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tangare [24]
4 years ago
14

Suppose A = {1, 7, 13, 17, 21, 25} and B = {7, ,14, 21, 28, 35, 42}. What is A∩B?

Mathematics
1 answer:
Lubov Fominskaja [6]4 years ago
8 0

A\cap B=\{7,21\}

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In a quadrilateral ABCD, angle A + angle D = 90°. Prove that AC^2 + BD^2 = BC^2 + AD^2​
olga2289 [7]

Answer:

AD^{2}+BC^{2}=AE^{2}+ED^{2}+BE^{2}+EC^{2}

AC^{2}+BD^{2}=AE^{2}+EC^{2}+BE^{2}+ED^{2}

Hence prove.

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Step-by-step explanation:

Given:

∠A + ∠D = 90°

We are prove to that

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Solution:

See required figure in attached file.

We know sum of the all angles of a triangle is 180°.

So, in triangle AED.

∠A + ∠E + ∠D = 180°

∠E + (∠A + ∠D) = 180°

Now, we substitute ∠A + ∠D = 90° in above equation.

∠E + 90° = 180°

∠E = 180° - 90°

∠E = 90°

Using Pythagoras Theorem for triangle ADE and triangle BEC.

AD^{2}=AE^{2}+ED^{2}

BC^{2}=BE^{2}+EC^{2}

Now, we add both above equations.

AD^{2}+BC^{2}=AE^{2}+ED^{2}+BE^{2}+EC^{2}--------(1)

Similarly, Using Pythagoras Theorem for triangle AEC and triangle BED.

AC^{2}=AE^{2}+EC^{2}

BD^{2}=BE^{2}+ED^{2}

Now, we add both above equations.

AC^{2}+BD^{2}=AE^{2}+EC^{2}+BE^{2}+ED^{2}--------(2)

We get From equation 1 and equation 2.

AC^{2}+BD^{2}=BC^{2}+AD^{2}

Hence prove,

AC^{2}+BD^{2}=BC^{2}+AD^{2}

4 0
3 years ago
Find the roots.<br> 3x2 - 5x+ 2 =0
tigry1 [53]

Answer:

see explanation

Step-by-step explanation:

Given

3x² - 5x + 2 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × 2 = 6 and sum = - 5

The factors are - 3 and - 2

Use these factors to split the x- term

3x² - 3x - 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x - 1) - 2(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(3x - 2) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = \frac{2}{3}

Roots are x = 1, x = \frac{2}{3}

5 0
3 years ago
Can someone please answer this algebra question thanks!
Goryan [66]

Answer:

Yes it does answer A_____

6 0
3 years ago
The city of Redmond is planning to build a new park by enlarging the current park by a scale factor of 3. The current park has a
Charra [1.4K]

Answer:  I think it’s Area of the new park is 602000 yd

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-5X +1 92 - 321+13 - 12X<br> Plz I need help
Alex73 [517]

Answer:

x= 116/17

Step-by-step explanation:

5x+192−321+13=−12x

Step 1: Simplify both sides of the equation.

5x+192−321+13=−12x

5x+192+−321+13=−12x

(5x)+(192+−321+13)=−12x(Combine Like Terms)

5x+−116=−12x

5x−116=−12x

Step 2: Add 12x to both sides.

5x−116+12x=−12x+12x

17x−116=0

Step 3: Add 116 to both sides.

17x−116+116=0+116

17x=116

Step 4: Divide both sides by 17.

17x/17=116/17

x = 116/17

6 0
3 years ago
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