Factorise 3x squared-13x-10

CD is perpendicular to AB and passes through point C5, 12).

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD $mCD = -\frac{1}{mAB}$

Hence we start from determining slope of AB

slope is given as

$m= \frac{y_2-y_1}{x_2-x_1}$

$m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1$

Hence $mAB=1$

There fore $mCD=-1$

(∵ Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

$m=\frac{y-y_1}{x-x_1}$

$-1=\frac{y-12}{x-5}$

$-x+5=y-12$

$y=-x+17$

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

$0=-x+17$

$x=17$

Hence the x intercept is 17

8 0

3 years ago

What is the prime factorization of 154?

kap26 [50]

Answer:

C. 2 × 7 × 11

Step-by-step explanation:

2 × 7= 14

14 × 11= 154

8 0

2 years ago

Read 2 more answers

Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a law

NARA [144]

Answer:

Slope of this line is given by:

Aaron’s rate for mowing lawns is 0.5 acres per hour

Step-by-step explanation:

It is given that time is tracked by Aaron related to x coordinate.

and the area of land mowed in acres is related to y coordinate.

Two of his points are given as:

(3, 1.5) and (5,2.5)

We know that the coordinates are represented in the form of (x,y)

i.e. first coordinate represents x coordinate and

second coordinate represents y coordinate.

So, it can be observed that:

$x_1=3, y_1=1.5\\x_2=5, y_2=2.5$

Change in x coordinate = $x_2-x_1=5-3 = 2$

i.e. total time taken is 2 hours.

Change in y coordinate = $y_2-y_1=2.5-1.5 = 1$

i.e. total land mowed taken is 1 acre.

In other words, it takes 2 hours for Aaron to mow 1 acre of land.

So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.

Rate of mowing lawn is the land mowed by Aaron in 1 hour.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = $\frac{1}{2}$ acre i.e. 0.5 acre

Also, slope of a line is given as:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

Here $y_2 - y_1 = 1$

$x_2 - x_1 = 2$

As per formula:

$m = \dfrac{1}{2} = 0.5$

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

6 0

3 years ago

Read 2 more answers

The product of 11/13 and 4 is:

kirza4 [7]

Answer:

11/13 x 4 = 3 5/13

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

If the tip of the arrow moves to (0,2), what is the center of rotation?

LiRa [457]

The answer is A. (2,2)....

8 0

3 years ago