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3 years ago

One number is eight more than twice another. If their sum is decreased by nine, the result is fourteen. Find the numbers

1 answer:

6 0

$x-\ first \ number\\
y-\ second\ number\\\\
x-8=2y\\
x+y-9=14\\\\
x=2y+8\\
x+y=23\\\\
2y+8+y=23\\
3y+8=23\ \ \ |subtract\ 8\\
3y=15\ \ \ |divide\ by\ 3\\
y=5\\\\x=18$ Answer here

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What is the answer to 6x = 54

Morgarella [4.7K]

Answer:

It's division because to get x by itself, you need to divide both sides. X = 9

Step-by-step explanation:

6x = 54

Divide both sides by 6

54/6 = 9

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What is the opposite of dividing by 1? O A. subtracting 1 B. multiplying by 1 C. adding 1 D. dividing by 1

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Answer:

B multiplying by

Step-by-step explanation:

Multiple is opposite from divide.

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3 years ago

Find the equation of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit.

leonid [27]

<u>Answer-</u>

The equations of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit are

$12x-5y+14=0 \\ 12x-5y-14=0$

<u>Solution-</u>

Let a point which is 1 unit away from the line 12x-5y-1=0 is (h, k)

The applying the distance formula,

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{12^2+5^2}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{169}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{13} \right |=1$

$\Rightarrow 12h-5k-1=\pm 13$

$\Rightarrow 12h-5k=\pm 14$

$\Rightarrow 12h-5k=14,\ 12h-5k=-14$

$\Rightarrow 12h-5k-14=0,\ 12h-5k+14=0$

$\Rightarrow 12x-5y-14=0,\ 12x-5y+14=0$

Two equations are formed because one will be upper from the the given line and other will be below it.

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3 years ago

Find the equation of a circle with a center at (0, -4) and a point on the circle is (6, 0).

EastWind [94]

Answer:

$x^2 + ( y + 4)^2 = 52$

Step-by-step explanation:

Equation of circle with center (a , b) and radius, r is :

$(x -a)^2 + ( y -b)^2 = r^2$

Given : a = 0 , b = - 4

Step 1 : Find the radius.

Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

$r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\$

$= \sqrt{ 36 + 16 } \\\\= \sqrt{52}$

Step 2 : Equation of circle.

$(x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52$

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3 years ago

I really need help with this question! And I need to show work

krek1111 [17]

Answer:

x=0.25 or -1/4

Step-by-step explanation:

120x + 21 = -9

120x = -30 (-21 from both sides of equation)

x = -0.25 or -1/4 (divide 120 from both sides of equation)

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