What is the equation of the line?

Answer:

[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]

Step-by-step explanation:

To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3[tex]\pi[/tex]/2]

Proof -

We know that,

Average value of f in the interval [a, b] is -

[tex]f_{ave}[/tex] = [tex]\frac{1}{b - a}\int\limits^b_a {f(x)} \, dx[/tex]

Now,

Here a = 0, b = [tex]\frac{3\pi }{2}[/tex], f(x) = [tex]5sec^{2}(\frac{x}{6} )[/tex]

Now,

[tex]f_{ave}[/tex] = [tex]\frac{1}{\frac{3\pi }{2} - 0}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]

      = [tex]{\frac{2 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]

      = [tex]{\frac{10 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {sec^2 ({\frac{x}{6} }) } \, dx[/tex]

      = [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ][/tex]

      = [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ][/tex]

      = [tex]{\frac{10 }{3\pi }}[ {1 - 0 } ][/tex]

      = [tex]{\frac{10 }{3\pi }[/tex]

⇒[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]

Answer:

Step-by-step explanation:

Answer:

square root of (2+10)²+(-5+3)²

square root of 144+4

square root of 148

Answer:

Step-by-step explanation:

Answer:

H 5 ft L 18 ft

Step-by-step explanation:

hight is 5 feet high legnth is 18 feet wide

Answer:

youbhave give me more information.

Answer:

incomplete question

please write the whole question or diagram of the question

Answer:

f(x) is translated 1 units left to give g(x)

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex]

[tex]g(x) = (x - 1)^2[/tex]

Required

How does f(x) transform to g(x)

[tex]f(x) = x^2[/tex]

When translated by b units left, it gives:

[tex]g(x) = f(x - b)[/tex]

In this case:

[tex]b = 1[/tex]

So:

[tex]g(x) = f(x - 1)[/tex]

If [tex]f(x) = x^2[/tex], then

[tex]f(x - 1) = (x - 1)^2[/tex]

Hence:

[tex]g(x) = (x - 1)^2[/tex]

This implies that; f(x) is translated 1 units left to give g(x)

Answer:

The answer for question 3 is D, number 4 is C

Answer:

Yeah me too buddy :(

Step-by-step explanation:

Answer:

JKM is not a right triangle because KL + LM ≠ 15.3.

Step-by-step explanation:

Given

[tex]JK = 13[/tex]

[tex]JL = 5[/tex]

[tex]JM = 8[/tex]

Required

Determine if JKM is right-angles or not

Calculate length KL using Pythagoras theorem.

[tex]JK^2 = JL^2 + KL^2[/tex]

[tex]13^2 = 5^2 + KL^2[/tex]

Collect like terms

[tex]KL^2 = 13^2 - 5^2[/tex]

[tex]KL^2 = 144[/tex]

[tex]KL = 12[/tex]

Calculate length LM using Pythagoras theorem.

[tex]JM^2 = JL^2 + LM^2[/tex]

[tex]8^2 = 5^2 + LM^2[/tex]

Collect like terms

[tex]LM^2 = 8^2 - 5^2[/tex]

[tex]LM^2 = 39[/tex]

[tex]LM = \sqrt{39[/tex]

[tex]LM = 6.2[/tex]

[tex]KM = KL + LM[/tex]

[tex]KM = 12 + 6.2[/tex]

[tex]KM = 18.2[/tex]

If JKM is right-angled, then:

[tex]KM^2 = JK^2 + JM^2[/tex]

[tex]KM^2 = 13^2 + 8^2[/tex]

[tex]KM^2 = 233[/tex]

[tex]KM = \sqrt{233[/tex]

[tex]KM = 15.3[/tex]

[tex]15.3 \ne 18.2[/tex]

i.e

[tex]KL + LM \ne 15.3[/tex]

Hence: JKM is not right-angled

Answer:

C-JKM is not a right triangle because KL + LM ≠ 15.3

Step-by-step explanation:

if right mark as brainliest

Answer:

13 hours

Step-by-step explanation:

Since Shawn mows lawns at a rate of 5 dollars an hour, if he mows for t hours, he earns 5t dollars. Also, he gets 10 dollars weekly allowance from his parents. Thus, the total amount he earns per week is thus 10 + 5t.

Since he needs to earn enough to buy 75 dollars pair of basketball shoes, the amount he earns must equal the price of the shoes. So,

10 + 5t = 75

We now solve for t to find the amount of hours  if takes him to earn enough to buy the shoes.

So,

10 + 5t = 75

Subtracting 10 from both sides, we have

10 - 10 + 5t = 75 - 10

5t = 65

dividing both sides by 5, we have

t = 65/5

t = 13 hours

So, it takes Shawn 13 hours to earn enough to buy the shoes.

Answer: 88

The unknown angle in the left triangle is 80 since the sum of the angles in a triangle is 180.(180-60-40=80)

The unknown angle (the one that doesn't have a "?") is 36 since there's a straight angle which equals 180.(180-80-64)

Therefore the angle with the "?" is 88 since the sum of the angles in a triangle are 180(180-36-56)

Hope this helps!

The list that represents the simulation is (d) 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153

The list is given as:

860583 785814 010122 337198 621549 034076 796495 978078 433330 333153

To illustrate the simulation of four free throws, then each number on the list must have 4 digits

So, we have:

8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153

Hence, the list that represents the simulation of four free throws is (d)

Read more about random numbers at:

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Answer:

y ≠ 9, y ≠ 3

Step-by-step explanation:

y² -12y +27 = (y - 9) (y - 3)

Denominator ≠ 0

y ≠ 9 or y ≠ 3

Answer:

circle

Step-by-step explanation:

Answer:

9.8 in²

Step-by-step explanation:

If A, B and C are the angles of a triangle and a, b, c are the repective sides opposite the angles, then the area of the triangle is given as:

Area = (1/2)absin(C)

In ΔQRS, the area is:

Area = (1/2)rqsin(S)

∠S + ∠Q + ∠R = 180° (sum of angles in a triangle)

∠S + 40 + 101 = 180

∠S = 39°

Using sine rule to find q:

[tex]\frac{q}{sinQ} =\frac{r}{sinR} \\\\\frac{q}{sin40}=\frac{6.9}{sin101} \\\\q=\frac{6.9*sin40}{sin101} =4.52 \ inches\\\\Area\ of\ triangle \ QRS=\frac{1}{2}rqsin(S) =\frac{1}{2}*6.9*4.52*sin(39)=9.8\ in^2[/tex]

Answer:

She need to wash 9 cars

Step-by-step explanation:

Answer:

Hey Mate!

tis is ur answrr!

Answer:

8

Step-by-step explanation: 6.20-4.20=2.00 2.00 divide by 25 for each mile = 8

Answer:

Yes

Step-by-step explanation:

Since 3 is less than 4, it would work in the inequality. It would look like this: 3 [tex]\leq[/tex] 4, which is true.

Answer:

see explanation

Step-by-step explanation:

The volume (V) of the cuboid is calculated as

V = (2x + 5)(3 - x)(x + 1)

   = (3 - x)(2x + 5)(x + 1) ← expand the pair of factors using FOIL

    = (3 - x)(2x² + 7x + 5)

    = 3(2x² + 7x + 5) - x(2x² + 7x + 5) ← distribute parenthesis

    = 6x² + 21x + 15 - 2x³ -7x² - 5x ← collect like terms and rearrange

    = 15 + 16x - x² - 2x³

The volume of the cuboid is 15 + 16x - x² - 2x³

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The volume (V) of the cuboid is calculated as

Volume of cuboid is length times width times height.

V = (2x + 5)(3 - x)(x + 1)

= (3 - x)(2x + 5)(x + 1)

Expand the pair of factors using FOIL

= (3 - x)(2x² + 7x + 5)

= 3(2x² + 7x + 5) - x(2x² + 7x + 5) ←

Distribute parenthesis

= 6x² + 21x + 15 - 2x³ -7x² - 5x

Combine like terms and rearrange

= 15 + 16x - x² - 2x³

Hence, the volume of the cuboid is 15 + 16x - x² - 2x³

To learn more on Three dimensional figure click:

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Answer:

#8

#9

Answer:

y = -5x - 23

Step-by-step explanation:

Write it in point - slope form:

y - 7 = -5(x + 6)

rearrange:

y - 7 = -5x - 30

y = -5x - 23

Answer:

d

Step-by-step explanation:

Option (b) 1.00

Step-by-step explanation:

3.4×1.00 = 3.4

Answer:

1.00

Step-by-step explanation:

1.00 equals one therefore the actual equation is 3.4x 1 = 3.4

Or 3.4x1.00=3.4

Hope this helps.

Answer:

4x + 18

Step-by-step explanation:

This is called a composite function, meaning passing the range of one function as a domain of another function.

For f(f(x)), the inner-function's range is passed as the domain of the outer function.

We can do so by substitution,

The range of f(x) can be written as 2x + 6 for any defined x values,

So we will substitute 2x  + 6 as the 'x' of another function which is in this case

f(x) again, so it looks like this 2(2x+6) + 6 which can be simplified into

4x + 18

Answer:

Step-by-step explanation:

This probability will be the area of the square divided by the area of the circle.

[tex]P=\frac{(4\sqrt{2})^2}{\pi 4^2}\\ \\ P=\frac{32}{16\pi}\\ \\ P=\frac{2}{\pi }\\ \\ \text{As a percentage}\\ \\ P=\frac{200}{\pi}\\ \\ P\approx 63.7\% [/tex]

Answer

62

Step-by-step explanation: