Answer:
x = 5.6
Step-by-step explanation:
So, lets first go over something:
What does it mean for two shapes to be similar?
It means that all their angles are the same, but their side lengths are different, or in other words, one triangle has a different ratio of side lengths to the other.
So how can we find this ratio difference?
We can take the lengths of the same sime on the two different traingles.
You could go with 4 : 3.2 or 2 : 1.6
When you simplfy this, you get 1 : 0.8
We can then find the value of x by multiplying the two ratios by 7, which is the side length of the similar triangle's unknown side:
7 : 5.6
This means that x = 5.6
Hope this makes sense!
Answer:
y = -2x + 12
Step-by-step explanation:
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
I will use the first point (1, 10) and the last point (5, 2)
Plug in these values:
(2 - 10) / (5 - 1)
Simplify the parentheses.
= (-8) / (4)
Simplify the fraction.
-8/4
= -2
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = -2x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the last point (5, 2). Plug in the x and y values into the x and y of the standard equation.
2 = -2(5) + b
To find b, multiply the slope and the input of x(5)
2 = -10 + b
Now, add 10 to both sides to isolate b.
12 = b
Plug this into your standard equation.
y = -2x + 12
This is your equation.
Check this by plugging in the other point you have not checked yet (1, 10).
y = -2x + 12
10 = -2(1) + 12
10 = -2 + 12
10 = 10
Your equation is correct.
Hope this helps!
Answer:
-4.745
Step-by-step explanation:
hope this is helpful.
Given:
The equation is:
To find:
The number that should be added to sides of the equation to complete the square.
Solution:
If an expression is in the form of , then we have to add to make it perfect square.
We have,
...(i)
To make it perfect square we need to add square of half of coefficient of x on both sides.
Coefficient of x is -10, so square of half of coefficient of x is:
On adding 25 on both sides of (i), we get
Therefore, we need to add 25 to both sides of the equation to complete the square.
multiply the left one by 2:
5/6 = 10/12