the principal likes to keep the ratio of students to teachers at 24:1 if he has hired 32 teachers then how many students are expected to enroll

Answer:

The rate of change of the distance between the airplanes is approximately 316.760 kilometers.

Step-by-step explanation:

The distance between both airplanes (r), in kilometers, can be determined by the Pythagorean Theorem, that is:

[tex]r^{2} = x^{2}+y^{2}[/tex] (1)

Where:

[tex]x[/tex] - Distance of the westbound airplane from airport, in kilometers.

[tex]y[/tex] - Distance of the southbound airplane from airport, in kilometers.

By Differential Calculus, we derive an expression for the rate of change of the distance between the airplanes ([tex]\dot r[/tex]), in kilometers per hour:

[tex]2\cdot r\cdot \dot r = 2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y[/tex]

[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)

Where:

[tex]\dot x[/tex] - Rate of change of the distance of the westbound airplane, in kilometers per hour.

[tex]\dot y[/tex] - Rate of change of the distance of the southbound airplane, in kilometers per hour.

If we know that [tex]x = 17\,km[/tex], [tex]y = 28\,km[/tex], [tex]\dot x = -164\,\frac{km}{h}[/tex] and [tex]\dot y = -271\,\frac{km}{h}[/tex], then the rate of change of the distance between the airplanes is:

[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex]

[tex]\dot r \approx -316.760\,km[/tex]

The rate of change of the distance between the airplanes is approximately 316.760 kilometers.

Answer:

485297

Step-by-step explanation:

Answer:

1680 ways

Step-by-step explanation:

From the question,

nPr = n!/(n-r)!.................. Equation 1

Where, n = Total number of books to chose from, r = number of books to be arranged in the shelf.

Given: n = 8 books,  r = 4 books.

Substitute into equation 1

8P4 = 8!/(8-4)!

8P4 = 8!/4!

8P4 = (8×7×6×5×4!)/4!

8P4 = 1680 ways.

Hence the number of ways 4 books can be arranged in a shelf if there are 8 books to chose from is 1680 ways

Answer: 210

Step-by-step explanation:

Answer:

11 feet

Step-by-step explanation:

Length of diagonal of square of side a = √2a

Here value of a = 8 feet

Therefore length of diagonal d = √2×8 = 1.414×8 =    11.312 feet

So after rounding to the nearest tenth the length of diagonal becomes 11 feet

Answer:

x = 9

Step-by-step explanation:

Formula

The secant and tangent lines bear the following relationship

(tangent line )^2 = the outside secant line * length of the whole line

Givens

tangent line = 15

outside secant line = x

length of whole secant line = x + 16

Solution

15^2 = x ( x + 16)

15^2 = x^2 + 16x

225 = x^2 + 16x

x^2 + 16x - 225 = 0

Answer and Discussion

The equation has two factors.

(x - 9)(x + 25) =0

x + 25 has no meaning. There cannot be a negative length in this level of geometry.

The answer is x - 9 = 0

x = 9

Given:

In triangle [tex]EFG, m\angle E = 5x, m\angle F=6x[/tex] and extirior angle G  is 110 degrees.

To find:

The measure of angle FEG.

Solution:

Exterior angle theorem, the sum of two interior angles of a triangle is equal to the opposite extirior angle.

Using extrior angle theorem in triangle EFG, we get

[tex]m\angle E+m\angle F=\text{Measure of extirior angle }G[/tex]

[tex]5x+6x=110^\circ[/tex]

[tex]11x=110^\circ[/tex]

[tex]x=\dfrac{110^\circ}{11}[/tex]

[tex]x=10^\circ[/tex]

Now,

[tex]m\angle FEG=5x[/tex]

[tex]m\angle EFG=5(10^\circ)[/tex]

[tex]m\angle EFG=50^\circ[/tex]

Therefore, the measure of angle FEG is 50 degrees. So, option C is correct.

Answer:

30 pieces.

Step-by-step explanation:

According to the word problem, Alex wants to cut all six of his candy bars into fifths.

5/5 = one whole candy bar.

If there will 5 pieces for every candy bar, we can multiply 5 by 6.

5 x 6 = 30.

There will be 30 of the 1/5 size pieces.

Answer:

48

Step-by-step explanation:

Answer:

The answer is going to be 13/5 or 2.6

Step-by-step explanation:

You are going to need to divide both sides by the constant of -5 in order to get s by itsef. After you divide both sides by -5, you will get -13/-5 which two negatives divided by a positive so it would be 13/5 or if you turn it into an integer, it would be 2.6

Answer: I think it's D.

Answer:

CE

Step-by-step explanation:

The smallest side is opposite the smallest angle.

Answer:

y=2 x=2  

Step-by-step explanation:

  x = -2y + 6

3•(-2y+6) - y = 4

  - 7y = -14

7y = 14

y = 2

x = -2y+6

   y = 2

x = -2(2)+6 = 2

x=2

Step-by-step explanation:

solve for y in both equations

subtract 3x from both sides

-y=4-3x

multiply the equation by -1

y=-1(4-3x)

subtract both sides by x

2y=6-x

divide both sides by 2

y=(6-x)/2

-1(3x-4)=(6-x)/2

-3x+4=(6-x)/2

multiply both sides by 2

-6x+8=6-x

add 6x to both sides and subtract 6 to both sides

2=x

put 2 back into x for y=(6-x)/2

y=2

Hope that helps :)

Answer:$1.08 cents.

Step-by-step explanation:

$6 - $4.52 = $1.08.

Answer:

20.04

Step-by-step explanation:

Answer:

20.04

Step-by-step explanation:

The three is in the hundredths place:

find your place (3)

look next door (8)

5 or greater add one more so 4

Step-by-step explanation:

For example, 2/4 and 3/6 both are equal to ½.

...

Equivalent Fractions Chart.

Unit Fraction Equivalent Fractions

1/2 2/4, 3/6, 4/8..

1/3 2/6, 3/9, 4/12..

1/4 2/8, 3/12, 4/16..

1/5 2/10, 3/15, 4/20,

Answer:

500/1000

Step-by-step explanation:

if you happen to simplify you will get 1/2. hope it helps.good day

Answer:

86 degrees

Step-by-step explanation:

Interior degrees of a triangle always add up to 180 degrees

What you would do is add the first two (52+31 = 84)

Subtract this number from 180 to get your remaining degrees

86 degrees

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

7 1/4 pounds

[tex]4\frac{7}{8} + 2\frac{3}{8}[/tex]

[tex]6\frac{7 + 3}{8}[/tex]

= [tex]6\frac{10}{8}[/tex]

convert the improper fraction to a mixed fraction

10/8 = 1 2/8 = 1 1/4

Add the 1 1/4 to 6 = 7 1/4

Step-by-step explanation:

Kelly buys 4 7/8 pounds of apples and 2 3/8 pounds of oranges. How many pounds of fruit does she buy altogether? Show Your work

Answer:

10 smoothies

Step-by-step explanation:

because each 3/8th yields 2 smoothies and the leftovers from each cup made 2 more.

Answer:

Q5: S.A = 216 cm²

Q6: S.A = 254 cm²

Step-by-step explanation:

Q5:

Surface area of a cube = 6a²

a = 6 cm

Plug in the value of a

Surface area of the cube = 6(6²)

= 6(36)

S.A = 216 cm²

Q6:

Given:

Length (L) = 9 cm

Width (W) = 4 cm

Height (H) = 7 cm

Required:

Surface area

Solution:

Surface area of the rectangular prism = 2(LW + LH + HW)

Plug in the values

S.A = 2(9*4 + 9*7 + 7*4)

= 2(36 + 63 + 28)

= 2(127)

S.A = 254 cm²

Answer:

105

Step-by-step explanation:

11×14= 154

7×7= 49

154-49= 105

Answer:

105 is ur answer!

you're welcome lol

Answer:

9.91%

Step-by-step explanation:

cost price= 400

selling price=444

profit made= 444-400

= 44

profit percentage= 44/444 ×100

=9.91%

Answer:

=12y+5x

Step-by-step explanation:

Answer:

12y+ 5x

Step-by-step explanation:

9y + 3y + 5x​

9y and 3y are like terms

9y+3y = 12y

12y+ 5x