determine the total number of roots of each polynomial function. f (x) = 3x6 + 2x5 + x4 - 2x3 f (x) = (3x4 + 1)2

Answer:

C 3x + 9.99 = 32.88

Step-by-step explanation:

The number of small boxes purchased = 4

and the number of large boxes purchased = 9

According to the given question, a contractor needs to buy nails to build a house.

The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought a total of 13 boxes that have 3350 nails altogether.

Let x be the number of small boxes and y be the number of large boxes.

The contractor bought a total of 13 boxes that have 3350 nails altogether.

x + y = 13                     ...............(1)

50x + 350y = 3350              ..........(2)

We solve above system of equations.

From equation (1),

x = 13 - y             ...........(3)

Substitute x = 13- y in equation (2)

50(13 - y) + 350y = 3350    

650 - 50y + 350y = 3350

300y = 2700

y = 9

Substitute above value of y in equation (3),

x = 13 - 9

x = 4

Therefore, the number of small boxes purchased = 4

and the number of large boxes purchased = 9

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Important notice:

/\2 = Power 2

Answer:

D. 1,047.2

Step-by-step explanation:

The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.

The silo is made up of a cylinder with the height of 10 feet and base radius of 5 feet and two cones, each having the height of 5 feet and base radius of 5 feet.

The formulas volume of cylinder πr /\2 h and volume of cone 1/3  πr/\2h can be used to determine the tatol volume of the silo.

Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is:

V = π(5)/\2 (10) + (2) ( 1/3) π(5) /\2 (5)

= ( 4/3 ) (250)π

= 1,047.2 cubic feet.

Answer:

a. -5 > 2 (This is false because -5 is not greater than 2.)

b. 3 > -8 (This is true because a positive is greater than a negative.)

c. -12 > -15 (This is true because -12 is closer to 0 than -15 on the number line.)

d. -12.5 > 12 (This is false because -12.5 is further away from 0 than -12.)

Answer:

Which word best completes the sentence?

Select the word from the drop-down menu.

Everybody enjoys  

Choose...

company.

Step-by-step explanation:

The curve will get shifted left side by four units. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = g(x)

If the g(x) is replaced with g(x + 4). Then the curve will get shifted left side by four units.

Thus, the correct option is A.

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Answer:

Scale factor is 2/5 or 0.4

Step-by-step explanation:

Divide radius of smaller circle (2) by radius of large circle (5)

Answer:

Scale factor is 2/5

Step-by-step explanation:

10 : 11 It is already in its simplest form

The area of the shaded region is 5π  

The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:

where θ is the central angle (in degrees) of the sector, r is the radius.  

Here we have

The length of arc FG = 5/3 π  and measure of ∠FEG = 50°

As we know Arc Length = θ × (π/180) × r  

=> Length of arc FG = 50 × (π/180) × r

From the given data,

=> 50 × (π/180) × r = 5π/3

=> 5 × (1/18) × r = 5/3

=>  (1/6) × r = 1

=> r = 6 units  

Hence, the radius of the circle is 6 units

By using the formula,

Area of a Sector of Circle = (θ/360°) × πr²

Area of shaded region = (50/360) × π(6)²  

= (5/36) × π(36)

= (5/36) × π(36)

= 5π  

The area of the shaded region is 5π  

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Answer:

equation;

\((x + 4) {}^{2} + (y - 2) {}^{2} = 27\)

Center (-4,2)

Radius is

\(3 \sqrt{3} \)

Step-by-step explanation:

Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of

\((x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} \)

Where (h,k) is center

r is the radius

So first we group like Terms together

\( {x}^{2} + 8x + {y}^{2} - 4y - 7 = 0\)

Add 7 to both sides

\( {x}^{2} + 8x + {y}^{2} - 4y = 7\)

\(( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7\)

Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem

\( (\frac{8}{2} ) {}^{2} = 16\)

and

\(( - \frac{4}{2} ) {}^{2} = 4\)

so we have

\( {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4\)

\( {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27\)

\((x + 4) {}^{2} + (y - 2) {}^{2} = 27\)

To find our center, h is -4 and k is 2

so the center is (-4,2)

The radius is

\( \sqrt{27} = 3 \sqrt{3} \)

So the radius is 3 times sqr root of 3.

Let us suppose that the farmer buys x cows, y pigs and z sheep. The total cost of cows, pigs, and sheep bought by the farmer is

10x + 3y + 0.5z.

The total number of cows, pigs, and sheep bought by the farmer is

x + y + z.

Given that the farmer spent exactly 100 and bought exactly 100 animals, we can write two equations as follows.

:\($10x + $3y + $0.5z = $100 ---(1)x + y + z = 100 ---(2).\)

Multiplying equation (2) by 10 on both sides, we get

:10x + 10y + 10z = 1000

Subtracting this equation from equation (1), we get

:7y + 9.5z = 500

The LHS of the equation

7y + 9.5z = 500

is an odd number. This means that either y or z has to be odd and the other even. If y is even, then z has to be odd and vice versa. However, both

3y and 0.5z

are integers.

The solutions are:

x =

52,

y = 8,

z = 40 ---(Option A)

or = 48,

y = 16,

z = 36

x = 44,

y = 24,

z = 32x

= 40,

y = 32

z = 28

The farmer buys 52 cows, 8 pigs, and 40 sheep.

Hence,

the answer is 52 cows, 8 pigs, and 40 sheep.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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| x

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|

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

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|

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B

|

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

work is shown and pictured

Answer: 1.11

Step-by-step explanation:

To find the range of the data set all you have to do is subtract the higher number with the lowest number, so in this math problem, we will take 1.75- 0.64 and we get 1.11 :]

(a) The dimensions of matrix A are 0x0.

(b) If the system has no solutions, the possible values are infinite.

The dimensions of matrix A being 0x0 indicates that there are no rows or columns in the matrix. In the context of a linear system of equations, this means that there are no equations or variables present in the system.

A standard augmented matrix for a linear system would typically have dimensions of mx(n+1), where m represents the number of equations and n represents the number of variables. However, with 0 rows and 0 columns, matrix A in this case is empty.

If the system represented by matrix A has no solutions, it implies that the equations in the system are inconsistent or contradictory. In such a scenario, there are no values for the variables that simultaneously satisfy all the equations. This results in an empty solution set.

When a linear system has no solutions, the possible values for the variables are infinite. Since there is no solution that satisfies all the equations, any value assigned to the variables would not satisfy the system as a whole. Therefore, the system is considered inconsistent, and the variables can take on any value.

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An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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1/36 (2.778%)

there is your answer

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The volume of the solid S is 162 pi.

Suppose that a solid is arranged along the x - axis from x = a to x = b and that the cross-sections perpendicular to the x-axis have area A(x). The volume of the solid is then \(\int\limits^b_a A{(x)} \, dx\).

If the region is arranged along the y-axis from y = c to y = d and the cross-sections perpendicular to the y-axis are A(y), then the volume is \(\int\limits^d_c A{(y)} \, dx\)

The region bounded by \(y = 9 - x^2\) and the x-axis can be described by

\(D={(x,y)|-\sqrt{9-y}\leq x\leq \sqrt{9-y},0\leq y\leq 9}.\)

Suppose that the cross-sections perpendicular to the y-axis are squares, they have side length

\(s =\sqrt{9-y}-(-\sqrt{9-y} )=2\sqrt{9-y}\)

The area of the cross-sections are then

\(A(y)=(2\sqrt{9-y} )^2=4(9-y)=36-4y\)

Therefore, the volume of the solid is

\(Volume = \int\limits^9_0 A{(y)} \, dy\\\)

             \(=\int\limits^9_0 {36-4y} \, dy\)

             \(=36y-2y^2|^9_0\)

             \(=36(9)-2(9)^2-(0-0)\)

             = 162

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Hello!

3 ≤ x - 2

3 + 2 ≤ x

5 ≤ x

x ≥ 5

x ∈ [5 ; +∞)

so the correct number line is E.

Answer:

?

Answer · 0 votes

To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how. Let's try it with the fractions 23 and 312 12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also. Now you have the following: 812 and 312 These fractions now have common denominators! Now they're all set for adding or subtracting fractions. Try another: 26 and 35: The least common multiple of 6 and 5 is 30. (the product of the denominators) Transform each fraction by multiplying by "1": 26⋅55 = 1030 and 35⋅66 = 1830 One last problem: 49 and 76 What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the L…

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Question

1.What’s the least common multiple (LCM) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.What’s the least common denominator (LCD) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.Insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 _____ 1/2 b. 13/15 _____ 7/10 c. 3/5 _____ 5/9 d. 3/8 _____ 10/16 4.On a hot summer day, John drank 5⁄11 of a quart of iced tea; Gary drank 7⁄10 of a quart; and Carter drank 3⁄5 of a quart. Which man was the most thirsty? 5.What’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9 6.Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365 7.What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? 8.In each pair, tell if the fractions are equal by using cross multiplication. a. 5⁄30 and 1⁄6 b. 4⁄12 and 21⁄60 c. 17⁄34 and 41⁄82 d. 6⁄9 and 25⁄36 9.This year, a baseball player made 92 hits out of 564 times at bat. Another player made 84 hits out of 634 times at bat. Did the two players have the same batting average? 10.On a test with 80 questions, Bob got 60 correct. On another test with 100 questions, he got 75 correct. Did Bob get the same score on both tests? 11.Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6 12.This handy application of LCMs is used by astronomers. All the planets in our solar system revolve around the sun. The planets occasionally line up together in their journeys, as shown in the illustration. The chart shows the time it takes each planet to make one trip around the sun. Now, imagine that the planets Earth, Mars, Jupiter, Saturn, Uranus, and Neptune aligned last night. How many years will pass before this happens again? (Hint—Find the LCM of the planets’ revolution times.) Solar System Planet Revolution Time Earth 1 year Mars 2 years Jupiter 12 years Saturn 30 years Uranus 84 years Neptune 165 years

Answer · 15 votes

1. a. 30b. 44c. 36d. 402. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's a. 24b. 20c. 4d. 53.a. =b. not =c. not =d. not =4. Gary5. a. 5/6b. 5/12c. 19/45d. 13/14e. 7/11f. 1/26.a. 2/3b. 8/9c. 3/10d. 9/11e. 3/4f. 1/57.a. 36/40b. c. 8.a. yesb. noc. nod. no9. no10. yes11. a. 40b. 48c. 77d. 4812. 4,620

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Wyzant

Question

what is the common denominator for 3/4 and 2/5

Answer · 0 votes

Hi Elikem! To find the common denominator. First check to see if one of the numbers is divisible by the other. In this case 4 is not divisible by 5 and 5 is not divisible by 4. So the next step is to find the common multiple. You do this by writing out the multiples of each. 4 8 12 16 20 24 28 5 10 15 20 25 When you find a common multiple, in this case 20, you have found the common denominator. Hope this helps!I am available for online tutoring for $35 per hour sessions.

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Brainly.ph

Question

What is the least common denominator of 2/6 and 5/12​

Answer · 3 votes

Answer:12Step-by-step explanation:Rewriting input as fractions if necessary: 2/6, 5/12 For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12. Calculations to rewrite the original inputs as equivalent fractions with the LCD:2/6 = 2/6 × 2/2 = 4/125/12 = 5/12 × 1/1 = 5/12

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People also ask

What is the LCM of 4/6 and 9?

What is the common denominator of 4 and 9?

What is the LCD of 4 and 6?

What is the lowest common denominator of 4 and 9?

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

snsnnsnsnnsnnnsn s s

You have the following operation:

958 ÷ 10

To determine what is the missing number, calculate the given division:

95

10 | 958

- 90

58

-50

8

as you can notice, the missing number is 58 in the given procedure of the division 958 ÷ 10.

Hence, the asnwer is C. 58

Answer:

The speed of the boat is approximately 0.704 m/s

Step-by-step explanation:

The time it takes the man in the boat to change the angle of elevation from 60° to 45°, t = 2 minutes = 120 seconds

The height of the light house = 200 m

Given that the angle of elevation is reducing, the direction of the man is away from the lighthouse

The initial distance of the man in the boat from the lighthouse = 200 m/(tan(60°)) = (200/√3) m

The final distance of the man in the boat from the lighthouse = 200 m/(tan(45°)) = 200 m

The distance traveled in 2 minutes, d = 200 m - (200/√3) m ≈ 84.53 m

The speed of the boat, v = d/t

∴ v = 84.53 m/(2 min × 60 s/min) ≈ 0.704 m/s

The speed of the boat, v ≈ 0.704 m/s.

Answer:

0.56%

Step-by-step explanation:

Percentage error

\( = \frac{2500 - 2486}{2500} \times 100 \\ \\ = \frac{1400}{2500} \\ \\ = 0.56\%\)

The crowd at a sporting event is estimated to be 2,500 people, the exact attendance is 2,486 people, the percentage error is, 0.56%

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

The crowd estimated to be 2,500 people

The exact attendance is 2,486 people

Percentage error = ?

Percentage error = (estimated value- exact value)/estimated value×100

Percentage error =   (2,500 - 2,486) /2500×100

                             =  0.56%

So, the percentage error is 0.56%

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Answer:

A C E

Step-by-step explanation:

The coordinates for the given point are:

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given:

According to the graph the normal coordinate is (-3, 2).

Now, according to the complex number the coordinates are (√13, 146.3) and (√13, -33.7)

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Answer:

6 units

Step-by-step explanation:

The claim that "a context level data flow diagram includes many detailed processes representing the computer programmes within the system" is false.

A context level data flow diagram (DFD) is a particular kind of diagram that shows how various system components interact with one another. The main objective of building a DFD is to visually depict the data flow and system activities.

The highest-level diagram that shows the system's overall operation without going into specifics about particular processes or data stores is a context level DFD, also referred to as a Level 0 DFD.

The statement that "a context level data flow diagram includes many detailed processes representing the computer programmes within the system" is untrue. This is so because the context level DFD reflects the total functionality of the system.

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Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

I can help you with that problem i just did that on my own.