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4 years ago

ABCD is a rectangle. Find the length of each diagonal.ac=2(5a+1) bd=2(a+1).

1 answer:

7 0

Rectangle diagonals are equal.

2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0

AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2 <span>
</span>BD = 2(a+1) = 2(0 + 1) = 2 <span>× 1 = 2
</span>
Ansver: AC = BD = 2

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What is the simplified form of the following expression? (n^5)(n^2)

tatiyna

$(n^5)(n^2)=n^{5+2} =\boxed{n^7}$

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4 years ago

The number of kilograms of water in a human body varies directly as the mass of the body. A 93-kg person contains 62-kg of water

slava [35]

We know that the variation is proportianal, that is we can relate the quantities as:

$y=kx$

where y is the mass of the body and x is the mass of water. From the values given we have that:

$\begin{gathered} 93=62k \\ k=\frac{93}{62} \\ k=\frac{3}{2} \end{gathered}$

hence the constant of proportionality is 3/2. Now, if the mass of the water is 75, then the mass of the body is:

$\frac{3}{2}\cdot75=112.5$

Therefore, the mass of the body is 112.5 kilograms

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1 year ago

IN A CLASS OF 60 STUDENTS, 25 PLAYS BASKETBALL, 2O PLAY VOLLEYBALL, AND 10 STUDENTS PLAY BOTH OF THEM. HOW MANY STUDENTS PLAY NE

I am Lyosha [343]

Answer:

Step-by-step explanation:

We'll compare it with the study of sets, the most noticeable operation of which is:

<u>n(A ∪ B) = n(A) + n(B) - n(A ∩ B)</u>

where,

n(A ∪ B) is the Union Set, i. e, the set that contains all the elements

n(A) is a subset of the Union Set

n(B) is another subset of the Union Set, and

n(A ∩ B) is the Intersection Set ,i.e, the set contains common elements from both A and B sets.

<h3><u>In the question:</u></h3>

n(A ∪ B) = ? (<em>the total number of students in the class who are into the above mentioned sports)</em>

Let set A contains the students who play basketball and set B, the students who play Volleyball.

n(A) = 25
n(B) = 20

10 students play both of them, i. e.,

n(A ∩ B) = 10 (<em>as 10 students have common sports - Volleyball and Basketball</em>)

<u>Using the above operation:</u>

=> n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

=> n(A ∪ B) = 25 + 20 - 10

=> n(A ∪ B) = 35

<h3><u>Final Step to the Answer:</u></h3>

<u>The total number of students in the class </u>

= students into the given sports + students who don't play any of them

Total number of students in the class is 60
Total number fo students playing basketball and volleyball is 35

The students who play neither = 60 - 35

= 25

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3 years ago

As the time___, the water___

Tasya [4]

Answer:

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3 years ago

Can someone please help with this

finlep [7]

Answer:

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Step-by-step explanation:

Draw a trend line (attached).

Reading from the graph, the resting hear rate, in bpm, of a person who exercises an average of 8 hours a week is approximately 47.

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2 years ago