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3 years ago

Solve for x thanks .

Mathematics

1 answer:

OleMash [197]3 years ago

8 0

Answer:

x = 3.87

Step-by-step explanation:

Using the right angle altitude theorem, we know that all three triangles are congruent, so the lengths of corresponding sides of the triangles are in proportion..

AD/DB = DB/DC

15/x = x/1

x² = 15

x = √15

x = 3.87

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In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

Bond [772]

Answer:

NS= 20

Step-by-step explanation:

4x / 3x-5 (2/1)

4x / 6x-10

-6x -6x

-2x / -10

X / 5

X=5

NS= 4x

NS= 4(5)

NS= 20

3 0

3 years ago

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What is the volume of the sphere below?

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Distance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 14 mph, and ship B sails east at 18 mph.

Murrr4er [49]

Answer:

c = 22.8 miles/hr

Step-by-step explanation:

The ship A sails north at the rate of 14 mile per hour , it represent the opposite side of a triangle. Ship B start at the same point and move east at the rate of 18 miles per hour, it represent the adjacent side.

The other rate telling you how fast the distance between them are changing can be computed using the Pythagorean theorem, since the change in time is 1 hour. From 12 noon to 1 pm.

c = ?

a = 14

b = 18

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c² = 14² + 18²

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5 0

3 years ago

What is the simplified form of the expression the quantity x squared minus 4x minus 21 end quantity divided by 4 times the quant

ExtremeBDS [4]

The simplified form of the given expression $\frac{x^2-4x-21}{4(x+3)}$ is $\frac{x-7}{4}$ .

<h3>How to simplify a fractional expression?</h3>

The steps to simplify a fractional expression are:

Factorize the expressions both in the numerator and the denominator using different methods
Remove the common terms in the numerator and denominator
Thus, the simplified expression will be obtained.

<h3>Calculation:</h3>

The given expression is $\frac{x^2-4x-21}{4(x+3)}$

Factorizing the numerator:

x² - 4x - 21 = x² - 7x + 3x - 21

= x(x - 7) + 3(x - 7)

= (x - 7)(x + 3)

Then,

$\frac{x^2-4x-21}{4(x+3)}$ = $\frac{(x-7)(x+3)}{4(x+3)}$

common factor (x + 3) is canceled out from both the numerator and the denominator

So,

$\frac{x^2-4x-21}{4(x+3)}$ = $\frac{x-7}{4}$

Therefore, the simplified expression is $\frac{x-7}{4}$ .

Learn more about simplifying an expression here:

brainly.com/question/13742517

#SPJ1

8 0

2 years ago

If (2i/2+i)-(3i/3+i)=a+bi, then a=<br>A. 1/10<br>B. -10<br>C. 1/50<br>D. -1/10

Verizon [17]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

$\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi$

We need to find the value of a.

The LCM of (2+i) and (3+i) is (2+i)(3+i)

$=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}$

Now rationalize the denominator by multiplying by 5-5i/5-5i

$=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}$

We are given

$\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi$

Now after solving we have:

$\frac{1}{10}-\frac{i}{10}=a+bi$

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

8 0

4 years ago