QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
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The possible rational roots of the given equation are 1 and -3

From the question, we are to determine all the possible rational roots of the given equation

The given equation is

x⁴ -2x³ -6x² +22x -15 = 0

To determine the rational roots, we will test for values that make the equation equal to zero

(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15

1 + 2 - 6 - 22 -15

= -40

∴ -1 is not a root of the equation

(1)⁴ -2(1)³ -6(1)² +22(1) -15

1 - 2 - 6 + 22 -15

= 0

∴ 1 is one of the roots of the equation

(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15

16 + 16 - 24 - 44 -15

= -51

∴ -2 is not a root of the equation

(2)⁴ -2(2)³ -6(2)² +22(2) -15

16 - 16 - 24 + 44 -15

= 5

∴ 2 is not a root of the equation

(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15

81 + 54 - 54 -66 -15

= 0

∴ -3 is one of the roots of the equation

(3)⁴ -2(3)³ -6(3)² +22(3) -15

81 - 54 - 54 + 66 -15

= 24

∴ 3 is not a root of the equation

The other roots of the equation are irrational roots.

Hence, the possible rational roots of the given equation are 1 and -3

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Answer:

Angle x= 60°

Step-by-step explanation:

For the triangle HIL, you're going to add 30+90=120

Angles in a triangle add up to 180.

So, therefore,

180-120=60   so angle L must equal 60.

HJ is a straight line and angles in a straight line add up to 180.

180-90=90

Angle JIL is equal to 90.

To find y you add 90+45 which equals 135.

Again, angles in a triangle add up to 180.

180-135=45

So,

y = 45

Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.

To find angle JLK we must add angle L and angle y.

60+45=105

Angles in a straight line add up to 180. So,

180-105=75

75 = Angle JLK

75+45=120

Angles in a triangle add up to 180 so,

180-120= 60

Angle x= 60°

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The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.

It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.

Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.

Hence, the positive square root of the number 151,321 is; 389.

Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.

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Answer:

0

Step-by-step explanation:

because 1-0=1*2^3=8

because2^3=8

If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].

The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].

So, the surface area is given by the definite integral

[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]

Answer:

80 in.²

Step-by-step explanation:

The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.

Square: area = s²

Square: side = 4 in.

Triangular side: area = bh/2

Triangular side: base = 4 in.; height = 8 in.

Area of the base: s² = (4 in.)² = 16 in.²

Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²

Surface area = 16 in.² + 64 in.² = 80 in.²

Answer:

Step-by-step explanation:

Answer:

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Answer:

  x = 8

Step-by-step explanation:

Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.

The measure shown is equal to the angle measure of 90°.

  14x -22 = 90

We can solve this 2-step linear equation in the usual way.

  14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone

  x = 112/14 = 8 . . . step 2, divide by the coefficient of x

The value of x is 8.

Answer:

125

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

We can write the following equation according to this information and that will help us find the value of x:

65 + 60 = x add like terms

125 = x is the answer we are looking for.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{equation:}[/tex]

[tex]\large\textsf{a = 60 + 65}[/tex]

[tex]\huge\textsf{solving:}[/tex]

[tex]\large\textsf{a = 60 + 65}[/tex]

[tex]\large\textsf{60 + 65 = a}[/tex]

[tex]\huge\textsf{simplify it:}[/tex]

[tex]\large\textsf{a = 125}[/tex]

[tex]\huge\textsf{therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.

First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;

(a+a+2+a+4+a+6+a+8+a+10)/6 = b

6b=6a+30

b=a+5

Also, let the average of the consecutive intergers ending with b be denoted by; x.

(b+b-1+b-2+b-3+b-4)/5 = x

=(5b-10)/5

=b–2

The average, x=b – 2 (where b = a-5)

Ultimately, the value of the required average is; = a+5-2 = a+3.

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Answer:

2x + 8

Step-by-step explanation:

(4x + 5) - (2x - 3)

4x + 5 - 2x + 3

2x + 8

Answer: 2x+8

Step-by-step explanation:

4x+5-2x+3

=2x+8

[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]

[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]

[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]

[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]

[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]

[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]

[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]

[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]

[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]

[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]

[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]

a. The arc length is given by the integral

[tex]L(r) = \displaystyle \int_3^\infty \sqrt{x'(t)^2 + y'(t)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\left(\frac{t\cos(t) - r\sin(t)}{t^{r+1}}\right)^2 + \left(-\frac{t\sin(t) + r\cos(t)}{t^{r+1}}\right)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\frac{(t^2+r^2)\cos^2(t) + (t^2+r^2)\sin^2(t)}{\left(t^{r+1}\right)^2}} \, dt \\\\ ~~~~~~~~ = \boxed{\int_3^\infty \frac{\sqrt{t^2+r^2}}{t^{r+1}} \, dt}[/tex]

b. The integrand roughly behaves like

[tex]\dfrac t{t^{r+1}} = \dfrac1{t^r}[/tex]

so the arc length integral will converge for [tex]\boxed{r>1}[/tex].

c. When [tex]r=3[/tex], the integral becomes

[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2+9}}{t^4} \, dt[/tex]

Pull out a factor of [tex]t^2[/tex] from under the square root, bearing in mind that [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex].

[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2} \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{|t| \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{t \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{\sqrt{1+\frac9{t^2}}}{t^3} \, dt[/tex]

since for [tex]3\le t<\infty[/tex], we have [tex]|t|=t[/tex].

Now substitute

[tex]s=1+\dfrac9{t^2} \text{ and } ds = -\dfrac{18}{t^3} \, dt[/tex]

Then the integral evaluates to

[tex]L(3) = \displaystyle -\frac1{18} \int_2^1 \sqrt{s} \, ds \\\\ ~~~~~~~~ = \frac1{18} \int_1^2 s^{1/2} \, ds \\\\ ~~~~~~~~ = \frac1{27} s^{3/2} \bigg|_1^2 \\\\ ~~~~~~~~ = \frac{2^{3/2} - 1^{3/2}}{27} = \boxed{\frac{2\sqrt2-1}{27}}[/tex]

a) The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].

b) r > 1 for a spiral with finite length.

c) The length of the spiral when r = 3 is (1 - 2√2) / 9 units.

a) The arc length formula for 2-dimension parametric functions is defined below:

L = ∫ √[(dx / dt)² + (dy / dt)²] dt, for [α, β]         (1)

If we know that [tex]\dot x (t) = \frac{t \cdot \cos t - r \cdot \sin t}{t^{r+1}}[/tex], [tex]\dot y(t) = \frac{t\cdot \sin t + r\cdot \cos t}{t^{r + 1}}[/tex], α = 0 and β → + ∞ then their arc length formula is:

[tex]L = \int\limits^{\infty}_{3} {\sqrt{\left(\frac{t\cdot \cos t - r\cdot \sin t}{t^{r + 1}}\right)^{2}+\left(\frac{t\cdot \sin t + r\cdot \cos t}{t^{r+1}}\right)^{2}} } \, dt[/tex]

By algebraic handling and trigonometric formulae (cos ² t + sin² t = 1):

[tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex]      (2)

The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].

b) By ratio comparison criterion, we notice that √(t² + r²) is similar to √t² = t and [tex]\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}}[/tex] is similar to [tex]\frac{t}{t^{r +1}} = \frac{1}{t^{r}}[/tex].

The integral found in part a) has a finite length if and only the governing grade of the denominator is greater that the governing grade of the numerator. and according to the ratio comparson criterion, the absolute value of the ratio is greater than 0 and less than 1. Therefore, r > 1 for a spiral with finite length.

c) Now we proceed to integrate the function:

L = ∫ [√(t² + 9) / t⁴] dt, for [3, + ∞].

L = ∫ [t · √(1 + 9 / t²) / t⁴] dt, for [3, + ∞].

By using the algebraic substitutions: u = 1 + 9 / t², du = - (18 / t³) dt → - (1 / 18) du.

L = ∫ √u du, for [3, + ∞].

L = - (1 / 9) · √(u³), for [3, + ∞].

L = - (1 / 9) · [√(1 + 9 / t²)³], for [3, + ∞].

L = - (1 / 9) · [√(2³) - √(1³)]

L = - (1 / 9) · (2√2 - 1)

L = (1 - 2√2) / 9

The length of the spiral when r = 3 is (1 - 2√2) / 9 units.

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Answer:   x = 2

Work Shown:

x+5 = 7

x+5-5 = 7-5

x = 2

Subtract 5 from both sides to isolate x. This is to undo the plus 5.

The missing value in the logarithm are as follows:

Using logarithm rule,

logₐ b - logₐ c = logₐ (b / c)

logₐ b + logₐ c = logₐ (b × c)

Therefore,

log₃ 7 - log₃ 2 = log₃ (7 / 2)

log₉ 7 + log₉ 4 = log₉ (7 × 4) =  log₉ 28

log₆ 1 / 81 = log₆ 81⁻¹ = log₆ 3⁻⁴ =  - 4 log₆ 3

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Answer:

3.2

Step-by-step explanation:

4 x 8 / 8 + 2

32/10

=3.2

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Answer:

-4

Step-by-step explanation:

7x^3 + 5x^2 - 2
= 7*-1 + 5*1 - 2

= -7 + 5 - 2

= -4

Answer:

c)  3 units

d)  g(x) - f(x) = x² + 2x

e)  (-∞, -2] ∪ [0, ∞)

Step-by-step explanation:

To calculate the length of FC, first find the coordinates of point C.

The y-value of point C is zero since this is where the function f(x) intercepts the x-axis.  Therefore, set f(x) to zero and solve for x:

[tex]\implies 1-x^2=0[/tex]

[tex]\implies x^2=1[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]

[tex]\implies x= \pm 1[/tex]

As point C has a positive x-value,  C = (1, 0).

To find point F, substitute the x-value of point C into g(x):

[tex]\implies g(1)=2(1)+1=3[/tex]

⇒ F = (1, 3).

Length FC is the difference in the y-value of points C and F:

[tex]\begin{aligned} \implies \sf FC& = \sf y_F-y_C\\ & = \sf 3-0\\ & =\sf 3\:units \end{aligned}[/tex]

Given functions:

[tex]\begin{cases}f(x)=1-x^2\\ g(x)=2x+1 \end{cases}[/tex]

Therefore:

[tex]\begin{aligned}\implies g(x)-f(x) & = (2x+1) - (1-x^2)\\& = 2x+1-1+x^2\\& = x^2+2x\end{aligned}[/tex]

The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):

Point A is the y-intercept of both functions, therefore the x-value of point A is 0.

To find the x-value of point E, equate the two functions and solve for x:

[tex]\begin{aligned}g(x) & = f(x)\\\implies 2x+1 & = 1-x^2\\x^2+2x & = 0\\x(x+2) & = 0\\\implies x & = 0, -2\end{aligned}[/tex]

As the x-value of point E is negative ⇒ x = -2.

Therefore, the values of x for which g(x) ≥ f(x) are:

Answer:

a)

A = (0, 1)

B = (-1, 0)

C = (1, 0)

D = (-0.5, 0)

b) E = (-2, -3)

c) FC = 3 units

d) x² + 2x

e) x ≤ -2 and x ≥ 0

Explanation:

This question displays one equation of a linear function g(x) = 2x + 1 and a parabolic function f(x) = 1 - x².

a)

A point is where the linear function cuts the y axis.

y = 1 - (0)²

y = 1

A = (0, 1)

B and C point is where the parabolic function cuts the x axis.

1 - x² = 0

-x² = -1

x² = 1

x = ±√1

x = -1, 1

B = (-1, 0), C = (1, 0)

D point is where the linear function cuts x axis.

2x + 1 = 0

2x = -1

x = -1/2 or -0.5

D = (-0.5, 0)

b)

E point is where both equations intersect each other.

y = y

2x + 1 = 1 - x²

x² + 2x = 0

x(x + 2) = 0

x = 0, x = -2

y = 1, y = -3

E = (-2, -3)

c)

C : (1, 0)

To find F point

y = 2(1) + 1

y = 3

F : (1, 3)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\sf d = \sqrt{(1 - 1)^2 + (3 - 0)^2}[/tex]

[tex]\sf d = \sqrt{0 + 3^2}[/tex]

[tex]\sf d = 3[/tex]

FC length = 3 units

d)

g(x) - f(x)

(2x + 1) - (1 - x²)

2x + 1 - 1 + x²

x² + 2x

e)

g(x) ≥ f(x)

2x + 1 ≥ 1 - x²

x² + 2x ≥ 0

x(x + 2) ≥ 0

[tex]\boxed{If \ x \ \geq \ \pm \ a \ then \ -a \ \leq x \ \ and \ x \ \geq \ a }[/tex]

x ≤ -2 and x ≥ 0

Answer:

Most you can do is factor out the x and turn it into   x (3x + 7)

roots would be x = 0 and x = -7/3

Answer:  x(3x+7)

Step-by-step explanation:

You would factor the x out of both of your values and put on the outside of the parenthesis. And you put the two numbers that you have left inside of the parenthesis. And that is as far down as this function can be factored.

Answer:

[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]

Step-by-step explanation:

[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]

Answer:

W = (P -2L)/2

Step-by-step explanation:

P = 2(L + W)  Distribute the 2

P = 2L + 2W   Subtract 2L from both sides

P - 2L = 2W  Divide both sides by 2

(P-2L)/2 = W  

Answer:

1. f(x) is reflected across the x-axis

2. f(x) is translated 1 unit up

3. f(x) is vertically scaled by a factor of 2

4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2

5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down

6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up

Solving question:

(1)  [tex]g(x) = -f(x)[/tex]

This graph has been reflected in the x axis. Equation:  [tex]\sf g(x) = -\dfrac{2}{x}[/tex]

(2) [tex]g(x) = f(x) + 1[/tex]

Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]

(3) [tex]g(x) = 2f(x)[/tex]

This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]

(4) [tex]g(x) = -2f(x)[/tex]

This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]

(5)  [tex]g(x) = 3f(x) - 1[/tex]

This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]

(6)   [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]

This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]

Answer:

D.

Step-by-step explanation:

We can solve by simply isolating x:

[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]

You can check by plugging in any value greater than -8

-122<-3(-2-8(-7))-8*-7

-122<-3(-2+56)+56

-122<-3(54)+56

-122<-162+56

-122<-106

The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.

From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.

Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.

This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.

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The best sampling strategy would be a stratified sample.

Samples may be classified as:

For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.

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C

1, -9 , 81 , -729 .....

ratio :-

R1 = -9/1 = -9

R2 = 81/-9 = -9

R3 = -729 / 81 =-9

so ,. R1= R2= R3

Answer:

2.8m²

Step-by-step explanation:

p = F / A

A = F / p

A = 84 / 30

A = 2.8m²

Answer:

x = 12cos(35)

Step-by-step explanation:

Well you have hyp and adj, meaning cosine. and u have the angle and need the adjacent, so side(cos(theta)).

12cos(35).