Can someone help with this math question

Mathematics

1 answer:

Bumek [7]3 years ago

3 0

We can find the y-intercept by writing the slope-intercept form of the equation. For that first we need to find the slope of the given line.

$Slope=m= \frac{17-3}{10-6}= \frac{7}{2}$

Using the slope m =7/2 and a point (6,3) we can write the equation of the line as:

$y-3= \frac{7}{2}(x-6) \\ \\ 
y= \frac{7x}{2}-21+3 \\ \\ 
y= \frac{7x}{2}-18$

The equation above is in the slope intercept form.Coefficient of x is the slope and constant term is the y-intercept.

So, the y-intercept for the line is -18. Therefore, option C is the correct answer

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Jack ran 13.5 miles in 1.5 hours. What was his speed in miles per minute?

Minchanka [31]

Answer:

Step-by-step explanation:

13.5 / 1.5 = 9

8 0

3 years ago

Read 2 more answers

Please help Need help

Anettt [7]

This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.

We know that the line passes through A(3,-6), B(1,2)

All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.

So we can check which line passes through which point:

a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok

b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****

c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok

d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.

Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.

8 0

3 years ago

Use a matrix to solve the system:

Romashka-Z-Leto [24]

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

$2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\$

Rewrite these equations in matrix form

$\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\$

we can write it like this,

$AX=B\\X=A^{-1}B$

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

$A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\$

now multiply the matrix with B

$X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\$