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creativ13 [48]
3 years ago
11

Just answer what it asks in the picture PLEASE

Mathematics
1 answer:
Molodets [167]3 years ago
7 0

m∠1 = 30° (by Vertical angle theorem)

m∠A = 80° (by Triangle sum theorem)

m∠D = 80° (by Triangle sum theorem)

The value of x is 7.5 and y is 9.

Solution:

∠ACB and ∠DCE are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

⇒ m∠DCE = m∠ACB

⇒ m∠1 = 30° (by Vertical angle theorem)

In triangle ACD,

Triangle sum property:

<em>Sum of the interior angles of the triangle = 180°</em>

⇒ m∠A + m∠C + m∠B = 180°

⇒ m∠A + 30° + 70° = 180°

⇒ m∠A + 100° = 180°

⇒ m∠A = 100° – 180°

⇒ m∠A = 80° (by Triangle sum theorem)

Similarly, m∠D = 80° (by Triangle sum theorem)

In ΔACD and ΔDCE,

All the angles are congruent, so ΔACD and ΔDCE are similar triangles.

<em>In similar triangle corresponding sides are in the same ratio.</em>

$\frac{9}{12}=\frac{x}{10}

Do cross multiplication.

90 = 12x

7.5 = x

Now, to find y:

$\frac{9}{12}=\frac{6}{y}

Do cross multiplication.

9y = 72

Divide by 9, we get

y = 8

Hence the value of x is 7.5 and y is 9.

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PLEASE HELP I WILL MARK YOU AS BRAINLEST
denpristay [2]

Answer:

(i) Five number summary: Minimum value = 1, Q_1=18,Median=18.5, Q_3=20.5, Maximum value = 26.

(ii) IQR = 2.5, upper fence = 24.25 and lower fence = 14.25.

(iii) 26 is an outlier of the data.

Step-by-step explanation:

The given data set is

19, 18, 23, 18, 18, 26, 19, 16, 20, 18, 17, 21

Arrange the data set in ascending order.

16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 23, 26

Divide the data set in 4 equal parts.

(16, 17, 18), (18, 18, 18), (19, 19, 20), (21, 23, 26)

Minimum value = 16

Q_1=\frac{18+18}{2}=18

Median=Q_2=\frac{18+19}{2}=18.5

Q_3=\frac{20+21}{2}=20.5

Maximum value = 26

The inter quartile range (IQR) of the data is

IQR=Q_3-Q_1=20.5-18=2.5

Upper fence :

Q_3+1.5(IQR)=20.5+1.5(2.5)=24.25

Lower fence :

Q_1-1.5(IQR)=18-1.5(2.5)=14.25

If the any element of the data set lies out side the upper fence and lower fence, then it is called an outlier.

26 ∉ [14.25, 24.25]

Therefore, 26 is an outlier of the data.

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