Answer:
If two figures are similar, then the correspondent sides are related by a constant factor.
For example, if the base of one side of one of the figures has a length L, then the correspondent side of the other figure has a length k*L where k is the scale factor.
Let's start with the two left triangles.
In the smaller one the base is 5, and the base of the other triangle is 15.
Then we will have:
15 = k*5
15/5 = k = 3
The scale factor is 3.
Then we will have that:
a = scale factor times the correspondent side in the smaller triangle:
a = k*3 = 3*3 = 9
a = 9
For the other two triangles, the base of the smaller triangle is 12, while the base of the larger triangle is 20.
Then we will have the relation:
12*k = 20
k = (20/12) = 10/6 = 5/3
The scale factor is 5/3
This means that the unknown side b is given by:
b*(5/3) = 15
b = (3/5)*15 = 3*3 = 9
b = 9.
Answer:
6
Step-by-step explanation:
It is ALWAYS helpful to sketch the appropriate figure.
That will make clear that 3x = x+4, by the definition of midpoint.
Then you solve the equation and you get x=2, so that PQ = 6.
Hey there! :)
Answer:
y + 32 = 3(x + 8)
Step-by-step explanation:
Begin by finding the slope of the line using the slope formula:
Plug in the coordinates of the points into the equation:
Simplify:
m = 3.
Point-slope form is:
y-y₁=m(x-x₁)
Plug in the coordinates of the first point, as well as the slope:
y - (-32) = 3(x - (-8)
y + 32 = 3(x + 8)
Answer:
a. 0.0000009 m
b. 6,130, 000, 000
c. 100,000 light years
d. 0.00001 mm
e. 0.0000010 kg
Step-by-step explanation:
Here, we want to come from the standard form to the decimal form
In doing this, we consider the power of 10 attached
If negative, we count leftwards, if positive, we count right-wards
The number of times we count is the power of 10 attached. The count means we are moving the decimal point
For numbers with out visible decimal point, it is at the back of the most right-ward number
Thus, we have these as;
a. 9 * 10^-7
= 0.0000009 m
b. 6.130 * 10^9
= 6,130, 000, 000
c. 1 * 10^5
= 100,000 light years
d. 1 * 10^-5 mm
= 0.00001 mm
e. 10^-7
= 0.0000010 kg
Answer:
Step-by-step explanation:
c and d
