Given:
The two points are (-5,8) and (-3,1).
To find:
The distance between the given two points in simplest radical form.
Solution:
Distance formula: The distance between two points is

Using distance formula, the distance between (-5,8) and (-3,1) is





Therefore, the distance between two points (-5,8) and (-3,1) is
units.
<u>Given</u>:
Given that the figure of similar triangles.
The altitude of the triangle is x.
The length of the left part is 30.
The length of the right part is 15.
We need to determine the value of x.
<u>Value of x:</u>
The value of x can be determined using the geometric mean theorem.
Thus, we have;

Substituting the values, we have;

Cross multiplying, we get;


Taking square root on both sides, we have;

Thus, the value of x is 15√2
Answer:
Value is x=8 and y=4
Step-by-step explanation:
Given : A right triangle 'A' hypotenuse length of x+4 and a leg of x,
and right triangle 'B' hypotenuse length of 3y and a leg length of y+4
To find : For what values of x and y are the triangles congruent by HL?
Solution :
Triangle A,
Hypotenuse: x+4
Leg: x
Triangle B,
Hypotenuse: 3y
Leg: y+4
Since the triangle A and B are congruent so, the sides of triangles are equal.
(Hypotenuse are equal) ..........[1]
and
(Legs are equal) ..........[2]
Solving the equation of system,
Put the value of x from [2] in [1],




Substitute y in [2],
Therefore, The value of x=8 and y=4
Verifying for the values of x and y:
Triangle A,
Hypotenuse: x+4=8+4=12
Leg: x=8
Triangle B,
Hypotenuse: 3y=3(4)=12
Leg: y+4=4+4=8
Both hypotenuses and both legs are equal hence they are congruent.
Answer: She will pay $52.68, including taxes
Step-by-step explanation: One can of tennis ball is $4 and there are no discount on it. Elena bought 3 cans, so:
can = 3 x 4 = 12
One tennis racket is $43 but it has a discount of 15%:
discount = 0.15 x 43 = 6.45
total racket = 43 - 6.45 = 36.55
Elena will have to pay:
pay = 12 + 36.55 = 48.55
She will also have to pay taxes, which are 8.5% over the price she paid:
pay + tax = 48.55 x 0.085 = 4.13
total to pay = 48.55 + 4.13 = 52.68
Buying 3 can of tennins ball and one racket, Elena paid $52.68, including taxes.
The third equation is linear