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4 years ago

Add. Express your answer in simplest form. 7 3/5 + 8 2/3???

Mathematics

1 answer:

Damm [24]4 years ago

6 0

The value is 244/15 or 16 + 4/15

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What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ subtract 2x from both sides

$3y=-2x+6$ divide both sides by 3

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ subtract 4/3 from both sides

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ multiply both sides by 3

$3y=-2x+5$ add 2x to both sides

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines k and l are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

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3 years ago

Write a numerical expression that represents the number of increments it will take Ashley to reach -60 feet.

tatyana61 [14]

Answer:

-60 divided by -10

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3 years ago

John and his son are building a boxcar for a group competition. According to the rules of the competition, the length of the car

kozerog [31]

Answer:

x ≥ y + 2

0.50 (x) (x+3) + 2.25 (4) (y) ≤ 50

Step-by-step explanation:

x = width of the car

x+3 = length of the car

y = radius of the car

The width must be at least 2 inches greater than the radius, so:

x ≥ y + 2

The total cost must be no more than $50, so:

0.50 (x) (x+3) + 2.25 (4) (y) ≤ 50

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4 years ago

Will give brainliest

erastovalidia [21]

Answer:

Step-by-step explanation:

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3 years ago

In a survey, it was reported 820 people will attend the concert. But, 1000 people attended the concert. What is the percent erro

Sergeu [11.5K]

18%.

820 - 1000 = -180 (Ignore minus sign)

180/1000 = 0.18

18 × 100 = 18

Add a percentage sign =18%

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4 years ago