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A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?

Answers

Answer 1

An equation can be written to determine the number of students that went on this trip is: C. [tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]

How to write an equation to determine the number of students that went on this trip?

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

[tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

Related Questions

Given the inscribed polygon, find the value of both x .and y.
X =
y =
please help!!!

Answers

X= 101
y= 107
This is because opposite angles in a cycling quadrilateral ( the inscribed polygon) are equal to 180

Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.

Answers

There exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2.

To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use the concept of the longest path in a tree and the properties of odd integers.

First, let's consider the longest path in the tree T.

Since the tree has n vertices, the longest path can have at most n-1 edges.

Let's denote this longest path as P.

Since n is an odd integer, we have n = 2k + 1, where k is a non-negative integer.

This implies that n-1 = 2k, which is an even number.

Now, consider the middle vertex x of the longest path P.

If P has an odd number of vertices, then x is unique.

If P has an even number of vertices, then there are two possible middle vertices, but we can choose any one of them.

Next, let's consider the distance between v and x along the longest path P. Since x is the middle vertex, this distance can be at most (n-1)/2.

This is because the longest path P divides the tree into two parts, each containing (n-1)/2 vertices at most.

Now, let's consider the subtree rooted at x, which consists of all vertices that can be reached from x.

Since the distance between v and x is at most (n-1)/2, it implies that v is within this subtree.

Therefore, we have found a vertex u (in this case, x) in the subtree rooted at x such that the distance between u and v is at most (n-1)/2.

By proving the existence of such a vertex u, we have shown that for any vertex v in the tree T, there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Please help i havent been able to get this for so long

Answers

Answer:

A) AAS

B) HL

C) SSS

E) SAS

Step-by-step explanation:

We cannot prove the triangles congruent by AAS because we would need another angle pair that is congruent to each other.

We can prove the triangles congruent by HL because the pairs of hypotenuses and shorter legs are shown to be congruent to each other.

We can prove the triangles are congruent by SSS because every side is congruent to its respective pair.

We cannot prove the triangles congruent by HA because we would need another angle pair that is congruent to each other, like with AAS.

We can prove the triangles are congruent by SAS because two pairs of sides in addition to their respective included angles (the right angles) are congruent to each other.

We cannot prove the triangles congruent by LA because we would need to know by the given information that ∠B≅∠E, but it's not provided.

Therefore, A, B, C, and E are the correct answers.

A salad dressing is made by mixing lemon juice and vinegar in the ratio of 4 : 3. Vicky makes 700ml of the salad dressing. How much lemon juice does she use?

Answers

Answer:

Vicky uses 400 ml of lemon juice in the salad dressing.

What is the volume of the sphere? Write your answer in terms of pi (for example, 25 pi cubic units).

Answers

Answer:

4/3 ×π×r³

4/3 × 22/7 ×3³

88/21 ×27

Please help i need this done as soon as possible will mark brainly!!!!!!!!

Answers

The number 5730 represents

(**the number of years it takes for half of the carbon-14 to decay.**)

It is the half-life of carbon-14, which is the amount of time it takes for half of the substance to undergo radioactive decay.

can someone help me solve this

Answers

Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

We have to given that;

Expressions are,

⇒ 12 - |2x + 15| > 3

And, (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

Now, We can simplify as;

⇒ 12 - |2x + 15| > 3

⇒ 12 - 3 > |2x + 15|

⇒ 9 > |2x + 15|

⇒ |2x + 15| < 9

⇒ - 9 < 2x + 15 < 9

This gives,

⇒ - 9 < 2x + 15

⇒ - 9 - 15 < 2x

⇒ - 24 < 2x

⇒ - 12 < x

And, 2x + 15 < 9

⇒ 2x < 15 - 9

⇒ 2x < 6

⇒ x < 3

Hence, Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Simplify the expressions ,

⇒ (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

⇒ (x - 3)² - x² + 3) ≥ 0

⇒ x² + 9 - 6x - x² + 3 ≥ 0

⇒ 12 - 6x ≥ 0

⇒ 12 ≥ 6x

⇒ 2 ≥ x

Hence, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

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(5^2+7)÷4 evaluate it

Answers

Answer:

Step-by-step explanation:

(5² + 7) ÷ 4 ← evaluate terms in parenthesis

= (25 + 7) ÷ 4

= 32 ÷ 4

= 8

Area + Arc length equations of a circle, can someone help me out with this problem

Answers

To find the area of a sector, you can use the formula A = (θ/2π) × πr^2 = (θ/2) × r^2.

The area of a circle is given by the equation A = πr^2, where r is the radius of the circle. The arc length of a circle is given by the equation L = rθ, where θ is the central angle in radians and r is the radius of the circle.

To find the arc length of a portion of a circle, you can use the formula L = (θ/2π) × 2πr = (θ/2π) × C, where C is the circumference of the circle. This formula is useful when you have a fraction of a circle, such as a sector.

These equations are fundamental in geometry and are used in many applications such as architecture, engineering, and physics.

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3x, 3x+7,4x,5x-8 What is the value of x

Answers

Hello

What is the value of x?^

[tex]\frac{3x}{4x} = \frac{3x+7}{5x-8} \\\\\frac{3}{4} = \frac{3x+7}{5x-8}\\\\\frac{3}{4}(5x-8) = 3x+7\\\\\frac{3(5x-8)}{4} = 3x + 7\\\\\frac{15x-24}{4} = 3x + 7\\\\15x - 24 = 4(3x + 7)\\\\15x - 24 = 12x + 28\\\\15x - 12x = 28 + 24\\\\3x = 52\\\\\boxed{x = 52/3}[/tex]

In circle J with m/HJK = 48 and HJ = 11 units, find the length of arc HK.
Round to the nearest hundredth.
H
K

Answers

The length of arc HK is approximately 3.86 units.

To find the length of arc HK, we need to know the circumference of circle J.

The formula for the circumference of a circle is C = 2πr,

where C is the circumference and r is the radius.

Since we don't have the radius directly given, we can find it using the given information.

We know that the measure of angle HJK is 48 degrees, and HJ is 11 units. The angle at the center of a circle is twice the angle at the circumference that intercepts the same arc.

Therefore, angle HJK at the center of the circle intercepts an arc HK with the same measure.

So, the circumference of the circle is C = 2πr = 2π(11 units).

To find the length of arc HK, we need to find the fraction of the circumference represented by the angle HJK.

We know that the total angle at the center of a circle is 360 degrees (the full circumference), so the fraction of the circumference represented by angle HJK is 48/360.

The length of arc HK is then calculated by multiplying the fraction of the circumference represented by the angle HJK by the total circumference of the circle:

Arc HK = [tex](48/360) \times 2\pi (11 units)[/tex]

Calculating this value, we get:

Arc HK ≈[tex](48/360) \times 2 \pi \times 11[/tex] ≈ 1.234π

To find the numerical value, we can approximate π as 3.14:

Arc HK ≈[tex]1.234 \times 3.14[/tex] ≈ 3.86 units (rounded to the nearest hundredth)

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1. Write down the next three numbers and describe each pattern: b) 1; 8; 15; 22; c) 7; 9; 8; 10; 9:0 a) 3; 6; 9; 12; d) 4; 1; 16; 1; 64; 1; e) 2; 4; 8; 16; 32; f) 3; 9; 27; 81; 2. Draw the next diagram in each pattern. Explain the rule. a) b) P 3. The diagrams below show artwork that the Nguni people paint c their houses. Describe the pattern in the sequence of artwork.