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slavikrds [6]
3 years ago
5

An arts academy requires there to be 4 teachers for every 100 students and 3 tutors for every 30 students. How many students doe

s the academy have per teacher? Per tutor? How many Tito’s does the academy need if it has 110 students?
Mathematics
1 answer:
jekas [21]3 years ago
6 0

Answer:

18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors

Step-by-step explanation:

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3y-6=3x and y+2x=5 solve the system of linear equations by graphing PLEASE SHOW WORK​
Dmitry_Shevchenko [17]

Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.

___

If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.

  <u>3y -6 = 3x</u>

To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.

  3x -3y = -6

  x/(-6/3) +y/(-6/-3) = 1

  x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.

Plot the intercept points and draw a line through them.

  <u>y +2x = 5</u>

The intercepts for this one are found by dividing by 5:

  x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.

The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.

  y = -2x + 5

The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).

  <u>Solution</u>

When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.

7 0
3 years ago
What is the correct inverse function for f(x)=ln(3x)?
Maslowich

Let y = f(x)

y = ln(3x)

Exchange place with x and y.

x = ln(3y)

Solve for y.

y = (e^x)/3

Replace y with the inverse notation.

f^(-1) x = (e^x)/3

Done.



5 0
3 years ago
Read 2 more answers
25 pts
Solnce55 [7]

Answer:

490lbs.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A 12 foot ladder is leaning up against a wall. If the angel made between the ladder and the ground is 80 degrees. How far up can
lorasvet [3.4K]

Answer:

<h3>11.8 feet</h3>

Step-by-step explanation:

Given

Length of the ladder = 12foot

angle of elevation = 80 degrees

Required

Height of the wall (opposite side)

The set up will form a right angled triangle where

length of the ladder is the hypotenuse

height of the wall is opposite;

Using SOH, CAH, TOA trig identity

According to SOH

sin 80 = opp/hyp

sin80 = opp/12

opp = 12sin80

opp = 11.82 feet

Hence the height of the wall is 11.8feet (to the nearest tenth)

5 0
3 years ago
Point X is at 2/3 on a number line. On the same number line, point Y is the sane distance for 0 as point X, but has a numerator
olga2289 [7]

Answer:

12

Step-by-step explanation:

4 0
3 years ago
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