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3 years ago

Eight less than four times a number is the same as 13 more than the number. What is the number?

Mathematics

1 answer:

Bas_tet [7]3 years ago

6 0

4n - 8 = n + 13
4n - n = 13 + 8
3n = 21
n = 21/3
n = 7....the number(n) = 7

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Please Help!!

Genrish500 [490]

Given

$a\sqrt{x+b}+c=d$

we have

$\sqrt{x+b}=\dfrac{d-c}{a}$

Squaring both sides, we have

$x+b=\dfrac{(d-c)^2}{a^2}$

And finally

$x=\dfrac{(d-c)^2}{a^2}-b$

Note that, when we square both sides, we have to assume that

$\dfrac{d-c}{a}>0$

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

$a=1,\ b=0,\ c=2,\ d=6$

and you'll have

$\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16$

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

$a=1,\ b=0,\ c=10,\ d=4$

and you'll have

$\sqrt{x}+10=4 \iff \sqrt{x}=-6$

Squaring both sides (and here's the mistake!!) you'd have

$x=36$

which is not a solution for the equation, if we plug it in we have

$\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4$

Which is clearly false

7 0

3 years ago

Determine whether 4 is a solution of the equation 9x+7=40. Is 4 a solution?

Allisa [31]

Plug in 4 for x

9(4) + 7 = 40

36 + 7 = 40

43 ≠ 40

No, 4 is not a solution

hope this helps

5 0

3 years ago

Read 2 more answers

A local food truck specializes in gourmet grilled cheese sandwiches. Each month, the owners of the truck have a constant total o

Citrus2011 [14]

B would be best answer. 5400s is rent

2.25s amount of sandwich cost and 9.00s selling prices. They all need s and has to be less then!

7 0

2 years ago

chegg evaluate the following integral using trigonometric substitution. dx/square root(x^2-81), x > 9

vesna_86 [32]

Integration will be ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c .

Given ∫ 1 dx / ( $x^{2}$ - 81 )

Put ,

x = 9 secθ

dx = 9 secθ tanθ dθ

and

$\sqrt{x^{2} - 9^{2} }$ = 9 tanθ

Substituting values in ∫ 1 dx / ( $x^{2}$ - 81 ) ,

∫ (9 secθ tanθ ) dθ / ( 9 tanθ )

∫ secθ dθ = ln | secθ + tanθ | + c

= ln | ( x /9 ) + ( $\sqrt{x^{2} - 9^{2} }$ / 9 ) | + c

= ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c

Hence , the integration will be ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c .

To learn more on integration follow link :

brainly.com/question/20156869

#SPJ4

6 0

1 year ago

ALGEBRA evaluate each eapression if x= -3, y=8, and z=-12 y-10 12-z 3-x z-24

Vinvika [58]

Answer:

-2
24
6
-36

Step-by-step explanation:

Put the numbers in place of the corresponding letter and do the arithmetic.

y -10 = 8 -10 = -2

12 -z = 12 -(-12) = 24

3 -x = 3 -(-3) = 6

z -24 = -12 -24 = -36

6 0

3 years ago