The graph of a quadratic relationship is in the shape of a parabola. Parabolas are symmetric arcs and are useful for modeling re

Answer:

The lines are parallel

Step-by-step explanation:

it's established that

To find the slope between two points, we use the formula

Keep in mind

If lines are parallel, their slopes must be identical

When lines are perpendicular, their slopes are negative reciprocals (the product equals -1)

step 1

Determine the slope of JK

we have

insert the values

step 2

Compute the slope of LM

we have

insert the values

step 3

Analyze the slopes

thus

hence

The lines are parallel

To address this issue, the procedure below should be utilized:

 1- The Law of sines can be applied as follows:

 The unknown angle can be determined by: 180°-65°-45°=70°

 - The <span>distance Jake travels to the store is:

 30/Sin(70°)=x/Sin(45°)
 x=22.57

 - The distance Maddie travels to the store is:

 </span>30/Sin(70°)=y/Sin(65°)
<span> y=28.93

 - The difference calculated is: 6.36

Thus, the result shows that the difference is 6.36 m.</span>

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

This represents a difference of squares:

(16a^4 - b^4)

= (4a^2 + b^2)(4a^2 - b^2)

Furthermore, the second bracket can be simplified as it is also a difference of two squares:

(4a^2 + b^2)(4a^2 - b^2)

= (4a^2 + b^2)(2a - b)(2a + b)

<span>As the restaurant owner, The likelihood of hiring Jun is 0.7 => p(J) The likelihood of hiring Deron stands at 0.4 => p(D) The chance of hiring at least one of them is 0.9 => p(J or D) We can formulate the probability equation: p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D) p(J and D) = 1.1 - 0.9 = 0.2 Thus, the probability that both Jun and Deron are hired is 0.2.</span>