Which choice is equivalent to the expression below?

Answer:

C. [tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]

Step-by-step explanation:

We want to find the equation of a polynomial the following properties;

i. Leading coefficient is 1

ii. roots (7 + i) and (5 – i) with multiplicity 1

Recall the complex conjugate properties of the roots of a polynomial.

According to this property, if

[tex]a+bi[/tex] is a root of a polynomial, then the complex conjugate, [tex]a-bi[/tex]  is also a root.

This means that:

(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.

The complete set of roots are:

[tex]x=(7+i),x=(7-i),x=(5-i),x=(5+i)[/tex]

Therefore the polynomial is:

[tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]

The correct choice is C.

Final answer:

The correct polynomial function with roots (7 + i) and (5 – i), each with multiplicity 1 and a leading coefficient of 1, is given by (c) f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i)).

Explanation:

The question asks which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1. For a polynomial to have these roots, its conjugates, (7 - i) and (5 + i), must also be roots because complex roots always come in conjugate pairs if the polynomial has real coefficients.

This leads us to option (c) as the correct answer. To form a polynomial with these roots, we take each root, turn it into a binomial by subtracting it from x, and then multiply these binomials together.

Doing so for the given roots, we get:

f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i))

This polynomial matches option (c), confirming it as the correct answer.

Answer:

What's the question? All you posted was the potential answers.

Step-by-step explanation:

This seems really easy, but

1)  0

2) 0

3) 0

Answer:

The measure of angle EYH is [tex]25\°[/tex]

Step-by-step explanation:

step 1

Find the measure of arc EH

we know that

[tex]arc\ EV+arc\ VL+arc\ HL+arc\ EH=360\°[/tex] ----> by complete circle

substitute the given values

[tex]130\°+110\°+40\°+arc\ EH=360\°[/tex]

[tex]280\°+arc\ EH=360\°[/tex]

[tex]arc\ EH=360\°-280\°=80\°[/tex]

step 2

Find the measure of angle EYH

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

[tex]m<EYH=\frac{1}{2}(arc\ EV-arc\ EH)[/tex]

substitute the values

[tex]m<EYH=\frac{1}{2}(130\°-80\°)=25\°[/tex]

there are two ways you can do

[tex]y = 5x + 15 \\ \\ 1. \: y - 15 = 5x \\ 2. \: \frac{y - 15}{5} = x \\ 3. \: x = \frac{y - 15}{5} \\ \\ \\ 1. \: 5x + 15 = y \\ 2. \: 5x + 15 + - 15 = y + - 15 \\ 5x = y - 15 \\ 3. \: \frac{5x}{5} = \frac{y - 15}{5} \\ x = \frac{1}{5} y - 3[/tex]

A solution of the equation y = 5x + 15 represents a specific moment during Kenneth's experiment, where 'x' is the time elapsed since he started adding the blue liquid, and 'y' is the total volume of the liquid mixture in the beaker.

The equation y = 5x + 15 provided is a linear equation, which is a mathematical expression showing a constant rate of change. In this context, Kenneth's experiment in the laboratory, 'x' is the number of minutes since Kenneth began adding drops of blue liquid to the beaker, and 'y' is the total amount of liquid, in milliliters, in the beaker.

A solution to this equation refers to specific values for 'x' and 'y' which make this equation true. For instance, if we choose x = 1 minute, then we can calculate 'y' by substituting 'x' into the equation which gives y = 5*1 + 15 = 20 mL. This means that after 1 minute, Kenneth has 20 mL of liquid in his beaker. Indeed, every solution to this equation reflects a specific moment (x, or number of minutes) in Kenneth's ongoing experiment and the corresponding total volume (y) of the mixture in the beaker.

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Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet

Answer:

  B.  3x -2y = 10

Step-by-step explanation:

The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.

Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...

  3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.

  y = 3/2x -5 . . . . . the coefficient of x is the slope

Answer:

B.  3x -2y = 10

Step-by-step explanation:

The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.

Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...

  3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.

  y = 3/2x -5 . . . . . the coefficient of x is the slope

Answer: -70 degrees difference

Step-by-step explanation:

Answer:

-70!!

Step-by-step explanation:hope this helped!

Answer:  C)  g(x) = 2ˣ⁻³ + 2

Step-by-step explanation:

The general form of an exponential equation is: g(x) = 2ˣ⁻ᵃ + b   where

The new function is shifted UP 2 units and RIGHT 3 units

--> g(x) = 2ˣ⁻³ + 2

ANSWER

Option D is correct

EXPLANATION

We resolve the forces into component forms.

[tex]F_1 = 400 \cos(30) i + 400 \sin(30) j[/tex]

[tex]F_1 = 200 \sqrt{3} i +200j[/tex]

Also the second is resolved to obtain,

[tex]F_2= 280 \cos(135) i + 280 \sin(135) j.[/tex]

[tex]F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j[/tex]

To find the resultant vector, V, We add the corresponding components of the two forces to get:

[tex]V=F_1+F_2 [/tex]

[tex] \implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j[/tex]

The correct answer is D.

Answer:

98

Step-by-step explanation:

If half the diagonal is 7 yd, then the full diagonal is 14 yd.

If we call the side length s, then using Pythagorean theorem:

c² = a² + b²

(14)² = s² + s²

196 = 2s²

s² = 98

The area of a square is s², so:

A = s²

A = 98

The area is 98 yd².

Answer:

  12 m

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh . . . . . b represents the base; h represents the height

We are told that the height is 5 m less than the base, so we have ...

  42 = (1/2)(b)(b -5)

  84 = b(b-5) . . . . . . . . multiply by 2

We want two factors of 84 that differ by 5. The factors are ...

  84 = 1·84 = 2·42 = 3·28 = 4·21 = 6·14 = 7·12

The relevant factors are 7 and 12, so now we know b-5 = 7 and b = 12.

The length of the base is 12 m.

A = person is under 20

B = person is over 60

P(A or B) = P(A) + P(B) ... works because A and B are mutually exclusive

P(A or B) = 0.30 + 0.17

P(A or B) = 0.47 = 47%

The probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.

Probability is a topic in mathematics  where the likeliness of an event is studied.

The range of probability is 0 to 1 .

0 indicates uncertainty to 1 indicating certainty.

It is given in the question that

30% of the U.S. population is under 20 years old

About 17% of the population is over 60

probability that a person chosen at random is under 20 or over 60 = ?

Let P(A) represents person under 20

Let P(B) represents person over 60

As a person is chosen at random and the events cannot happen together so they are mutually exclusive events.

The probability for mutually exclusive event is given by

P(A or B) = P(A) + P(B)

P(A) = 17% = 0.17

P(B) = 30% = 0.3

P(A or B) = 0.30 + 0.17

P(A or B) = 0.47 = 47%

Therefore , the probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.

To know more about Probability

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probability of drawing a blue marble is 1/3

actually box 3 is correct.

because their radiuses are easy to find

but the tangent line is x=-4 or x=4

The option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have two circles in the graph plot:

From the graph plot:

For the circle:A the radius is 4

For the circle:B the radius is 3

The point of intersection point (4, 3)

The tangent line will be:

x = 4

Thus, the option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.

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Answer:

The answer is 1/4.

Step-by-step explanation:

5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).

Answer:

The odds that he choose a country CD is 1/3

Step-by-step explanation:

12/12 ÷ 3 = 1/3

Answer:

x ≈ 11.68 ( to 2 dec. places )

Step-by-step explanation:

Given

[tex]6^{(x-8)}[/tex] = 730 ( take log of both sides )

log [tex]6^{(x-8)}[/tex] = log730

(x - 8)log6 = log730 ( divide both sides by log6 )

x - 8 = [tex]\frac{log730}{log6}[/tex] ≈ 3.68 ( add 8 to both sides )

x ≈ 11.68 ( to 2 dec. places )

Answer:

6^ 3.679648309

Step-by-step explanation:

Don't really have one. Went with trial and error. Set calculator to 2 d.p by the way

Answer:

Final answer in simplified form is [tex]3x^2-17x-30[/tex]

Step-by-step explanation:

Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]

Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]

First we can distribute the negative sign and remove the parenthesis the combine like terms

[tex](3x^2-8x-24)-(9x+6)[/tex]

[tex]=3x^2-8x-24-9x-6[/tex]

[tex]=3x^2-17x-30[/tex]

Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]

Answer:

See below.

Step-by-step explanation:

Values are excluded if they make the denominator zero, so one rational expression could be:

(x^2 - 9) /  (x + 4)(x + 7)

- when x = -4 or -7 then the denominator is zero so the values of the function is undefined for these values.

Your answer would be C.

Step-by-step explanation:

250 dollars. 250-100= 150. 150/20 equls 7.5. 7.5 will round to 8. It iwll be 8 hours hey will have to pay for.

Answer:

A' because it is translated to another position.

Hope this helps

Answer: A'

Step-by-step explanation:

From the given figure , it can be seen that the quadrilateral ABCD is translated to produce A'B'C'D' by some distance in a particular direction.

We can see that the point A' in the image is corresponding to the point A in the pre-image.

Hence, the image of point A is A' .

Answer:

3, 7

Step-by-step explanation:

Since we are asked for the known solutions to f(x) = g(x), we need to consider the values of the functions where x's are the same.

If you look at the table, you will see that f(-9) = g(-9) = 3 and f(2) = g(2) = 7.

The value of x where f(x) = g(x) is 3

According to the given question, we are to find the value of x for which the function f(x) is equal to g(x)

From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.

Therefore from the table, the value of x where f(x) = g(x) is 3

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Answer:

d.(-2,0)

Step-by-step explanation:

The given parametric equation is:

[tex]x=4t[/tex]

[tex]y=12t^2+4t-1[/tex]

We make t the subject in the first equation;

[tex]t=\frac{x}{4}[/tex]

We substitute into the second equation to get:

[tex]y=12(\frac{x}{4})^2+4(\frac{x}{4})-1[/tex]

[tex]y=\frac{3}{4}x^2+x-1[/tex]

When x=4 , [tex]y=\frac{3}{4}(4)^2+4-1=15[/tex]

When x=-2 , [tex]y=\frac{3}{4}(-2)^2+-2-1=0[/tex]

Therefore the point (-2,0) lies on the given parametric  curve.

Answer:

Last option

[tex]y = 3cos(\pi(x+2)) + 5[/tex]

Step-by-step explanation:

The general cosine function has the following form  

[tex]y = Acos(b(x-\phi)) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

[tex]\phi[/tex] is the shift phase

In this problem :

[tex]A = 3[/tex]

[tex]\frac{2\pi}{b}=2\\\\ b=\frac{2\pi}{2}\\\\ b=\pi[/tex]

[tex]\phi =-2\\\\k = 5[/tex]

So  The function is:

[tex]y = 3cos(\pi(x+2)) + 5[/tex]

The yellow and orange triangle is AA

It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.

Answer:

AA

Step-by-step explanation:

For the 2 triangles to be similar we require 2 corresponding angles to be congruent.

There are 2 angles of measure 30°

If we consider the yellow triangle the the third angle is

180° - ( 41 + 30)° = 180° - 71 = 109°

The 2 triangles have therefore 2 corresponding congruent angles

Hence the triangles are similar by the postulate AA

For #11, the answer is C, I’m pretty sure.

For #12, KM = LN, and LM = KN.

I can’t help with the others though, sorry :/

Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]

              2) Quadrant: III, reference angle: 85°

              3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]

Step-by-step explanation:

Reference angle is the angle closest to the x-axis

1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π

Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.

The angle closest to the x-axis is the same as the given angle.

2) The given angle is -95°. It is measured clockwise since it is a negative angle.  Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.

The angle closest to the x-axis is 85°.

3) The given angle is (23/4)π.  Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.

The angle closest to the x-axis is π/4

Answer:

see explanation

Step-by-step explanation:

1

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus

phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]

2

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

Final answer:

The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.

Explanation:

To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.

To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.

You can factor -80 as

[tex]-80 = (-1)\cdot 16 \cdot 5[/tex]

So, we have

[tex]\sqrt{-80} = \sqrt{(-1)\cdot 16 \cdot 5}[/tex]

The square root of a product is the product of the square roots:

[tex]\sqrt{-80} = \sqrt{(-1)}\sqrt{16}\sqrt{5}[/tex]

Since [tex]i^2=-1[/tex] and [tex]4^2=16[/tex], we have

[tex]\sqrt{-80} = 4i\sqrt{5}[/tex]

The equivalent expression of the complex expression √(-80) will be 4i√5. Then the correct option is C.

A complex number is a number that is made up of both real and imaginary numbers. The complex number can be given as a + ib where a is the real part and ib is the imaginary part.

The expression is given below.

⇒ √(-80)

And we know that √(-1) = i

Then the expression can be written as

⇒ √(-1 x 16 x 5)

⇒ 4i√5

More about the complex number link is given below.

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Answer:

$36.00

Step-by-step explanation:

The cost performance index (CPI) is a measure of the financial effectiveness and efficiency of a project. As a ratio it is calculated by dividing the budgeted cost of work completed, or earned value, by the actual cost of the work performed, that is to say:

CPI = Budgeted cost of work / Actual cost of work

From the statement we know that:

CPI = 1.94

Budgeted cost of work= $69.85

Cost of work in 1983 = Budgeted cost of work / CPI

Cost of work in 1983 = $69.85 / 1.94 = $36.00

Answer:

The answer is C

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

because while solving a probability question you divide it by thee full number