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devlian [24]
2 years ago
6

Find the arc length shown in red. Give your answer in terms of . A 10 cm

Mathematics
1 answer:
salantis [7]2 years ago
3 0

Answer:

5π/2 cm

Step-by-step explanation:

Given,

Radius ( r ) = 10 cm

Since, the angle is 90, the length of the the arc is π r/ 4

π * 10 / 4

= 10π/4

= 5π/2

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Last time, one out of every 4 students in our class was absent. This time, after Jen came back, only one out of every 5 students
VMariaS [17]

Answer: There are 20 students and 4 students are not here today.

Step-by-step explanation:

If the number of students = 4

Let the number of students be 'x'.

Fraction of students absent = \dfrac{x}{4}

If the number of students = 5

Fraction of students absent = \dfrac{x}{5}

And Jen came back,

So, the fraction of student absent is also written as

\dfrac{x}{4}-1

According to question, it becomes,

\dfrac{x}{5}=\dfrac{x}{4}-1\\\\\dfrac{x}{5}=\dfrac{x-4}{4}\\\\4x=5(x-4)\\\\4x=5x-20\\\\4x-5x=-20\\\\-x=-20\\\\x=20

Hence, there are 20 students in our school.

And number of students are not here today is \dfrac{20}{5}=4

3 0
3 years ago
I need help fast what is 9m−​(3+7​m) simplified?
iogann1982 [59]

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

4 0
3 years ago
150 tissues to fill an area 3 ft long and 2 ft wide. they want to fill an area of 8 ft long and 7 ft wide. what is the total num
Mamont248 [21]
I'm not sure I'm not good at things :/
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3 years ago
In order to give a souvenir table tennis ball to each participant in a youth table tennis tournament, a city recreation departme
professor190 [17]
6 boxes (add the cumulatively)
each box bas 5 pkgs so 10w,5o
1st box: 10w,5o
2nd box:20w,10o
3rd box:30w,15o
4th box:40w,20o
5th box:50w,25o
6th box:60w,30o
You need a min. of 48w and 27o
8 0
3 years ago
F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,
svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

so

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

g(x)=2x^2+8x+6

Find the vertex

Factor the leading coefficient

g(x)=2(x^2+4x)+6

Complete the square

g(x)=2(x^2+4x+4)+6-8

g(x)=2(x^2+4x+4)-2

Rewrite as perfect squares

g(x)=2(x+2)^2-2

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

0=2(x+2)^2-2

2(x+2)^2=2

(x+2)^2=1\\x+2=\pm1\\x=-2\pm1

so

The roots or x-intercepts are

x=-1 and x=-3

<u><em>Verify each statement</em></u>

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true  (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

7 0
3 years ago
Read 2 more answers
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