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makkiz [27]
3 years ago
11

Write an equation in standard form for the line that passes through the point (2,-3) and is perpendicular to the line y + 4 = -2

/3(x-12)
Mathematics
1 answer:
sineoko [7]3 years ago
5 0

For this case we have that by definition, the standard form of a linear equation is given by:

ax + by = c

By definition, if two lines are perpendicular then the product of their slopes is -1. That is to say:

m_ {1} * m_ {2} = - 1

We have the following point-slope equation of a line:

y+4 = -\frac {2} {3}(x-12)

The slope is:

m_ {1} = - \frac {2} {3}

We find the slope m_ {2}of a perpendicular line:

m_ {2} = \frac {-1}{m_ {1}}\\m_ {2} = \frac {-1} {-\frac {2} {3}}\\m_ {2} = \frac{3} {2}

Thus, the equation is of the form:

y-y_ {0} = \frac {3} {2} (x-x_ {0})

We have the point through which the line passes:

(x_ {0}, y_ {0}) :( 2, -3)

Thus, the equation is:

y - (- 3) = \frac {3} {2} (x-2)\\y + 3 = \frac {3} {2} (x-2)

We manipulate algebraically:

y + 3 = \frac{3} {2} x- \frac {3} {2} (2)\\y + 3 = \frac{3} {2} x-3

We add 3 to both sides of the equation:

y + 3 + 3 = \frac {3} {2} x\\y + 6 = \frac {3} {2} x

We multiply by 2 on both sides of the equation:

2(y + 6) = 3x\\2y + 12 = 3x

We subtract 3x on both sides:

2y-3x + 12 = 0

We subtract 12 from both sides:

2y-3x = -12

ANswer:

-3x + 2y = -12

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umka2103 [35]

The amount that will be expected to be paid for the bonds that are bought will be C. $3,318.33

<h3>How to calculate the amount of bonds?</h3>

From the information given, the bonds from the city of tavel gorge worth $1,000 each are selling at 110.611 and Sean wishes to purchase three such bonds.

Therefore, the amount for the bonds will be:

= 1110.611 × 3

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In conclusion, the correct option is C.

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8 0
2 years ago
Solve x2 − 10x = −13.
aev [14]

Answer:

B

Step-by-step explanation:

First, let's rearrange the given equation into something more recognizable. If we add 13 to both sides, we now have the polynomial x^{2}-10x+13. We can now use the quadratic formula to solve.

Remember that the quadratic formula is

\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}

Substitute the numbers from the equation into the formula.

\frac{-(-10)+/-\sqrt{(-10)^{2}-4(1)(13) } }{2(1)}

Simplify:

\frac{10+/-\sqrt{100-52} }{2}

\frac{10+/-\sqrt{48} }{2}

Here, I'm going to assume that there was a mistype in option B because if we divide out the 2 we end up with 5+/-\sqrt{48}.

Hope this helps!

6 0
2 years ago
Use the commutative property of Multiplication to write a related number sentence. 4 times 9=36
aev [14]
 a possible answer would be 36/9=4
7 0
3 years ago
Kala takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit
masya89 [10]

Answer:

T=98W-115W+1840

Step-by-step explanation:

$98 per credit at Westside (W)

$115 per credit at Pinewood (P)

Expression 1 : 98W+115P=T

Expression 2 : W+P=16

Combined: if W=16-P

Total=98W+115(16-W)

T=98W-115W+1840

3 0
2 years ago
Identify the vertex of the quadratic function in standard form y=2x^2 -16x+31
lapo4ka [179]

Answer:

(4,1)

Step-by-step explanation:

The vertex of the quadratic can be found using -b/2a. The vertex is the point (-b/2a, f(-b/2a)).

To find the x coordinate of the quadratic, define its a,b, and c. The quadratic has a = 2, b=-16, and c=31. Then -b/2a is -(-16)/2(2) = 16/4 = 4.

To find the y-coordinate, input the x=4 and solve for y.

y=2(4)^2-16(4)+31\\y=2(16)-64+31\\y=32-64+31\\y=1

The vertex is (4,1).

8 0
3 years ago
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