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2 years ago

A right triangle has legs of length 4x and 20x. What is an expression for the hypotenuse of the right triangle

Mathematics

1 answer:

kherson [118]2 years ago

5 0

Answer:

$4x\sqrt{26}$ .

Step-by-step explanation:

Given information:

$Leg_1=4x$

$Leg_2=20x$

According to the Pythagoras theorem,

$(hypotenuse)^2=(Leg_1)^2+(leg_2)^2$

Using Pythagoras theorem, we get

$(hypotenuse)^2=(4x)^2+(20x)^2$

$(hypotenuse)^2=16x^2+400x^2$

$(hypotenuse)^2=416x^2$

Taking square root on both sides.

$hypotenuse=\sqrt{416x^2}$

$hypotenuse=4x\sqrt{26}$

Hence, the expression of the hypotenuse is $4x\sqrt{26}$ .

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5 minutes

Step-by-step explanation:

9/6=40 mins per patient

8/6=45 mins per patient

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2 years ago

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On a class test, Lesley scored 4.5 points more than her friend Cathy. Lesley scored 81.5 points. Cathy's score, x, can be found

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Answer: B

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2 years ago

Organisms A and B start out with the same population size. Organism A's population doubles every day. After 5 days, the populati

Zigmanuir [339]

Answer:

The number of times organism B's population is larger than organism A's population after 8 days is 32 times

Step-by-step explanation:

The population of organism A doubles every day, geometrically as follows

a, a·r, a·r²

Where;

r = 2

The population after 5 days, is therefore;

Pₐ₅ = = 32·a

The virus cuts the population in half for three days as follows;

The first of ta·2⁵ he three days = 32/2 = 16·a

The second of the three days = 16/2 = 8·a

After the third day, Pₐ = 8/2 = 8·a

The population growth of organism B is the same as the initial growth of organism A, therefore, the population, P₈ of organism B after 8 days is given as follows;

P₈ = a·2⁸ = 256·a

Therefore, the number of times organism B's population is larger than organism A's population after 8 days is P₈/Pₐ = 256·a/8·a = 32 times

Which gives, the number of times organism B's population is larger than organism A's population after 8 days is 32 times.

3 0

2 years ago

Al purchases a speedboat costing $24,500. State taxes are 5.5% and federal excise tax is 13%. What is the total purchase price?

trapecia [35]

Answer: The total purchase price is $ 29,032

Step-by-step explanation:

Hi, to solve this problem you have to solve the percentages of each taxes first.

So :

state taxes =$24,500 × 5.5% = $1,347.5

federal tax = $24,500 × 13% = $3,185

The next step is adding the taxes results to the speedboat cost.

so:

speedboat = $24,500

speedboat + taxes = $24,500 + $1,347.5 +$3,185 = $29,032

The total purchse price for the speedboat is $29,032.

8 0

2 years ago

A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 cus

IRINA_888 [86]

Answer:

3 customers brought all the three papers.

Step-by-step explanation:

Let, D, O and N represents the three newspapers.

D = The daily times

O = The observer

N = The new Nigeria.

According to the given information,

$n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50$

$n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16$

We know that,

$n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)$

Using this formula, we get

$n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)$

$135 =70+60+50-17-15-16 +n(D\cap O\cap N)$

$135 =132+n(D\cap O\cap N)$

$135 -132=n(D\cap O\cap N)$

$3=n(D\cap O\cap N)$

Therefore, 3 customers brought all the three papers.

5 0

2 years ago