All categories

2 years ago

What is the solution to this system of linear equations? 12q + 3r = 15 –4q – 4r = –44 (–18, 29) (–2, 13) (8, –1) (15, –44)

Mathematics

2 answers:

beks73 [17]2 years ago

8 0

Answer:

(-2,13)

I believe this is the answer.

VMariaS [17]2 years ago

7 0

Answer: The correct option is (B) (-2, 13).

Step-by-step explanation: We are given to find the solution of the following system of equations :

$12q+3r=15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4q-4r=-44~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (ii) by 3, we have

$3(-4q-4r)=-44\times3\\\\\Rightarrow -12q-12r=-132~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Adding equations (i) and (iii), we get

$(12q+3r)+(-12q-12r)=15+(-132)\\\\\Rightarrow 3r-12r=15-132\\\\\Rightarrow -9r=-117\\\\\Rightarrow r=\dfrac{-117}{-9}\\\\\Rightarrow r=13.$

From equation (ii), we get

$-4q-4\times13=-44\\\\\Rightarrow -4q-52=-44\\\\\Rightarrow -4q=-44+52\\\\\Rightarrow -4q=8\\\\\Rightarrow q=\dfrac{8}{-4}\\\\\Rightarrow q=-2.$

Thus, the required solution is (q, r) = (-2, 13).

Option (B) is CORRECT.

You might be interested in

Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the so

Georgia [21]

In order to construct this equation, we will use the variables:
V to represent mixture volume (40 ml)
C to represent mixture concentration (0.32)
v₁ to represent volume of first solution (40 / 4 = 10 ml)
c₁ to represent concentration of first solution (0.2)
v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml)
c₂ to represent the concentration of the second solution

We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus:
VC = v₁c₁ + v₂c₂
40(0.32) = 10(0.2) + 30c

6 0

2 years ago

Read 2 more answers

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each r

bulgar [2K]

Answer:

The answer to your question is 8 h

Step-by-step explanation:

Data

length of the ladder = 200 cm

distance between each rung = 20 cm

rate = 10 cm/h

fifth rung = ?

Process

1.- Calculate the total distance the tide must rise

distance = 20 cm x 4

= 80 cm because the first rung touches the water

2.- Calculate the time

rate = distance / time

-Solve for time

time = distance / rate

-Substitution

time = 80 cm / 10cm/h

-result

time = 8 h

3 0

1 year ago

Find the value of y for a given value of x, if y varies directly with x.

stepan [7]

Answer:

5.46

Step-by-step explanation:

3.24/5.4 = y/9.1

7 0

2 years ago

A coin jar contains 12 quarters, 15 dimes, and 23 nickels. find the probability that a karen will choose a dime from the jar and

Darina [25.2K]

Karens possabilty is 15/50 chance

Makiah possability is 12/50 chance

Have a nice day

7 0

2 years ago

A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

2 years ago