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3 years ago

Write the standard form of the equation of the line through the given point with the given slope. Simplify as much as possible.

Mathematics

2 answers:

Mashutka [201]3 years ago

6 0

Answer:

$y =-\frac{2}{3} x - \frac{2}{3}$

Step-by-step explanation:

Equation of line in point slope form is given as

$y-y_1=m(x-x_1)$

Here

m=-2/3 and $(x_1, y_1)=(-1, 0)$

Equation of the line passing through the point (-1, 0) with slope -2/3 is

$y-0=-\frac{2}{3} (x-(-1))$

$y =-\frac{2}{3} (x+1)$

$y =-\frac{2}{3} x - \frac{2}{3}$

adoni [48]3 years ago

4 0

Answer:

y = -2/3x - 1

Step-by-step explanation:

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In a certain Algebra 2 class of 25 students, 13 of them play basketball and 11 of them play baseball. There are 4 students who p

Flauer [41]

Answer:

$\frac{4}{5}$

Step-by-step explanation:

Given: There are 2 classes of 25 students.

13 play basketball

11 play baseball.

4 play neither of sports.

Lets assume basketball as "a" and baseball as "b".

We know, probablity dependent formula; P(a∪b)= P(a)+P(b)-p(a∩b)

As given total number of student is 25

Now, subtituting the values in the formula.

⇒P(a∪b)= $\frac{13}{25} +\frac{11}{25} -\frac{4}{25}$

taking LCD as 25 to solve.

⇒P(a∪b)= $\frac{13\times 1+11\times 1-4\times 1}{25} = \frac{20}{25}$

∴ P(a∪b)= $\frac{4}{5}$

Hence, the probability that a student chosen randomly from the class plays both basketball and baseball is $\frac{4}{5}$ .

6 0

3 years ago

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D

polet [3.4K]

Given:
A has coordinates (-6,5)
C has coordinates (3.6,-0.4).
C divides AB in the ratio 3:2.

Refer to the diagram shown below.
The coordinates of B are determined by
$\frac{3.6-(-6)}{x-(-6)} = \frac{3}{3+2} \\ \frac{9.6}{x+6} = \frac{3}{5} \\ 3(x+6) = 48 \\ 3x +18=48 \\ x=30/3=10$
Also,
$\frac{5-(-0.4)}{5-y} = \frac{3}{5} \\ 3(5-y) = 27 \\ 15-3y=27 \\ y= \frac{12}{-3} =-4$

Answer:
The coordinates of B are (10,-4).

Now, we know the coordinates of line segment AB as A (-6, 5) and B (10,-4).
D (x,y) divides AB in the ratio 4:5.
Therefore
$\frac{x-(-6)}{10-(-6)} = \frac{4}{4+5} \\ \frac{x+6}{16} = \frac{4}{9} \\ 9(x+6)=64 \\ 9x+54=64 \\ x=1.11$
Also,
$\frac{5-y}{5-(-4)} = \frac{4}{9} \\ 5-y = 4 \\ y = 1$

Answer:
The coordinates of D are (1.11, 1)