How many numbers from 1 through 200 have a 2 in the units place and are divisible by 4?

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

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Plz reanswer it If (x+4): (3x+1) is the duplicate ratio of 3:4 find the value of x.

Rzqust [24]

Answer: x = 13/5

Explanation:

(x+4)/(3x+1) = 3/4

Cross multiply:

4(x+4) = 3(3x+1)
4x + 16 = 9x + 3
4x - 9x = 3 - 16
-5x = -13
x = -13/-5
x = 13/5

3 0

3 years ago

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There are 15 students on a yearbook committee. 40% of the students are females. How many students on the committee are males?

Andrei [34K]

Answer:

9 students on the committee are males

Step-by-step explanation:

As per the statement:

There are 15 students on a yearbook committee.

⇒Total students on a yearbook committee = 15

⇒ $\text{Male students} +\text{Female students} = 15$ ....[1]

It is given that:

40% of the students are females

⇒ $\text{Female students} = \frac{40}{100} \cdot 15 = 6$

Substitute in [1] we have;

$\text{Male students} + 6 = 15$

Subtract 6 from both sides we have;

$\text{Male students}= 9$

Therefore, 9 students on the committee are males

8 0

3 years ago

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64, –48, 36, –27, ...<br><br> Which formula can be used to describe the sequence?

nordsb [41]

Answer:

$\boxed{a_n \: = \: 64 \: \times \: ( - \frac{3}{4} ) ^{n \: - \: 1} }$

Step-by-step explanation:

We first compute the ratio of this geometric sequence.

$r \: = \: \frac{ - 48}{64} \\ \\ r \: = \: \frac{36}{ - 48} \\ \\ r \: = \: \frac{ - 27}{36}$

We simplify the fractions:

$r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4}$

We deduce that it is the common ratio because it is the same between each pair.

$r \: = \: - \frac{3 }{4}$

We use the first term and the common ratio to describe the equation:

$a_1 \: = \: 64; \: r \: = \: - \frac{3 }{4}$

<h3>We apply the data in this formula:</h3>

$\boxed{a_n \: = \: a_1 \: \times \: {r}^{ n \: - \: 1} }$

_______________________

<h3>We apply:</h3>

$\boxed {\bold{a_n \: = \: 64 \: \times \: {( - \frac{3}{4} )}^{ n \: - \: 1} }}$

<u>Data</u>: The unknown "n" is the term you want

<h3><em><u>MissSpanish</u></em></h3>

4 0

2 years ago

Mrs teed bought 22 packs of hot dog rolls at the store for the 4th-grade picnic there were 12 rolls in each pack how many hot do

creativ13 [48]

Answer:

Step-by-step explanation:

To find out

22 x 12 = 264 rolls

5 0

2 years ago