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1 year ago

Which value of x would make LK ∥ OM? x = 2 x = 2.4 x = 4.8 x = 8

Mathematics

1 answer:

goldenfox [79]1 year ago

6 0

Answer:

x=8

Step-by-step explanation:

The figure is shown in the attached figure.

We have, LK║OM. We need to find the value of x.

It is based on side-splitter theorem. If a line is parallel to third side of a triangle, then the points that intersects the two lines, it divides proportionally.

Using it in given problem. So,

$\dfrac{\text{NK}}{\text{KM}}=\dfrac{\text{NL}}{\text{LO}}$

Nk = x+2, KM = x-3, NL = x and LO = x-4

So,

$\dfrac{x+2}{x-3}=\dfrac{x}{x-4}$

Cross multiplying, we get :

$(x+2)(x-4)=x(x-3)\\\\x^2-4x+2x-8=x^2-3x\\\\-2x+3x=8\\\\x=8$

So, the value of x is 8.

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John and Belinda played a nine holes of golf. John's score was 10 less than two times Belinda's score. If Johns score was 54 str

polet [3.4K]

Answer:

Belinda's score is 32 strokes.

Step-by-step explanation:

Let the score of John be "x" and Belinda be "y".

It is given that, in the game of golf, John's score was 10 less than two times Belinda's score.

Also, John's score is 54 strokes.

The above equation can be written as ;

$x = 2(y) -10$

Here, x = 54,

$54 = 2(y) -10$

$64 = 2(y)$

$y = 32$

Thus, Belinda's score is 32 strokes.

6 0

1 year ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

: adam and melissa went fly-fishing and caught a total of 32 salmon. melissa caught three times as many salmon as adam. how many

nadya68 [22]

A=Adam
m= Melissa

a+m = 32
m= 3a
Then 3a + a = 32 or 4a =32 then a = 8

5 0

1 year ago

Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?

Ugo [173]

The given expression can be simplified in many ways by grouping like terms. The simplest form is obtained by factoring out a²b which gives us the following expression.

a²b(7 + 10b +14b²)

4 0

2 years ago

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Suppose the radius of a circle is \color{purple}{3}3start color purple, 3, end color purple. what is its circumference?either en

Vlada [557]

$\text{Consider the circle of radius 3.}\\
\\
\text{we need to find the cirumference of the circle.}\\
\\
\text{we know that the circumference of the circle of radius r is given by}\\
\\
\text{circumference}=2\pi r\\
\\
\text{so using this formula, the circumference of the given circle is}$

$\text{Circumference}=2\pi r\\
\\
=2\pi \times 3\\
\\
=6\pi
\\
\text{so the circumference of the circle is}=6\pi\\
\\
\text{and in decimals, it gives}=6\times 3.14\\
\\
\Rightarrow \text{circumference}=18.84$

Hence the circumference of the circle is: 6π or 18.84 units

6 0

2 years ago

Read 2 more answers