What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?

Answer:

[tex]y=6\sqrt{3}[/tex].

Step-by-step explanation:

It is given that,

Hypotenuse : AB=6 units.

Perpendicular : BC=y units.

[tex]\angle BAC=30^{\circ}[/tex]

We know that, in a right angle triangle,

[tex]\tan \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In triangle ABC,

[tex]\tan A=\dfrac{BC}{AB}[/tex]

[tex]\tan (60^\circ)=\dfrac{y}{6}[/tex]

[tex]\sqrt{3}=\dfrac{y}{6}[/tex]     [tex][\because \tan (60^\circ)=\sqrt{3}][/tex]

Multiply both sides by 6.

[tex]6\sqrt{3}=y[/tex]

Therefore, [tex]y=6\sqrt{3}[/tex].

Answer:

3

Step-by-step explanation:

you can solve this 2 different ways:

You can use the sine ratio or, since the triangle is a 30 60 90,you can solve it that way.

1:

sine 30 = opposite/hypotenuse

sin 30 = y/6

(sin 30)6 = (y/6)6

sin 30 (6) = y

y = 0.5 (6)

y = 3

2:

Since triangle ABC is a 30 60 90 triangle, the hypotenuse will always be 2 times the shorter leg:

hypotenuse = 2(shorter leg)

6 = 2y

6/2 = 2y/2

3 = y

y = 3

Answer:

Step-by-step explanation:

x=✓64*36=✓8^2*6^2

x=8*6

x=48

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

the amount of fuel consumed every 100 kilometers is 62.5 litres.

Step-by-step explanation:

To determine the amount of fuel consumed every 100 kilometers.

Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.

From the graph, the amount of fuel consumed for the first 100 kilometers is;

[tex]F = F_0 - F_{100} .........................1[/tex]

[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]

substituting into equation 1.

[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]

Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.

Answer:500

Step-by-step explanation:got it on Kahn

Answer:

Reflect the points across the y-axis and then translate them 7 units down.

Step-by-step explanation:

Let's look at Points A and A''. We notice that to transform A into A'', we need to reflect the point across the y-axis and then translate it down 7 units. We know this because 3 and -3 are opposite numbers are 8 - 7 = 1.

Answer:

D

Step-by-step explanation:

The points The points

A (3, 8),

B (6, 8),

C (6, 3),

D (5, 3)

need to be transformed to points

A'' (–3, 1),

B'' (–6, 1),

C'' (–6, –4),

D'' (–5, –4).

What transformations are made to make Building 4?

Answer:

The probability that the weight of a candy randomly selected is more than 0.8537 is 0.7486

Step-by-step explanation:

The given parameters are;

The mean candle weight = 0.8552 g

The standard deviation = 0.0519 g

The number in the sample, n = 442 candles

By central limit theorem, the sample standard deviation, [tex]\sigma _{\bar x}[/tex] is given by the relationship;

[tex]\sigma _{\bar x} = \dfrac{\sigma}{\sqrt{n} } = \dfrac{0.0519}{\sqrt{442} } = 0.002469[/tex]

The probability is given by the relation;

[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-\mu }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-\mu }{\dfrac{\sigma }{\sqrt{n}}} \right )[/tex]

[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-0.8552 }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-0.8552 }{\dfrac{0.0519 }{\sqrt{442}}} \right )[/tex]

[tex]P\left (\bar{X}>0.8537 \right )= P\left (z>-0.6076\right )[/tex]

The from the z-score table we have = 0.2514

The probability of P (z > -6076) = 1 - 0.2514 =  0.7486

The probability that the weight of a candy randomly selected is more than 0.8537 = 0.7486.

Drop a perpendicular from [tex]\overline{AK}[/tex] to $\overline {DE}$.

Let $l(AK)=h$ and $l(AB)=l(DC)=L$

$h$ is the height of the parallelogram and the triangle.

$L$ is the length of the base of the triangle and one of the sides of parallelogram.

We have area of parallelogram $=A_{para}=hL$

And the area of triangle is:

$A_{tria}=\frac{1}{2} h\times (L+L)=hL$

Thus we can see that they are equal.

Answer:

See below

Step-by-step explanation:

Given:

ABCD is a parallelogram

DC = CE

To Prove:

area of the ADE triangle is equal to the area of the parallelogram​.

Proof:

Let The Point between B and C be F

To prove that area of the ADE triangle is equal to the area of the parallelogram​, we'll first prove that ΔADF ≅ ΔECF

Statements                             |               Reason

DC ≅ CE                                  |                Given

But,  CD ≅ AB                         |    Opposite sides of a ║gm

So,  CE ≅ AB                           |   Transitive Property of Equality

∵  ΔABF ↔ ΔECF                    |

 CE ≅ AB                                |       Already Proved

  ∠CFE ≅ ∠ BFE                     |       Vertical Angles

  ∠ECF ≅ ∠ABF                      |      Alternate Angles

So, ΔABF ≅ ΔECF                   |    S.A.A.  Postulate

Now,                                         |

Area of ║gm = Area of            |

quad ADCF + ΔABF                |

But,    ΔABF ≅ ΔECF               |        Already Proved

So,                                            |

Area of ║gm = Area of            |

quad ABCF + ΔECF                 |

But Area of ΔADE = Area of   |

quad ABCF + ΔECF                 |

So,                                            |

Area of ║gm = Area of ΔADE |     Hence Proved

Answer:

Substitution

Step-by-step explanation:

The subtraction property of equality is when you subtract from both sides, they will still be equal. The multiplication property is the same thing but with multiplication.

Answer:

Substitution

Step-by-step explanation:

Substitution: If a = b, then either a or b may be substitued for the other in any equation (or inequality).

Multiplication: If a =b, then ca = cb.

Subtraction: If a=b and c=d, then a-c=b-d

Substitution is the closest.

Answer: draw a straight line trough point B, same thing with the second one,for the third you must draw a straight line from the angle across to the segment. (make sure all of the intersections are 90 degrees

Answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

5. cut the five fruits into 3 equal parts....

5x3=15 pieces

15/3(bowls)=5 pieces in each bowl

cut the fruits in multiples of 5 divisible by 3....that many ways possible

(similarly 4th qstion can be done)!!

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Answer:

The length of the missing segment is 36

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]

[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]

Cross Multiply

[tex]20 * (24 + x) = 24 * 50[/tex]

[tex]20 * (24 + x) = 1200[/tex]

Divide both sides by 20

[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]

[tex](24 + x)= \frac{1200}{20}[/tex]

[tex]24 + x= 60[/tex]

Subtract 24 from both sides

[tex]24 - 24 + x = 60 - 24[/tex]

[tex]x = 60 - 24[/tex]

[tex]x = 36[/tex]

Hence, the length of the missing segment is 36

Answer:

a

Step-by-step explanation:

its straight

Answer:

Hello I am from India.

Step-by-step explanation:

Can you pls chat with me

I am requesting you a lot

pls dear

Answer:

Step-by-step explanation:

x + 2x + 4x = 49

7x = 49

x = 7

2(7)= 14 hours he worked on Wednesday

Answer:

1st blank: substitution property of equality

2nd blank: linear pair theorem

3rd blank: substitution property of equality

Step-by-step explanation:

1st blank

∠EIJ ≅ ∠GJI (eq. 1)

∠EIJ ≅ ∠IKL (eq. 2)

∠GJI ≅ ∠JLK (eq. 3)

Substituting eq. 3 into eq. 1:

∠EIJ ≅ ∠JLK

and then, substituting eq. 2:

∠IKL ≅ ∠JLK

which means that m∠IKL = m∠JLK

2nd blank

The Linear Pair Theorem states that two angles that form a linear pair are supplementary

3rd blank

m∠JLK + m∠JLD = 180°

Substituting with the previous result:

m∠IKL + m∠JLD = 180°

Answer:

1st blank: substitution property of equality

2nd blank: linear pair theorem

3rd blank: substitution property of equality

Step-by-step explanation:

there u go

Answer:

15

Step-by-step explanation:

Try 1, 2, 3, or 4 blue pencils. Then green is 6 times as many. Red must be the rest to make up 20 total.

No. of blue        No. of green      No. of red

1                          6                           13

2                        12                           6

3                        18                           -1

You can't have 3 blue pencils because 3 blue + 18 green = 21 pencils, and there are only 20.

If you have 1 blue and 6 green, then there must be 13 red, but red must be less than green, and 13 is not less than 6.

The only possibility is

2 blue, 12 green, 6 red

If you start taking out pencils, when you take out the first 14 they may be all blues or green, so only when you take out the 15th pencil do you know for sure there must be 1 green pencil.

Answer:

Step-by-step explanation:

let width=x

length=3x

area=3x×x=3x²

3x²=192

x²=192/3=64

x=√64=8

width=8 m

length=3×8=24 m

Answer:

Solution,

Let the length be 3x meter.

Let the width be X meter

Area of rectangle= 192 square metres

Now,

Area of rectangles= length * breath

[tex]192 = 3x \times x \\ 192 = 3 {x}^{2} \\ {x}^{2} = \frac{192}{3} \\ x^{2} = 64 \\ x = \sqrt{64} \\ x = 8 \: meter[/tex]

Replacing value,

[tex] \: \: \: 3 \times x \\ \: \: = 3 \times 8 \\ \: \: \: \: = 24[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

y=5x-4

Step-by-step explanation:

Write in slope-intercept form.

y= mx +b

To find the slope [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Your points are (5,21) and (-5,-29)

[tex]y_2[/tex] = -29

[tex]y_1[/tex] = 21

[tex]x_2[/tex] = -5

[tex]x_1[/tex] = 5

[tex]\frac{-29-21}{-5-5}[/tex]=[tex]\frac{-50}{-10}[/tex]=5

The slope is 5.

y= 5x+b

Insert a point. Let's use (5,21)

21 = 5(5) +b

21 = 25+ b

b=-4

y=5x-4

Answer:

Step-by-step explanation:

7 + 3i / 2 - 5i would be clearer if written as (7 + 3i) / (2 - 5i).  We must remove the symbol i from the denominator, and that can be accomplished by multiplying both 7 + 3i and 2 - 5i by the conjugate 2 + 5i:

(2 + 5i)(7 + 3i)

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

     4 + 29

which simplifies to     14 + 6i + 35i - 15 over 33, or

-1 + 41i

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

    33

Answer:

i would say the answer is C) simple random sampling

Step-by-step explanation:

this is because an example of a simple random sample would be the names of 25 employees being chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen. This is similar to your question where it chooses 100 random people.

hope this helps ;)

Answer:

That's right in the end we will get only zeros.

Step-by-step explanation:

We can do a test:

-We choose two numbers for example 2 and 7; making the difference or subtraction would give a value of 5; Now when you start to make differences between two following numbers, it will give a value that will be repeated in double position, which will determine that at some point you will start to make differences in which the only value on the board is zero. .

1-2-3-4-5-6-7-8-9-10.   We subtract and replace the value obtained in two         positions.(7-2)=5;  

Now we get:

1-5-3-4-5-6-5-8-9-10;  

If we subtract 5 minus 5 we will obtain zero, and so we proceed to do the same with two following numbers, we replace the obtained value and then we make the difference between them.

Answer:

4).  (x + 2)^2 + (y - 1)^2 = 25.

Step-by-step explanation:

x^2 + y^2 + 4x - 2y - 20 = 0

x^2 + 4x + y^2 - 2y = 20

Completing the square on the x and y terms:

(x + 2)^2  - 4 + (y - 1)^2 - 1 = 20

(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1

(x + 2)^2 + (y - 1)^2 = 25.

The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

The given circle equation is x²+ y²+4x-2y-20=0.

Here, x²+ y²+4x-2y=20

By completing the square on the x and y terms:

Now, add 4 on both the sides of an equation, we get

x²+ y²+4x-2y+4=20+4

x²+4x+4+y²-2y=24

Add 1 on both the sides of an equation, we get

(x+2)²+y²-2y+1=24+1

(x+2)²+(y-1)²=25

The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.

To learn more about an equation of a circle visit:

https://brainly.com/question/23799314.

#SPJ2

Answer:

The volume of the cone is 1006.9in³

Step-by-step explanation:

Given

[tex]Height = 18.8\ in[/tex]

[tex]Diameter = 14.3\ in[/tex]

Required

Calculate the volume;

The volume of a cone is calculated as thus;

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where V represents volume; r represents radius; and h represents height

The radius is calculated as thus;

[tex]r = \frac{1}{2}Diameter[/tex]

[tex]r = \frac{1}{2} * 14.3[/tex]

[tex]r = 7.15[/tex]

Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]

[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes

[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]

[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]

[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]

[tex]V = \frac{21144.266}{21}[/tex]

[tex]V = 1006.86980952[/tex]

[tex]V = 1006.9\ in^3[/tex] (Approximated)

Hence, the approximated volume of the cone is 1006.9in³

Answer:1006.5

Step-by-step explanation:

Answer:

The correct statements are:

1: mEFD = mEGD

3: mED = mFD

5: mFD = 120°

Step-by-step explanation:

Let's analyse each statement:

1: mEFD = mEGD

Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:

[tex]60 + 90 + 90 + mECD = 360[/tex]

[tex]mECD = 120\°[/tex]

The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.

The angle EFD inscribes the arc ED, so we have:

[tex]mEFD = mED/2[/tex]

[tex]mEFD = 120/2 = 60\°[/tex]

So the angles mEFD and mEGD are equal. The statement is TRUE.

2. mEGD = mECD

This statement is FALSE, because mEGD = 60° and mECD = 120°

3. mED = mFD

If mED is 120° and mEF = mFD, we have:

[tex]mED + mEF + mFD = 360[/tex]

[tex]2*mFD = 360 - 120[/tex]

[tex]mFD = 120\°[/tex]

So the statement is TRUE, both arcs have 120°.

4. mEF = 60°

This statement is FALSE, because we calculated before that mEF = mFD = 120°

5. mFD = 120°

This statemente is TRUE, because we calculated before that mFD = 120°.

So the correct statements are 1, 3 and 5

The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Start by calculating the measure of angle ECD.

We have:

[tex]\angle ECD = 2 * \angle EGD[/tex]

So, we have:

[tex]\angle ECD = 2 * 60[/tex]

[tex]\angle ECD = 120[/tex]

The above means that:

[tex]\overset{\huge\frown}{ED} = 120[/tex]

So, the measure of angle EFD is:

[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]

[tex]\angle EFD = 0.5 * 120[/tex]

[tex]\angle EFD = 60[/tex]

From the question, we have:

[tex]\angle EGD = 60[/tex]

So, it is true that:

[tex]\angle EFD =\angle EGD[/tex]

To calculate the measure of arc FD, we have:

[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]

Lengths EF and DE are congruent.

So, we have:

[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]

[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]

So, we have:

[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]

Divide through by 2

[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]

Subtract 60 from both sides

[tex]\overset{\huge\frown}{FD} =120[/tex]

This means that:

[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true

Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Read more about cyclic theorems at:

https://brainly.com/question/26168678

Answer:

134 will be heads.

Step-by-step explanation:

200÷3 = 66.66

Round that of to the nearest whole number = 67

67 x 2 = 134

Answer:

75

Step-by-step explanation:

i took the semester exam

Answer:

To answer the question above,

If you entered your test scores correctly, then your choices are off the wall.  

The median is 87  

The mode is 89  

The mean is 85.833...  

There is not a mode of 91 !  

I hope this helps

Step-by-step explanation:

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

so applying this law here, we get as,

2X + (3X-10) = 180°

=> 5X - 10° = 180°

=> 5X = 190°

=> X = 190°/5

=> X = 38°

thus the angle X= 38°.

Answer:

$0.56/lb

Step-by-step explanation:

Given

Cost of a chicken = $2.15 per pound

26 pound of a chicken = $41.34

Required

Calculate how much saved.

The first step is to calculate the unit price of a chicken when 26 pound of chicken was bought.

Unit Price = Price ÷ Weight

Unit Price = $41.34 ÷ 26lb

Unit Price = $1.59/lb

The next step is to calculate the difference between these two prices

Difference = |$1.59/lb - $2.15/lb|

Difference = |-$0.56/lb|

Difference = $0.56/lb

The calculated difference is the amount saved per pound of chicken when I bought 26 pound of chicken.