In a plane, if a line is _____ to one of two parallel lines, then it is perpendicular to the other.

What is the vertex of the equation, y= -3x^2+2x-7?

Genrish500 [490]

A

Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then

The x-coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

y = - 3x² + 2x - 7 is in standard form

with a = - 3, b = 2 and c = - 7, hence

$x_{vertex}$ = - $\frac{2}{-6}$ = $\frac{1}{3}$

Substitute this value into the equation for y-coordinate

y = - 3 ( $\frac{1}{3}$ )² + 2 ( $\frac{1}{3}$ ) - 7

= - $\frac{1}{3}$ + $\frac{2}{3}$ - $\frac{21}{3}$ = - $\frac{20}{3}$

vertex = ( $\frac{1}{3}$ , - $\frac{20}{3}$ ) → A

4 0

3 years ago

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5•9-10 ———— 5-(-2).

Alenkinab [10]

Answer:

35/7 or 5

Step-by-step explanation:

so you multiply 5 and 9 which is 45- 10 which is 35 but then its 5-(-2) which when doing this a variable minus a negative makes it a positive so then its 5+2 which is 7 then you have 35/7 or 5

4 0

3 years ago

3 What is 27x + 8 ——————- 3x-2

marissa [1.9K]

Answer:

34 Step-by-step explanation:

6 0

3 years ago

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What is the qoutient of 1/6 and 2/9

beks73 [17]

Answer:

$\frac{3}{4}$

Step-by-step explanation:

To find the quotient, we first need to know what quotient means.

Quotient is the solution to division problems.

So here is how we have to do this, first we identify our fractions:

$\frac{1}{6} and \frac{2}{9}$

Next, we must turn the fraction we are dividing by into a reciprocate:

$\frac{2}{9} turns into \frac{9}{2}$

Now we have $\frac{1}{6} and \frac{9}{2}$

Next, we multiply!:

$\frac{1}{6} x \frac{9}{2} = \frac{9}{12}$

Simplified:

$\frac{3}{4}$

8 0

3 years ago

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6(m-1) = 3(3m + 2) Show all work

nordsb [41]

Answer:

$\boxed{\sf m = -4}$

Step-by-step explanation:

$\sf Solve \: for \: m: \\ \sf \implies 6 (m - 1) = 3 (3 m + 2) \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \sf \implies 6 m - 6 = 3 (3 m + 2) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies 6 m - 6 = 9 m + 6 \\ \\ \sf Subtract \: 9 m \: from \: both \: sides: \\ \sf \implies (6 m - 9 m) - 6 = (9 m - 9 m) + 6 \\ \\ \sf 6 m - 9 m = -3 m: \\ \sf \implies -3 m - 6 = (9 m - 9 m) + 6 \\ \\ \sf 9 m - 9 m = 0: \\ \sf \implies -3 m - 6 = 6 \\ \\ \sf Add \: 6 \: to \: both \: sides: \\ \sf \implies (6 - 6) - 3 m = 6 + 6 \\ \\ \sf 6 - 6 = 0: \\ \sf \implies -3 m = 6 + 6 \\ \\ \sf 6 + 6 = 12: \\ \sf \implies -3 m = 12 \\ \\ \sf Divide \: both \: sides \: of \: -3 m = 12 \: by \: -3: \\ \sf \implies \frac{ - 3m}{ - 3} = \frac{12}{ - 3} \\ \\ \sf \frac{ - 3}{ - 3} = 1: \\ \sf \implies m = \frac{12}{ - 3} \\ \\ \sf - \frac{12}{3} = - 4 : \\ \sf \implies m = - 4$

7 0

3 years ago