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2 years ago

Jan 258:00:56 AM

Mathematics

1 answer:

horsena [70]2 years ago

8 0

Answer:

The equation of the straight line in point-slope form

$y - 4 = \frac{7}{9} (x-0)$

The equation of the straight line

7x -9y +36 =0

Step-by-step explanation:

Given that the points (0,4) and (-9,-3)

The slope of the line

$m = \frac{y_{2} - y_{1} }{x_{2}- x_{1} } = \frac{-3-4}{-9-0} = \frac{7}{9}$

Equation of the straight line passing through the point (0,4) and having slope m = 7/9

$y - y_{1} = m (x-x_{1} )$

$y - 4 = \frac{7}{9} (x-0)$

9 y - 36 = 7x

9y = 7x + 36

$y = \frac{7x}{9} +\frac{36}{9}$

Slope - intercept form

$y = \frac{7x}{9} +4$

<u><em>Final answer:-</em></u>

The equation of the straight line in point-slope form

$y - 4 = \frac{7}{9} (x-0)$

The equation of the straight line

7x -9y +36 =0

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Becca and Kimberly are running at a constant speed in a marathon. Becca runs at 4.5 miles per hour. Kimberly’s progress is shown

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Answer:

Part A: Kimberly

Part B:

Becca = 22.5 miles, Kimberly = 25 miles

Step-by-step explanation:

Part A:

Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.

Let x = time

y = distance

k = speed = y/x

Equation for each person can be written as: y = kx

Therefore:

✔️Equation for Becca if k = 4.5

y = 4.5x

✔️Find k (speed) of Kimberly using (2, 10):

Speed (k) = y/x

k = 10/2

k = 5 miles per hour

Equation for Kimberly would be:

y = 5x

Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.

Part B:

For Becca, substitute x = 5 into Becca's equation, y = 4.5x

Thus:

y = 4.5*5 = 22.5 miles

For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x

Thus:

y = 5*5 = 25 miles

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2 years ago

Diane has a hospital appointment. when she arrives at the hospital, the car park is nearly full. there are a total of 534 car pa

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In total there are 534 spaces, but 476 are occupied.
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3 years ago

Can someone good with math help out ?

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Sry i suck in math brother

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3 years ago

The volumes of a water balloon and an air balloon after they are punctured are represented by the

spin [16.1K]

Answer:

Both air balloon and water balloon data are best modeled by an exponential function.

Step-by-step explanation:

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0 95

3 69

6 50

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12 27

The relation Volume variation/time is constant for lines, In this case, this value change from point to point, as can be seen next.

(69 - 95)/3 = -8.67

(50 - 69)/3 = -6.33

(37 - 50)/3 = -4.33

(27 - 37)/3 = -3.33

Water balloon

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3 15.8

6 7.8

9 4

12 2

(30 - 15.8)/-3 = -4.73

(15.8 - 7.8)/-3 = -2.67

(7.8 - 4)/-3 = -1.27

(4 - 2)/-3 = -0.67

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2 years ago

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andre [41]

Answer:

13) Rectangle

14) parallelogram

15) co ordinates areD (0,a) andE (c,b)

16) co ordinates are D(0,b) and E(a,0)

17)(-1,1) (4,1) (-1,4)

18)(0,0) (a,0) (a,a) (0,a)

Step-by-step explanation:

<h3>13)</h3><h3>Rectangle</h3>

The opposite sides of a rectangle are parallel and equal

left height = right height

(by using distance formula)

(0,3),(2,-2) = (5,5),(7,0)

√(2-0)²+(-2-3)² = √(7-5)²+(0-5)²

√(2)²+(-5)² = √(2)²+(-5)²

√4+25 = √(2)²+(-5)²

√29 = √29 hence equal

<h3>14)</h3><h3>parallelogram</h3>

The opposite sides of a rectangle are not equal

left height = right height

(by using distance formula)

(0,0),(3,-4) = (3,4),(7,0)

√(3-0)²+(-4-0)² = √(7-3)²+(0-4)²

√(3)²+(-4)² = √(5)²+(-4)²

√9+16 = √(25)+(16)

√(25) ≠√41

5 ≠ √41

<h3>15)</h3><h3>co ordinates are D(0,a) and E(c,b)</h3><h3>16)</h3><h3>co ordinates are D(0,b) and E(a,0) </h3>

since rhombus have equal opposite sides

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3 years ago