Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2

Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + x2 − x − 1
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 6x − 12

To simplify negative 5 minus the square root of negative 44, you need to use imaginary numbers. The expression simplifies to -5 minus 2i√11. Hence, the correct answer is Option B.

To simplify
negative 5 minus the square root of negative 44, we need to work with imaginary numbers. Recall that the square root of -1 is defined as i, which is the imaginary unit. Using this, we can simplify the given expression step-by-step:

Recognize that
√-44 can be written as
√(-1 × 44).

Since
√(-1 × 44) = √(-1) × √44, and
√(-1) = i, we get
i × √44.

Now, we simplify
√44:
√44 = √(4×11) = 2√11.

Therefore,
i × √44 = 2i√11.

Putting it all together,
-5 - √-44 becomes
-5 - 2i√11.

Hence, the correct answer is
Option B. negative 5 minus 2 i times the square root of 11.

The fully simplified form of the expression is [tex]-25 - 14i \sqrt{11}[/tex]

To simplify the expression [tex]-5 - \sqrt{-44} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \cdot \sqrt{11} - 5 - 2 \cdot \sqrt{11} i[/tex], we will follow these steps:

Understanding Square Roots of Negative Numbers:
The square root of a negative number can be written using the imaginary unit [tex]i[/tex], where [tex]i = \sqrt{-1}[/tex].

Thus, we can rewrite [tex]\sqrt{-44}[/tex] as follows:
[tex]\sqrt{-44} = \sqrt{-1 \cdot 44} = \sqrt{-1} \cdot \sqrt{44} = i \cdot \sqrt{44}[/tex]
Note that [tex]\sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11}[/tex].

Thus,
[tex]\sqrt{-44} = 2i \sqrt{11}[/tex]
Now substituting this into the expression gives us:
[tex]-5 - 2i \sqrt{11} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \sqrt{11} - 5 - 2\sqrt{11} i[/tex]  

Combining Like Terms:
Now combine all the real parts and the imaginary parts separately in the expression:  

Real Part:
[tex]-5 - 5 - 5 - 5 - 5 = -25[/tex]

Imaginary Part:
[tex]-2i\sqrt{11} - 4i\sqrt{11} - 4i\sqrt{11} - 2i\sqrt{11} - 2i\sqrt{11}[/tex]
Combining these gives:
[tex]-2i \sqrt{11} - 4i \sqrt{11} - 4i \sqrt{11} - 2i \sqrt{11} - 2i \sqrt{11} = -14i\sqrt{11}[/tex]

Final Result:
Combining the real and imaginary parts, we get:
[tex]-25 - 14i \sqrt{11}[/tex]

To solve the inequalities by graphing, transform each inequality into an equation form, plot the lines on the graph, and identify the overlapping region that satisfies both inequalities. The lines are 5x + 2y ≥ 3 and y ≥ x, with appropriate slopes and y-intercepts.

To solve the inequalities by graphing, we need to transform each inequality into a graphable equation form and then use the properties of the lines to find the solution set. The inequalities in question are:

Let's graph each inequality one by one:

The solution to the system of inequalities will be the region on the graph where both conditions are satisfied, typically above the lines in this case because both inequalities are greater than or equal to.

Always label your graph with f(x) and x, and select an appropriate scale for the x and y axes to ensure all important points and lines are visible on the graph.

The provided figures and instructions on slope and graphing help us understand how to plot each line based on their equations. Using the slope-intercept form, we graph the lines and identify the intersection or overlapping regions that satisfy both inequalities.

[tex]

S=14\times14+4(\frac{14}{2}\times18) \\

S=196+4(7\times18) \\

S=196+4\times126 \\

S=196+504 \\

S=\boxed{700}

[/tex]

Answer:

B. [tex]700\text{ inches}^2[/tex].

Step-by-step explanation:

We have been given an image of a pyramid. We are asked to find the total surface area of the given pyramid.

[tex]\text{Surface area of pyramid}=A+\frac{1}{2}*ps[/tex], where,

A = Area of base of pyramid.

p = Perimeter of base,

s = Slant height,

Upon substituting our given values, we will get:

[tex]\text{Surface area of pyramid}=14^2+\frac{1}{2}*4*14*18[/tex]

[tex]\text{Surface area of pyramid}=196+2*14*18[/tex]

[tex]\text{Surface area of pyramid}=196+504[/tex]

[tex]\text{Surface area of pyramid}=700[/tex]

Therefore, the total surface area of given pyramid is 700 square inches and option B is the correct choice.

Answer:D

Step-by-step explanation:

The function g(x) = x + 8 is the result of the linear parent function f(x) = x shifting 8 units to the left. The addition of a positive constant to x corresponds to a leftward shift on the graph. Hence correct option A.

The student's question pertains to the transformation of a linear parent function, which is f(x) = x, to the function g(x) = x + 8. In analyzing the transformation, we must identify what changes were made to the parent function to obtain the new function. The addition of 8 to the independent variable x in the function indicates that there should be a shift along the x-axis.

Shifting the graph of a function parallel to the x-axis is denoted by the form f(x - a). If a positive constant is subtracted from x, the graph shifts to the right. Thus, f(x - 8) would represent a shift of 8 units to the right. Conversely, adding a positive constant to x, which is the case in g(x) = x + 8, signifies a shift of 8 units left. Therefore, the correct answer is:

A. Shift: 8 units left.

Answer:

49 minutes

Step-by-step explanation:

knowing that the more people, the lower the time (divide), and the more walls, the more time (multiply)

1. find how long it takes 1 person to paint 1 wall:

63 minutes/9 walls = 7 minutes/wall with 4 people

7 minutes * 4 people = 28 minutes/wall with 1 person

2. Find for 7 people and 4 walls: 28 minutes * 7 people/4 walls = 196/4 =

49 minutes

Answer:

The correct answer is 16 minuets!

Step-by-step explanation:

You can use the formula PRT=w

(P=people) (R=rate) (T=time) (w-work)

You would start by plugging the numbers in for the given information:

(4 people)*(r)*(63min)=9walls

then solve for r

in this case r=.035714286

You can use this infromation to find what is being asked and the previously mentioned formula:

(7 people)*(.035714286)*(t) = 4 walls

Now all you have to do is solve for t to get the answer.

In this case t=16

(I also just had this question asked on an online quiz and got it correct so I know the answer is right)

Hope this helps!

120/2=60

160/4=40

60+40=100

100 boxes/1 hour=600 boxes/x

x= 6 hours

Answer:

Step-by-step explanation:

"opposite" and "opposites" are confusing when encountered in algebra and arithmetic.

In this case, the correct description of graphs of functions and their inverses follows:  the graphs are reflections of each other in the line y = x.  To call these graphs "opposites" would be misleading and incorrect.

Answer:

D

Step-by-step explanation:

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence

(BC)² = 10² + 30² → D

The equation that is needed to find the length of BC is [tex]BC^2 = 10^2 + 30^2[/tex].

The correct option is D.

To find the length of side BC in the triangle ABC, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, triangle ABC has a right angle at angle BAC.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can use this theorem to find the length of BC.

Let BC be denoted as x. According to the Pythagorean theorem, we have:

[tex]BC^2 = AB^2 + AC^2[/tex]

Substituting the given values, we get:

[tex]BC^2 = 10^2 + 30^2[/tex]

To learn more about the Pythagoras theorem;

https://brainly.com/question/343682

#SPJ2

Answer:

12%

Step-by-step explanation:

We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 4 inches. We need to determine the percent of men whose height falls between 65 and 67 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 65 and 67 inches;

This can be done in stat-crunch;

Click Stat, highlight on Calculators then click Normal

In the pop-up window that appears click Between

Enter the given values of mean and standard deviation; 70 and 4 respectively

Enter the values 65 and 67 in the next set of boxes in that order

Finally, click on compute;

Stat-Crunch returns a probability of 0.12097758. Therefore, the percent of men whose height falls between 65 and 67 inches is 12.10%. Therefore, the solution is 12%.

Answer:

A) left 6 units, up 4 units, reflection about the x-axis  

Step-by-step explanation:

The given absolute value function is

ƒ(x) = –|(x + 6)| + 4

The base function is

[tex]g(x)=|x|[/tex]

There is a transformation of the form;

[tex]-g(x+b)+c[/tex]

The base function is shifted left 6 units. (+b means left shift) and shifted up 4 units (+4 means upward vertical shift), and reflected in the x-axis , (-g(x)) means reflection in the x-axis.

The correct choice is A.

Answer:

A) left 6 units, up 4 units, reflection about the x-axis

Step-by-step explanation:

[tex]f(x) = -|x + 6| + 4[/tex]

For absolute function , the parent function is [tex]f(x)=|x|[/tex]

f(x) ---> f(x+a) , the graph will be shifted 'a' units to the left

6 is added with x so, we move graph 6 units left.

f(x) ---> f(x)+a , the graph will be shifted 'a' units up

4 is added with x. So, we move graph 4 units up

f(x) ---> -f(x) , the graph will be reflected over x-axis

we have negative sign in the front of the equation, so there will be a reflection about the x-axis

The order of transformation is

moving left 6 units, moving up by 4 units and a reflection about x-axis

Answer:

Step-by-step explanation:

The population doubles every 20 minutes, so:

x = 200 (2)^(t / 20)

Answer:

(-3, 8)

Step-by-step explanation:

We are given two equations and we have to find the solution to the given equations. We can do this by using substitution method as shown below:

[tex]2x+y=2[/tex]                                          Equation 1

[tex]x-3y=-27[/tex]                                     Equation 2

From Equation 1, we can get the value of y as:

[tex]y=2-2x[/tex]                                          Equation 3

Using this value of y in equation 2, we get:

[tex]x-3(2-2x)=-27\\\\ x-6+6x=-27\\\\ 7x=-21\\\\ x=-3[/tex]

Thus value of x is -3. Using this value in Equation 3, we get:

[tex]y=2-2(-3)\\\\ y=2+6\\\\ y=8[/tex]

Thus the solution to the given equations is (-3, 8)

First combine the roots:

[tex]\sqrt[7]{x^5}\cdot\sqrt[7]{x^5}=\sqrt[7]{x^5\cdot x^5}=\sqrt[7]{x^{10}}[/tex]

Now use the fact that [tex]\sqrt[n]{x^n}=x[/tex] (for odd [tex]n[/tex]):

[tex]\sqrt[7]{x^{10}}=\sqrt[7]{x^7\cdot x^3}=\sqrt[7]{x^7}\cdot\sqrt[7]{x^3}=x\sqrt[7]{x^3}[/tex]

Answer:

[tex]Area=121\pi ft^2[/tex] in terms of [tex]\pi[/tex].

Step-by-step explanation:

A 360 degree rotating sprinkler will water a full circular region of the lawn.

The area of this circular region is calculated using the formula:

[tex]Area=\pi r^2[/tex]

where r=11 feet is the radius of the circular region covered.

We substitute the value of the radius into the formula to get:

[tex]Area=\pi \times 11^2[/tex]

[tex]Area=121\pi ft^2[/tex] in terms of [tex]\pi[/tex].

This is approximately [tex]380.1 ft^2[/tex] to the nearest tenth

Answer:

45

Step-by-step explanation:

Two tangents drawn to a circle from an outside point form arcs and an angle, and this formula shows the relation between the angle and the two arcs.

m<EYL = (1/2)(m(arc)EVL - m(arc)EHL)      Eq. 1

The sum of the angle measures of the two arcs is the angle measure of the entire circle, 360 deg.

m(arc)EVL + m(arc)EHL = 360

m(arc)EVL = 360 - m(arc)EHL      Eq. 2

We are given this:

m<EYL = (1/3)m(arc)EHL       Eq. 3

Substitute equations 2 and 3 into equation 1.

(1/3)m(arc)EHL = (1/2)[(360 - m(arc)EHL) - m(arc)EHL]

Now we have a single unknown, m(arc)EHL, so we solve for it.

2m(arc)EHL = 3[360 - m(arc)EHL - m(arc)EHL]

2m(arc)EHL = 1080 - 6m(arc)EHL

8m(arc)EHL = 1080

m(arc)EHL = 135

Substitute the arc measure just found in Equation 3.

m<EYL = (1/3)m(arc)EHL

m<EYL = (1/3)(135)

m<EYL = 45

ANSWER

The area of the floor is 696 square feet.

EXPLANATION

It was given that, the volume inside a rectangular storage room is 2,088 cubic feet.

The rectangular room is a rectangular prism.

The volume of a rectangular prism is

[tex]V = floor \: area \times height[/tex]

The height of the room is 3 ft.

This implies that,

[tex]2088= floor \: area \times3[/tex]

Divide both sides by 3.

[tex] \frac{2088}{3} = floor \: area [/tex]

[tex]floor \: area = 696 {ft}^{2} [/tex]

The area of the floor is 696 square feet.

Answer:

They are clearly written to be able to find a clear solution, it clearly tells you what to do, and how, you just have to find out the way to be able to use the hints in a simple word problem, so it finds its way to be solved

Step-by-step explanation:

the difference between 100,000,000 and -100,000,000 is greater than a hyphen. Mathematical sentences without symbols would be as nonsensical as regular sentences without verbs: they tell you what to do

Answer:

The result [tex]6x^4-x^3-19x^2+2x+12[/tex].

is a polynomial.

Step-by-step explanation:

The first polynomial is [tex]3x^2-2x-4[/tex].

The second polynomial is [tex]2x^2+x-3[/tex]

The closure property of multiplication states that if we multiply two polynomials the result must be a polynomial.

The product of these two polynomials is :

[tex](3x^2-2x-4)(2x^2+x-3)=6x^4-x^3-19x^2+2x+12[/tex].

We can see that the result is still a polynomial.

Answer: I believe the answer is C) The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. !!!!!!!!

Answer:

Here's what I get.

Step-by-step explanation:

9. (6, -8)

The reference angle θ is in the fourth quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = 6² + (-8)² = 36 + 64 = 100

OB = √100 = 10  

[tex]\sin \theta = \dfrac{-8}{10} = -\dfrac{4}{5}\\\\\cos \theta =\dfrac{6}{10} = \dfrac{3}{5}\\\\\tan \theta = \dfrac{-8}{6} = -\dfrac{4}{3}\\\\\csc \theta = \dfrac{10}{-8} = -\dfrac{5}{4}\\\\\sec \theta = \dfrac{10}{6} = \dfrac{5}{3}\\\\\cot \theta = \dfrac{6}{-8} = -\dfrac{3}{4}[/tex]

10. cot θ = -(√3)/2

The reference angle θ is in the second quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = (-√3)² + (2)² = 3 + 4 = 7

OB = √7

[tex]\sin \theta = \dfrac{2}{\sqrt{7}} = \dfrac{2\sqrt{7}}{7}\\\\\cos \theta = \dfrac{-\sqrt{3}}{\sqrt{7}} = -\dfrac{\sqrt{21}}{7}\\\\\tan \theta = \dfrac{2}{-\sqrt{3}} = -\dfrac{2\sqrt{3}}{3}\\\\\csc \theta = \dfrac{\sqrt{7}}{2} \\\\\sec \theta = \dfrac{\sqrt{7}}{-\sqrt{3}} = -\dfrac{\sqrt{21}}{3}\\\\\cot \theta = -\dfrac{\sqrt{3}}{2}[/tex]

Answer:

(-7 , 7/2)

Step-by-step explanation:

Given in the question,

point E(-4,14)

x1 = -4

y1 = 14

point G(-8,-2)

x2 = -8

y2 = -2

Location of point F which is 3/4 of the way from E to G

which means ratio of point F from E to G is 3 : 1

a : b

3 : 1

xF = [tex]x1+\frac{a}{a+b}(x2-x1)[/tex]

yF = [tex]y1+\frac{a}{a+b}(y2-y1)[/tex]

Plug values in the equation

xF = -4 + (3)/(3+1) (-8+4)

xF = -7

yF = 14 + (3)/(3+1)(-2-14)

yf = 7/2

Answer:

(x+5)^2-20

(-5,-20)

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term to complete the square.

[tex]\sin\theta=\dfrac13>0[/tex], so

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}<0\implies\cos\theta<0[/tex]

Recall that

[tex]\cos^2\theta+\sin^2\theta=1[/tex]

for all [tex]\theta[/tex], and knowing that [tex]\cos\theta<0[/tex] we have

[tex]\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt2}3[/tex]

Answer:

Final answer is C. 28°.

Step-by-step explanation:

Given equation is [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex].

Now we need to find the missing value of [tex]\theta[/tex] using cosine formula. So let's compare the given equation [tex]15^2+17^2-2\left(15\right)\left(17\right)\cos\left(\theta \right)=8^2[/tex] with cosine formula [tex]b^2+c^2-2\left(b\right)\left(c\right)\cos\left(A\right)=a^2[/tex].

we get [tex]\theta =A[/tex]

which is basically the angle between given sides 15 and 17

Hence A=28°.

So the final answer is 28°.

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x-----> the number of snacks

we  know that

The inequality that represent this situation is

[tex]9.50+3.50x\leq 35[/tex]

Solve for x

[tex]3.50x\leq 35-9.50[/tex]

[tex]3.50x\leq 25.50[/tex]

[tex]x\leq 7.3\ snacks[/tex]

The maximum number of snacks is 7

The solution for the inequality is all real numbers less than or equal to 7.3 snacks

The solution for the problem situation is all whole positive numbers less than or equal to 7 snacks

Verify each case

case 1) 4 snacks

Is a solution to both the inequality and the problem situation

case 2) 314 snacks

Is not a solution

case 3) 912 snacks

Is not a solution

case 4) 4.25 snacks

Solution to the inequality ONLY

Answer:

solution to both: 2,4

solution to inequality ONLY: -2,4.25,3 1/4

NOT a solution: 9 1/2

Step-by-step explanation:

yw ;)

Answer:

option B and option D

0 and 2

Step-by-step explanation:

Given in the question two functions

f(x) = x² - 4x + 3

g(x) = -x² + 3

f(x) = g(x)

x² - 4x + 3 = - x² + 3

Rearrange the like terms, x terms to the left and constant term to the right.

x²+ x² - 4x = 3 - 3

2x² - 4x = 0

Divide by two

2x²/2 - 4x/2 = 0/2

x² - 2x = 0

Take x as a common term

x(x-2) = 0

so

x = 0

or

(x-2) = 0

x = 2

Answer:

0

3

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2-4x+3[/tex]

We can rewrite this function in the vertex form to obtain;

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

This is the graph of the parent function [tex]h(x)=x^2[/tex] shifted, 2 units to the right and 1 unit down.

The second function is

[tex]g(x)=-x^2+3[/tex]

This is the graph of the parent function [tex]h(x)=x^2[/tex] reflected in the x-axis and shifted up 3 units.

The graph of the two functions are shown in the attachment.

The solution to f(x)=g(x) is where the two graphs meet.

The two graphs intersected at

(0,3) and (2,-1)

Answer:Add T with e and thats your answer.

Step-by-step explanation:

Answer:

The height of the pyramid is [tex]50\ in[/tex]

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

we have

[tex]V=1,800\ in^{3}[/tex]

The area of the base B is equal to

[tex]B=\frac{1}{2}(12)(18)=108\ in^{2}[/tex]

substitute and solve for H

[tex]1,800=\frac{1}{3}(108)H[/tex]

[tex]5,400=(108)H[/tex]

[tex]H=5,400/(108)=50\ in[/tex]

Answer:

Step-by-step explanation:

You can use the same formula in each case. The area of a triangle with sides "a" and "b" separated by angle α is ...

  A = (1/2)ab·sin(α)

1. The area of the square is 4 times the area of the right triangle whose legs are radii of the square:

  square area = 4·(1/2)·(13 m)(13 m)sin(90°) = 2·(13 m)² = 338 m²

__

2. The area is ...

  A = (1/2)(8 cm)(12 cm)sin(81°) ≈ 47.4 cm²

For this one, you don't need to work out the answer in detail. You know it will be less than, but nearly, 48 cm², which is half the product of the side lengths.

Answer:

2/3 cup

Step-by-step explanation:

Add 1/6 cup and 3/6 cup, obtaining 4/6 cup of sugar, total.

4/6 reduces to 2/3.

The total amt of sugar in the recipe is 2/3 cup.

Answer:

Dave rode his bicycle 17 miles in the morning

Dave rode his bicycle 40 miles in the afternoon

Step-by-step explanation:

* Lets study the information to solve the question

- Dave rod his bicycle in the morning and again in the afternoon

- Six more than twice as many miles in the afternoon as in the morning

  means the distance in the afternoon is 6 more than twice the distance

  in the morning

- The entire trip was 57 miles means the total distance in the morning

  and in the afternoon was 75

* To solve the question let the distance in the morning is x miles

∵ The distance in the morning = x miles

∵ The distance in the afternoon is 6 more than twice the distance

  in the morning

∴ The distance in the afternoon = 2x + 6 miles

∵ The distance in entire trip = 57 miles

- The distance in the morning and the distance in the afternoon = 57 miles

∴ x + (2x + 6) = 57 ⇒ simplify

∴ 3x + 6 = 57 ⇒ subtract 6 from both sides

∴ 3x = 51 ⇒ divide both sides by 3

∴ x = 17 miles

∵ The distance in the morning is x miles

∴ Dave rode his bicycle 17 miles in the morning

∵ The distance in the afternoon = 2x + 6 miles

- Substitute the value of x

∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles

∴ Dave rode his bicycle 40 miles in the afternoon