There are two right angled triangles given that, №17886059, 16.09.2022 07:28

Mathematics

There are two right angled triangles given that Tan A = Tan B Find the value of X

Step-by-step answer

P Answered by PhD

$x = \frac{2}{3}$

Step-by-step explanation:

Given

See attachment for triangles

Required

Find x

First, calculate tan A

From the first triangle:

$tan\ A= \frac{x + 2}{x}$

Next, calculate tan B

From the second triangle:

$tan\ B= \frac{4}{3x-1}$

$tan\ A = tan\ B$

So, we have:

$\frac{x + 2}{x}= \frac{4}{3x-1}$

Cross Multiply

(x + 2)(3x - 1) = 4 * x

Open brackets

3x^2 + 6x - x - 2 = 4x

3x^2 + 5x - 2 = 4x

Collect Like Terms

3x^2 + 5x - 4x- 2 =0

3x^2 + x- 2 =0

Expand

3x^2 + 3x - 2x- 2 =0

Factorize:

3x(x + 1) - 2(x+ 1) =0

Factor out x + 1

(3x - 2)(x +1) = 0

Split:

$3x - 2 = 0\ or\ x + 1 = 0$

$x = \frac{2}{3}\ or\ x = -1$

x can not be negative, so:

$x = \frac{2}{3}$

Mathematics

NEEDED ASAP WILL MARK AS BRAINLIEST Here are two right-angled triangles. Given that tan a = tan b find the value of x. You must show all your working.

Step-by-step answer

P Answered by Specialist

Explanation:

This might not be how you are supposed to do it but,

We can see the two triangles are similar because AA similarity.

We know that the sides are proportional so we can make:

$\frac{x+2}{x}=\frac{4}{3x-1}$

We get,

$3x^2+5x-2=4x\\3x^2+x-2\\(3x-2)(x+1)=0\\x=2/3, x=-1$

Because sides can't be negative, x = 2/3

Mathematics

NEEDED ASAP WILL MARK AS BRAINLIEST Here are two right-angled triangles. Given that tan a = tan b find the value of x. You must show all your working.

Step-by-step answer

P Answered by Specialist

Explanation:

This might not be how you are supposed to do it but,

We can see the two triangles are similar because AA similarity.

We know that the sides are proportional so we can make:

$\frac{x+2}{x}=\frac{4}{3x-1}$

We get,

$3x^2+5x-2=4x\\3x^2+x-2\\(3x-2)(x+1)=0\\x=2/3, x=-1$

Because sides can't be negative, x = 2/3

Mathematics

16. photon lighting company determines that the supply and demand functions for its most popular lamp are as follows: s(p) = 400 - 4p + 0.2p4 and d(p) = 2,800 - 0.0012p3, where p is the price. determine the price for which the supply equals the demand. a) $93.24 b) $100.24 c) $96.24 d) $99.24 17. write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 2, -4, and 1 + 3i (1 point) a) f(x) = x4 - 2x2 + 36x - 80 b) f(x) = x4 - 3x3 + 6x2 - 18x + 80 c) f(x) = x4 - 9x2

Step-by-step answer

P Answered by PhD

80

QUESTION 16

If the demand and supply are equal, then we equate the two functions in p and solve for p.

That is

S(p)=D(p)

$400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}$

We can rearrange to obtain,

$0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0$

$2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0$

The real roots of this polynomial equation are:

$p = - 118.26 \: p = 96.24$

Since price can not be negative, we discard the negative value ,

p = 96.24

The correct answer for question 16 is C.

QUESTION 17

We were given the solution to this polynomial as

x=2,x=-4, x=1+3i

We need to recognize the presence of the complex root and treat it nicely.

There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if

a + bi

is a solution to

p(x)

then the complex conjugate

a - bi

is also a root.

Since

x = 1 + 3i

is a solution then,

x = 1 - 3i

is also a solution.

Therefore we have

f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)

$f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))$

We expand to obtain,

$( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)$

Note that:

${i}^{2} = - 1$

$f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)$

We now expand to obtain,

$f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80$

We simplify further to obtain,

$f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80$

The correct answer for question 17 is A.

QUESTION 18

If

-2i

is a zero of the polynomial,

f(x)=x^4-45x^2-196

then the complex conjugate

is also a zero,

This means that ,

(x+2i), (x-2i)

are factors of the polynomial.

The product of these two factors,

(x+2i), (x-2i) =x^2-(2i)^2=x^2+4

is also a factor , so we use it to divide and get the remaining factors.

see diagram for long division.

The above polynomial can therefore factored completely as,

f(x)=(x^2+4)(x^2-49)

Applying our knowledge from difference of two squares, we obtain,

f(x)=(x+2i)(x-2i))(x-7)(x+7)

Hence all the zeroes of these polynomial can be found by setting

(x+2i)(x-2i))(x-7)(x+7)=0

This implies,

x=-2i,x=2i,x=7,x=-7

The correct answer for question 18 is B

QUESTION 19

We were asked to find the horizontal and vertical asymptote of

$f(x)=\frac{2x^2+1}{x^2-1}$

To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,

$y=\frac{2x^2}{x^2}=2$

For vertical asymptote, equate the denominator to zero and solve for x.

x^2-1=

$\Rightarrow x=-1, x=1$

None of the options is correct, so the correct answer for question 19 is A.

QUESTION 20

We are converting,

$\frac{5\pi}{6}$

to degrees .

To convert from radians to degrees, multiply by,

$\frac{180\degree}{\pi}$

That is,

$\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}$

We simplify to obtain,

$\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree$

The correct answer is B.

QUESTION 21

Recall the mnemonics, SOH CAH TOA

The sine ratio is given by,

$\sin(B)=\frac{21}{75}=\frac{7}{25}$

From the diagram,

$\tan(B)=\frac{21}{72}=\frac{7}{24}$

The correct answer is C.

QUESTION 22

From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.

Using the cosine ratio, we obtain,

$\cos(58\degree)=\frac{17}{x}$

We can simply switch positions to make x the subject.

$x=\frac{17}{\cos(58\degree)}$

$x=\frac{17}{0.5299}$

x=32.08

Hence the correct answer is A.

QUESTION 23

Coterminal angles have the same terminal sides.

To find coterminal angles, we keep adding or subtracting 360 degrees.

See diagram.

$x=202\degree$

is coterminal with

$202\degree +360\degree =562\degree$

or

$202\degree -360\degree =-158\degree$

The correct answer is D.

See the attached file for continuation.

16. photon lighting company determines that the supply and demand functions for its most popular lam

Mathematics

What s the exact value of cos 75°? Question 1 options: A) B) C) D) Question 2 (5 points) What s a radian? Question 2 options: A) The distance halfway around a circle B) The ratio between a circle s diameter and its radius C) An angle made at the center of a circle by an arc whose length is equal to the radius of the circle D) The ratio between a circle s circumference and its radius Question 3 (5 points) image Determine the value of x. Question 3 options: A) 54.45 B) 16.32 C) 17.51 D) 35.54 Question 4 (5 points) image Which of the following is

Step-by-step answer

P Answered by Specialist

The exact value of cos 75º is $\frac{\sqrt{6} - \sqrt{2}}{4}$

Step-by-step explanation:

We have to know the sine and cosine of three fundamental angles: 30º, 45º,60º. So

$\sin{30} = \frac{1}{2}, \cos{30} = \frac{\sqrt{3}}{2}$

$\sin{45} = \cos{45} = \frac{\sqrt{2}}{2}$

$\sin{60} = \frac{\sqrt{3}}{2}, \cos{60} = \frac{1}{2}$

The cosine of the sum of two angles is given by:

$\cos{a + b} = \cos{a}\cos{b} - \sin{a}\sin{b}$

In this question:

75º is the sum if 30º and 45º. So

$\cos{75} = \cos{30 + 45} = \cos{30}\cos{45} - \sin{30}\sin{45} = \frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2} - \frac{1}{2}\frac{\sqrt{2}}{2} = \frac{\sqrt{6} - \sqrt{2}}{4}$

The exact value of cos 75º is $\frac{\sqrt{6} - \sqrt{2}}{4}$

Mathematics

16. photon lighting company determines that the supply and demand functions for its most popular lamp are as follows: s(p) = 400 - 4p + 0.2p4 and d(p) = 2,800 - 0.0012p3, where p is the price. determine the price for which the supply equals the demand. a) $93.24 b) $100.24 c) $96.24 d) $99.24 17. write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 2, -4, and 1 + 3i (1 point) a) f(x) = x4 - 2x2 + 36x - 80 b) f(x) = x4 - 3x3 + 6x2 - 18x + 80 c) f(x) = x4 - 9x2

Step-by-step answer

P Answered by PhD

80

QUESTION 16

If the demand and supply are equal, then we equate the two functions in p and solve for p.

That is

S(p)=D(p)

$400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}$

We can rearrange to obtain,

$0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0$

$2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0$

The real roots of this polynomial equation are:

$p = - 118.26 \: p = 96.24$

Since price can not be negative, we discard the negative value ,

p = 96.24

The correct answer for question 16 is C.

QUESTION 17

We were given the solution to this polynomial as

x=2,x=-4, x=1+3i

We need to recognize the presence of the complex root and treat it nicely.

There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if

a + bi

is a solution to

p(x)

then the complex conjugate

a - bi

is also a root.

Since

x = 1 + 3i

is a solution then,

x = 1 - 3i

is also a solution.

Therefore we have

f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)

$f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))$

We expand to obtain,

$( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)$

Note that:

${i}^{2} = - 1$

$f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)$

We now expand to obtain,

$f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80$

We simplify further to obtain,

$f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80$

The correct answer for question 17 is A.

QUESTION 18

If

-2i

is a zero of the polynomial,

f(x)=x^4-45x^2-196

then the complex conjugate

is also a zero,

This means that ,

(x+2i), (x-2i)

are factors of the polynomial.

The product of these two factors,

(x+2i), (x-2i) =x^2-(2i)^2=x^2+4

is also a factor , so we use it to divide and get the remaining factors.

see diagram for long division.

The above polynomial can therefore factored completely as,

f(x)=(x^2+4)(x^2-49)

Applying our knowledge from difference of two squares, we obtain,

f(x)=(x+2i)(x-2i))(x-7)(x+7)

Hence all the zeroes of these polynomial can be found by setting

(x+2i)(x-2i))(x-7)(x+7)=0

This implies,

x=-2i,x=2i,x=7,x=-7

The correct answer for question 18 is B

QUESTION 19

We were asked to find the horizontal and vertical asymptote of

$f(x)=\frac{2x^2+1}{x^2-1}$

To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,

$y=\frac{2x^2}{x^2}=2$

For vertical asymptote, equate the denominator to zero and solve for x.

x^2-1=

$\Rightarrow x=-1, x=1$

None of the options is correct, so the correct answer for question 19 is A.

QUESTION 20

We are converting,

$\frac{5\pi}{6}$

to degrees .

To convert from radians to degrees, multiply by,

$\frac{180\degree}{\pi}$

That is,

$\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}$

We simplify to obtain,

$\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree$

The correct answer is B.

QUESTION 21

Recall the mnemonics, SOH CAH TOA

The sine ratio is given by,

$\sin(B)=\frac{21}{75}=\frac{7}{25}$

From the diagram,

$\tan(B)=\frac{21}{72}=\frac{7}{24}$

The correct answer is C.

QUESTION 22

From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.

Using the cosine ratio, we obtain,

$\cos(58\degree)=\frac{17}{x}$

We can simply switch positions to make x the subject.

$x=\frac{17}{\cos(58\degree)}$

$x=\frac{17}{0.5299}$

x=32.08

Hence the correct answer is A.

QUESTION 23

Coterminal angles have the same terminal sides.

To find coterminal angles, we keep adding or subtracting 360 degrees.

See diagram.

$x=202\degree$

is coterminal with

$202\degree +360\degree =562\degree$

or

$202\degree -360\degree =-158\degree$

The correct answer is D.

See the attached file for continuation.

Mathematics

What s the exact value of cos 75°? Question 1 options: A) B) C) D) Question 2 (5 points) What s a radian? Question 2 options: A) The distance halfway around a circle B) The ratio between a circle s diameter and its radius C) An angle made at the center of a circle by an arc whose length is equal to the radius of the circle D) The ratio between a circle s circumference and its radius Question 3 (5 points) image Determine the value of x. Question 3 options: A) 54.45 B) 16.32 C) 17.51 D) 35.54 Question 4 (5 points) image Which of the following is

Step-by-step answer

P Answered by Specialist

The exact value of cos 75º is $\frac{\sqrt{6} - \sqrt{2}}{4}$

Step-by-step explanation:

We have to know the sine and cosine of three fundamental angles: 30º, 45º,60º. So

$\sin{30} = \frac{1}{2}, \cos{30} = \frac{\sqrt{3}}{2}$

$\sin{45} = \cos{45} = \frac{\sqrt{2}}{2}$

$\sin{60} = \frac{\sqrt{3}}{2}, \cos{60} = \frac{1}{2}$

The cosine of the sum of two angles is given by:

$\cos{a + b} = \cos{a}\cos{b} - \sin{a}\sin{b}$

In this question:

75º is the sum if 30º and 45º. So

$\cos{75} = \cos{30 + 45} = \cos{30}\cos{45} - \sin{30}\sin{45} = \frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2} - \frac{1}{2}\frac{\sqrt{2}}{2} = \frac{\sqrt{6} - \sqrt{2}}{4}$

The exact value of cos 75º is $\frac{\sqrt{6} - \sqrt{2}}{4}$

Mathematics

Which of the following best describes a bisector of an angle? a. the set of all points included between two sides of a given angle b. the set of all points in a plane that are equidistant from the two sides of a given angle c. the set of all points in a plane that are equidistant from the vertex of a given angle d. the set of all points in a plane that are equidistant from two other points

Step-by-step answer

P Answered by Master

41

That would be B.

The set of points are all on the line which is a bisector.

Mathematics

A(n) is the common side of two consecutive angles in a polygon.2.a statement you can probe and then use as a reason in later proofs is a(n) .a(n) divides an angle into two congruent angles.4.a(n) compares two numbers by division.5.a(n) has at least one non-rectangular lateral face prism. 6.a name given to matching angles of congruent triangles is 7.a(n) is a quadrilateral with four congruent sides.8.the is used to write the equations of a line with a given slope that passes through a given point. 9.a polygon is if no diagonal contains points in

Step-by-step answer

P Answered by PhD

6

1. Included side

2. Theorem

3. Midpoint

4. Ratio

5. Oblique prism

6. Corresponding triangle

7. Rhombus

8. Slope intercept form

9. Convex

10. Proportion

11. Conjecture

12. Transversal

13. Dependent event

14. Supplementary angles

15. Counterexample

16. Alternate interior angles

17. Vertex

18. Base

Step-by-step explanation:

1. An included side is the common side of two consecutive angles in a polygon.

2. A statement you can probe and then use as a reason in later proofs is a theorem.

3. A midpoint divides an angle into two congruent angles.

4. A ratio compares two numbers by division.

5. A oblique prism has at least one non-rectangular lateral face prism.

6. A name given to matching angles of congruent triangles is corresponding triangle.

7. A rhombus is a quadrilateral with four congruent sides.

8. The slope intercept form is used to write the equations of a line with a given slope that passes through a given point.

9. A polygon is convex if no diagonal contains points in the exterior.

10. An equation stating that two ratios are equal is called a proportion

11. A statement you believe to be true based on inductive reasoning is called a conjecture.

12. A transversal is a line that intersects two coplanar lines at two points.

13. The outcomes of dependent events affect each other.

14. Supplementary angles are two angles whose measures have the sum of 180°.

15. A counterexample is a case in which a conjecture is not true.

16. Angles on opposite sides of transversal and between the lines it intersects are alternate interior angles.

17. The common endpoint of two sides of a polygon is a vertex.

18. Each of the parallel sides of a trapezoid is called a base.

Mathematics

24) draw a line segment of any length and label it pq. if you were to construct a line segment congruent to pq, what would be your first step? a) put one end of the compass on point p and the other end on point q. b) measure pq using a ruler. c) draw an arc the size of pq below the segment. d) draw a new segent below the line the same length as pq. 25) describe the transformation that maps the pre-image a to the image a . a) translated 10 units to right and then 10 units up b) translated 5 units to left and then reflected across the x-axis c) translated

Step-by-step answer

P Answered by PhD

11

24) A

25) picture is missing

26) C

27) B

28) C

29) D

30) D

31) D

32) A

Step-by-step explanation:

24) You have to put one end of the compass on point P and the other end on point Q, so that, you have the measure of the segment.

25) The figure is missing, so I will answer the question in general terms.

translation 10 units to right and then 10 units up transforms point (x, y) into (x +10, y+10)translation 5 units to left and then reflected across the x-axis transforms point (x, y) into (x-5, -y)translation 10 units to right and then reflected across the x-axis transforms point (x, y) into (x+10, -y)translation 10 units to right and then reflected across the y-axis transforms point (x, y) into (-x-10, y)

26) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.

27) The ratio length/width must be the same

original case: 36/9 = 4

A) 30/6 = 5

B) 44/11 = 4

C) 64/8 = 8

D) 72/12 = 6

28) The angle '?' must be equal to the acute angle of the original figure

29) As shown in the picture, three sides are equal

30) The following proportion must be satisfied:

12/6 = 13/y = 5/x = 2, which is the scale factor

31) Since B is on the perpendicular bisector of AC and ∠ADB is a right angle, BD is the perpendicular bisector of AC. All of these is shown in the picture

32) ∠V ≅ ∠W. This is a property of isosceles triangles

There are two right angled triangles

given that Tan A = Tan B

Find the value of X

Step-by-step answer

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