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3 years ago

4 out of every 5 students made it to class on Monday. If there are 7500 students enrolled how many made it to class?

Mathematics

1 answer:

astraxan [27]3 years ago

4 0

Answer:

6000

Step-by-step explanation:

7500x4/5=6000

7500/5=1500

1500x4=6000

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Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

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2 years ago

Read 2 more answers

How many different 5-letter codes can you make from the letters in the word "company"?

____ [38]

Answer:

any, camp,man,and,pan

8 0

3 years ago

Read 2 more answers

ANYONE SOMEONE PLEASE

ladessa [460]

Answer:

I'm fairly positive the answer is 90 degrees.

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4 years ago

Use the Law of Sines to solve each triangle with the given measures. Round answers to the nearest tenths. A = 38°, a = 41 in, b

julia-pushkina [17]

Use the Law of Sines and set up the equation sin A/side a = sin B/side b. So you have sin 38/41 = sin B/54. Cross-multiply to get 54 sin 38 = 41 sin B. Make sure your calculator is in degree mode and the left side comes out to be 33.246. Now divide both sides by 41 to get an equation of .8109=sin B. Use the inverse sin function on your calculator to get that sin^-1(.8109) = 54.18 degrees

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3 years ago

What are the values of x and y ? Log(3)x-log(3)3=log(3)y

Step2247 [10]

Answer:

Step-by-step explanation:

$log_{3} x-log_{3}3=log_{3}y\\log_{3}(\frac{x}{3})=log_{3}y\\\frac{x}{3}=y\\x=3y\\y\geq 0,x \geq 0$

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4 years ago

4 out of every 5 students made it to class on Monday. If there are 7500 students enrolled how many made it to class?​

4 out of every 5 students made it to class on Monday. If there are 7500 students enrolled how many made it to class?