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Answer: 12 < x < 15

Step-by-step explanation:

Answer:

The sensory somatic nervous system controls all voluntary responses of the body.

Step-by-step explanation:

The sensory somatic nervous system controls all voluntary responses of the body.

The movements includes muscles and organs movements and reflex movements. Here the sensory neurons carry impulses to the brain and the spinal cord.

Answer:

Height of the kite from ground is 77 m.

Step-by-step explanation:

Given: Length of the kite string = 80 m

           Angle of elevation = 75°

To find: Height of the kite from the ground.

Figure is attached.

In ΔABC

using trigonometric ratio,

[tex]sin\,75^{\circ}=\frac{AB}{AC}[/tex]

[tex]0.97=\frac{AB}{80}[/tex]

[tex]AB=0.97\times80[/tex]

AB = 77.27 m

AB = 77 m (approx.)

Therefore, Height of the kite from ground is 77 m.

The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option  B is correct.

Use the concept of polynomial defined as:

An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.

The given polynomial is:

f(x) = 5(x + 8)²(x - 8)³

To find its root equate this polynomial to 0.

Then,

5(x + 8)²(x - 8)³ = 0

(x + 8)²(x - 8)³ = 0

(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0

Therefore,

x = -8, -8, 8, 8, 8

Hence,

It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.

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The complete question is:

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 5(x + 8)²(x - 8)³

A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3

B. -8, multiplicity 2; 8, multiplicity 3

C. -8, multiplicity 3; 8, multiplicity 2

D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

Step-by-step explanation: First, notice that this line is in slope intercept or more commonly known as y = mx + b form because y is by itself on one side of the equation.

Our slope or m therefore is the coefficient of the x-term which in this case is 3/4. Our b or y-intercept is the constant term which in this case is -2.

To graph a line given the slope and y-intercept, we will first start with its y-intercept. The y-intercept of a line is the point where the line crosses the y-axis. Since our y-intercept is -2, we start by plotting the point that is down 2 units on the y-axis and we call that point A.

From there we take our slope of 3/4 so our rise is 3 and our run is 4 and we end up at point B. Now we can connect the two points and we have our line.

I attached the image of the line in the image provided.

cos4x = cos2x

We know that:

cos2x = 1-2cos^2 x

==> cos4x = 1-2cos^2 (2x)

Now substitute:

==> 1-2cos^2 (2x) = cos2x

==> 2cos^2 (2x) + cos2x - 1 = 0

Now factor:

==> (2cos2x -1)(cos2x + 1) = 0

==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3

==> x1= pi/6 , 7pi/6

==> x1= pi/6 + 2npi

==> x2= 7pi/6 + 2npi

==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.

==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}

The solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.

Here, we have to solve the equation cos(4x) + cos(2x) - 2 = 0, we can use trigonometric identities to simplify it.

We know the following trigonometric identities:

[tex]cos(2x) = 2cos^2(x) - 1\\cos(4x) = 2cos^2(2x) - 1[/tex]

Now, let's rewrite the equation using these identities:

[tex]2cos^2(2x) - 1 + 2cos^2(x) - 1 - 2 = 0[/tex]

Combine like terms:

[tex]2cos^2(2x) + 2cos^2(x) - 4 = 0[/tex]

Divide the entire equation by 2:

[tex]cos^2(2x) + cos^2(x) - 2 = 0[/tex]

Now, let's simplify further:

We can rewrite [tex]cos^2(2x)[/tex] as [tex](1 - sin^2(2x))[/tex]using the Pythagorean identity: [tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]

So, the equation becomes:

[tex](1 - sin^2(2x)) + cos^2(x) - 2 = 0[/tex]

Rearrange the terms:

[tex]cos^2(x) - sin^2(2x) - 1 = 0[/tex]

Now, use the double-angle identity: [tex]sin^2(2x) = 2sin(x)cos(x)[/tex]

[tex]cos^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]

Now, we can rewrite [tex]cos^2(x) as (1 - sin^2(x))[/tex] using the Pythagorean identity:

[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]

[tex](1 - sin^2(x)) - 2sin(x)cos(x) - 1 = 0[/tex]

Now, simplify further:

[tex]1 - sin^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]

We can see that [tex](1 - sin^2(x))[/tex] cancels out:

-2sin(x)cos(x) = 0

Divide both sides by -2:

sin(x)cos(x) = 0

Now, there are two possible solutions for this equation:

sin(x) = 0

cos(x) = 0

Let's solve each case:

sin(x) = 0

This occurs when x is an integer multiple of π (π, 2π, 3π, ...). So the solutions are x = nπ, where n is an integer.

cos(x) = 0

This occurs when x is an odd multiple of π/2 (π/2, 3π/2, 5π/2, ...). So the solutions are x = (2n + 1)π/2, where n is an integer.

Therefore, the solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.

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Answer:

x = 3

Step-by-step explanation:

  Given:[tex]\log _{x-1}\left(16\right)=4[/tex]

We have to solve for x.

Consider the given expression [tex]\log _{x-1}\left(16\right)=4[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}[/tex]

[tex]\log _{x-1}\left(16\right)=\frac{\ln \left(16\right)}{\ln \left(x-1\right)}[/tex]

Thus, the expression becomes,

[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}=4[/tex]

Multiply both side by [tex]\ln \left(x-1\right)[/tex]

[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}\ln \left(x-1\right)=4\ln \left(x-1\right)[/tex]

Simplify, we get,

[tex]\ln \left(16\right)=4\ln \left(x-1\right)[/tex]

Divide both side by 4, we have,

[tex]\frac{4\ln \left(x-1\right)}{4}=\frac{\ln \left(16\right)}{4}[/tex]

[tex]\frac{\ln \left(16\right)}{4}:\quad \ln \left(2\right)[/tex]

Thus, [tex]\ln \left(x-1\right)=\ln(2)[/tex]

[tex]\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]

thus, x - 1 = 2

simplify for x, we have,

x = 3

Answer:

then f the teacher

Step-by-step explanation:

Answer:

This is an equation in which we have to find the slope of the line. We are supposed to draw the line for the two given points.

Step-by-step explanation:

The equation and the graph are solved as:

Now the Graphical data and the results are attached to the answer, given hope it helps out.

According to the properties of a perpendicular bisector, XY will form four right angles with JK, XY is perpendicular to JK, and it must bisect JK into two equal parts, making statements A, D, E, and F true.

The question tells us that XY is the perpendicular bisector of JK. This tells us a few things about the relationship between the two lines and the points on them:

The options regarding P being the midpoint of XY and the statement that includes an undefined variable 'm' were ignored due to lack of context.

Final answer:

The statements that must be true when XY is the perpendicular bisector of JK are: XY and JK form four right angles, P is the midpoint of XY, XP = YP, and XY is perpendicular to JK.

Explanation:

To determine which of the statements must be true, we need to understand the properties of a perpendicular bisector. A perpendicular bisector of a line segment is a line that divides the line segment into two equal parts and forms a right angle with the line segment.

From this definition, we can conclude that the following statements must be true:

A. XY and JK form four right angles - Since XY is the perpendicular bisector of JK, it forms a right angle with JK at each point of intersection.

B. P is the midpoint of XY - The perpendicular bisector passes through the midpoint of the line segment it bisects.

C. XP = YP - Since P is the midpoint of XY, XP and YP have equal lengths.

F. XY is perpendicular to JK - This is the definition of a perpendicular bisector.

The value of AC + BD will be 70.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangle ABCD,

AB = 21

AD = 28

Now,

Since, ABCD is a rectangle.

Hence, We get;

⇒ AC = BD

Here, In rectangle ABCD,

AB = 21

AD = 28

So, By using definition of Pythagoras theorem, we get;

⇒ BD² = AB² + AD²

⇒ BD² = 21² + 28²

⇒ BD² = 441 + 784

⇒ BD² = 1225

⇒ BD = 35

Thus, The value of BD + AC is find as;

⇒ AC + BD = 35 + 35

                 = 70

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