PLEASE HELP!!!The points A, B, C, and D are plotted on a line, consecutively. AB = BC = CD = 6 cm. Find the distance between M and N, which are the midpoints of segments AB and CD , respectively. Fill in the blanks of the Statement/Reason solution.

The number of students who attended the museum opening is 80.

What is a linear equation?

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, A group of 100 people, some students and some faculty, attended a museum opening.

Assuming no. of students to be x and no. of faculty to be y.

∴ x + y = 100...(i)

Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance and the total cost is $1300.

∴ 10x + 25y = 1300...(ii)

Now multiplying eqn(i) by 10 we get 10x + 10y = 1000...(iii)

Subtracting eqn(iii) from eqn(ii) we get 15y = 300 ⇒ y = 20 and substitting value of y in eqn(iii) we get x = 80.

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STUDENTS               X              10               

FACULTY           100-X              25

                                   10X + 25(100-X) = 1300

                                    10X + 2500 -25X = 1300

                                    10X - 25X = -2500 + 1300

                                             -15X = -1200

                                               15X = 1200

                                                    X = 1200/15

                                                    X = 80 STUDENTS <--------SOLUTION

Final answer:

The results of the modulo operations are: 290 mod 26 results in 2; 9^{-1} mod 26 is equivalent to 3; and -15 mod 26 equals 11.

Explanation:

To simplify each of the following with justifications:

1. 290 mod 26: When you divide 290 by 26, the remainder is 2. Therefore, 290 mod 26 = 2.
2. 9^{-1}  mod 26: First, you need to find the multiplicative inverse of 9 in mod 26. The multiplicative inverse of an integer a modulo m is an integer b such that (ab) mod m = 1. For 9, the multiplicative inverse is 3, since (9*3) mod 26 = 27 mod 26 = 1. Therefore, 9^{-1} mod 26 = 3.
3. -15 mod 26: In modular arithmetic, if you end up with a negative number, you add the modulus until you get a positive result. Here, adding 26 once to -15 gives you 11. Therefore, "-15 mod 26 = 11".

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Answer:

y = 1

Step-by-step explanation:

The line of reflection will be a parallel line midway between y = - 3 and y = 5

y = = = 1

line of reflection is y = 1

Answer:

y=1

Step-by-step explanation:

the line of reflection will be a parallel line midway between y=-3and y=5

y=-3+5/2

=2/2=1

Answer:

She can buy 50 cherry candies if she wishes to spent the entire $25 on cherry candies

Step-by-step explanation:

Cost of each licorice sticks = $0.75

Cost of each cherry candy = $0.50

Total budget = $25

Equation to represent her expenses is 0.75x + 0.5y = 25

where x is the number of licorice sticks and y is the number of cherry candies

Let the number of cherry candies she can buy be c.

So,

Cost of each cherry candy * Number of cherry candies = Total budget

=> 0.50 x c = 25

We get

0.50c = 25

We need to eliminate 0.50 from the left so we divide both sides by 0.50

Cancelling out 0.50 from the top and bottom of the left side we get,

c = 50

So, she can buy 50 cherry candies if she wishes to spent the entire $25 on cherry candies.

Answer:

The answer is D

Step-by-step explanation: