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2 years ago

10

(

t{6} +\sqrt{3})(\sqrt{2}-2)" alt="(\sqrt{6} +\sqrt{3})(\sqrt{2}-2)" align="absmiddle" class="latex-formula">

1 answer:

Marta_Voda [28]2 years ago

7 0

Answer:

-2.453

Step-by-step explanation:

sqrt(6) * sqrt(2) = 3.461

sqrt(6) * -2 = -4.899

sqrt(3) * sqrt(2) = 2.449

sqrt(3) * -2 = -3.464

sum of numbers equals

-2.453

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What is the vertex of the graph of y = 1/3 (x-9)2 + 5 Question 1 options: (9,5) (3,3) (3,5) (-9,5)

svlad2 [7]

ANSWER

The vertex of the graph of
$y = \frac{1}{3} {(x - 9)}^{2} + 5$
is

$(9,5)$

EXPLANATION

The vertex form of a parabola is given by

$y = a {(x - h)}^{2} + k$

where
$V(h,k)$
is the vertex of the parabola.

The function given to us is

$y = \frac{1}{3} {(x - 9)}^{2} + 5$
This is already in the vertex form.

When we compare this to the general vertex form, we have,

$a = \frac{1}{3}$

$h = 9$
and

$k = 5$

Therefore the vertex of the parabola is

$V(9,5)$

Hence the correct answer is option A.

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Answer:

Step-by-step explanation:

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Equation of a line that is perpendicular to given line is $y=\frac{-7}{4} x+\frac{7}{4}$ .

Equation of a line that is parallel to given line is $y=\frac{4}{7} x-\frac{69}{7}$ .

Solution:

Given line $y=\frac{4}{7} x+4$ .

Slope of this line, $m_1$ = $\frac{4}{7}$

$$\text{Slope of perpendicular line} = \frac{-1}{\text{Slope of the given line} }$

$$m_2=\frac{-1}{m_1}$

$$=\frac{-1}{\frac{4}{7} }$

Slope of perpendicular line, $m_2=\frac{-7}{4}$

Passes through the point (–7, 5). Here $x_1=-7, y_1=5$ .

Point-slope formula:

$y-y_1=m(x-x_1)$

$$y-(-7)=\frac{-7}{4} (x-5)$

$$y+7=\frac{-7}{4} x+\frac{35}{4}$

Subtract 7 from both sides, we get

$$y=\frac{-7}{4} x+\frac{7}{4}$

Equation of a line that is perpendicular to given line is $y=\frac{-7}{4} x+\frac{7}{4}$ .

To find the parallel line:

Slopes of parallel lines are equal.

$m_1=m_3$

$$m_3=\frac{4}{7}$

Passes through the point (–7, 5). Here $x_1=-7, y_1=5$ .

Point-slope formula:

$$y-(-7)=\frac{4}{7} (x-5)$

$$y+7=\frac{4}{7} x-\frac{20}{7}$

Subtract 7 from both sides,

$$y=\frac{4}{7} x-\frac{69}{7}$

Equation of a line that is parallel to given line is $y=\frac{4}{7} x-\frac{69}{7}$ .

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2 years ago