HD = 10.5
Step-by-step explanation:
Given BH = 3, GH = 2, BF = 10
Step 1: To find HF:
HF = BF – BH
HF = 10 – 3
HF = 7
Step 2: To find HD:
We know that if two chords intersects inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.
⇒ GH × HD = BH × HF
⇒ 2 × HD = 3 × 7
⇒ HD = 10.5
Hence, the value of HD = 10.5.
The attached graph represents the solution set of 
<h3>How to determine the graph?</h3>
The complete options are not given.
So, I would plot the graph that represents the solution set
The inequality is given as:
Start by splitting the inequalities as follows:
The above means that we plot the graphs of f(x) and g(x) to represent the solution set
See attachment
Read more about inequalities at:
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Answer:
64
Step-by-step explanation:
What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°
What we are looking for:
Toby's Angle = ?
The distance x = ?
We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.
Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle = 180° - (40° + 30°)
Toby's Angle = 110°
Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
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x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
x = 69.31m
∴The distance, x, between two landmarks is 69.31m
Answer:
- check below for explanation.
explanation:
➢ Given coordinates:
- A( 1, 3 )
- B( 1, 6 )
- C( 4, 6 )
- D( 5, 2 )
➢ after a dilation with a scale factor of 1/2:
- A( 1, 3 ) ÷ 2 ☛ A'(0.5,1.5)
- B(1, 6 ) ÷ 2 ☛ B'(0.5, 3)
- C( 4, 6) ÷ 2 ☛ C'( 2, 3 )
- D( 5, 2) ÷ 2 ☛ D'( 2.5, 1)
➢ Plot the after dilation coordinates on the graph:
