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Mashutka [201]
3 years ago
5

A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.

Mathematics
1 answer:
brilliants [131]3 years ago
3 0

Answer:  a=24

Step-by-step explanation:

Lets find the line's  formula (equation of the line).

As known the general formula of any straight line (linear function) is

y=kx+b

Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7

(Xb;Yb)- are the coordinates of point B

(Xa;Ya) are the coordinates of point A

Now lets find the coefficient b.  For this purpose we gonna use the coordinates of any point A or B.

We will use A

7=-2/7*3+b

7=-6/7+b

b=7 6/7

So the line' s  equation is y= -2/7*x+7 6/7

Now we gonna find the value of a usingcoordinates of point C.

Yc=1,  Xc=a

1=-2/7*a+7 6/7

2/7*a= 7 6/7-1

2/7*a=6 6/7

(2/7)*a=48/7

a=48/7: (2/7)

a=24

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Lemur [1.5K]

Answer:

(0,3)

Step-by-step explanation:

y = 3x^2 +3

This is in the form

y = a(x-h)^2 +k

Where the vertex is (h,k)

y = 3(x-0)^2 +3

The vertex is (0,3)

6 0
3 years ago
Find the average rate of change<br> f(x)=x^2−6x+8 when x2=1 and x1=3
sergeinik [125]

Answer:

Average rate of change for given function is: -2

Step-by-step explanation:

Given function is:

f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3

The formula for finding the rate of change is:

Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}

Putting the values, we get

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Hence,

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3 0
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A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism ha
KonstantinChe [14]
Yes they are. Given that a volume of a rectangular prism is V=l•w•h, we can plug them into an equation and compare them. I'll call the Right rectangular prism figure R and the oblique rectangular prism O


For Figure R, We know all the basic needs to find the volume. This means we can plug it in.

V=l•w•h
V=12•3•5
Now We can solve for V
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The volume of the right rectangular prism is 180in^3


Now, For figure O.
V=9•4•5
V=9•20
V= 180.


With this in mind, We now can say that the volumes of both the rectangular prisms are the same.
8 0
3 years ago
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sergeinik [125]

Answer:

16

Step-by-step explanation:

Area of circle Formula: A = πr²

d = 2r

Simply plug in what you know:

201.0624 = 3.1416r²

64 = r²

r = 8

d = 2(8)

d = 16

8 0
3 years ago
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