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2 years ago

Use the rule to enter the first five terms of the pattern in order. Rule: Add 9, subtract 6 First term: 56

Mathematics

1 answer:

miskamm [114]2 years ago

3 0

Answer:

The first five terms in the pattern are 56, 59, 62, 65 and 68.

Step-by-step explanation:

Here, the first term in the pattern = 56

Rule : Add 9, Subtract 6

Second term :

First term + 9 - 6 = 56 + 9 - 6 = 59

Third Term :

Second term + 9 - 6 = 59 + 9 - 6 = 62

Fourth Term :

Third term + 9 - 6 = 62 + 9 - 6 = 65

Fifth Term :

Fourth term + 9 - 6 = 65 + 9 - 6 = 68

Hence, the first five terms in the pattern is 56, 59, 62, 65 and 68.

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If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 wi

Dmitry [639]

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴ ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

$Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}$

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

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2 years ago

7) Shannon is selling some embroidered jackets on a Web site. She wants 10 points

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Answer: A

Step-by-step explanation:

Nothing you a bum

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2 years ago

The midpoint of AB is M(1, -4). If the coordinates of A are (-3,-6), what are the coordinates of B?

kramer

Answer:

The coordinates of B is (5,-2)

Step-by-step explanation:

In order to find the coordinates of B, you have to use midpoint formula. Then substitute the following values into the formula :

$m = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

Let (x1,y1) be A (-3,-6),

Let (x2,y2) be B,

Let midpoint be M (1,-4),

$(1, - 4) = (\frac{ - 3 + x2}{2} , \frac{ - 6 + y2}{2} )$

$by \: comparison, \:$

$\frac{ - 3 + x2}{2} = 1$

$- 3 + x2 = 2$

$x2 = 5$

$\frac{ - 6 + y2}{2} = - 4$

$- 6 + y2 = - 8$

$y2 = - 2$

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2 years ago

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iren [92.7K]

Answer:

(7, 5)

Step-by-step explanation:

When reflecting over the x-axis, the only position that moves is the y-coordinate as it is going above the axis it was previously below. Since point F's original position was (7, -5) it is 5 spaces away from the x-axis. We move 5 places up to be even with the x-axis, then move up another 5 places to reflect the point to get F'.

Hope this Helps!

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2 years ago

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Is 2000 1 tenth of 200?

Iteru [2.4K]

Answer:No

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2 years ago