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Elanso [62]
3 years ago
14

Find the values of x and y.

Mathematics
1 answer:
kotykmax [81]3 years ago
6 0

Answer:

y=9 and x=18

Step-by-step explanation:

You know that y+3=12 so 12-3=9

You know that x-3=15 so 15+3=18

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HELP!!!!!! 100 POINTS!!!!!!
Artyom0805 [142]

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

  • Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class.
  • Lauren has 5 classes with g students in each class and 10 classes with h students in each class.
  • If Kyle has a total of 62 students and Lauren has a total of 70 students,

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

To know more about expression follow

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3 0
2 years ago
Find n. Perimeter = 46 in.<br>8 in.​
Lana71 [14]

Answer: 108 inches

Step-by-step explanation:

If length = 46, width = 8

Perimeter of rectangle = 2(l+w)

= 2 (46 + 8)

= 2 x 54

= 108 inches

6 0
3 years ago
What is the essence of calculus? <br>*friendship​
iragen [17]

Differential Calculus, or Differentiation

If we have a function of one variable, ie of the form y=f(x), then in its most basic form differentiation is the study of how a small change in one variable x affects the other variable y.

As an real life example, consider the average speed of a moving car:

average speed = distance travelled/ time taken

Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.

Similarly if we wanted to find the gradient of the tangent to a curve at some particular point A we would estimate the gradient by using a chord to a nearby point B. As we move this nearby point B  closer to the tangent point A the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point B infinitesimally close to the point A o that we can calculate the actual gradient of the tangent.

Integral Calculus, or Integration

Suppose we wanted to calculate the area under a curve, y=f(x),  bounded the x =axis, and two points a and b. We could start by splitting the interval  [a,b]  into n regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase n then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.

The Fundamental Theorem of Calculus

Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.

Visual for  Fundamental Theorem of Calculus for integrals:

\int\limits^b_af {(x)} \, dx =F(b)-F(a).

where F is an antiderivative of f

Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.

Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.

All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.

Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.

4 0
2 years ago
Read 2 more answers
Given f ( x ) = 3 x 2 + k x − 13 f(x)=3x 2 +kx−13, and the remainder when f ( x ) f(x) is divided by x + 4 x+4 is 15 15, then wh
Varvara68 [4.7K]

Answer:

k=5

Step-by-step explanation:

We are provided with function, f ( x ) = 3 x^{2} + kx − 13

which is divided by x+4 gives 15.

Here,

since f(x) is divided by x+4 so we can put :

x+4 = 0

x= -4

Putting this in f(x) -----> f(-4)

f(x) = f(-4) = 3 (-4^{2}) + k(-4) − 13

f(-4) = 3(16) - 4k - 13

f (-4) = 48 - 4k - 13                ------------------------------------------Equation 1

Since, when f(x) is divided by x+4 , the remainder is 15 so we can say,

f(-4) = 15

putting in equation 1

f (-4) = 15 = 48 - 4k - 13

48 -4k - 13 = 15

35 - 4k = 15                      

35 - 15 = 4k                         (Moving - 4k on right hand side and 15 on the left)

or 20 = 4k

or 4k = 20

k = \frac{20}{4}

<h2>k = 5</h2>

4 0
3 years ago
Dont trust breekall indian hacker/and help please
ollegr [7]

Answer:

ok....

Step-by-step explanation:

3 0
2 years ago
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