All categories

2 years ago

If students sit 3 per bench, we are short 3 benches. If they sit 5 per bench,

1 answer:

8 0

An expression is defined as a set of numbers, variables, and mathematical operations. There are a total of 10 benches in the class.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let the total number of benches be represented by x. If students sit 3 per bench, we are short 3 benches. Therefore, the total number of students can be written as,

Total number of students = 3x + 9

If they sit 5 per bench, 2 benches are left empty, and one bench only has 4 students.

Total number of students = 5(x-1) - 10 +4

Now, the total number of students can be written as,

3x + 9 = 5(x-1) - 10 +4

3x + 9 = 5x - 11

20 = 2x

x = 10

Hence, there are a total of 10 benches in the class.

Learn more about Expression:

brainly.com/question/13947055

#SPJ1

You might be interested in

Abcd is a rectangle if DB=26 and DC=24 find bc

Anettt [7]

Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first establish that triangle BCD is a right-angle triangle.

Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:

a^2 + b^2 = c^2

Where c = hypotenus of right-angle triangle

Where a and c = other two sides of triangle

Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:

Let a = BC

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

a^2 + 24^2 = 26^2

a^2 = 26^2 - 24^2

a = square root of ( 26^2 - 24^2 )

a = square root of ( 676 - 576 )

a = square root of ( 100 )

a = 10

Therefore, as a = BC, BC = 10.

If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:

a = BC = 10

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

FINAL ANSWER:

Therefore, BC is equivalent to 10.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3

7 0

3 years ago

The sum of the digits of a two-digit number is 5. If the number is multiplied by 3, the result is 42. Write and solve a system o

Elenna [48]

A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit

"The sum of the digits is 5"
x + y = 5

The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]

The number is: 10x + y
3(10x + y) = 42

The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42

Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out

-3x - 3y = -15
30x + 3y = 42
------------------
27x + 0 = 27
x = 1

then plug x = 1 into either equation to find y

1 + y = 5
y = 4

remember the x and y represent digits so the number xy is 14

6 0

3 years ago

Solve: 3 + √x+2 = 11<br><br> 62<br> 64<br> ()

klemol [59]

Answer: its 62

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

3 0

3 years ago

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

denis23 [38]

Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)

Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is $f(x)=-0.03x^{2}+3x$ .
Plugging 15 and 35 in x, we can find the values of the function, i.e.
$f(15)=38.25$ and $f(35)=68.25$ .
Then, the average change is $\frac{68.25-38.25}{35-15}=1.5$

4 0

3 years ago

Read 2 more answers

Please help! The volume of an inflated spherical water balloon is 121,500 pi millimeters to the third. What is the radius of the

irga5000 [103]

Answer:

The radius of the inflated spherical balloon is 45 millimeters.

Step-by-step explanation:

Volume of the spherical water balloon = 121,500 pi cubic millimeters

Let the radius of the balloon = r

Now, Volume of a Sphere = $\frac{4}{3} \pi r^{3}$