Help help help help math

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0   ⇒   x = 2   and   x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

[tex]|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}[/tex]

Then from our previous analysis, this definition tells us that

[tex]|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}[/tex]

So, in the integral, we have

[tex]\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx[/tex]

Then

[tex]\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3[/tex]

[tex]\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43[/tex]

[tex]\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3[/tex]

and the overall integral would be

20/3 - (-4/3) + 20/3 = 44/3

Answer:

60

Step-by-step explanation:

Since the angles A, D, and G are congruent then sum of given angles is eaqual to 180 degrees

x + 20 + 2x + x  = 180 add like terms

4x + 20 = 180 subtract 20 from both sides

4x = 160 divide both sides by 4

x = 40

Angles B, E, and H are congruent so E is also  = x + 20 and x = 40 so angle E = 60

Answer: {x,y} = {-3,-4}

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 inches  = 3 ft

max height of lumber stack is 7 - 3 = 4 ft.

4 ft = 48 inches

48 inch / 1.5 inch/board = 32 boards

Answer:

49%.

Step-by-step explanation:

2205      100        220500

........... x ..........  =  ..................  = 49 (49%).

4500        1              4500

The theater filled up with 49% of seats with 6th grade students.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a middle school that took all of its 6th grade students on a field trip to see a symphony at a theater that has 4500 seats. The students filled 2205 of the seats in the theater.

Assume that the theater filled up [x]% of seats at the theater. Then, we can write -

[x]% = (2205/4500) x 100

[x]% = 0.49 x 100

[x]% = 49%

Therefore, the theater filled up with 49% of seats with 6th grade students.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

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Answer:

C (-3 + 5i) (-3 + 5i) = -16-30i

Step-by-step explanation:

EDGENUNITY

Step-by-step explanation:

the slope is the ratio of "y coordinate difference / x coordinate difference".

so, let's find 2 good points (I mean by that with integer coordinates). I see e.g.

(-1, -1) and (0, -7)

x changes by +1 (from -1 to 0).

y changes by -6 (from -1 to -7).

so, the slope is -6/1 = -6.

D is the right answer.

Answer

First one is A

Second one is B

Third one is D

Problem 1

Answer: Choice A

(30, 225); Rocket reaches max height of 225 ft after 30 seconds.

-------------------

Explanation:

Distribute the 0.25 through to get

y = 0.25(60x-x^2)

y = 15x - 0.25x^2

y = -0.25x^2 + 15x

This is in standard form y = ax^2+bx+c with a = -0.25, b = 15 and c = 0.

The first two values mentioned lead to this x coordinate of the vertex.

h = -b/(2a)

h = -15/(2*(-0.25))

h = -15/(-0.5)

h = 30

This tells us the answer is between A and C.

If you were to plug x = 30 into the original equation, you'll get y = 225. It means that after x = 30 seconds, the rocket has reached its max height of 225 feet. Therefore, the answer must be choice A.

===========================================================

Problem 2

Answer:  Choice B

(x-3)^2 = -8(y-6)

-------------------

Explanation:

vertex = base of the bulb = (3,6)

focus = top of the bulb = (3,4)

This flashlight is pointed downward, which forms a downward opening parabola.

The distance from the vertex to the focus is p = 2 units. This is known as the focal distance.

We'll plug that in along with the vertex (h,k) = (3,6) in the formula below

4p(y-k) = (x-h)^2

4*2(y-6) = (x-3)^2

8(y-6) = (x-3)^2

Unfortunately that equation above produces a parabola that opens upward. To fix things, we stick a negative out front on either side, which will reflect the parabola over the x axis to make the parabola open downward. That leads us to choice B.

===========================================================

Problem 3

Answer:  D) square

-------------------

Explanation:

We can form a point by intersecting the plane through the point where the two cones meet. The plane needs to be parallel to the base of each cone.

We can also form a line. To do so, we intersect the plane at exactly  along the edge of the cone. Make the plane tangent to the cone.

Lastly, we can form a circle by intersecting any plane parallel to the cone's base. This plane cannot pass through the meeting point of the two cones. Rather, the plane passes through one of the cones.

Those three previous paragraphs mean that we can rule out choices A,B,C. The only thing we can't form is a square. We can form straight lines, but we cannot form perpendicular lines needed to get a square. Nice work on selecting the correct answer.

Answer:

See explanation

Step-by-step explanation:

Dilation of 4

G (0, 1) G' (0, 4)

F (1, 1) F' (4, 4)

Gx'/Gx = 0 / 0 = 0

Gy' / Gy = 4 / 1 = 4

Fx' / Fx = 4 / 1 = 4

Fy' / Fy = 4 / 1 = 4

Answer:

The answer is 4

Step-by-step explanation:

(-2.4)(10) / -3(2)

-24/-6

=4

Answer:

The answer will be 4! Hope this helps

Answer:

Step-by-step explanation:

opposite angles = equal angles

so

106 = 6s - 8

114 = 6s

s = 114 : 6

s = 19°

--------------- check

106 = 6 * 19 - 8

106 = 106

the answer is good

Answer:

2/11

Reasoning, there are 36 possible (and equally likely) combinations that we can obtain from two dice. Of these 11 (1,5 2,5 3,5 4,5 5,5 6,5 5,6 5,4 5,3 5,2 5,1) would allow us to ‘know’ that “one dice (not necessarily the first) has shown a 5”. Of these 11 possibilities only two also contain a 4. So the probability is 2/11

Step-by-step explanation: have a good day

Answer:

<4 = 67 degrees

Step-by-step explanation:

Find <3

30+37+x=180

subtract 37 and 30

x = 180 - 30 - 37

x = 150 - 37

x= 113

Find <4

180 - 113

67

Answer:

The coordinates of the focus are [tex](-3,0)[/tex]

Step-by-step explanation:

Since [tex]B^2-4AC=0^2-4(1)(0)=0[/tex], the conic section is a parabola.

Convert general form into standard form by completing the square:

[tex]x^2+6x-4y+5=0[/tex]

[tex]x^2+6x+5=4y[/tex]

[tex]x^2+6x+9=4y+4[/tex]

[tex](x+3)^2=4(y+1)[/tex]

Now that the equation is in the form of [tex](x-h)^2=4p(y-k)[/tex], we can see that [tex]h=-3[/tex] and [tex]k=-1[/tex] which tells us that the vertex is at [tex](-3,-1)[/tex]. To determine the coordinates of the focus, we need to solve the equation [tex]4p=4[/tex] and plug the value of [tex]p=1[/tex] into [tex](h,k+p)[/tex] to get [tex](-3,-1+1)[/tex] which is [tex](-3,0)[/tex].

In conclusion, the coordinates of the focus for the conic section are [tex](-3,0)[/tex].

Answer:

the value of x must be 71°

Step-by-step explanation:

180° - (38° + 33°) = 109°

x = 180° - 109°

x = 71°

Answer:

x = 71

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 38 + 33 = 71

Answer: C

Step-by-step explanation: x represents the number of classes, not the cost of classes.

Answer:

the answers are <1 = 118°, <2 = 62°

Answer:

∠ 1 = 118° , ∠ 2 = 62°

Step-by-step explanation:

∠ 1 and 118° are corresponding angles and are congruent, then

∠ 1 = 118°

∠ 1 and ∠ 2 are adjacent angles on a straight line and sum to 180°

∠ 2 + 118° = 180° ( subtract 118° from both sides )

∠ 2 = 62°

Hey there!

The expression 26-(-17) can be rewritten as

26+17

Remember:

Hope it helps. Use the comment section to clarify your doubts.

Answered by

~A felicitous teen who is preparing for the New Year's Day

Good luck. :-)

Answer:

Not a solution.

Step-by-step explanation:

[tex]-6x + 6y = - 9\\\rule{150}{0.5}\\-6(\frac{1}{2}) + 6(2) = -9\\\\-3 + 12 = -9\\\\9 =-9[/tex]

The final result is a contradiction. It is not a solution to the equation, and therefore, will not be on the line.

Answer:

The 2 dollars has $1.80 more than the two dimes.

Step-by-step explanation:

2.00-0.20=1.80

Answer:

Step-by-step explanation:

Let the price is x.

With 17% discount it becomes:

The number we need is 0.83

Solution,

Assume That The Price is x

When Will Put It in Equation,

[tex] \frak{ \bigstar}{ \rm{ {We \: Will \: Get,}}}[/tex]

Hence, Required Price is “0.83”

Answer:

.....,....................

Answer:

y = 10; x = -2

Step-by-step explanation:

Because both are equal to y, you can set them equal to each other.

-9x - 8 = -6x - 2

- 6 = 3x

x = -2

y = -9(-2) - 8 = 10

Answer:

true

Step-by-step explanation:

i learned this in like 7th grade