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Alexus [3.1K]
3 years ago
5

Solve the system of equations below. A. B. C. D.

Mathematics
1 answer:
timofeeve [1]3 years ago
7 0

Answer:

  A.  (-7 -2)

Step-by-step explanation:

You can eliminate y by multiplying the first equation by 7 and subtracting 6 times the second equation:

  7(-3x +6y) -6(5x +7y) = 7(9) -6(-49)

  -21x +42y -30x -42y = 63 +294 . . . . eliminate parentheses

  -51x = 357 . . . . . . . . collect terms

  x = -7 . . . . . . . divide by -51. This matches answer choice A.

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In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta
Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let x,\ x\ge 0 be the number of students and y,\ y\ge 0 be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

15x+25y\ge 3,750

2. The auditorium can accommodate up to 180 spectators, hence

x+y\le 180

3. We get the system of inequalities:

\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise \$(15\cdot 50+25\cdot 125)=\$3,875

8 0
3 years ago
Show that the sum of the first 2n natural numbers is n(2n+1)
Leokris [45]

Answer:

This sum is the sum of an arithmetic sequence.  There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.

A nice approach for this sequence is the following.  Notice  that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.

There are n of these pairs.  So the desired sum is n x (first number + last number).   But the first number is 1 and the last on is 2n.   Thus the desired sum is n(1 + 2n).

Hope this helps!!

Mark Brainleast!!!!!!!!!!!

7 0
2 years ago
Read 2 more answers
The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of
Lostsunrise [7]

Answer:

$15 + x = $

Step-by-step explanation:

4 0
3 years ago
A factory packed 9600kg of flour in to small bags and large bags. Each small bag contained 3kg of flour and each large bag conta
yawa3891 [41]

Answer:

696 large bags of flour were packed.

Step-by-step explanation:

Let large bags of flour be 'y'

Let small bags of flour be 'x'. That is x=2040 (according to the question)

(3 \times x) + (5 \times y) = 9600

(3 \times 2040) + ( 5 \times y) = 9600

(6120) + (5 \times x) = 9600

(5 \times x) = 9600 - 6120

(5 \times x) = 3480

x = 3480  \div 5

x = 696

HOPE IT HELPS

#PEACE

5 0
2 years ago
Simplify the expression 6 + 3(2x - 4(3x - 2)].​
I am Lyosha [343]

Answer:

-30x + 30

Step-by-step explanation:

6 + 3 × [2x - 12x + 8]

6 + (-30x) + 24

-30x + 24

hope its correct if not sorry

8 0
3 years ago
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