greater than size of Δ ABC, that means k > 1
∵ AC = 2 units
∵ DF = 6 units
∵ 
∴ 
∴ 3 = k
∵ The scale factor of dilation is equal to the constant ratio k
∵ k = 3
∴ The scale factor was used in the dilation is 3
Answer:
y value
Step-by-step explanation:
For question number one:
We know that in similar triangles, corresponding sides are proportional.
In this scenario we have two triangles- one made by a stop sign and a shadow and one by a tree and its shadow.
The side of the triangle that is represented by the shadow of the stop sign is proportional to the side of the larger triangle represented by the shadow of the tree.
Also, the side of the smaller triangle that is represented by the height of the stop sign is proportional to the side of the bigger triangle represented by the height of the tree.
Using this information we can conclude that 12/42=18/h
By cross multiplying: 12h=42(18)
solve for h: (42)(18)/(12)=h
calculate: h=63
The height of the tree is 63 ft.