How can one 1/4x − 3 = 1/2x + 8 be set up as a system of equations?

a. 4y + 4x = −12
2y + 2x = 16

b.4y − x = −12
2y − x = 16

c.4y + x = −12
2y + x = 16

d.4y − 4x = −12
2y − 2x = 16

Sam's gas usage is a proportional relationship because he gets a constant 25 miles per gallon in both given scenarios.

Yes, this is a proportional relationship. To determine proportionality, we can calculate the gas mileage for each scenario. Gas mileage is calculated by dividing the number of miles driven by the number of gallons used. For the first scenario, the gas mileage is 50 miles / 2 gallons = 25 miles per gallon. In the second scenario, the gas mileage is 100 miles / 4 gallons = 25 miles per gallon. Since the gas mileage is the same in both cases, it indicates a proportional relationship.

Answer:

60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.

Step-by-step explanation:

Consider the provided information.

60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich.

40 Out of 60 people who order grilled chicken sandwich got a chocolate milk to drink.

Let say x number of people out of 90 got chocolate milk drink.

Now we need to find the people who ordered the spicy fried chicken sandwich got a chocolate milk.

The above information can be written as:

[tex]\frac{40}{60}=\frac{x}{90}[/tex]

[tex]\frac{40}{60}\times 90=x[/tex]

[tex]x=20\times 3[/tex]

[tex]x=60[/tex]

Hence, 60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.

The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is calculated as 50.

The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is to be determined.

Step-by-step explanation:

Answer:

The correct option is D.

Step-by-step explanation:

From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.

The length of line segment AC is

[tex]AC=C-A=8-0=8[/tex]

The length of line segment CF is

[tex]CF=F-C=20-8=12[/tex]

The ratio of line segment AC to CF is

[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]

Cancel out the common factors.

[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]

The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.

Therefore the correct option is D.

Answer:

5.586

Step-by-step explanation:

Answer:

probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

Step-by-step explanation:

Given: A jar contains "x" black and "y" white balls.

To find: What is the probability that a random draw is black.

Solution: We have given that black balls  = x

                                                 white balls = y

                                     total balls = x + y

probability that a random draw is black = [tex]\frac{Number\ of\ outcome happen}{Total numer of outcomes}[/tex]

probability that a random draw is black = [tex]\frac{Ball\ drawn\ is\ black}{Total\ number\ of\ ball}[/tex].

probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

Therefore, probability that a random draw is black = [tex]\frac{x}{x+y}[/tex].

By using the quadratic formula, the roots of the equation are,

⇒ x = 2 ± (√3/2) i

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The quadratic equation is,

⇒ x² - 4x + 13 = 0

Now, By using the quadratic formula, the roots of the equation are,

⇒ x² - 4x + 13 = 0

⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2

⇒ x = 4 ± √16 - 52 / 2

⇒ x = 4 ± √- 36 / 2

⇒ x = 4 ± √6 i / 2

⇒ x = 2 ± (√3/2) i

Thus, We get;

⇒ x = 2 ± (√3/2) i

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Final answer:

The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.

Explanation:

To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:

x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)

This simplifies to:

x = 4 ± √(16 – 52) / 2

x = 4 ± √(-36) / 2

Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:

x = (4 ± 6i) / 2

x = 2 ± 3i

Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.

Answer:

D

Step-by-step explanation:

Answer:

The graph shows the given straight line.    

Step-by-step explanation:

We are given an equation:

[tex]y = \displaystyle\frac{1}{3}x + 3[/tex]

The attached image shows the graphical plot for the given equation.

If we compare the given equation to the

[tex]y = mx+c[/tex]

where m is the slope and c is the y-intercept of the straight line.

Comparing, we get:

[tex]m = \displaystyle\frac{1}{3}\\\\c = 3[/tex]

The line will pass by the points (-3, 2), (0, 3), and (3, 4)

Given is an equation y = x/3+3 we need to graph it,

Let's pick a few x-values and determine the y-values that go with them:

Y equals (1/3) when x = -3(-3) + 3 = -1 + 3 = 2

Y = (1/3)(0) + 3 = 0 + 3 = 3 when x = 0.

Y = (1/3)(3) + 3 = 1 + 3 = 4 for x = 3.

The points (-3, 2), (0, 3), and (3, 4) can now be plotted on the coordinate plane.

A straight line running across these locations will form the graph.

The line will have a positive slope because the value of x is positive (1/3).

Given that the y-intercept is 3, the line will cross the y-axis at (0, 3).

The plotted points (-3, 2), (0, 3), and (3, 4) lie on the line, and the line continues indefinitely in both directions.

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A trapezoid becomes an isosceles trapezoid when its non-parallel sides, or legs, are of equal length. Thus, for a given length x, an isosceles trapezoid requires both legs to be x in length.

A trapezoid is a geometric shape with one pair of parallel sides. A trapezoid becomes an isosceles trapezoid when the non-parallel sides (the legs) are equal in length. If we denote the length of the legs as x, then the trapezoid becomes an isosceles trapezoid when both legs are of equal length, meaning x equals x.

Without additional information such as the lengths of the base and height of the trapezoid or the angles within it, we cannot provide a specific numerical value for x. The key to remember here is that an isosceles trapezoid has equal length legs - so whatever value you have for one leg, the other leg must be the same for it to qualify as an isosceles trapezoid.

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ITS 10

Then 1.5% thank this

To find out how much cement was delivered to each team, we can set up an equation based on the information provided and solve for the unknowns.

Let's denote the amount of cement delivered to the second team as x kg. According to the question, the first team received 50 kg less, so they received x - 50 kg of cement.

The first team used 150 kg of cement every hour for 3 hours, so they used a total of 150 * 3 = 450 kg of cement. Therefore, they had 1.5 times as much remaining cement as the second team, which means they had 1.5 * (x - 50) kg of cement remaining.

Since we know that the remaining cement of the first team is equal to 450 kg, we can set up the following equation: 1.5 * (x - 50) = 450. Solving this equation will give us the amount of cement delivered to each team.

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The first team received 750 kg of cement, and the second team received 800 kg of cement.

Let's denote the amount of cement delivered to the first team as [tex]\( x \)[/tex]kg and to the second team as[tex]\( y \)[/tex] kg. According to the problem, we have the following information:

1. The first team received 50 kg of cement less than the second team: [tex]\( x = y - 50 \)[/tex].

2. The first team uses 150 kg of cement per hour, and the second team uses 200 kg per hour.

3. After three hours of work, the first team has 1.5 times as much remaining cement as the second team.

Let's calculate the amount of cement used by each team after three hours:

- The first team uses [tex]\( 150 \times 3 = 450 \)[/tex] kg of cement.

- The second team uses [tex]\( 200 \times 3 = 600 \)[/tex] kg of cement.

Now, let's denote the remaining cement for the first team as [tex]\( R_1 \)[/tex] and for the second team as [tex]\( R_2 \)[/tex]. We can set up the following equations:

For the first team: [tex]\( R_1 = x - 450 \)[/tex].

For the second team: [tex]\( R_2 = y - 600 \)[/tex].

According to the problem, the remaining cement for the first team is 1.5 times that of the second team: [tex]\( R_1 = 1.5 \times R_2 \).[/tex]

Substituting the expressions for[tex]\( R_1 \)[/tex] and [tex]\( R_2 \)[/tex] into the equation, we get:

[tex]\( x - 450 = 1.5 \times (y - 600) \).[/tex]

Now, we can substitute[tex]\( x = y - 50 \)[/tex] into the equation:

[tex]\( (y - 50) - 450 = 1.5 \times (y - 600) \),[/tex]

[tex]\( y - 500 = 1.5y - 900 \),[/tex]

[tex]\( 0.5y = 400 \),[/tex]

[tex]\( y = 800 \).[/tex]

Now that we have [tex]\( y \)[/tex], we can find [tex]\( x \)[/tex]:

[tex]\( x = y - 50 \),[/tex]

[tex]\( x = 800 - 50 \)[/tex],

[tex]\( x = 750 \).[/tex]

Answer:

11+c=15

Step-by-step explanation:

4 pups have their eyes closed

Answer:

y1= |x-12|

y2= 22

Which graph represents the two functions? Graph 3

Step-by-step explanation: