Answers
[tex]\huge\bold{Given :}[/tex]
Angle AOD = [tex]x[/tex] - 10°
Angle DOC = 3[tex]x[/tex] + 25°
Angle BOC = [tex]x[/tex] + 5°
[tex]\huge\bold{To\:find :}[/tex]
The value of [tex]x[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{The\:value\:of\:x\:is\:32°}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ ∠ AOD + ∠ DOC + ∠ BOC = 180°
➪ [tex]x[/tex] - 10° + 3[tex]x[/tex] + 25° + [tex]x[/tex] + 5° = 180°
Combining like terms, we have
➪ 5[tex]x[/tex] + 20° = 180°
➪ 5[tex]x[/tex] = 180° - 20°
➪ 5[tex]x[/tex] = 160°
➪ [tex]x[/tex] = [tex]\frac{160}{5}[/tex]
➪ [tex]x[/tex] = 32°
Therefore, the value of [tex]x[/tex] is 32°.
Now,
I) ∠ AOD = [tex]x[/tex] - 10° = 32° - 10° = 22°
2) ∠ DOC = 3[tex]x[/tex] + 25° = 3 x 32° +25° = 96° + 25° = 121°
3) ∠ BOC = [tex]x[/tex] + 5° = 32° + 5° = 37°
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
∠ AOD + ∠ DOC + ∠ BOC = 180°
✒ 22° + 121° + 37° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
Related Questions
the numerator of a fraction is 2 less than the denominator . If one is added to its denominator ,it becomes 1/2 ,find the fraction.
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Answers
Answer:
numerator = 2 and denominator is 4
Step-by-step explanation:
let the denominator be x
numerator = x-2
according to the question
[tex]\frac{x-2}{x} = \frac{1}{2}[/tex]
do cross multiplication
x*1 = 2(x-2)
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4 = 2x - x
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therefore denominator is 4
numerator = x-2
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Step-by-step explanation:
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Answer:
[tex]AB[/tex] is parallel to [tex]CD[/tex] ([tex]AB ||CD[/tex])
Step-by-step explanation:
In a set of parallel lines cut by the traversal, [tex]\angle AHG[/tex] and [tex]\angle DGH[/tex] are alternate interior angles. In a set of parallel lines cut by a traversal, alternate interior angles are always equal. Therefore, since [tex]\angle AHG=\angle DGH=115^{\circ}[/tex] (they are equal), the lines AB and CD must be parallel.
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Answer: The equation is h(x) = 45(1/5)^x
This is the same as h(x) = 45(0.2)^x because 1/5 = 0.2
=======================================================
Explanation:
We'll start with y = a*b^x, and plug in x = 0 to find that,
y = a*b^x
y = a*b^0
y = a*1
y = a
The table says that y = 45 is the case when x = 0. So that must mean a = 45.
The value of ''a' is the y intercept and it's the initial value.
---------
So the equation y = a*b^x updates to y = 45*b^x
Let's plug in (x,y) = (1,9) and solve for b
y = 45*b^x
9 = 45*b^1
9 = 45b
45b = 9
b = 9/45
b = 1/5
b = 0.2
Therefore, the equation in fraction form is y = 45(1/5)^x
That same equation in decimal form is y = 45(0.2)^x
---------
To verify the equation, plug in various values of x and you should get y values that are shown in the table.
For instance, plug in x = 2 to find that
y = 45(0.2)^x
y = 45(0.2)^2
y = 45(0.04)
y = 1.8
which matches with the table. That verifies the 5th row. I'll let you verify the other rows.
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The value of ( - 2 / 3 ) will be ……
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Answer:
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Answers
Step-by-step explanation:
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Answer:
cost of 1 kg mango = rupees 29.4
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis
Answers
Answer:
the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)
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after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)
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Step-by-step explanation:
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2-4 6 8 10 12
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Hope this is straightforward.
Each unit in the graph above is one block. How far would you have to walk from the party supply store to the art gallery and then continue on to the dry cleaners?
Options:
A)
6 blocks
B)
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C)
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D)
10 blocks
Answers
Answer:
11 blocks
Step-by-step explanation:
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Answers
Answer:
The lateral area of a cone is 141.4 square centimeters
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Compré un TV que costó 35.000 pesos. Si en la aduana debo pagar 10 % por impuesto de nacionalización y 12 % sobre el precio nacionalizado de IVA. ¿Cuánto dinero pagué en total solo en impuestos?
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7700 in taxes
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Step-by-step explanation:
I bought a TV that cost 35,000 pesos. If at customs I must pay 10% for nationalization tax and 12% on the nationalized VAT price. How much money did I pay in total just in taxes?
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Answers
Answer:D
Step-by-step explanation:
Darryl was shopping for a new camera. He found one with an original price of $125.00 and is marked 45% off. Sales tax for the item is 5.2%. What is the final price of the camera, including tax?
Answers
Answer:
$75.25
Step-by-step explanation:
Given data
Original price =$125
Discount =45%
Tax=5.2%
Let us find the discount
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56.25
Let us find the tax
5.2/100*125
0.052*125
6.5
Hence the amount is
125-56.25+6.5
=$75.25
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Answers
Answer:
Maybe 1 out the 10 possibilities
Step-by-step explanation:
I remember learning this a few years back but I'm not 100% sure.
The equation SA = 6s can be used to calculate the surface area, SA, of a cube with side length S. What is the
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Answers
=6 • 6 = 36
36 sq ft.
