Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
The slope- intercept is y> (1-4x) / 5 and y< 2x + 6
<h3 /><h3>What is inequality?</h3>
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
4x – 5y < 1 and 1/2y – x < 3
Solving
4x – 5y < 1
-5y < 1- 4x
-y < (1-4x) / 5
y> (1-4x) / 5
Now, the second inequality,
1/2y – x < 3
1/2y< 3+x
y< 2x + 6
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Answer:
39.27
Step-by-step explanation:
The area of a semi-circle is pi times the radius squared divided by 2. So basically standard area of a circle formula (pi times the radius squared) but then you add in the extra step of dividing it by 2.
The formula looks like this:
π × r² ÷ 2
The radius is half the diameter of the circle. So basically think of it as a line to the middle of the circle. Our diameter is 10, (the diameter is the entire length of the circle. It gives us this already. If you need diameter and only have the radius add the radius together twice or multiply it by 2 to get the diameter. Fun fact..?)
and it tells us to substitute pi for 3.142.
So, plugging our numbers in we get:
3.142 x 5^2 ÷ 2 = 39.275.
Cut out the 3rd decimal place (5) as it tells us to only include the first 2 decimal places, and we finally end up with 39.27.
<u>Hope this helps and have a nice day!</u>
This exercise is about a proof in Euclidian geometry. See the explanation below.
<h3>What is Euclidian Geometry?</h3>
The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).
<h3>What is the statement that completes the above proof?</h3>
Given that S is the midpoint of 
:
Hence QS = TS ......................1
It is right to indicate that
PQ = TV ........................2
And ∠RSQ is vertically opposite to ∠TSV
Hence
∠RSQ = ∠TSV.........................3
Given 1, 2, and 3,
Δ QRS ≅ ΔVTS
Therefore,
Δ QRS ≅ ΔVTS
and ∠ RSQ can be termed to be congruent to ∠TSV.
<h3>What does it mean for an angel to be congruent?</h3>
It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.
The angles of a regular polygon will always be congruent, regardless of its size or scale.
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