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Gennadij [26K]
2 years ago
13

What is the equation of the line that passes through the point (6,-1) and has a slope of 1?

Mathematics
1 answer:
Brut [27]2 years ago
6 0

Answer:y

=

4

3

x

−

9

Explanation:

Given -

x

1

=

6

y

1

=

−

1

Slope

m

=

4

3

Given the slope and a point, the formula for the straight line equation is

(

y

−

y

1

)

=

m

(

x

−

x

1

)

y

−

(

−

1

)

=

4

3

(

x

−

6

)

y

+

1

=

4

3

x

−

6

.

4

3

y

+

1

=

4

3

x

−

8

y

=

4

3

x

−

8

−

1

y

=

4

3

x

−

9

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the length of a rectangle is 8 units greater than its width . find the dimensions when its area is 105 square units.
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Estimate by rounding the first factor to the nearest thousand. 1,912 x 8
Vika [28.1K]

Answer:

15,000

Step-by-step explanation:

1912* 8 =15,296

To the nearest thousand = 15,000

5 0
3 years ago
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(I WILL GIVE YOU BRAINLIEST AND ANSWER ALL YOU CAN IDC) a market researcher tracks the number of people who visits a company's w
lawyer [7]

Part A: The exponential function is the best model for the given data. The data shows that every month the number of visitor approximately doubles from previous month. In other words the number is some base value (2, in this case) with the number of month (t) being in the exponent. This the a key characteristic of an exponential growth.  

Part B: (also explained above). Every month the number of visitors approximately doubles. Starting with 5.74 at month 8, the numbers goes up by about the same amount to 12.0 at month 9. At month 10, a similar increase occurs (doubling would be 24, and the data shows 25, so this is all "aproximate"). This trend continues throughout the table.

Part C:

Month 7 will be estimated as half of month 8 (going backward):

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5 0
3 years ago
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8 0
2 years ago
The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m
Keith_Richards [23]

Answer:

a) \left(x,y\right)=\left(4.95,-4.95\right)

b) r\angle\theta = 7\angle0.5236\,\text{radians}

Step-by-step explanation:

Polar coordinates are represented as: r\angle\theta, where 'r' is the length (or magnitude) of the line, and '\theta' is the angle measured from the positive x-axis.

in our case:

7\angle\dfrac{3\pi}{4}

to covert the polar to cartesian:

x = r\cos{\theta}

y = r\sin{\theta}

we can plug in our values:

x = 7\cos{\dfrac{3\pi}{4}} = -7\dfrac{\sqrt{2}}{2}

y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}

the Cartesian coordinates are:

\left(x,y\right)=\left(-7\dfrac{\sqrt{2}}{2},7\dfrac{\sqrt{2}}{2}\right)

\left(x,y\right)=\left(4.95,-4.95\right)

(b) to convert (x,y) = (6.06,-3.5)

we'll use the pythagoras theorem to find 'r'

r^2 = x^2+y^2

r^2 = (6.06)^2+(-3.5)^2

r = \sqrt{48.97} \approx 7

the angle can be found by:

\tan{\theta} = \dfrac{y}{x}

\tan{\theta} = \dfrac{3.5}{6.06}

\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}

\theta = 0.5236 \text{radians}

to convert radians to degrees:

\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ

writing in polar coordinates:

r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}

5 0
3 years ago
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