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elena-14-01-66 [18.8K]

1 year ago

12

A construction worker needs to put in a rectangular window in the side of a building. He knows from measuring that the top and b

ottom of the window has a width of 5ft and the sides have a length of 12ft. He also measured a diagonal of 13 ft. What is the length of the other diagonal?

1 answer:

maksim [4K]1 year ago

7 0

Answer:

13

Step-by-step explanation:

The diagonals of a rectangle are congruent.

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In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is . The area of polygon ABCDE is s

Gekata [30.6K]

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

$P=2b+2h$

In this problem

$b=ED=2\ units$

$h=AE=6\ units$

substitute

$P=2*2+2*6=16\ units$

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

$P=BD+DC+BC$

In this problem we have

$BD=AE=6\ units$

$DC=BC$

Applying the Pythagoras theorem

$DC^{2}=4^{2}+3^{2}$

$DC^{2}=25$

$DC=5\ units$

substitute

$P=6+5+5=16\ units$

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

$P=16\ units$

the perimeter of the triangle is

$P=16\ units$

so

the ratio is equal to

$\frac{16}{16} =1$

therefore

<u>the answer Part 1) is the option B</u>

$1$

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

$A=AE*BD=6*2=12\ units^{2}$

Area of the triangle is equal to

$A=\frac{1}{2}AEh$

the height h of the triangle is equal to $4\ units$

substitute

$A=\frac{1}{2}(6)(4)=12\ units^{2}$

The area of polygon is

$12\ units^{2}+12\ units^{2}=24\ units^{2}$

therefore

<u>the answer part 2) is the option C</u>

$24\ units^{2}$

7 0

2 years ago

Read 2 more answers

Suri's age is 4 less than 3 times her cousin's age. Suri is 17 years old. Which method can be used to find c, her cousin's age?

Mila [183]

Answer:

7 years

Step-by-step explanation:

Suri's age=17 years

Her cousin's age =c

Suri's age is 4 less than 3 times her cousin's age

4 less than 3 times her cousin's age means subtract 4 from 3 times her cousin's age

17=3c - 4

Find c which is her cousin's age

Add 4 to both sides

17+4=3c - 4 + 4

17+4=3c

21=3c

Divide both sides by 3

21/3=3c/3

7=c

Therefore,

C= 7

Her cousin's age = 7 years

4 0

1 year ago

What is the ninth term in the binomial expansion of (X-2y)^13?

vlada-n [284]

Answer:

$329472\cdot x^5\cdot y^8$

Explanation:

Binomial expansion is:

$(a+b)^n=a^n+n\cdot a^{n-1}{\cdot b}+\frac{n(n-1)}{2}\cdot a^{n-2}\cdot b^2+------+b^n$

Here in given expression we have a=x , b=-2y and n = 13

general formula for binomial expansion is:

$T_{r+1} =^nC_r\cdot a^{n-r}\cdot b^r$

Since, $T_{r+1}$

r should be one number less than the term we need to find so it will become the number we need to find like here we have to find 9th term so, r=8

substituting the values in the genral formula we will get

$^13C_8\cdot x^{13-8}\cdot (-2y)^8$

After substituting the values we will get

$\frac{13!}{8!\cdot 5!}\cdot x^5\cdot (-2y)^8}$

After simplification we will get

$329472\cdot x^5\cdot y^8$ which will be the 9th term of the expansion

5 0

1 year ago

Read 2 more answers

Which linear inequality will not have a shared solution set with the graphed linear inequality? y < Five-thirdsx – 2 y < N

elena-14-01-66 [18.8K]

Answer:

the third option

Step-by-step explanation:

idk :/

8 0

1 year ago

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9 out of 10 people at a game are rooting for the home team. What is the probability that exactly 6 of 8 people sitting together

scZoUnD [109]

A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.

Choosing 6 out of 8 supporters who root for the home team has probability

$\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14$

7 0

2 years ago