Mr. Turney wrote the value statement "x = 2" on the whiteboard. He asked his students to create an equation or inequality with t
1 answer:
Answer:
Some of the equations can be written as-
1. 2x = 4
2. 3x + 9 = 15
3. x + 5 = 7
4. 5x - 2 = 8
Step-by-step explanation:
Given - Mr. Turney wrote the value statement "x = 2" on the whiteboard.
To find - He asked his students to create an equation or inequality with
this value as a solution.
Proof -
Given that, The value statement is ''x = 2''
We have to find out that equation in such a way that if we solve the equation , we get the value x = 2
There can be infinite many equation that give the value statement '' x = 2''
Some of the equations can be written as-
1. 2x = 4
2. 3x + 9 = 15
3. x + 5 = 7
4. 5x - 2 = 8
And many more.
Verification -
1. 2x = 4
⇒x =
⇒x = 2
Verified
2. 3x + 9 = 15
⇒3x = 15 - 9
⇒3x = 6
⇒x =
⇒x = 2
Verified
3. x + 5 = 7
⇒x = 7 - 5
⇒x = 2
Verified
4. 5x - 2 = 8
⇒5x = 8 + 2
⇒5x = 10
⇒x =
⇒x = 2
Verified
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Answer:
∠HGJ = 35°
Step-by-step explanation:
Although the question is somewhat incomplete, I have tried to reconstruct the question as much as possible to aid understanding (attached is the pictorial representation of the rhombus).
Firstly, it is important to note that rhombuses are parallelograms which have all sides equal and whose diagonals are perpendicular to each other. In addition to this, their diagonals bisect one other.
Mathematically, |EF| = |FG| = |GH| = |HE|
Another property which rhombuses have is that their opposite angles are equal.
Mathematically, ∠E = ∠G, ∠H = ∠F
The adjacent angles in a rhombus are supplementary. This means that the sum of angles closest to each other is 180°.
Mathematically, ∠E + ∠F = 180°, ∠F + ∠G = 180°, ∠G + ∠H = 180°,
∠H + ∠E = 180°
The question gave us ∠GHE and asked us to find ∠HGJ (denoted as θ in the picture attached). Note that ∠GHE means ∠H. That is, ∠GHE ⇒ ∠H
∠GHE or ∠H = 110°
From the properties of rhombuses (earlier stated), we know that adjacent angles in a rhombus are supplementary
Mathematically,
∠GHE + ∠FGH ⇒ 110° + ∠FGH = 180° ⇒ ∠FGH = 180° - 110°
∠FGH or ∠G = 70°
To calculate for ∠HGJ, we divide ∠FGH by 2, we have:
∠HGJ = ∠FGH ÷ 2 = 70° ÷ 2
∠HGJ = 35°
