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vladimir1956 [14]

2 years ago

12

the mean of "n" numbers is "x" . if one more is added the mean is "y" . write an algebraic expression for the value of the numbe

r added?

1 answer:

vaieri [72.5K]2 years ago

3 0

Answer:

yn +y -xn

Step-by-step explanation:

Mean= sum of numbers ÷number of numbers

x= sum of n numbers ÷n

<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>n</em><em>:</em>

xn= sum of n numbers

sum of n numbers= xn -----(1)

Let the number added be a.

After a has been added,

y= (sum of n numbers +a) ÷(n+1)

<em>Multiply</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>(</em><em>n</em><em> </em><em>+</em><em>1</em><em>)</em><em>:</em>

y(n +1)= sum of n numbers +a

sum of n numbers= y(n +1) -a -----(2)

Substitute (1) into (2):

xn= y(n +1) -a

<em>Expand</em><em>:</em>

xn= yn +y -a

a= yn +y -xn

<u>Let's check!</u>

Let the numbers be 1, 2, 3 and 4.

mean, x= 10 ÷4= 2.5

n= 4

Let the new number added, a, be 7.

a= 7

mean, y= 17 ÷5= 3.4

a= yn +y -xn

a= 3.4(4) +3.4 -2.5(4)

a= 7

Thus, the expression is true.

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3 years ago

Which of the following shows the graph of the inequality y > –2x + 9?

Ira Lisetskai [31]

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2 years ago

Read 2 more answers

Look at this cone:<br><br>,,

Assoli18 [71]

Slant height=l=3ft
Radius=r=2ft

We know

$\boxed{\sf \star TSA_{(Cone)}=\pi r(r+\ell)}$

$\\ \sf\longmapsto TSA_{(Old\:Cone)}=2 \dfrac{22}{7}\times 2(2+3)$

$\\ \sf\longmapsto TSA_{(Old\:Cone)}=\dfrac{44}{7}(5)$

$\\ \sf\longmapsto TSA_{(Old\:Cone)}=\dfrac{220}{7}$

$\\ \sf\longmapsto TSA_{(Old\:Cone)}=31.4ft^2$

Now

New slant height =2(3)=6cm
New radius=2(2)=4cm

$\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{22}{7}\times 4(4+6)$

$\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{88}{7}(10)$

$\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{880}{7}$

$\\ \sf\longmapsto TSA_{(New\:Cone)}=125.7cm^2$

So

$\\ \sf\longmapsto \dfrac{TSA_{(New\:Cone)}}{TSA_{(Old\:Cone)}}=\dfrac{125.7}{31.4}$

$\\ \sf\longmapsto \dfrac{TSA_{(New\:Cone)}}{TSA_{(Old\:Cone)}}=\dfrac{4}{1}$

$\\ \sf\longmapsto\underline{\boxed{\bf{ {TSA_{(New\:Cone)}}:{TSA_{(Old\:Cone)}}=4:1}}}$

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2 years ago

Solve the equation x+3/x-4 = x-5/x+4

Serga [27]

Answer:

$\large\boxed{x=\dfrac{1}{2}}$

Step-by-step explanation:

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}$

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D$

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2 years ago

A 6-foot tall man casts a shadow that is 12 feet long. What is the measure of the sun's angle of elevation? Enter your answer, r

Masteriza [31]

Answer:

$27^{\circ}$

Step-by-step explanation:

Let x represent the sun's angle of elevation.

We have been given that a 6-foot tall man casts a shadow that is 12 feet long.

Upon looking at our attachment we can see that man and his shadow forma a right triangle with respect to ground, where height of man is opposite side and his shadow is adjacent side.

Since tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(x)=\frac{6}{12}$

$\text{tan}(x)=\frac{1}{2}$

Using arctan we will get,

$x=\text{tan}^{-1}(\frac{1}{2})$

$x=26.565051177078^{\circ}\approx 27^{\circ}$

Therefore, the measure of the sun's angle of elevation is 27 degrees.

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3 years ago