What are the zeros of the function? f(x)=x(x−2)(x+6)

Select each correct answer.

−6​
−2
0
2
6

Answer:

The function has no undefined points nor domain constraints, therefore the Domain is (-∞ < x < ∞). Since your answers don't match the real results, the interval notation is (-∞,∞)

Step-by-step explanation:

Answer: 4/8

Step-by-step explanation:

Equation: 1/8+x=5/18

                 -1/8     -1/8

                      x=4/8

Double Check: 4/8+1/8=5/8

Answer:

x + y = z

y=5

z=10

x = z - y =10-5 =5

Step-by-step explanation:

Answer:

1. B (obtuse)

2. Obtuse

3. 20.92

Step-by-step explanation:

1.

We need to use the converse of the pythagorean theorem to solve this problem. Given that c is the longest side of a triangle, and a and b are the other two sides. The triangle is right triangle if  [tex]c^2=a^2 +b^2[/tex]

The triangle is acute triangle if  [tex]c^2 < a^2 + b^2[/tex]

The triangle is obtuse triangle if  [tex]c^2 > a^2 + b^2[/tex]

the longest side of this triangle is 47, so we check:

[tex]47^2=2209[/tex], and

[tex]34^2 + 20 ^2 =1556[/tex]

Hence, c^2 is GREATER than a^2 + b^2, so the triangle is obtuse.

2. Using the points we showed above, we can again summarize:

This triangle's c (longest side) is 5. Let's check:

5^2 = 25, and

[tex](1.2)^2 + (4.6) ^2=22.6[/tex]

Hence, c^2 is GREATER than a^2 +b^2, so the triangle is obtuse.

3.

The side opposite of the 90 degree angle is the "hypotenuse", that is x. The side opposite the 35 degree angle is "opposite" side.

The trigonometric ratio that related "opposite" side to "hypotenuse" side is SINE. So we can write:

[tex]Sin(35)=\frac{Opposite}{Hypotenuse}\\Sin(35)=\frac{12}{x}[/tex]

Now, cross multiplying and solving:

[tex]Sin(35)=\frac{12}{x}\\x*Sin(35)=12\\x=\frac{12}{Sin(35)}\\x=20.92[/tex]

The first triangle is obtuse since the square of the longest side is greater than the sum of the squares of the other sides. The second triangle is acute since the square of the longest side is less than the sum of the squares of the other sides. Both answers provided are correct.

To determine the type of triangle (acute, obtuse, or right) based on the side lengths, you can apply the Pythagorean theorem. For the triangle with side lengths of 34 in., 20 in., and 47 in., you compare the square of the largest side (472) with the sum of the squares of the other two sides (342 + 202). If the square of the largest side is greater, the triangle is obtuse. Calculating gives us 2209 (472) and 1556 (342) + 400 (202), equaling 1956, thus 2209 > 1956 and the triangle is indeed obtuse. Your answer is correct.

For the second triangle with side lengths of 1.2, 4.6, and 5, we again apply the Pythagorean theorem. If the square of the largest side (52) is equal to the sum of the squares of the other two sides (1.22 + 4.62), the triangle is right. If it’s less, the triangle is acute.

Calculating gives us 25 (52) and 1.44 (1.22) + 21.16 (4.62), equaling 22.60, thus 25 > 22.60 and the triangle is acute. Your answer is correct.

Answer:

Step-by-step explanation:

It would help you if you drew charts of what is happening. The red tank is loosing volume. It's chart is on the left.

The blue tank is gaining water (the same amount as the red is loosing)

The red graph is the red tank.

The blue graph is the blue tank.

All  you really have to understand is the the slopes (3 and - 3) and the same numerically and the rates are the same numerically. So the negative slope means loose. and the positive slope (blue) gains.

The graphs have to start somewhere. You can't make a graph like one without a starting point.

The blue container starts at 0,0. I think that's easy enough to understand. At the beginning of your experiment, the blue container is empty.

The red container starts (arbitrarily) at 3 (the y intercept).  It is just a number. It means that the red container starts with 3 gallons.

Neither graph should go into a negative region. I don't know how to make desmos not go into a negative region. Just block them out in your mind. Everything should take place in quadrant 1 bound by the +x and + y axis.

Answer: A. The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.

Step-by-step explanation: Most of the Data is on the right so it is skewed left, and most of the emails are on 11 and 12 so that is why A is correct.

Answer: 8

Step-by-step explanation:

 The triangle shown in the image attached is a right triangle.

Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:

[tex]a^2=b^2+c^2[/tex]

Where a is the hypotenuse and b and c are the legs.

The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from [tex]a^2=b^2+c^2[/tex], as following:

[tex]17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8[/tex]

Therefore, the lenght of the missing side is: 8

Answer:

The value of third side= 8 units

Step-by-step explanation:

It is given a right angled triangle with base = 15 and hypotenuse = 17

We have to find the height of given triangle.

Points to remember

By Pythagorean theorem

Base² + Height² = Hypotenuse²

To find the third side

Here base = 15 and hypotenuse = 17

We have,

Base² + Height² = Hypotenuse²

Height² = Hypotenuse² - Base² = 17² - 15² = 64

Height = √64 = 8 units

Therefore the value of third side = 8 units

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h. k) are the coordinates of the centre and r is the radius

here (h, k) = (- 1, 10) and r = 2, thus

(x - (- 1))² + (y - 10)² = 2², that is

(x + 1)² + (y - 10)² = 4 → C

Answer:

Step-by-step explanation:

If N is midpoint between Q and R, then use the formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points Q(0, 2b) and R(2c, 0). Substitute:

[tex]x=\dfrac{0+2c}{2}=\dfrac{2c}{2}=c\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b[/tex]

Trigonometry

[tex]Sin\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite}[/tex]

[tex]S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]

You know the hypotenuse and you want to find the opposite therefore you use, sine.

[tex]Opposite = Sin(70) *{20}[/tex]

Opposite = 18.79385242

Answer:

(1,0)

Step-by-step explanation:

The given logarithmic function is

[tex]y=\log_ax[/tex]

When [tex]x=1[/tex], the logarithmic function becomes;

[tex]y=\log_a1[/tex]

[tex]\Rightarrow y=\log_aa^0[/tex]

[tex]\Rightarrow y=0(\log_aa)[/tex]

[tex]\Rightarrow y=0(1)[/tex]

[tex]\Rightarrow y=0[/tex]

Therefore the graph always passes through;

[tex](1,0)[/tex]

Answer:

option D

(1,0)

Step-by-step explanation:

Given in the question an expression

y = [tex]log_{a}x[/tex]

This function's graph will always pass through x-axis where y will always be 0

 y = [tex]log_{a}x[/tex]

 0 =  [tex]log_{a}x[/tex]

This situation is only possible when x = 1

0 = [tex]log_{a}1[/tex]

Secondly, x can never be zero

As,

[tex]y = log_{a}0[/tex] is undefined

so this eliminate option (A) and (C)

y = 120 + 75x

y is total charge

75x where 75 is monthly charge and x is number of months

120 is installation charges.

Dish television charges modeled by the equation represents,

Linear equation is the equation in which the highest power of the unknown variable is one. Linear equation are used to model the real life problem in the mathematical expressions.

The linear equation with dependent variable y and independent variable x can be written as,

[tex]y=mx+c[/tex]

Here,  [tex]m[/tex] is the slope of the equation and [tex]c[/tex] is the y intercept.

Given information-

The total cost is modeled by the equation

[tex]y=120+75x[/tex]

In the above equation the, variable y is dependent variable and the variable x is independent variable. The constant term 120 is fixed.

Hence,

Learn more about the linear equation here;

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Answer:

3/32 of a cup of food

Step-by-step explanation:

Sammy's dog eats 3/4 cup of food at each meal. His cat eats 1/8 of that.

This comes out to (1/8)th of (3/4 cup), or:

 1        3

----- · ----- cup  =  3/32 cup

  8      4

The cat eats 3/32 of a cup of food.

Final answer:

Sammy's cat eats 3/32 cup of food per meal, which is calculated by multiplying the dog's portion, 3/4 cup, by 1/8.

Explanation:

Solving the question involves a basic understanding of fractional multiplication. Since Sammy's cat eats 1/8 of what the dog eats, we calculate the cat's portion by multiplying the dog's portion by 1/8.

Sammy's dog eats 3/4 cup of food at each meal. To find out what fraction of a cup Sammy's cat eats, we multiply 3/4 by 1/8.

Here's the calculation: 3/4 × 1/8 = 3/32

Therefore, Sammy's cat eats 3/32 cup of food at each meal.

Answer:

Step-by-step explanation:

#1.

228 ÷ 6 = 38 in

#2.

186 ÷ 3 = 62 ft

#3.

360 ÷ 8 = 45 yd

#4.

119 ÷ 7 = 17 ft

I hope I helped you.

Answer:

Perimeter is the total outside dimension.

To find the length of one side, divide the total perimeter by the number of sides.

1. 228 / 6 = 38 inches.

2. 186 / 3 = 62 feet.

3. 360 / 8 = 45 yards

4. 119 / 7 = 17 feet.

Answer:

-60 people

Step-by-step explanation:

The change in population was -300 people.

The change in population was -300 people/5 yr or -60 people/yr.

Answer:150

Step-by-step explanation:75 on 100 multiply by 400 u will get 300.then 50 on 100 multiply 300 .your answer is 150.check???

Answer:

150.

Step-by-step explanation:

Answer:

y = 3x^2 + 1/3

Step-by-step explanation:

The first step is the easiest. Find the value of c. That means that all you are left with is c and y because x and a disappear when x = 0.

y = ax^2 + c

Givens

Solution

1/3 = a(0)^2 + c

1/3 = 0 + c

c = 1/3

Second Given

Second Solution

82/3 = a*(-3)^2 + 1/3            Subtract 1/3 from both sides

82/3 - 1/3 = a*(9) + 1/3 - 1/3

81/3 = 9a                              Reduce the left

27 = 9a                                Divide by 9

27/9 = a

3 = a

Answer

y = 3x^2 + 1/3

Answer:

d 7(8 + 3)

Step-by-step explanation:

Answer:

  5

Step-by-step explanation:

The horizontal distance between the points is 3 units; the vertical distance is 4 units. The straight-line distance is the length of the hypotenuse of a right triangle with those side lengths. So, the distance between the two points is ...

  √(3² +4²) = √(9+16) = √25 = 5 . . . . units

_____

Comment on this triangle

The numbers 3, 4, 5 are the smallest set of integers that satisfy the relation of the Pythagorean theorem. They are also the only set of sequential numbers or numbers in arithmetic sequence that satisfy the Pythagorean theorem. As a consequence, they show up often in geometry and algebra problems. The "3-4-5 triangle" is worth remembering. So, anytime you see numbers that have these ratios, such as 9, 12, 15, for example, you know they can be the sides of a right triangle.

Answer:

Not enough info.

Step-by-step explanation:

Not enough information, how big is the fence perimeter wise? What is the shape of the fence? If the fence is square and 2,000 feet long, of course there's room. If its a square fence that's 2 feet long, there is no room at all.

The answer is 2.58

See attached picture of graph with the solution:

The approximate zeros of the function f(x)=-2x^3+5x^2+1, to the nearest tenth, are x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7.

To find the zeros of the function f(x)=−2x3+5x2+1, one uses a graphing calculator or similar piece of technology. After entering this function and graphing it, you locate the points where the curve intersects the x-axis. These points are the function's zeros or roots, as the function equals zero at these x-values.

For the function given, the zeros are approximately x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7 when rounded to the nearest tenth. These values represent the x-coordinates of the points where the graph of the function intersects the x-axis.

Please note that because we're rounding to the nearest tenth, the actual zero could slightly differ.

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Answer:

[tex]\frac{4\sqrt{3} }{3}[/tex]

Step-by-step explanation:

4sqrt3/3

The answer is 150 to this question

Answer:

(32/15, -2/5)

Step-by-step explanation:

(1) ³/₂x   -    2y =  4

(2)   x  +    ⅓y =  2

(3)  3x   -     4y =  8              Multiplied (1) by 2

(4)  3x  +       y =  6              Multiplied (2) by 3

                  5y = -2              Subtracted (3) from (4)

(5)                 y = -⅖             Divided each side by 5

       x + ⅓(-⅖) =  2              Substituted (5) into (2)

       x  -  ²/₁₅    =  2

       x              =  2 + ²/₁₅     Added ²/₁₅ to each side

      x              = 32/15

The system of equations has only one solution: (32/15, -2/5).

We can use the fact that, for [tex]|x|<1[/tex],

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

Notice that

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}[/tex]

so that

[tex]f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right][/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=1}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty(n+1)x^n[/tex]

By the ratio test, this series converges if

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right|=|x|\lim_{n\to\infty}\frac{n+2}{n+1}=|x|<1[/tex]

so the series has radius of convergence [tex]R=1[/tex].

The Maclaurin series for the function 5(1 − x)⁻² is obtained by applying the binomial series theorem, resulting in the series: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The radius of convergence for the series is 1.

The function given is f(x) = 5(1 − x)−2. The Maclaurin series of a function f is the expression of that function as an infinite sum of terms calculated from the values of its derivatives at a single point. Here, we can use the binomial theorem as a starting point. It states that (1+x)ⁿ = 1 + nx + (n(n-1)/2!)x² + ..., where n is a real number and -1

Now, f(x) is similar to the binomial series: if we let n=-2, and x become -(x-1), we have f(x) = 5(1 – x)⁻² = 5*(1 + 2(x-1) + 3*(x-1)² + 4*(x-1)³ + ...)

So the Maclaurin series for the function is: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The next step is to find the radius of convergence. The series has a radius of convergence R such that for all x in the interval -R

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Answer:

The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 4x² + 5y² = 20

∵ A = 4 , B = 0 , C = 5

∴ B² - 4 AC = (0)² - 4(4)(5) = -80

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* Now lets study T(5 , -6), that means the graph will translate

 5 units to the right and 6 units down

∴ x will be (x - 5) and y will be (y - -6) = (y + 6)

* Lets substitute the x by ( x - 5) and y by (y + 6) in the equation

∴ 4(x - 5)² + 5(y + 6)² = 20

* Use the foil method

∴ 4(x² - 10x + 25) + 5(y² + 12y + 36) = 20

* Open the brackets

∴ 4x² - 40x + 100 + 5y² + 60y + 180 = 20

* Collect the like terms

∴ 4x² + 5y² - 40x + 60y + 280 = 20

∴ 4x² + 5y² - 40x + 60y + 280 - 20 = 0

∴ 4x² + 5y² - 40x + 60y + 260 = 0

* The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0

Answer:

BBBBBB

Step-by-step explanation:

BBBBB

Answer:

The approximate height of the paint can is 8.2 in

Step-by-step explanation:

we know that

The volume of the cylinder ( can of paint) is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=231\ in^{3}[/tex]

[tex]r=3\ in[/tex]

[tex]\pi=3.14[/tex]

Substitute the values and solve for h

231=(3.14)(3)^{2} h

h=231/(3.14*9)=8.2 in

Answer is :    

      8

For IM..

Answer:

The asnwers for your two question problem are

1. $625

2. 90 building blocks

Step-by-step explanation:

First problem

The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost?

* The fabric has 100 pieces

* Each piece costs $6.25

Total amount for the fabric  = $6.25*100 = $625

Second problem

A student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold?

* 6  layers of blocks fit in the box

* Each layer has 15 blocks

Total amount of blocks = 6*15 blocks  = 90 blocks

[tex]f(x)=\ln(x^2+2x+4)\implies f'(x)=\dfrac{2x+2}{x^2+2x+4}[/tex]

The numerator determines where the derivative vanishes (the denominator has a minimum value of 3, since [tex]x^2+2x+4=(x+1)^2+3\ge3[/tex]).

[tex]2x+2=0\implies x=-1[/tex]

At this critical point, we have

[tex]f(-1)=\ln((-1)^2+2(-1)+4)=\ln3\approx1.099[/tex]

At the endpoints, we have

[tex]f(-2)=\ln4\approx1.386[/tex]

[tex]f(2)=\ln12\approx2.485[/tex]

so [tex]f[/tex] attains a maximum value of [tex]\ln12[/tex] and a minimum value of [tex]\ln3[/tex].

The absolute minimum of the function f(x) = ln(x2 + 2x + 4) is at x=-2 where the value is ln(4) and the absolute maximum is at x=2 where the value is ln(8). There are no critical numbers within the selected interval.

The given function is

f(x) = ln(x

2

+ 2x + 4)

, for which we need to find the absolute maximum and minimum in the interval [-2, 2]. Firstly, we find the derivative of the function:

f '(x) = (2x + 2) / (x

2

+ 2x + 4)

. To find the critical points, we set the derivative equal to zero and solve for x, finding no real solutions, indicating there are no critical numbers within the given interval. Thus, the extrema must occur at the endpoints. So, we find f(-2) = ln(4) and f(2) = ln(8).

The absolute minimum is ln(4) at x = -2 and the absolute maximum is ln(8) at x = 2

.

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