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3 years ago

The sum of three consecutive numbers is 72. What are the smallest of these numbers?

Mathematics

1 answer:

spayn [35]3 years ago

6 0

Answer: 23,24,25

Step-by-step explanation:

Obviously the numbers are about 72÷3 = 24 so see if 23,24,25 works. It does. No need to solve

(i-1) + (i) + (i+i) = 72, 3i=72, i=24.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

Will give brainlest if u slove

grin007 [14]

Answer:

Step-by-step explanation:

6 0

2 years ago

Which situation can be represented by 16 x 4?

Alex787 [66]

Answer:

the answer should be c.

Step-by-step explanation:

here's why....A uses 4 more which is adding. B uses 4 fewer which is subtracting and D does not complete so it should be C.

6 0

3 years ago

There are 4 jacks and 13 clubs in a standard, 52-card deck of playing cards. What is the probability that a card picked at rando

ale4655 [162]

Answer:

16/52, or 4/13.

Step-by-step explanation:

First, since we know that the question is asking for the probability of a club <u>or</u> a jack, we know that we have to add the two probabilities. The first probability is that of picking a club, which is 13/52. The probability of picking a jack (be sure not to overlap; don't double count the jack of clubs) is 3/52. Adding these two gives us 13/52+3/52=16/52, which simplifies to 4/13.

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3 years ago

The expression (3r+5)(2r-6) is equivalent to ?

Sholpan [36]

Is the answer 5r-1? I'm not sure tho sorry if it's wrong!

5 0

3 years ago