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3 years ago

The greatest common factor of 24,40 and 56

1 answer:

7 0

The factors of 24 are 1,2,3,4,6,8,12, and 24. The factors of 40 are 1,2,4,5,8,10,20, and 40. The factors of 56 are 1,2,4,7,8,14,28, and 56. 24÷8=3. 40÷8=5. 56÷8=7. Therefore, the GCF of 24,40, and 56 is $\boxed{8}$

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1. Based on the information given, can you determine that the quadrilateral must be a

zhenek [66]

Solving Q1: Given BE = ED and AE = EC.

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)

Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)

Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

Solving Q2: The parallelogram has the angle measures shown in the diagram.

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

7 0

3 years ago

The Apple harvest produced 2,350kg of Apple's. A farmer packs 36 apples in the box. One apple weighs approximately 250 grams how

jenyasd209 [6]

Answer:

Step-by-step explanation:

The total number of apples produced at the apple harvest is 2,350kg.

1 kg = 1000 grams. Therefore,

2350 kg = 2350 × 1000 = 2350000kg

A farmer packs 36 apples in the box. If one apple weighs approximately 250 grams, the total weight of 36 apples would be

36 × 250 = 9000 grams

Therefore, the number of boxes that are needed to pack the apples would be

2350000/9000 = 261.11

It means that 262 boxes would be needed.

5 0

3 years ago

Solve the inequality if possible 4(3-2x)>2(6-4x)

GenaCL600 [577]

Final Answer: No Solution

Steps/Reasons/Explanation:

Question: $4(3- 2x) > 2(6- 4x)$

Step 1: Divide both sides by $2$ .

$2(3 - 2x) > 6 - 4x$

Step 2: Expand.

$6 - 4x > 6 - 4x$

Step 3: Since $6 - 4x > 6 - 4x$ is false, we have no solution.

No Solution

~I hope I helped you :)~

6 0

3 years ago

Read 2 more answers

With reference to the figure, sin X equals? 1.) 0.250 2.)0.447 3.)0.894 4.)1

Flura [38]

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

$sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894$ (nearest thousandth)

6 0

3 years ago

What does it mean to evaluate an expression in math?

Ymorist [56]

It mainly means 'simplifying an expression down to a single numerical value', I believe.

7 0

3 years ago

Read 2 more answers