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oksano4ka [1.4K]
3 years ago
11

Construct a trapezium ABCD such that AD is parallel to BC, AB = 4.8 cm, BC = 6.8 cm, CD = 5.4 cm and ∠ABC = 60°. Measure and wri

te down the length of AC.

Mathematics
1 answer:
lara31 [8.8K]3 years ago
5 0

Answer:

AC = 6.05 cm

Step-by-step explanation:

We can draw two different trapeziums with the information given.

The possible drawings of the trapezium ABCD are in the image attached.

In both trapeziums, the length of AC is the same, and we can calculate this length using the law of cosines in the triangle ABC:

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(B)

AC^2 = 4.8^2 + 6.8^2 - 2 * 4.8 * 6.8 * cos(60)

AC^2 = 23.04 + 46.24 - 65.28 * 0.5

AC^2 = 36.64

AC = 6.05 cm

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Determine whether the point (3,3) is in the solution set of the system of inequalities below.
Radda [10]

Answer:

      The ordered pair is not a solution of the system D

explanation:

A.

y < -3

y ≤ 2/3x - 4

B.

y > -3

y ≥ 2/3x - 4

C.

y < -3

y ≥ 2/3x - 4

D.

y > -2

y ≤ 2/3x - 4

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each case

Case A) we have

----> inequality A

----> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

----> inequality A

----> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

----> is true

Inequality B

----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

----> inequality A

----> inequality B

Substitute the value of x and  y of the point (3,-2) in both inequalities and then compare the results

Inequality A

 ----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

y > -2 ----> inequality A

----> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

----> is not true

therefore

The ordered pair is not a solution of the system D

3 0
4 years ago
The area of a rectangle is 150 in². The ratio of the length to the width is 3:2. Find the length and the width.
kap26 [50]

Answer:

Width = 10 in

Length = 15 in

Step-by-step explanation:

L / W = 3 / 2

L = 3/2 W

L * W = 3/2 W *W = 3/2 W² = 150

w² = 150 * 2/3 = 100

W = 10 in

L = 15 in

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2 dollar bills, one nickel, and three pennies ($2.08) :)

8 0
3 years ago
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Kay [80]

Answer:

100%

Step-by-step explanation:

The problem states that all pencils are yellow and no other color, so the only outcome is yellow.

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Answer:

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