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3 years ago

Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?

Mathematics

2 answers:

mihalych1998 [28]3 years ago

7 0

Answer:

Step-by-step explanation:

The general formula of the linear equation is:

y = mx + c

where m is the slope and c is the y-intercept

1- getting the slope:

We are given the two points:

(6,10) representing (x1 , y1)

(12,7) representing (x2 , y2)

The slope of the line will be calculated as follows:

m = (y2-y1) / (x2-x1) = (7-10) / (12-6) = -3/6 = -0.5

The equation of the line now becomes:

y = -0.5x + c

2- getting the value of the y-intercept:

To get the value of the y-intercept (c), we will use any of the given points, substitute in the equation of the line and solve for c. I will use the point (6,10) as follows:

y = -0.5x + c

10 = -0.5(6) + c

10 = -3 + c

c = 13

Based on the above, the equation of the line would be:

y = -0.5x + 13

Hope this helps :)

Anvisha [2.4K]3 years ago

7 0

Answer:

Step-by-step explanation:

take the frickin answer

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What is the solution to -3/4 x + 2 ≤ -7 ?

Dvinal [7]

Answer:

x ≥ 12

Step-by-step explanation:

Step 1: subtract 2 from both sides

Now you have; -3/4 x ≤ -9

Step 2: divide both sides by -3/4

Now you have x ≥ 12

(when dividing an inequality by a negative you have to flip the sign)

Therefore the answer is x ≥ 12

6 0

3 years ago

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If XY=18, YZ=14, and XZ=20, find the radius of each circle.

Pachacha [2.7K]

Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.

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3 years ago

13 points!!! <br><br> 34ft 4in - 8=

vredina [299]

If feet:
34' 4" - 8' = 26' 4"

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5 0

3 years ago

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(10-P) Help please, thanks.

Anuta_ua [19.1K]

The formula of linear equation is:
$y1 - y2 = m(x1 - x2)$
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope

We can then choose a point from the line to find the eqaution.

We need to first find the slope:
$\frac{y1 - y2}{x1 - x2}$
In this case:
$\frac{ - 2 - 10}{ - 1 - 3} \\ = \frac{ - 12}{ - 4} \\ = 3$

In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :

y-(-2) = 3(x-(-1))
y+2 = 3(x+1)

Therefore
$y + 2 = 3x + 1$
is the answer.

Hope it helps!

7 0

3 years ago

The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an i

melisa1 [442]

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

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3 years ago