Daniel Capo
Solve System of Equations from Context
Jan 21,7:26:04 PM
Sydney is going to a carnival that has games and rides. Each game costs $1.25 and
each ride costs $2.25. Sydney spent $24.25 altogether at the carnival and the number
of rides she went on is 3 more than the number of games she played. Determine the
number of games Sydney played and the number of rides Sydney went on.
Sydney played
games and went on
rides rides.
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Answer:

  x = -3 or +2

Step-by-step explanation:

Such an equation resolves into two equations. The argument of the absolute value function can be either positive or negative, so there is one equation for each case.

4x +2 = 10

  4x = 8 . . . . subtract 2

  x = 2 . . . . . divide by 4

4x +2 = -10

  4x = -12 . . . subtract 2

  x = -3 . . . . . divide by 4

The two solutions are x=-3 and x=2.

Answer:

The solution of the system of equations is the point (1,2)

Step-by-step explanation:

It is required to solve the system of equations:

y= -3x + 5

5x - 4y = -3

So, substitute with y from the first equation at the second equation:

∴ 5x - 4(-3x + 5) = -3

Solve for x

∴ 5x + 12x - 20 = -3

∴ 17x = -3 +20 = 17

∴ x = 17/17 = 1

∴ y = -3 * 1 + 5 = -3 + 5 =2

So, the solution of the system of equations (1,2)

Another solution:

The give system of equations can be solved by graph both of them.

So, the solution will be the intersection between the lines.

See the attached figure.

Answer:0.6 cents

Step-by-step explanation:

Answer:

Step-by-step explanation:

add all numbers together

all of them should equal 88

then divide it by how many numbers there are. so 8.

this equals 11

The median of the given data set, 11, 16, 12, 7, 23, 9, 5, 5, is 10. This is found by arranging the data in numerical order, identifying the two middle numbers, and finding their average.

The subject of this question is the calculation of the median of a given data set in mathematics. The data given is: 11, 16, 12, 7, 23, 9, 5, 5. To find the median, the data must first be arranged in numerical order from smallest to largest. Once arranged: 5, 5, 7, 9, 11, 12, 16, 23, it can be seen that this data set contains an even number of data points.

In these instances, the median is found by taking the average of the two middle numbers. Here, the middle numbers are 9 and 11. The median is found by adding these numbers together and dividing by 2. Thus, the median for this data set is 10.

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Answer:

Sometimes true.

Step-by-step explanation:

The statement is sometimes true and sometimes false depending on the values of x and y.

Here's an example that shows it to be true.

|x+y|=|x|+|y|

Let x = 5 and y = 6.

|x+y|=5 + 6 = 11

|x|+|y| = |5| + +|6| = 5 + 6 = 11

In this case, both sides equal 11, and the expression is true.

Here's an example that shows it to be false.

|x+y|=|x|+|y|

Let x = -5 and y = 5.

|x+y|= |-5 + 5| = |0| = 0

|x|+|y| = |-5| + |5| = 5 + 5 = 10

The left side equals 0, and the right side equals 10. The sides are different, and the expression is false.

Answer:

Anything with a numerator (top) greater then the denominater (bottom) here are some examples:

[tex] \frac{11}{2} [/tex]

[tex] \tfrac{8}{5} [/tex]

[tex] \frac{399}{7} [/tex]

[tex] \frac{6}{2} [/tex]

Hope this information helps my friend!

Answer:

16

Step-by-step explanation:

You have to find y in the answer

Final answer:

The volleyball court is 16 meters long, which was calculated by using the formula for the perimeter of a rectangle and the given width of 9 meters.

Explanation:

To find the length of the volleyball court, we need to use the formula for the perimeter of a rectangle which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since we know the perimeter is 50 meters and the width is 9 meters, we can substitute these values into the formula to solve for the length l.

First, we calculate the total contribution of the width to the perimeter, which is 2w, so 2 times 9 meters = 18 meters. We then subtract this from the total perimeter to find the combined contribution of both lengths: 50 meters - 18 meters = 32 meters. Finally, we divide by 2 to find the length of one side: 32 meters / 2 = 16 meters.

Therefore, the volleyball court is 16 meters long.

Answer:

Pythagorean theorem theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle

Answer:

[tex]y = -\frac{1}{2}x -\frac{5}{2}[/tex]

Step-by-step explanation:

We are given;

We are required to determine the equation of the line;

Taking another point (x, y)

Then; (x, y) , ( 3, -4) and slope -1/2 can give us the equation;

That is;

[tex]\frac{y+4}{x-3}=-\frac{1}{2}[/tex]

Cross multiplication;

[tex]2(y+4) = -1 (x-3)[/tex]

[tex]2y + 8 = -x +3[/tex]

Combining the like terms;

[tex]2y=-x-5\\y = -\frac{1}{2}x-\frac{5}{2}[/tex]

Thus, the equation of the line is; [tex]y = -\frac{1}{2}x -\frac{5}{2}[/tex]

Answer:

240.3

Step-by-step explanation:

Remember SohCahToa for the trig. ratios. You always divide two sides.

'o' is opposite side. 'a' is adjacent side. 'h' is hypotenuse side.

Using alternating angles you can find the angle I marked blue (see diagram below). Because the 31° is parallel to the bottom side of the triangle, you can use alternating angles (Z pattern), where both 'insides' of the Z have the same measure.

The blue angle will be our angle of reference (angle we are talking about) represented by this symbol θ.

Since we need to find 'y', the opposite side, and we know 400ft is the adjacent side, use the tangent ratio.

tanθ = opposite / adjacent

tan31° = y / 400ft           Substitute what you know.

y = (400ft)tan31°          Isolate 'y'. Multiply 400ft and tan31°.

y = 240.344......ft      Exact answer on calculator

y ≈ 240.3ft      Answer rounded to nearest tenth

The nearest tenth is the first decimal. Since the second decimal is '4 or less', you round down, keeping the digit of the first decimal the same.

If the second digit was '5 or more', then you would round up.

A system of equations can be used to represent the situation. The system can be set up with x representing the price of a T-shirt and y representing the price of a pair of jeans.

To represent this situation, we can set up a system of equations. Let x represent the price of a T-shirt and y represent the price of a pair of jeans.

The first equation will be: 4x + 3y = 181, since Salazar bought 4 T-shirts and 3 pairs of jeans for $181.

The second equation will be: x + 2y = 94, since Jenna bought 1 T-shirt and 2 pairs of jeans for $94.

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The value of f(1) is 31

Solution:

Given that the sequence is defined by formula:

[tex]f(n+1) = f(n) - 3[/tex]

To find: f( 1 )

Also given that,

[tex]f(4) = 22[/tex]

So, we can say,

[tex]f(4) = f(3+1) = 22[/tex]

Substitute n = 3 in given formula

[tex]f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25[/tex]

Now we got, f(3) = 25

Use the similar steps to find for f(2)

Substitute n = 2 in given function

[tex]f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28[/tex]

Use the similar steps to find for f(1)

Substitute n = 1 in given function

[tex]f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31[/tex]

Thus value of f(1) is 31

Answer:

Please read the answer below.

Step-by-step explanation:

To eliminate the fractions before solving, each term can be multiplied by:

Answer:

I don't think you are doing anything wrong. Just ignore it and write the repeating decimal. If you're asked to do it, round it up instead.

Answer:

No you aren't doing anything wrong, it's just that the calculator is rounding the answer. So yes 1.6 repeating is correct

Answer:

284

Step-by-step explanation:

when the number to the left is 5 and up then the number is rounded up

The round off is 284.

what is rounding off?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

given number:

283.57

To round off nearest ones place we have to focus on the place value of tenth place.

If the number at tenth place value is greater than 5 then round off will be 284 otherwise if it less than 4 then the round off will be 283

hence, the rounding off is 284.

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Answer:

Let x = the number of small boxes purchased

Let y = the number of large boxes purchased

​

​150x+400y&=1950

​x=y+2

​

The system of equations is as follows:

Equation 1: Total nails from small boxes = 150s

Equation 2: Total nails from large boxes = 400l

Equation 3: Total boxes = s + l

Equation 4: Total nails = 150s + 400l = 1950

To determine the number of small boxes and large boxes the contractor purchased, we can set up a system of equations. Let's define the variables: let "s" represent the number of small boxes and "l" represent the number of large boxes.

Now, let's break down the information given into equations:

Equation 1: The total number of nails from the small boxes is 150 times the number of small boxes, which is 150s.

Equation 2: The total number of nails from the large boxes is 400 times the number of large boxes, which is 400l.

Equation 3: The total number of boxes is the sum of small and large boxes, so the total boxes are s (number of small boxes) plus l (number of large boxes).

Given that the contractor bought 2 more small boxes than large boxes and the total number of nails purchased is 1950, we can express this as an equation:

4. Equation 4: The total number of nails purchased is 1950.

Now, we can write the system of equations:

Equation 1: 150s

Equation 2: 400l

Equation 3: s + l

Equation 4: 150s + 400l = 1950

In this system, Equation 1 represents the total number of nails from the small boxes, Equation 2 represents the total number of nails from the large boxes, Equation 3 represents the total number of boxes, and Equation 4 represents the total number of nails purchased.

To find the solution, we can solve this system of equations using various methods, such as substitution or elimination, to determine the values of "s" and "l," representing the number of small and large boxes the contractor purchased, respectively.

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Answer:

D

Step-by-step explanation:

Given

2x(x - 4) + 7(x - 4) ← factor out (x - 4) from each term

= (x - 4)(2x + 7) → D

Answer:

First, find the area of each side, and the just add them together. It sounds like a lot of work, but getting the question right is totally worth it.

Step-by-step explanation:

The steps to find the Surface Area of different 3D shapes is discussed below:

Surface area refers to the total area of the outer surface of a three-dimensional object.

To find the surface area of 3D shapes, you need to calculate the sum of the areas of all the individual faces of the shape.

The specific formulas for each shape vary, so let's go through some common 3D shapes and their surface area formulas:

1. Cube:

The surface area of a cube is given by the formula: SA = 6s², where s² is the area of square faces.

2. Rectangular Prism:

The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder:

The surface area of a cylinder is given by the formula: SA = 2πrh + 2πr², where 2πrh is area of side circular and 2πr² is Area of base.

4. Sphere:

The surface area of a sphere is given by the formula: SA = 4πr², where r is the radius of the sphere.

5. Cone:

The surface area of a cone is given by the formula: SA = πr(r + √(r² + h²)), where r is the radius of the base and h is the height of the cone.

6. Pyramid:

The surface area of a pyramid depends on the shape of its base. For example, the surface area of a square pyramid is given by the formula: SA = l² + 2lw, where l is the slant height and w is the base width.

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Answer:number 1 is x<6750number 2 is $22.05 number 3 is $105

Step-by-step explanation:

To find the percent error, calculate the absolute difference between the estimated height and the actual height, and divide it by the actual height. Finally, multiply the result by 100 to get the percentage.

To find the percent error, we need to calculate the absolute difference between the estimated height and the actual height, and then divide it by the actual height.

Finally, we multiply the result by 100 to get the percentage.

Step 1: Determine the difference between estimated and actual height.

Difference = Actual height - Estimated height

Difference = 54 inches - 50 inches

Difference = 4 inches

Step 2: Calculate the absolute value of the difference.

Absolute value of the difference = |4 inches|

Absolute value of the difference = 4 inches

Step 3: Divide the absolute difference by the actual height and multiply by 100% to get the percent error.

Percent Error = (Absolute difference / Actual height) × 100%

Percent Error = (4 inches / 54 inches) × 100%

Percent Error ≈ 7.41%

Therefore, the percent error in your estimation of your friend's height is approximately 7.41%.

22 bouquets must Maria sell to break even.

bouquet costs  per unit $7

vendor  permit $150

number of bouquet need to  sell to meet break even  22 item (150/7)

22 item need to selled to meet the break even.

A sale is a deal involving two or more people when tangible or intangible commodities, services, or assets are exchanged for cash. A seller may occasionally receive assets in addition to money.

In the financial markets, a sale can also be defined as an agreement between a buyer and a seller specifying the purchase price and delivery details of a financial security.

A sale is essentially a contract between a seller of a certain good or service and a buyer who is willing to pay for that good or service, regardless of the environment.

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Answer:

I have attached a graph of such a system. The two lines have the same slopes but different y-intercepts, this means the lines are parallel, and therefore the system of equations that they represent  has no solutions because the lines never intersect.

Going into your next question, there are three ways the system of equations can be classified: the ones that have a solution, with infinitely many solutions, with no solutions.

The graphs of the system of equations that have a solution intersect exactly at one point.

The graphs of the system of equations that have infinitely many solutions are mapped onto each other (are on top of each-other), and therefore have infinite points of intersection.

The graphs of the system of equations that have no solutions never intersect;  these are represented by lines that are parallel.

Hope this helps!

The range of the function y = -3, graphed over the domain {x | -8 < x < 8}, is a singular value, which is y = -3.

The question asks for the range of the function y = -3 which is graphed only over the domain {x | -8 < x < 8}. This function is a horizontal line, which means that for any value of x within the domain, the value of y will always be -3.

Therefore, the range of this function is simply the single value y = -3, because no matter what x-value we have (as long as it's between -8 and 8), the y-value remains constant at -3.

Answer:

Therefore the value is

[tex]m<\dfrac{1}{9}[/tex]

Step-by-step explanation:

Given:

[tex]6m-2(7+3m)>5(2m-3)-m[/tex] ....Given

Step 1. Applying Distributive Property A(B+C)=AB+AC we get

[tex]6m-2\times7-2\times 3m>5\times 2m-5\times 3-m[/tex]

[tex]6m-14-6m>10m-15-m\\-14>9m-15[/tex]

Step 2. Add 15 both the side

[tex]-14+15>9m-15+15\\1>9m[/tex]

Step 3. Dividing both the side by 9

[tex]\dfrac{1}{9}>\dfrac{9m}{9}\\\\\dfrac{1}{9}>m[/tex]

Therefore the value is

[tex]m<\dfrac{1}{9}[/tex]

Answer:

x=-1, y=-3. (-1, -3).

Step-by-step explanation:

x+y=-4

3x-6y=15

---------------

x=-4-y

3(-4-y)-6y=15

-12-3y-6y=15

-12-9y=15

9y=-12-15

9y=-27

y=-27/9

y=-3

x+(-3)=-4

x-3=-4

x=-4+3

x=-1

Answer:

Step-by-step explanation:

Total number on the trip is 24

Let the number of girls be x

Then the boys are x + 8

So... x + x + 8 = 24

2x + 8 = 24.......... This is the equation

2x = 24 - 8

2x = 16

x = 16/2

x = 8

Number of girls = 8

And number of boys = x + 8

Which is = 8+8 = 16

There were 8 girls and 16 boys on the trip.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Bradley and 23 of his classmates went on a trip to the aquarium.

∴ There are a total of 24 students.

There are 8 more boys than girls on the trip.

Assuming the no.of girls to be x, hence no. of boys is (x + 8).

So, x + (x + 8) = 24.

2x + 8 = 24.

2x = 16.

x = 8.

So, no. of girls on the trip is 8, and no. of boys on the trip is (8 + 8) = 16.

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Answer:

14.

Step-by-step explanation:

The number of neutrons = the mass number - atomic number

= 27 - 13 = 14.

The correct answer is that Aluminium (Al), with an atomic number of 13 and a mass number of 27, has 14 neutrons.

To find the number of neutrons in an atom, one subtracts the atomic number (which is the number of protons) from the mass number (which is the sum of the number of protons and neutrons).

For Aluminium:

- The atomic number (Z) is 13, which means it has 13 protons.

- The mass number (A) is 27, which means the total number of protons and neutrons is 27.

The number of neutrons (N) can be calculated using the formula:

[tex]\[ N = A - Z \][/tex]

[tex]\[ N = 27 - 13 \][/tex]

[tex]\[ N = 14 \][/tex]

Therefore, Aluminium has 14 neutrons.

Answer:

Proportional: Mike, a plumber charges $5 per hour for his service.

Non-proportional: Mike charges a initial cost of $10 plus $3 for each hours of service.

Step-by-step explanation:

Let us assume that Mike, a plumber charges $5 per hour for his service.

So, the number of hours (h) of service and the total charge (C) are proportional, which is  

C(h) = 5h ....... (1)

If the condition changes like, Mike charges an initial cost of $10 plus $3 for each hour of service.

Here, the equation that models the situation is  

C(h) = 10 + 3h .......... (2)

Now, relation (1) is non-proportional.  (Answer)

Final answer:

Real-world examples of directly proportional relationships include the relationship between distance and time at a constant speed, and cost and weight of fruit. These relationships become nonproportional when a base charge or flat fee is introduced, respectively.

Explanation:

Two real-world quantities that have a proportional linear relationship are speed and distance traveled in a given amount of time, assuming constant speed. For example, the farther you travel at a steady speed, the longer it takes. This relationship can be represented by y = kx, where y is the distance, x is the time, and k is the constant speed.

To make this relationship nonproportional, we could introduce a starting fee or base charge, making the total cost not just dependent on the distance but also an additional amount. Another example of a directly proportional relationship is the cost of fruit, where cost and weight are proportional (y = kx). By adding a flat packaging charge regardless of weight, the relationship between cost and weight becomes nonproportional.

Answer:

Therefore NFC won 28 games and AFC won 25 games.

Step-by-step explanation:

i) let the number of Super Bowls won by NFC be x

ii) let number of Super Bowls won by AFC be y

iii) therefore it is given that  x + y = 53

iv) and also it is given that x = y + 3

v) substituting the equation in iv) into the equation in iii) we get

  (y +3) + y  =  53    ⇒  2y = 50   therefore y = 25.

vi) substituting the value of y from v) into the equation iv) we get

    x  = 25 + 3 = 28.

Therefore NFC won 28 games and AFC won 25 games.

To solve this mathematics problem, we formulate an equation based on the information that total Super Bowls were 53 and NFC won 3 more than AFC. By solving the equation, we find that NFC won 28 games and AFC won 25 games.

To solve this problem, let's start with the total number of games, which is 53. If the NFC has won 3 more Super Bowls than the AFC, that means the number of games won by both conferences adds up to 53. Let's denote the number of games won by the AFC as 'x'. So, the equation will be:

By combining like terms, we get:

Subtracting 3 from both sides, we have:

Finally, when we divide by 2, we solve for x:

This means that the AFC has won 25 games, and the NFC, having won 3 more, has won 28 games.

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