Question 2 Determine if (x-3) is a factor to the polynomial P(x) = 2x³ +5x²-28x - 15. (3 marks)​

Answer:

9: 50

10: 90

11: 60

12: 25 and 115

13: 130 and 40

Thats all i can do, im sorry but i hope this helps ^^

Answer:

Step-by-step explanation:

BASICALLY ANYTHING WITH 3

Step-by-step explanation:

Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.

For example,

[tex] \frac{1}{x - 5} [/tex]

Set the expression in the denominator equal to 0, because you can't divide by 0.

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

So the vertical asymptote is x=5.

Disclaimer if you see something like this

[tex] \frac{(x - 5)(x + 3)}{(x - 5)} [/tex]

x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.

Horizontal:

If we have a function like this

[tex] \frac{1}{x} [/tex]

We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.

Remember a constant can be represent by

[tex]a \times {x}^{0} [/tex]

For example,

[tex]1 = 1 \times {x}^{0} [/tex]

[tex]2 = 2 \times {x}^{0} [/tex]

And so on,

and

[tex]x = {x}^{1} [/tex]

So our equation is basically

[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]

Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.

So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.

Consider the function

[tex] \frac{3 {x}^{2} }{ {x}^{2} + 1} [/tex]

As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator

So in this case,

[tex]x = \frac{3}{1} [/tex]

Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.

(a) The precision of this measurement is 17.64 mm ± 0.01 mm.

(b) he uncertainty of the measurement is 0.057%.

(c) The tolerance of the measurement is 0.02 mm.

(d) The acceptable diameter in the format, nominal value uncertainty is 17.64 mm ± 0.057%.

A micrometer screw gauge is used in the measurement of a wire. The measuring accuracy of a micrometer screw gauge is 0.01 mm.

The precision of the measurement is 17.64 ± 0.01 mm.

The uncertainty of the measurement is calculated as follows;

uncertainty = (error/actual measurement) x 100%

uncertainty =  (0.01/17.64) x 100% = 0.057%

Tolerance = maximum measurement - minimum measurement

                 = (17.64 + 0.01)mm - (17.64 - 0.01)mm

                 = 0.02 mm

0.057% of 17.64 mm = 0.01 mm

Range of uncertainty = (17.64 mm - 0.01 mm) to (17,64 mm + 0.01 mm)

                                    = 17.63 mm to 17.65 mm

Acceptable diameter format, = 17.64 mm ± 0.057%

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Answer:

  yes, it can be of odd degree

Step-by-step explanation:

The local maxima and minima correspond to zeros in the derivative of the function. The degree of the polynomial will be 1 more than some multiple of 2 greater than the number of zeros in the derivative.

__

For 2 each of local maxima and minima, the derivative will have 2+2 = 4 real zeros. The degree of the polynomial will be 1 greater, hence of degree 5 (or more). The polynomial must be of odd degree.

__

The local extrema must alternate: a maximum must be followed by a minimum, or vice versa. When there are an even number of each kind, the end extrema will be of opposite kinds. The end behavior of the function will be upward from a minimum and downward from a maximum. Hence the end behaviors must be in opposite directions--characteristic of an odd-degree polynomial.

The polynomial must be of odd degree.

_____

Additional comment

A polynomial with real coefficients will have an even number of complex roots. The complex roots of the derivative of a polynomial have no effect on the number or kind of extrema.

__

Attached is an example of a polynomial with 2 maxima and 2 minima. It is of 5th degree.

For the given function h(x), we have:

a) at x = -2 and x = 2.

b) y = 0 and y = 3.

First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.

By looking at the horizontal axis, we can see that the maximums are at:

x = -2 and at x = 2.

Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.

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I think it's 12 because here it comes out

The volume of the triangular base prism is 120 centimetre cube.

volume of a triangular prism = BH

where

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 4 × 6 = 24 / 2 = 12 cm

Hence,

volume of a triangular prism = 12 × 10

volume of a triangular prism = 120cm²

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The value of y based on the values given ib the equilateral triangle will be 4.

From the information given, MN is one of the sides of the equilateral triangle. Therefore, side MR will be:

= 1/2 × 8 = 4

In the above, it should be noted that MR was calculated since it's half of the value of MN which is 8.

Here, value of y based on the values given ib the equilateral triangle will be 4.

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Answer:

Step-by-step explanation:

4

Applying the tangent ratio, the angle of elevation of the sun, to the nearest degree, is: 36°.

In a right triangle, tan ∅ = opposite length / adjacent length is the tangent ratio.

Given the following:

Apply the tangent ratio:

tan ∅ = 125/172

tan ∅ = 125/172

∅ = tan^(-1)(125/172)

∅ ≈ 36°

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Explanation:

Given f(x) : (2, -3)

f(x) + 2 then graph translates up by 2 units up =  [tex]\boxed{\sf (2, -1)}[/tex]

f(x) - 3 then graph translates down 3 units down = [tex]\boxed{\sf (2, -6)}[/tex]

f(x + 5) then graph translates left 5 units = [tex]\boxed{\sf (-3, -3)}[/tex]

-f(x) then graph reflects over x axis = [tex]\sf \boxed{\sf (2, 3)}[/tex]

f(-x)  then graph reflects over y axis = [tex]\sf \boxed{\sf (-2,-3)}[/tex]

f(2x) then graph has horizontal compression = (2/2, -3) = [tex]\boxed{\sf (1, -3)}[/tex]

2f(x) then graph has vertical compression = (2, (-3)2) = [tex]\boxed{\sf (2, -6)}[/tex]

-f(x - 4) then graph reflects over x axis, moves 4 units to right = [tex]\sf \boxed{\sf (6, 3)}[/tex]

Parent function: y = x²

Graph function: f(x) = (x + 8)² - 4

After Identification:

D. The graph has a translation of 8 units left and 4 units down.

Answer:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Given:  [tex]f(x)=(2,-3)[/tex]

[tex]f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)[/tex]

[tex]f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)[/tex]

[tex]f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)[/tex]

[tex]-f(x) \implies (x,-y)=(2,-(-3))=(2,3)[/tex]

[tex]f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)[/tex]

[tex]f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)[/tex]

[tex]2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)[/tex]

[tex]-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)[/tex]

[tex]\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}[/tex]

Parent function:  [tex]y=x^2[/tex]

Given function:  [tex]f(x)=(x+8)^2-4[/tex]

[tex]f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}[/tex]

[tex]f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}[/tex]

Therefore, a translation 8 units to the left and 4 units down.

Answer:

57 f

Step-by-step explanation:

-16t² + vt + h

-16(4 s)² + (72 f/s)(4 s) + (25 f)

-256 + 288 + 25 = 57

The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]

[tex]\rm x^4 = 81^5\\x = 243[/tex]

[tex]\rm x^4 = 625^3\\x = 125\\[/tex]

[tex]x^5 = 32^3\\x = 8\\[/tex]

[tex]\rm x ^3 = 64^4\\x = 256[/tex]

Therefore for each radical the value of x is determined.

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Answer:

y = 6l + 43

Step-by-step explanation:

y=mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers

b = 43

The slope is you purchase one pair of laces, it increases by 6 each time

m = 6

The y coordinate will represent the total cost spent

y

The x coordinate will represent the total number of laces purchase and we are told that the variable is l

x = l

combine:

y = 6l + 43

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

Answer:

(x + 5)^2 + (y + 8)^2 = 6^2

Step-by-step explanation:

A circle formula: (x - h)^2 + (y - k)^2 = r^2

We are given diameter. To find the radius divide diameter by 2.

d = 12

12/2 = r = 6

H and K are given to be (-5 , -8)

(x - (-5))^2 + (y - (-8))^2 = 6^2

(x + 5)^2 + (y + 8)^2 = 6^2

I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.

Answer:

c

Step-by-step explanation:

I took the test, and that was the correct answer. I hope this helps!

Answer:

Answer will be 50

Step-by-step explanation:

Let us suppose, present age of Nuri be ‘x’ years and present age of Sonu be ‘y’ years.

Now, it is given that five years ago, Nuri was thrice old as Sonu. Hence,

Five years ago,

Nuri’s age = x-5 years

Sonu’s age = y-5 years

And relation between ages can be given as

Nuri’s age = 3×sonu’s age or

x-5 = 3(y-5)

x-5 = 3y-15

x-3y+10 = 0 ………..(i)

Another relation is given in the problem that ten years later, Nuri is twice as old as Sonu.

So, ten years ago,

Nuri’s Age = x+10

Sonu’s Age = y+10

And relation between ages can be written as

x+10 = 2(y+10)

x+10 = 2y+20

x-2y-10 = 0 …………..(ii)

Now we can solve the equation (i) and (ii) to get values of x and ‘y’ or present ages of Nuri and Sonu.

Value of ‘x’ from equation (i) be

x = 3y-10 ……….(iii)

Putting value of ‘x’ from equation (iii) in equation (ii) we get,

3y-10-2y-10 = 0

y = 20

Now, from equation (iii) value of ’x’ can be given as,

x= 3(20)-10

x = 50

Hence, the present ages of Nuri and Sonu are 50 years and 20 years respectively.

Step-by-step explanation:

7

4

1

----

12

reality

6.833

3.594

1.369

----------

11.796

Hi Student!

Looking at the problem statement, we are asked to find the place value of the 1 in the number 742.513.  Let's go from right to left and name each of the place values.  7 is in the hundreds place, 4 is in the tens place, 2 is in the ones place, 5 is in the tenths place, 1 is in the hundredths place, 3 is in the thousandths place.

Therefore, our final answer for which place value the number 1 in 742.513 is, we come to the conclusion of the hundredths place.

The interval which the function is negative is (-∞, -6)

The equation of the function is given as:

[tex]g(x) = \sqrt[3]{x + 6}[/tex]

When the function is negative.

It means that g(x) is less than 0

i.e. g(x) < 0

So, we have:

[tex]\sqrt[3]{x + 6} < 0[/tex]

Take the cube of both sides

x + 6 < 0

Subtract 6 from both sides

x < -6

The above represents a value from negative infinity to -6

i.e.  (-∞, -6)

Hence, the interval which the function is negative is (-∞, -6)

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The linear equation will be 2x + 10 = 5(x - 6). Then the value of the variable x will be 23.33.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Translate then Solve for the variable:

The sum of two times a number and 10 is five times the difference between a number and six.

Let the number be x.

Then the equation will be

2x + 10 = 5(x - 6)

Then the value of x will be

2x + 10 = 5x - 60

5x - 2x = 60 + 10

      3x = 70

        x = 23.33

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The number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]

From the question, we are to determine which of the given options is not irrational

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.

[tex]1.\overline{45}[/tex]  is a repeating decimal and it can be expressed as a fraction

[tex]1.\overline{45} = \frac{144}{99}[/tex]

∴ [tex]1.\overline{45}[/tex] is not an irrational number. It is a rational number

The other options cannot the expressed as a fraction.

Hence, the number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]

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Answer:

Step-by-step explanation:

hope this helps !

Answer:

Step-by-step explanation:

10+u-17u=14

Starts by combining like terms:

u-17u=14-10

Solve:

-16u=4

u=-16/4

u= -4

Answer: [tex]\sqrt{109} \text{ m }[/tex]

Step-by-step explanation:

If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.

Answer:

56.52

Step-by-step explanation:

The formula for circumference is C=2πr

So, C=2(3.14)(9)

C=56.52 answer

The arc length can be found using the formula, ∅ × r, which is: (5π)/3.

Arc length = ∅ × r, where ∅ is the central angle in radians, and r is the radius of the circle.

Given the following:

Length of the arc = 60° × π/180 × 5 = (60 × π × 5)/180

Length of the arc = (300π)/180 = (5π)/3

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Hi Student!

This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression.  So let's plug in the values and solve.

Plug in the values

Factor out the exponent

Combine

Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

Solving the quadratic equation w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]

  [tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5

Answer:

8

Step-by-step explanation: