According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 - 33x2 – 12x + 20.
Which is an actual root of f(x)?

a) -5/2
b) -2
c) 1
d) 10/3
​

Answer:

[tex]24\sqrt{5}\ yards[/tex]

Step-by-step explanation:

Let A1 be the area of one square and A2 be the area of second square

So,

A1 = s^2

where s is side of square

[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]

So side of one square is [tex]5\sqrt{5}[/tex]

To calculate the length of fence we need to find the perimeter of the square

So,

P1 = 4 * s

[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]

For second square:

[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]

The perimeter will be:

[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]

So the total fence will be: P1+P2

[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]

First divide 6 to both sides to isolate q. Since 6 is being multiplied by q, division (the opposite of multiplication) will cancel 6 out (in this case it will make 6 one) from the right side and bring it over to the left side.

18 ≥  6q

18 ÷ 6 ≥ 6q ÷ 6

3 ≥  1q

3 ≥  q

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

3 ≥ q OR q ≤ 3

aka 3 is greater then q OR q is less then 3

This means that the graph will have an colored circle and the arrow will go to the left of 3. Look at image below.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

1. Write all the equations in standard form, leaving out decimals or fractions.

2. Select the variables to be eliminated; And then you take two of these equations, and you eliminate the variables.

3. Select a different set of two equations and eliminate the same variables as in step 2.

4. Solve two equations containing two variables from steps 2 and 3.

5. Substitute the answer to step 4 into any equation that contains the remaining variables.

6. Check the solution with three original equations.

To solve a system of three equations using the elimination method, pair up the equations, eliminate a variable from each pair, solve for the remaining variable and substitute this value into other equations to find the values of other variables.

To solve a system of three equations using the elimination method, the process involves eliminating one variable at a time to eventually have one equation with one variable left, which you can then solve.

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Answer:

x=21

y= 7

Step-by-step explanation:

x+y = 28

x = 3y

Substitute the second equation into the first

3y+y = 28

4y = 28

Divide by 4

4y/4 = 28/4

y = 7

Now we need to find x

x = 3*y

x = 3*7

x = 21

The graph of k(x)=2(x-8)², a quadratic function, will be an upwards-opening parabola with a vertex at (8,0). To compare it with the graph of f(x), we need more details about f(x), which could be linear, quadratic, or a different type of function entirely. The comparison can focus on attributes like shape, orientation, position, steepness, continuity, differentiability, or periodicity.

The function k (x) = 2 (x-8)² is a quadratic function where 2 is the coefficient, and 8 is the amount that the graph is shifted to the right in the x coordinate. This graph will be a parabola that opens upwards, with a vertex at the point (8,0) due to the transformation in the x term (x-8).

To compare the graph of f(x) with the graph of k(x), we first need to understand the characteristics of f(x). For example, if f(x) is also a quadratic function, we can compare their shapes, orientations (upward or downward opening), positions (based on vertex and line of symmetry), and steepness (determined by the absolute value of the coefficient -- in this case, 2).

If f(x) is a linear function, it will be a straight line and we can compare the orientation, steepness (slope), and position (y-intercept). Or if f(x) is a different type of function entirely, the comparison will focus more generally on attributes like continuity, differentiability, periodicity, etc. Therefore, without additional details about f(x), a complete comparison isn't possible.

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Step-by-step explanation:

∠YXZ and ∠VXU are vertical angles, and therefore are congruent.

∠YXZ ≅ ∠VXU, Vertical ∠'s ≅

Next, we're given that lines YZ and UV are parallel.  That means that ∠YZV and ∠UVZ are alternate interior angles, and therefore congruent.

∠YZV ≅ ∠UVZ, If lines ||, then alternate interior ∠'s ≅

If two triangles have two pairs of congruent angles, then the third pair must also be congruent, making the two triangles similar.

△XYZ ~ △XUV, AA

Since the triangles are similar, then by definition, their sides are proportional.

XY/XU = YZ/UV, Definition of Similar Polygons

YZ || UV - Given

YXZ = VXU - Vertical triangles =

YZV = UVZ - If lines ||, alternate internal triangles =

XYZ ~ XUV - AA

XY/XU = YZ/UV - Definition of Similar Polygons

Step-by-step explanation:

If the B is the middle of the segment AC,

AC= AB+BC

AC=7+12= 19.

If I'm wrong, correct me please. I would be pleased.

Answer: A is correct, an = 5(−2)n − 1

Step-by-step explanation:

The formula for geometric sequences is an=a(r)^n-1

a is the first term, which is 5 in this case

r is the common ratio, which is -2 because (5)(-2)=-10

Answer: The number before the decimal

Step-by-step explanation:

The digit in the ones place is 9, in the given number 409.21.

The given number is 409.21

⇒ 400 + 00 + 9 + 2×(1/10) + 1×(1/100)

⇒ 4×100 + 0×10 + 9×1 + 2×(1/10) + 1×(1/100)

So, the digit in ones place is 9.

Learn more about the place value system here:

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Answer:  The overall percent loss is 28%.  

Step-by-step explanation:  Given that a stock loses 10% of its value on Monday and on Tuesday it loses 20% of the value it had at the end of the day on Monday.

We are to find the overall percent loss in value from the beginning of Monday to the end of Tuesday.

Let x represents the value of a stock at the beginning of Monday.

Then, the value of the stock at the end of Monday is given by

[tex]x-10\%\times x=x-\dfrac{10}{100}x=x-\dfrac{x}{10}=\dfrac{9}{10}x.[/tex]

So, the value of the stock at the beginning of Tuesday is [tex]\dfrac{9}{10}x.[/tex]

Therefore, the value of the stock at the end of Tuesday is given by

[tex]\dfrac{9}{10}x-20\%\times\dfrac{9}{10}x\\\\\\=\dfrac{9}{10}x-\dfrac{20}{100}\times\dfrac{9}{10}x\\\\\\=\dfrac{9}{10}-\dfrac{9}{50}x\\\\\\=\dfrac{36}{50}x\\\\\\=\dfrac{18}{25}x\\\\\\=x-\dfrac{7}{25}x\\\\\\=x-\dfrac{28}{100}x\\\\\\=x-28\%x.[/tex]

Thus, the overall percent loss is 28%.  

Answer:

x = 11.2

Step-by-step explanation:

-5x - 12y = -8  

5x + 2y = 48

you can combine all like terms from both equations together:

0x-10y=40

simplified:

-10y=40

y=-4

now you plug in the value of y into either equation:

5x+2(-4)=48

simplify

5x-8=48

add 8

5x=56

divide by 5

x=56/5=11.2

Answer:

[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]

Step-by-step explanation:

We need to find the product of: [tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex]

We have that:

[tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex] = [tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]

We can't simplify more the expression, therefore, the solution is:

[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex].

Answer:

The answer is 27 patients.

Step-by-step explanation:

There are 3 patients per floor. There are 9 floors.

3 x 9 = 27

There are 27 patients in all.

I hope this helped! :)

The slope is 0. y  = 7 makes a horizontal line, therefore there is no rise only a run.

Remember: If it creates a horizontal line the slope is zero

Hope this helped!

~Just a girl in love with Shawn Mendes

The distance of the line segment joining the points (5, 4) and (-2, 1) is found using the distance formula. Substituting the given points into the formula, we calculate the distance to be approximately 7.62 units.

The distance between two points (x1, y1) and (x2, y2) in a 2-dimensional Cartesian plane is given by the distance formula: √[(x2-x1)² + (y2-y1)²].

Substituting the given points (x1, y1) = (5, 4) and (x2, y2) = (-2, 1), we get:

Distance = √[(-2 - 5)² + (1 - 4)²] = √[( -7)² + (-3)²] = √[49 + 9] = √58 ≈ 7.62.

Therefore, the distance of the line segment joining the two points (5, 4) and (-2, 1) is approximately 7.62 units.

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Answer: B) .47

Step-by-step explanation: As all of those numbers have a decimal with no whole number, we look past the decimal. Then you realize 4 is greater than 1, 0, 1 and 0. You ignore the numbers past it and read it from left to right all the time.

The greatest value is 0.47. Then the correct option is B.

Let the number will be a, b, c, d, and e.

If the value of the arbitrary constant d has a maximum value then the greatest value will be of d.

The numbers are given below.

0.1, 0.47, 0.049, 0.192, and 0.0864.

Then the greatest value is 0.47.

Then the correct option is B.

More about the greatest value link is given below.

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Answer:

The 17th term in arithmetic sequence is 68

Step-by-step explanation:

The general formula of arithmetic sequence is:

aₙ = a₁ + (n – 1)d.

We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇

To find the term a₁₇ we should know a₁ and d. So we would find both

a₆ = a₁ +(6-1)d

101 = a₁ +(5)d

101 = a₁ +5d     eq(1)

and

a₉ = a₁ +(9-1)d    

83 = a₁ + 8d       eq(2)

Subtracting eq(2) from eq(1)

101 = a₁ +5d

83 = a₁ + 8d

-       -     -

__________

18 = -3d

=> d = 18/-3

=> d = -6

Putting value of d in eq(1)

101 = a₁ + 5d

101 = a₁ + 5(-3)

101 = a₁ -15

=> a₁ = 101+15

=> a₁ = 116

Now finding a₁₇:

aₙ = a₁ + (n – 1)d.

a₁₇ = 116 +(17-1)(-3)

a₁₇ = 116+(16)(-3)

a₁₇ = 116 - 48

a₁₇ = 68

So, the 17th term in arithmetic sequence is 68

Answer:

[tex]A=400\ people[/tex]

Step-by-step explanation:

we have

[tex]Q=600+\sqrt{A+41}[/tex]

where

Q -----> is the daily output

A -----> is the number of people

For Q=621

Find the value of A

substitute and solve for A

[tex]621=600+\sqrt{A+41}[/tex]

Subtract 600 both sides

[tex]621-600=\sqrt{A+41}[/tex]

[tex]21=\sqrt{A+41}[/tex]

squared both sides

[tex]21^{2} ={A+41}[/tex]

[tex]441={A+41}[/tex]

Subtract 41 both sides

[tex]441-41=A[/tex]

Rewrite

[tex]A=400\ people[/tex]

Answer:

250, -1250

Step-by-step explanation:

Geometric Sequence is a hint to think multiplication:

What can you multiply to -2 to get 10

or what is 10/-2

I hope you said -5.

So just multiply -5 to a term to get the term right after!

So

-50(-5)=250

250(-5)=-1250

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. In this case, the answer is 9/4.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, the reciprocal of 1/3 is 3/1. So, we have:

3/4 ÷ 1/3 = 3/4 * 3/1 = 9/4.

The answer, 9/4, cannot be further reduced to lowest terms since 9 and 4 do not have any common factors other than 1.

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Answer: n + 2 = 2n

Step-by-step explanation:

sum = add

number and two = n, 2

twice the number = 2 x n

Answer:  n + 2 = 2n

Step-by-step explanation:

In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.

[tex]692,119[/tex]

[tex]2,119[/tex]

[tex]1<5[/tex]

[tex]= 2000[/tex]

[tex]= 692,000[/tex]

Which means your answer is "692,000."

Hope this helps.

The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.

The given number is 692,119

The digit in the thousands place of the given number is 2.

The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.

Therefore, the rounded number is 692,000.

Learn more about rounding off here:

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Check the picture below.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]

[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]

Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.

To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.

Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.

[tex](x + 10)(x + 10) = 0\\x+10=0\\x=-10[/tex]

ANSWER

[tex]x = - 10[/tex]

EXPLANATION

We have the quadratic equation

[tex](x + 10)(x + 10) = 0[/tex]

This quadratic equation is in the factored form.

According to the zero product principle either the first factor is zero or the second is zero.

We apply the zero product principle to obtain:

[tex](x + 10) = 0 \: \: or \: \: (x + 10) = 0[/tex]

This is a repeated factor therefore,

[tex]x = - 10[/tex]

is the repeated root.

Answer: 60

Step-by-step explanation:

A circle is 360 degrees, so 360/6 is your answer.

To find the total profit for both wallets sold by Efficient Homemakers Ltd., use the equation P = 40x + 25y, where x is the number of leather wallets and y is the number of canvas wallets sold.

The question involves writing a function for the total profit from selling canvas wallets and leather wallets made by Efficient Homemakers Ltd.

To calculate the total profit, we denote x as the number of leather wallets and y as the number of canvas wallets.

The company makes a profit of $40 for each leather wallet, and $25 for each canvas wallet.

Thus, the total profit P can be represented by the equation:

P = 40x + 25y

This equation represents the total profit as a function of the number of leather wallets (x) and the number of canvas wallets (y) sold.

Answer:

1 hour 54 minutes

Step-by-step explanation:

1 hour and 9 minutes + 45 minutes gives your answer. However, since 45+9=54, this is convenient, since now we don't need to carry. Thus, 1 hour and 54 min is your answer.

Hope this helps!

Answer: 114 minutes or  1 hour and 54 minutes.

Step-by-step explanation:

You need to analyse the exercise.

You know that it takes 45 minutes from Helflin to Pale City.

Driving back to Alabama takes 1 hour and 9 minutes. You need to remember that there are 60 minutes in an hour, therefore, this time in minutes is:

[tex]60\ minutes+9\ minutes=69\ minutes[/tex]

To find the total time, you need to add 45 minutes and 69 minutes. Then you get:

[tex]Total=45\ minutes+69\ minutes=114\ minutes[/tex] or 1 hour and 54 minutes.

Answer:

[tex]\frac{15}{8}[/tex]

Step-by-step explanation:

"the quotient of 1 and 2/3 " expressed mathematically is,

1 ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{2}[/tex]

"divided by 4/5"

[tex]\frac{3}{2}[/tex] ÷ [tex]\frac{4}{5}[/tex]

=[tex]\frac{3}{2}[/tex] x [tex]\frac{5}{4}[/tex]

= [tex]\frac{15}{8}[/tex]

Answer: 29 degrees is the answer

Step-by-step explanation:

The bisector is the line that divides the angle, and rhombus diagonally. So, basically you're just dividing 58 in half. Which is 29 degrees.

The measure of each of the two angles formed by the bisector of the diagonal of a rhombus will be 29 degree.

Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

We have,

A Rhombus with one of its angle equal to 58°.

Now,

Bisector of an angle, divides an angle into two equal parts.

So,

From the above mentioned definition,

i.e.

[tex]=\frac{58}{2} = 29^0[/tex]

So, the measure of each angle is 29°.

Hence, we can say that the measure of each of the two angles formed by the bisector of the diagonal of a rhombus will be 29 degree.

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Check the picture below.

[tex]\bf \stackrel{\textit{triangles' area}}{\cfrac{1}{2}(6)(1)+\cfrac{1}{2}(6)(1)}+\stackrel{\textit{front side}}{(6\cdot 2)}+\stackrel{\textit{left and right sides}}{(4\cdot 2)+(4\cdot 2)}\implies 3+3+12+8+8[/tex]