It takes a jet 2 hours to fly 1,100 miles. At this rate, how far does it fly in 8 hours?
2 answers:
You might be interested in
Answer:
A. Solutions are: x = 2, y = 1.
B. Solutions are: x = 3, y = 2.
C.
1. Inconsistent
2. Inconsistent
3. Consistent
Step-by-step explanation:
A. Solutions of each system of linear equations by substitution method:
Equation 1: 3x - 2y = 4
Equation 2: x = 2y
<u>Step 1:</u> Substitute x = 2y into the Equation 1:
3(2y) - 2y = 4
6y - 2y = 4
4y = 4
Step 2: Divide both sides of the equation by 4 to isolate y:
y = 1.
<u>Step 3:</u> For Equation 2, x = 2y, substitute y = 1 into the equation to solve for x:
x = 2y
x = 2(1)
x = 2
Therefore, the solutions are: x = 2, y = 1.
B. Find the solutions of each system of linear equations by elimination method:
Equation 1: 2x + y = 8
Equation 2: x + y = 5
<u>Step 1:</u> Multiply Equation 2 by 2:
2(x + y) = 5(2)
2x + 2y = 10
<u>Step 2:</u> Subtract Equation 1 from the equation derived from Step 1, 2x + 2y = 10:
2x + 2y = 10
- <u>2x + y = 8</u>
y = 2
Step 3: Plug in y = 2 into Equation 1, 2x + y = 8 to solve for x:
2x + y = 8
2x + (2) = 8
<u>Step 4:</u> subtract both sides of the equation by 2 to isolate x:
2x + 2 - 2 = 8 - 2
2x = 6
<u>Step 5:</u> Divide both sides of the equation by 2 to solve for x:
x = 3.
The solutions are: x = 3, y = 2.
C:
1. Inconsistent
2. Inconsistent
3. Consistent (infinitely many solutions)
(C) fraction of the marbles now in the bag is blue.
- A fraction is a portion of a whole or, more broadly, any number of equal parts.
- In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
- A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line.
- Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
To find what fraction of the marbles now in the bag is blue:
- Important information is that immediately before the last step blue marbles formed
from the marble in the bag.
- That means that there were
blue and
other marbles, for some
- When we double the number of blue marbles, there will be
blue and
- Hence, blue marbles now form
all marbles in the bag.
Therefore, (C) fraction of the marbles now in the bag is blue.
Know more about fractions here:
SPJ4
Complete question:
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 1/2