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3 years ago

A portable electronic typewriter cost £180 in 1988. Its price rose by 5% in 1989. What was the new price?

1 answer:

5 0

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 180}}{\left( \cfrac{5}{100} \right)180}\implies 9~\hfill \stackrel{\textit{new price}}{180+9\implies 189}$

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How do i write a two column proof for this?? Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST

Nikolay [14]

Answer:

PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)

Step-by-step explanation:

Given: PG ≅ SG and PT ≅ ST

To Prove: ∠GPT ≅ ∠GST

Proof: PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).

SSS Congruency Axiom: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Congruence: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

7 0

4 years ago

Does it matter what order you add the numbers in the problem

EastWind [94]

Answer:no it doesn’t matter what order you add the number.

Step-by-step explanation:

2 plus 3 equals 5

3 plus 2 equals 5

No matter the way you add 3 and 2, you still get 5

5 0

3 years ago

Consider the two data sets below:

alina1380 [7]

Answer:

Option c) The data sets will have the same values of their interquartile range.

Explanation:

1. The values are in order: they are in increasing oder, from lowest to highest value.

2. Calculate the interquartile range.

Interquartile range, IQR, is the third quartile, Q3, less the first quartile Q1:

IQR = Q3 - Q1

To find the first and the third quartile, first find the median:

Data Set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59

[19, 25, 35, 38], 41, [49, 50, 52, 59]

↑

median = 41

Data Set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99

[19, 25, 35, 38] , 41, [49, 50, 52, 99]

↑

median = 41

Now find the median of each subset: the values below the median and the values above the median.

Data set 1: First quartile

[19, 25, 35, 38],

↑

Q1 = [25 + 35] / 2 = 30

Third quartile

[49, 50, 52, 59]

↑

Q3 = [50 + 52] / 2 = 51

IQR = Q3 - Q1 = 51 - 30 = 21

Data set 2: First quartile

[19, 25, 35, 38]

↑

Q1 = [25 + 35] / 2= 30

Third quartile

[49, 50, 52, 99]

↑

Q3 = [52 + 50]/2 = 51

IQR = 51 - 30 = 21

Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)

This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.

An outlier will change the range because the range is the maximum value less the minimum value.

5 0

3 years ago

Elevii clasei a IV-a au fost la patinoar. Stiind ca numarul baietilor reprezinta jumatate plus 3 din numarul copiilor si ca numa

Shalnov [3]

Step-by-step explanation:

Fie x numărul de copii

$f = 10$ $=\:fete$

$b\:=\:\frac{x}{2}\:+\:3$

$f\:+\:b\:=\:x$

$10\:+\:\frac{x}{2}\:+\:3\:=\:x$

$20\:+\:x\:+\:6\:=\:2x$

$x\:=\:26\:copii\:au\:fost\:la\:patinoar$

$b=\frac{26}{2}+\:3$

$b\:=\:16\:baieti$

7 0

3 years ago

Help me answer these PLEASE ASAP

Hoochie [10]

Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

Sheet 1: Question 5

Step 1: Find the value of x

Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

Step 2: Find angles

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° (because it is vertically opposite to angle SOP)

Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)

Angle SOR = 130°

Angle POQ = 130° (because it is vertically opposite to angle SOR)

Sheet 1: Question 6

Angle 1 = 72° (because vertically opposite angles)

∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

Sheet 2: Question 3

Step 1: Find the value of x

Sum of complementary angles is equal to 90°

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

Step 2: Find angle A and angle B using x

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

Step 2: Find angle A and angle B using x

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

Sheet 3: Question 4

Sum of supplementary angles is equal to 180°.

Step 1: Find x

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

Step 2: Find both angles with the help of x

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

Sheet 4: Question 1

All angles on a straight line are equal to 180°

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

Sheet 4: Question 2

Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)

Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)

Sheet 4: Question 3

Step 1: Find the value of x

All angles on a straight line are equal to 180° or linear pairs are equal to 180°

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

Step 2: Find angles using the value of x

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

Sheet 4: Question 4

Linear pairs are equal to 180°.

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

Take LCM = 6

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

7 0

4 years ago