The ages of people on the camp bus are listed.

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

grandymaker [24]

Answer:

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

$m=\frac{6-4}{3+3}$

$m=\frac{2}{6}$

simplify

$m_a=\frac{1}{3}$

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

$m=\frac{3+3}{-8+10}$

$m=\frac{6}{2}$

$m_b=3$

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

$m=\frac{-4-5}{3-0}$

$m=\frac{-9}{3}$

$m_c=-3$

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

$m=\frac{-4+7}{13-4}$

$m=\frac{3}{9}$

simplify

$m_d=\frac{1}{3}$

Part 5) Compare the slopes

Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

$m_a=\frac{1}{3}$

$m_b=3$

$m_c=-3$

$m_d=\frac{1}{3}$

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

Lines d and c are perpendicular (slopes are opposite reciprocal)

6 0

3 years ago

How do you solve for area and perimeter

OverLord2011 [107]

Find the measure of the third angle

Use your trig functions the get the sides

Then calculate area and perimeter

8 0

3 years ago

Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old

Alinara [238K]

Answer:

actually it is

Step-by-step explanation:

i skipped the whole question except the last sentence's few words

6 0

3 years ago

The vertices of quadrilateral MNPQ are M(−3,−2),N(−1,4),P(2,4), and Q(4,−2). Translate quadrilateral MNPQ using the vector ⟨3,−4

timofeeve [1]

Answer:

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

Step-by-step explanation:

We are given that the vertices of quadrilateral MNPQ are M(-3,-2),N(-1,4),P(2,4) and Q(4,-2).

We have to translate the quadrilateral MNPQ using vector <3,-4>

The translate the coordinates of vertices (x,y) using the vector <a,b> is given by the rule

$(x,y)\rightarrow (x+a,y+b)$

Using the rule

The new coordinates of M

$(-3,-2)\rightarrow (-3+3,-4-2)$

$(-3,-2)\rightarrow (0,-6)$

The new coordinates of N

$(-1,4)\rightarrow (2,0)$

The new coordinates of P

$(2,4)\rightarrow (5,0)$

The new coordinates of Q

$(4,-2)\rightarrow (7,-6)$

Hence, after translation the new vertices of quadrilateral are

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

5 0

3 years ago

Find 41% of 48. Round to the nearest tenth of necessary

pshichka [43]

Answer:

19.7

Step-by-step explanation:

1. Change the percent to a decimal

0.41 of 48

2.Multiply the two numbers together.

0.41 of 48 = 19.68

3. Round to nearest tenth

19.68 = 19.70 = 19.7

8 0

3 years ago