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NeX [460]
3 years ago
6

What are the x and y-intercepts of the line described by the equation? −6x+3y=18.9

Mathematics
1 answer:
belka [17]3 years ago
5 0
<span> -6x+3y=(189/10) </span>Geometric figure: Straight Line<span>  Slope = 2  x-intercept = -63/20 = -3.15000  y-intercept = 63/10 = 6.30000</span>

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "18.9" was replaced by "(189/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     -6*x+3*y-((189/10))=0 

Step by step solution :<span>Step  1  :</span> 189 Simplify ——— 10 <span>Equation at the end of step  1  :</span> 189 (3y - 6x) - ——— = 0 10 <span>Step  2  :</span>Rewriting the whole as an Equivalent Fraction :

<span> 2.1 </span>  Subtracting a fraction from a whole 

Rewrite the whole as a fraction using <span> 10 </span> as the denominator :

3y - 6x (3y - 6x) • 10 3y - 6x = ——————— = —————————————— 1 10

<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole 

<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator

<span>Step  3  :</span>Pulling out like terms :

<span> 3.1 </span>    Pull out like factors :

   3y - 6x  =   -3 • (2x - y) 

Adding fractions that have a common denominator :

<span> 3.2 </span>      Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-3 • (2x-y) • 10 - (189) -60x + 30y - 189 ———————————————————————— = ———————————————— 10 10 <span>Step  4  :</span>Pulling out like terms :

<span> 4.1 </span>    Pull out like factors :

   -60x + 30y - 189  =   -3 • (20x - 10y + 63) 

<span>Equation at the end of step  4  :</span> -3 • (20x - 10y + 63) ————————————————————— = 0 10 <span>Step  5  :</span>When a fraction equals zero :<span><span> 5.1 </span>   When a fraction equals zero ...</span>

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.

Here's how:

-3•(20x-10y+63) ——————————————— • 10 = 0 • 10 10

Now, on the left hand side, the <span> 10 </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   -3  •  (20x-10y+63)  = 0

Equations which are never true :

<span> 5.2 </span>     Solve :    -3   =  0

<span>This equation has no solution.
</span>A a non-zero constant never equals zero.

Equation of a Straight Line

<span> 5.3 </span>    Solve  <span> 20x-10y+63 </span> = 0 

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). 

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

<span>In this formula :

</span><span>y </span>tells us how far up the line goes
<span>x </span>tells us how far along
<span>m </span>is the Slope or Gradient i.e. how steep the line is
<span>b </span>is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the<span> line properties.</span> We shall now graph the line <span> 20x-10y+63  = 0</span> and calculate its properties

Graph of a Straight Line :<span> </span>Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 63/10 so this line "cuts" the y axis at y= 6.30000

  y-intercept = 63/10 = 6.30000 Calculate the X-Intercept :

When y = 0 the value of x is -63/20 Our line therefore "cuts" the x axis at x=-3.15000

  x-intercept = -63/20 = -3.15000 Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 6.300 and for x=2.000, the value of y is 10.300. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 10.300 - 6.300 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

  Slope = 2Geometric figure: Straight Line<span>  Slope = 2  x-intercept = -63/20 = -3.15000<span>  y-intercept = 63/10 = 6.30000 </span></span>
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NISA [10]
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2.In this case, feet to meters and seconds to minutes</span> <span>
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5 0
3 years ago
You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Truck can carry a 3/4 - ton load. H
Olin [163]

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

6 0
3 years ago
Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the dat
Tems11 [23]

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

7 0
3 years ago
Please answer correctly! I will mark you as Brainleist!
timofeeve [1]

Answer:

1047.2 cubic inches

Step-by-step explanation:

V = 4(pi)(r³/3)

V = 4(pi)(125/3)

V = 523.6 cubic inches (1 ball)

V = 2(523.6) = 1047.2 cubic inches (total)

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3 years ago
A caterpillar crawling in a straight line across a coordinate plane starts at point (-3,
Irina18 [472]

9514 1404 393

Answer:

  15

Step-by-step explanation:

In vector form, the equation of point p on the line can be written as ...

  p = (-3, -4) +t(25 -(-3), 38 -(-4)) . . . . . for some scalar t

  p = (-3, -4) +t(28, 42)

  p = (-3, -4) +14t(2, 3)

where t takes on any value between 0 and 1.

If we let t = n/14 for some integer 0 ≤ n ≤ 14, then the coordinates of point p will be integers.

There are 15 values that n can have in the allowed range.

The caterpillar touches 15 points with integer coordinates.

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3 years ago
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