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3 years ago

Find the solution of the system of equations. 3x – 3y = 18 3x – 8y = -2

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

x=10, y=4

Step-by-step explanation:

3x-3y=18

(-)3x-(-)8y=-(-)2 -3x+8y=2 add to first equation to eliminate x

5y=20

y=4

substitute y with 4

3x-3(4)=18

3x=30

x=10

x=10,y=4

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For f(x) = 4x + 2 and g(x) = x^2 - 6, find (f+g)(x)

Margaret [11]

Answer:

$(f+g)(x) = x^2 + 4x - 4$

Step-by-step explanation:

We are given these following functions:

$f(x) = 4x + 2$

$g(x) = x^2 - 6$

(f+g)(x)

We add the common terms. Thus:

$(f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4$

Thus:

$(f+g)(x) = x^2 + 4x - 4$

3 0

2 years ago

A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and

nasty-shy [4]

Answer:

correct option is C) 2.8

Step-by-step explanation:

given data

string vibrates form = 8 loops

in water loop formed = 10 loops

solution

we consider mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = $\rho$

case (1)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

so here

$l = \frac{8 \lambda _1}{2}$ ..............1

$l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}$

and we know velocity is express as

velocity = frequency × wavelength .....................2

$\sqrt{\frac{Tension}{mass\ per\ unit \length }}$ = f × $\lambda_1$

here tension = mg

$\sqrt{\frac{mg}{\mu}}$ = f × $\lambda_1$ ..........................3

and

case (2)

when 8 loop form with 2 adjacent node is $\frac{\lambda }{2}$

$l = \frac{10 \lambda _1}{2}$ ..............4

$l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}$

when block is immersed

equilibrium eq will be

Tenion + force of buoyancy = mg

T + v × $\rho$ × g = mg

and

T = v × $\rho$ - v × $\rho$ × g

from equation 2

f × $\lambda_2$ = f × $\frac{1}{5}$

$\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}$ .......................5

now we divide eq 5 by the eq 3

$\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}$

solve irt we get

$1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}$

relative density $\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}$

relative density = 2.78 ≈ 2.8

so correct option is C) 2.8

3 0

3 years ago

Gavin plans to mix a batch of tangerine paint. He expects to have a total of 5 3/10 ounces of paint after he mixes the amounts o

SVEN [57.7K]

Tangerine is simply color orange, which is an addition of red and yellow colors. To analyze if the portions written below are reasonable, the given sum must equal to the sum of the individual red and yellow parts.

Total Red + Total Yellow = 5(3/10)
3(9/10) + 2(3/8) ? 5(3/10
3.45 ? 1.5
3.45 ≠ 1.5

Since they are not equal, then it means the portions are unreasonable.

3 0

3 years ago

You and your friend collect football cards. You tell your friend that you have 3 times the number of cards he has. Your friend r

fiasKO [112]

Easy I guess ..
I ll try to help ..
Here we go ..
The cards you have is N
The cards he has is n
you have 3 times the number of cards he has
This means N=3n
 you only have 80 more football cards then he does
This means N=n+80
But we already know that N=3n
So 3n=n+80
which is 2n=80
n=40
So your friend has only 40 cards and you have 3*40= 120 cards

Best luck

Wise

4 0

3 years ago

Solve x/5 - 1=7? help please !!

xxTIMURxx [149]

First, add 1 on both sides of the equation to begin to isolate x

x/5 = 8

Now, to isolate x, multiply both sides of the equation by 5/1

$\frac{x}{5}$ · $\frac{5}{1}$ = $\frac{5x}{5}$ = x

x= 7 · 5/1 = 7 · 5 = 35

x = 35

6 0

3 years ago