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:
B) Only (-3, 5)
Step-by-step explanation:
Slot in the options into the equation
(-2, 4),
Compare with (x, y)
x = -2, y =4
y =-3x - 4
4 =( -3 * -2 ) - 4
4 = 6 - 4
This is not true hence, option A is wrong
Using (-3, 5)
x = -3, y= 5
5 = (-3*-3) - 4
5 = 9 - 4
This is correct hence, option B is correct
Option c is wrong because (-2,4) is not a solution to the equation
Option D is wrong because option B is correct
Hello!
We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:
A1 + A2 + A3 = 180
With this knowledge, we can successfully find the missing measurements.
We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:
(90) + (65) + A3 = 180
155 + A3 = 180
Now subtract 155 from both sides of the equation:
A3 = 25
We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:
25 + 80 = 105
We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:
(105) + (50) + A3 = 180
155 + A3 = 180
Now subtract 155 from both sides of the equation:
A3 = 25
We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:
(25) + (25) + (x) = 180
50 + x = 180
Now subtract 50 from both sides:
x = 130
we have now proven that the missing angle (x) has a measure of 130 degrees.
I hope this helps!
second angle which has a value of 65 degrees.
Answer:
Step-by-step explanation:
The answer is geosphere and hydrosphere
Answer:
2+5x>47 or 2+5x=47
