suppose you go to a concert and purchase 3 identical t-shirts and a hat. the hat cost $21 and you spend $60 in all how much does each t-shirt cost ?

The value of x in the given equation is 41.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15, 9x+9 = 9, 3x+9 = 7, ax+by = z etc.

Based on the degree, equations can be classified into the following three types: Linear equation, Quadratic equation or Cubic equation

Given that, an equation 2x+12 = 3x-31

Solving for x,

2x+12 = 3x-31

Combining the like terms, by transposing,

3x-2x = 31+12

x = 41

Hence, the value of x in the given equation is 41.

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Answer: The volume of water in the pool over time from when the hose is placed in the pool until the pool is full is defined by the equation [tex]V(t)=5000+1250t[/tex] and its graph is given below.

Explanation:

The total capacity of the pool is 20,000 gallon.

It is given that the pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour. So the initial volume of water is 5000.

Let the time is defined by t. So, the volume of water in the pool after time t is defined as,

[tex]V(t)=5000+1250t[/tex]

The capacity of the pool is 20,000 gallon, therefore the maximum value of V(t) is 20,000.

[tex]20,000=5000+1250t[/tex]

[tex]15000=1250t[/tex]

[tex]12=t[/tex]

The maximum value of t is 12, since the time is always positive, therefore we can say that,

[tex]0\leq t\leq 12[/tex]

The below graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full. The initial point is (0,5000) and the other point is (12,20000).

The plot of the graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full is shown below.

The volume of water in the pool over time from when the hose is placed in the pool until the pool is full is defined by the equation  [tex]V(t)=5000+1250x[/tex] and its graph is given below.

According to the question, [tex]\rm Volume=20,000\; gallons[/tex]

Let the time be defined by [tex]x[/tex].

So, volume of water is defined as,

[tex]V(t)=5000+1250x[/tex]

[tex]20000=5000+1250x[/tex]

[tex]x=12[/tex]

So, the range is

[tex]0\leq t \leq 12[/tex]

The graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full. The initial points is [tex](0,5000)[/tex]  and the other point is [tex](12,20000)[/tex]

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The provided data is insufficient to accurately calculate the area of the polygon. With an assumption that the shape is a rectangle and the lengths are 15m and 8m, the area would be 120 square meters.

To calculate the area of a polygon, it's ideal to break down the polygon into simpler shapes like rectangles or triangles, for which we have well established formula for area. However, the information you've provided is inadequate to define a specific polygon shape like a rectangle or a square. Four sides could suggest a rectangle or a quadrilateral, but we don't know two essential properties: the arrangement of these sides and the measure of angles. For instance, if it was a rectangle, we'd look for pairs of equal lengths. If your shape is indeed a rectangle, and we assume that 15m and 8m are the length and width (or vice versa), we could calculate the area. For a rectangle, the area is calculated as length multiplied by width. In this case, it would be 15m*8m = 120 square meters.

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The pair of corresponding angles in the given figure are ∠ 3 and ∠ 7

Any pair of angles, each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Given that, a figure,

Here, ∠ 3 and ∠ 7 are the angles that are formed when two lines are intersected by the transversal.

Hence, ∠ 3 and ∠ 7 are making corresponding angles,

Hence, The pair of corresponding angles in the given figure are ∠ 3 and ∠ 7

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Final answer:

The distance between the points (9, -7) and (9, 4) is calculated by finding the absolute difference between the y-coordinates since the x-coordinates are the same. The distance is 11 units.

Explanation:

To calculate the distance between two points on a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem. However, in this particular case, since the x-coordinates of the points (9, -7) and (9, 4) are the same, the distance is simply the absolute difference between the y-coordinates.

The formula to find the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

So, substituting the known values:

d = √((9 - 9)² + (4 - (-7))²) = √(0 + 11²) = √121 = 11

Therefore, the distance between the points (9, -7) and (9, 4) on a coordinate plane is 11 units.

We have that for the Question ,it can be said that The speed pf the river is

3mph

From the question we are told

Bob can row 14 mph in still water. The total time to travel downstream and return upstream to the starting point is 2.8 hours. If the total distance downstream and back is 36 miles, determine the speed of the river (current speed).

Generally the equation for the time  is mathematically given as

[tex]t=\frac{d}{v}\\\\Therefore\\\\3=\frac{12}{9+x}+\frac{12}{9+x}[/tex]

[tex]1/4=\frac{12}{9^2=x^2}\\\\x^2=81-71\\\\\x=\pm 3\\\\x=3[/tex]

Therefore

The speed pf the river is 3mph

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A real-world situation that can be solved using a two-step equation is calculating the total cost of a shopping trip. Let's say you go to a store and buy some items. Each item costs $5, and you buy 3 items. You also have a $10 coupon. To find the total cost, we can use a two-step equation: 3 * 5 - 10 = x. Solving the equation, we get x = 15.

A real-world situation that can be solved using a two-step equation is calculating the total cost of a shopping trip. Let's say you go to a store and buy some items. Each item costs $5, and you buy 3 items. You also have a $10 coupon. To find the total cost, we can use a two-step equation:

Step 1: Write the equation. Let x be the total cost.

Step 2: Solve the equation. The cost of the items is $5 per item, so the first step is to multiply 3 (number of items) by 5 (cost per item). Then subtract the $10 coupon from the total cost. The equation becomes 3 * 5 - 10 = x. Solving the equation, we get x = 5. Therefore, the total cost of the shopping trip is $15.

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Answer:

The cost of one ounce of cereal is $0.24

Step-by-step explanation:

We are given the following information in the question:

Amount of cereals a box contain = 23.4 ounces

Cost of one box = $5.94

Cost of cereal per ounce =

Formula:

[tex]\text{Cost of one ounce of cereal} = \\\\\displaystyle\frac{\text{Cost of cereal}}{\text{Amount of cereal in a box}}[/tex]

Putting the values, we have:

[tex]\text{Cost of one ounce of cereal} = \displaystyle\frac{5.49}{23.4} = 0.2347 \approx 0.24[/tex]

Hence, the cost of one ounce of cereal is $0.24

Answer:

2 x /3 − 9/ 2

− y + 36

The measure of angle E is 0 degrees not provided in the options (A, B, C, or D), and the correct answer is "Cannot be determined."

To find the measure of angle E in degrees that the sum of angles in a triangle is 180 degrees.

From the given triangle, two angles with measures 50 degrees each (angle A and angle B), and one angle with a measure of 80 degrees (angle D).

To find the measure of angle E, we can use the equation:

Angle E = 180° - (angle A + angle B + angle D)

Angle E = 180° - (50° + 50° + 80°)

Angle E = 180° - 180°

Angle E = 0°

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