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alina1380 [7]
3 years ago
13

Properties of rectangle

Mathematics
2 answers:
Alexandra [31]3 years ago
8 0

4. y = 5

5. DB = 27

6. AC = 18

7. m<ABD = 53

Nat2105 [25]3 years ago
6 0

For this case we have:

Question 1:

BC = 24\\AD = 5y-1

By definition, one of the properties of the rectangle states that:

The opposite sides of a rectangle have the same length, that is, they are equal, then:

BC = AD

So:

24 = 5y-1

Clearing "y" we have:

24 + 1 = 5y\\25 = 5y\\y = \frac {25} {5}\\y = 5

Thus, the value of "y" is 5.

Answer:

y = 5

Question 2:

AC = 2x + 13\\DB = 4x-1

By definition, one of the properties of the rectangles states that:

 The diagonals of a rectangle have the same lengths, that is:

AC = DB\\2x + 13 = 4x-1

We clear the value of "x":

13 + 1 = 4x-2x\\14 = 2x\\x = \frac {14} {2}\\x = 7

We must find DB:

DB = 4x-1 \\DB = 4 (7) -1\\DB = 28-1\\DB = 27

ANswer:

DB = 27

Question 3:

AE = 3x + 3\\EC = 5x-15

By definition, one of the properties of the rectangles states that:

The diagonals of a rectangle intersect and at the point of intersection they are divided in half, that is:

AE = EC\\3x + 3 = 5x-15

Clearing the value of "x" we have:

3 + 15 = 5x-3x\\18 = 2x\\x = \frac {18} {2}\\x = 9

We know that:

AC = AE + EC\\AC = 3x + 3 + 5x-15\\AC = 8x-12\\AC = 8 (9) -12\\AC = 60

ANswer:

AC = 60

Question 4:

m

By definition, one of the properties of the rectangles states that:

The 4 angles of the rectangles are straight. From there it turns out that:

m

We clear the value of "x":

7x-4x = 5 + 31\\3x = 36\\x = \frac {36} {3}\\x = 12

So:

m

Answer:

m

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2 years ago
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How to put 5/27 into a <br> percentage
leonid [27]

Answer:

18.5185%

Step-by-step explanation:

(7/27) * 100% = (0.185185) * 100% = 18.5185%

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What is the answer too this,it’s rational numbers - 3.3(6)= ?
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Answer:

the answer is -19.8.

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On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 ho
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Answer:

45.29 miles per hour

Step-by-step explanation:

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Avg. Speed = 45.29 miles per hour

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Cheddar Cheese
disa [49]

Complete question :

Cheddar Cheese

$3/lb

Swiss Cheese

$5/lb

Keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Answer:

10 lbs of cheddar cheese

6 lbs of Swiss cheese

$3a + $5b = $30

Step-by-step explanation:

Given that :

Cheddar cheese = $3/lb

Swiss cheese = $5/lb

Total amount budgeted for cheese = $30

How many pounds of cheese can Keisha get if she buys only Cheddar cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of cheddar cheese

$30 / 3 = 10 pounds of cheedar cheese

Only Swiss cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of Swiss cheese

$30 / 5 = 6 pounds of Swiss cheese

A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Let amount of cheddar cheese she can get = a

Let amount of Swiss cheese she can get = b

Hence,

(Cost per pound of cheddar cheese * number of pounds of cheddar) + (Cost per pound of Swiss cheese * number of pounds of Swiss cheese) = total budgeted amount

(3 * a) + (5 * b) = $30

$3a + $5b = $30

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