Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 fee
t wide by 8 feet long.
Which quadratic equation can be used to determine the thickness of the frame, x?
(See picture attached below)
Answer Choices:
A. x2 + 15x − 2 = 0
B. x2 + 15x + 58 = 0
C. 4x2 + 30x − 2 = 0
D. 4x2 + 30x + 58 = 0
Which quadratic equation can be used to determine the thickness of the frame, x?
(See picture attached below)
Answer Choices:
A. x2 + 15x − 2 = 0
B. x2 + 15x + 58 = 0
C. 4x2 + 30x − 2 = 0
D. 4x2 + 30x + 58 = 0
2 answers:
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Answer:
= 12
Step-by-step explanation:
The shape ABCDEF is an irregular polygon.
The sum of the interior angles of any regular or irregular polygon = (n - 2) x 180 (where n is the number of sides of the polygon).
Therefore, the sum of the interior angles of shape ABCDEF = (6 - 2) x 180 = 720°
So to find the value of , we need to add together all the interior angles and equal it to 720, then solve for
.
Before we do that, we need to determine angle F.
From inspection, we can see that angle F and 52° are a linear pair. We know that a linear pair of angles add up to 180°, so F + 52 = 180 ⇒ F = 180 - 52 = 128°
Therefore:
A + B + C + D + E + F = 720
(10 - 5) + 108 + (8
- 3) + (14
- 25) + 133 + 128 = 720
Collect like terms:
10 + 8
+ 14
- 5 + 108 - 3 - 25 + 133 + 128 = 720
Combine like terms:
32 + 336 = 720
Subtract 336 from both sides:
32 = 384
Divide both sides by 32:
= 12
From the given figure ,
RECA is a quadrilateral
RC divides it into two parts
From the triangles , ∆REC and ∆RAC
RE = RA (Given)
angle CRE = angle CRA (Given)
RC = RC (Common side)
Therefore, ∆REC is Congruent to ∆RAC
∆REC =~ ∆RAC by SAS Property
⇛CE = CA (Congruent parts in a congruent triangles)
Hence , Proved
<em>Additional</em><em> comment</em><em>:</em><em>-</em>
SAS property:-
"The two sides and included angle of one triangle are equal to the two sides and included angle then the two triangles are Congruent and this property is called SAS Property (Side -Angle-Side)
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