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vlada-n [284]
2 years ago
11

This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of

proportionality?
1/25
1/20
1/15
1/10

Mathematics
2 answers:
alisha [4.7K]2 years ago
8 0
(60,4)(120,8)
slope = (8 - 4) / (120 - 60) = 4/60 = 1/15 <== the constant of proportionality is the slope
Ilya [14]2 years ago
4 0

Answer:

The correct option is 3.

Step-by-step explanation:

Form the given figure it is noticed that the line is passing through the points (60,4) and (120,8).

y\propto x

y=kx

Where, k is the constant of proportionality or slope.

The slope of a line is defined as

k=\frac{y_2-y_1}{x_2-x_1}

k=\frac{8-4}{120-60}

k=\frac{4}{60}

k=\frac{1}{15}

Therefore option 3 is correct.

You might be interested in
What is the expansion of (3+x)^4
Vlad1618 [11]

Answer:

\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81

Step-by-step explanation:

Considering the expression

\left(3+x\right)^4

Lets determine the expansion of the expression

\left(3+x\right)^4

\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i

a=3,\:\:b=x

=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i

Expanding summation

\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}

i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0

i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1

i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2

i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3

i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4

=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4

=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4

as

\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81

\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x

\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2

\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3

\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4

so equation becomes

=81+108x+54x^2+12x^3+x^4

=x^4+12x^3+54x^2+108x+81

Therefore,

  • \left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81
6 0
3 years ago
Please help!! How do you do number 1?
alisha [4.7K]
Do a ratio tall over shadow. How tall is tree / shadow. How tall is person / shadow then cross multiply. X/7.5 =5/3. 37.5=3x. Divide by 3 answer 12.5
6 0
3 years ago
Pleaseee helpp meeee
Marta_Voda [28]

Answer and Step-by-step explanation:

[] means to take the absolute version of the number. That means if the number is negative or positive, the outcome is always positive.

14.

-[3] = -3

15.

[5 + 9] = 14

16.

[17 - 8] = 9

#teamtrees #WAP (Water And Plant)

6 0
2 years ago
In 2010, the population of a city was 161,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 6.7%.
solniwko [45]

Answer:

99%

Step-by-step explanation:

2010 population = 161,000

From 2010 to 2015, the population grew by 8%.

2010 to 2015 = 161,000 + (8% of 161,000)

= 161,000 + (0.08 * 161,000)

= 161,000 + 12,880

= 173,880

2010 to 2015 = 173,880

From 2015 to 2020, it fell by 6.7%

2015 to 2020 = 173,880 - (6.7% of 173,880)

= 173,880 - (0.067 * 173,880)

= 173,880 - 11,649.96

= 162,230.04

2015 to 2020 = 162,230.04

what percent did the city grow from 2010 to 2020.

= 161,000 / 162,230.04 × 100

= 0.9924179270374 × 100

= 99.241792703743

Approximately, 99% to the nearest whole number

4 0
2 years ago
The area of a triangle is 30 square feet. If<br> the base is 4 feet, then what is the height?
ExtremeBDS [4]
Height=15

Explanation:
Area of a triangle= 1/2base x height
Plug in information
30=1/2 x 4 x h
Solve 1/2 x 4 = 2
30= 2 x h
Divide both side by two
30/2=2 x h/2
Solve:
15= h
6 0
3 years ago
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