Find a degree 3 polynomial with real coefficients having zeros 2 and 3 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) = .

Answer:

A (6)

Step-by-step explanation:

first, let's rearrange the polynomial (just to make it more clear)

[tex]P(x)=-2^2+x^6-4x+1[/tex]

p(x) = [tex]x^6-4x-4+1[/tex]

the highest exponent here is 6, meaning that the correct option is A (6)

hope this helps!

Because 6*6 = 36, we conclude that 36 is the only square number.

A square number is a number that is equal to the product of a whole number and itself.

For example, the square numbers are:

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

7*7 = 49

etc...

From the given numbers: {5, 8, 15, 30, 36}

The only one that belongs to the above list is 36, that is the only square number, so that is the correct option.

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Answer:

Make a graph with bug repellent as x, and bug bites as y

Step-by-step explanation:

This just makes the most sense to me, depending on how many people use bug repellent, how many bug bites they get.

The required limits for the heads (a), (b), (c) are given by 4, 1, 4 respectively.

[tex]f(x)\left \{ {{4x-3} ,x < 1\atop {3x+1},x\geq 1} \right.[/tex]

Limit, can be defined nearby values of a variable at which the function has their exists.

a)  [tex]\lim_{x \to 1+\y}3x+1\\[/tex]

⇒ 4
b) [tex]\lim_{x \to -1\y}4x-3\\[/tex]

⇒ 1

c) [tex]\lim_{x \to 1\y}3x+1\\[/tex]

⇒4

Thus, The required value of limits of a, b, c is given by 4, 1 ,4 respectively.

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Answer:

Step-by-step explanation:

3/4 * 1/8 = 3*1 / 4*8

3 / 32 is the solution.

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

The altitude of an object with respect to a reference plane or point is termed its height. This includes all parts of the object that add up to its height. Therefore, the height of the wall would be 100.5 inches.

The height of a given object implies the altitude of the object from a reference plane or point.

Therefore given that concrete blocks are 8 inches, then;

total height of mortar required to hold each concrete block = 3/8 inches

Thus, since there are 12 concrete blocks, then 12 sections of mortar would be required to hold 12 blocks starting from the ground.

So that;

total height of mortar required = 3/8 x 12

                                         = 4.5 inches

Total height of all concrete blocks required = 12 x 8

                                                             = 96 inches

Therefore, the height of the wall of 12 courses of concrete blocks = 96 + 4.5

                                                   = 100.5 inches

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The time to hit the ground is 1.9 seconds

The height equation is given as:

d = -16t^2 + h0

A stone thrown from 60 feet has an initial height of 60.

This means that:

h0 = 60

So, we have:

d = -16t^2 + 60

When the stone hits the ground, d = 0

So, we have:

-16t^2 + 60 = 0

Evaluate the like terms

-16t^2 = -60

Divide by -16

t^2 = 3.75

Evaluate the square root

t = 1.9

Hence, the time to hit the ground is 1.9 seconds

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The side of the small triangle that will correspond to the side of HI is side IK.

Similar triangles are triangles that have the same shape but different size.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are equal.

Therefore, the side of the small triangle that will correspond to the side of HI is side IK.

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Answer: 294.34 m^3

Step-by-step explanation: The formula for the volume of a hemisphere is 2/3 * 3.14 * radius cubed (r^3). Plugging in the values, we have 2/3 * 3.14 * 5.2^3, and we get roughly 294.339 m^3, or rounded to the nearest hundredth, 294.34 m^3.

Hope this helped!

Answer:

Your answer is 31808.6 but if your rounding the answer will be 31809

Step-by-step explanation:

The eqaution would be " v = 3.14 x r^2 x h"

The true statement about a ladder is; the ladder has parallel line segments and perpendicular line segments.

Parallel lines are lines that never meet on the same plane which have equal distance apart from each other.

They are lines that intersect each other to form a right angle.

Therefore, the ladder has parallel line segments and perpendicular line segments.

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The sum is given by -  f(y) = 4(y -1).

We have the following expression -

(y + 5) + (3y - 9)

We have to evaluate the above sum.

Now -

f(x) + g(x) = 3x + 9 - (6 - x)  

f(x) + g(x) = 3x + 10 - 6 + x

f(x) + g(x) =  4x + 4

f(x) + g(x) = 4(x + 1)

According to the question, we have -

(y + 5) + (3y - 9)

Assume that the sum is represented by the function f(y).

Solving, we get -

f(y) = y + 5 + 3y - 9

f(y) = y + 3y + 5 - 9

f(y) = 4y - 4

f(y) = 4(y - 1)

Hence, the sum is given by -  f(y) = 4(y -1).

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Answer:

6

Step-by-step explanation:

I believe so because the 20 pole took away six so im guessing the 41 pole will to the same

The length of the shadow cast by the 14-foot pole is 8.4 shadows.

We have,

From the figure given,

The two triangles are similar since the corresponding sides and angles are given equal.

This means,

The ratio of the corresponding sides is equal.

So,

20/14 = 12/x _______(1)

Where x is the length of the shadow cast by the 14-foot pole.

Now,

Solving for x from (1).

20/14 = 12/x

Divide 12 on both sides.

20 / (14 x 12) = 1/x

20/168 = 1/x

Cross multiply.

x = 168/20

x = 8.4 shadow.

Thus,

The length of the shadow cast by the 14-foot pole is 8.4 shadows.

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Answer:

Your answer should be D. $48,856.11

Step-by-step explanation:

This formula is for Compound Continuously.

[tex]A=P*e^{rt}[/tex]

P = 40,000

e = 2.71...

r = 2.5% = 0.025

t = 8 years

Plug in our variables and solve for the money of the account within 8 years.

A = 40,000*e^(0.025*8)

A = 40,000*e^(0.2)

A = 48,856.11033

A = $48,856.11

Flowers/week is the unit of measurement for the composite function s(W(h)).

Given that the function w(h) indicates the number of hours per week that Matthew spends picking flowers and the function s(t) approximates how many flowers he collects every hour.

The process of combining two or more functions into one function is known as the composition of functions. The output of the function enclosed in parenthesis becomes the input of the function outside of them in a composition of functions.

Hours of flowers is the unit of function s(t).

Additionally, consider that W(h) denotes the number of hours per week that Matthew spends gathering flowers.

W(h) = hours/week as a unit.

The unit of the composite function s(W(h)) will be = (Flowershours)(hoursweek) = Flowersweek.

Hence, the units of measurement for the composite function s(W(h))where the function s(t) approximates how many flowers Matthew picks per hour and the function w(h) represents how hours per week Matthew spends picking flowers is flowers/week.

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If the area is 90 square units. Then the dimension of the rectangle will be 5 units and 18 units.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L×W square units

The width of a rectangle is 13 units less than the length.

If the area is 90 square units.

W = L – 13

Then we have

                           90 = L(L – 13)

         L² – 13L – 90 = 0

L² – 18L + 5L – 90 = 0

L(L – 18) + 5(L – 18) = 0

         (L – 18)(L + 5) = 0

                             L = -5, 18

Then the width will be

W = 18 – 13

W = 5 units

Then the dimension of the rectangle will be 5 units and 18 units.

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The product of f(x) and g(x) is 3x²-6x+3

A function is a law that relates a dependent and independent variable with each other.

The domain of f(x) and g(x) is all real numbers

f(x) = 2x + x - 3 and g(x) = x - 1.

Then f(x).g(x) = (2x + x - 3) * ( x - 1)

f(x).g(x) = 2x² -2x +x²-x-3x+3

f(x).g(x) =3x²-6x+3

Therefore, the product of f(x) and g(x) is 3x²-6x+3.

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Using simpler trigonometric identities, the given identity was proven below.

Remember that:

[tex]sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}[/tex]

Then the identity can be rewritten as:

[tex]sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\[/tex]

Now we can multiply both sides by cos⁴(x) to get:

[tex]\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)[/tex]

Now we can use the identity:

sin²(x) + cos²(x) = 1

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

Thus, the identity was proven.

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The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ

Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]

Using the identity a² - b² = (a + b)(a - b), we have

(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]

= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =

= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)

Also, Using the identity a² - b² = (a + b)(a - b), we have

(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]

= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]

= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]

= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]

= 1 × cos⁴θ

= cos⁴θ

So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ

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Answer:

Step-by-step explanation:

[tex]F(2)=\frac{1}[3} \cdot 4^{2}=\frac{16}{3}[/tex]

The standard error for the distribution of sampling proportions will be 0.0686.

In mathematics, the difference between a data set and the populace's true average is known as primary data deviation from the mean.

According to the National Postsecondary Student Aid Study conducted by the U.S.

Department of Education in 2008, 62% of graduates from public universities had student loans.

We randomly select 50 students at a time.

Then the standard error for the distribution of sampling proportions will be

[tex]\rm Standard\ error = \sqrt{\dfrac{p(1-p)}{n}}\\\\Standard\ error = \sqrt{\dfrac{0.62(1-0.62)}{50}}\\\\Standard\ error = 0.0686[/tex]

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D.

Step-by-step explanation:

because cos0 = b/h

so cos0 = 8/15

Answer:

73 minutes and 30 seconds

Step-by-step explanation:

Answer:

y >_ - 29/8

Step-by-step explanation:

The measure of arc BEC in circle D is 134°

From the question, we are to determine the measure of arc BEC

Measure of arc BEC = 2 × m∠BAC

First, we will determine the measure of angle ACB

From one of the circle theorems,

The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference

∴ m∠ACB = 1/2 × 76°

m∠ACB = 38°

Then,

m∠BAC + m∠ACB + m∠ABC = 180° (Sum of angles in a triangle)

m∠BAC + 38° + 75° = 180°

m∠BAC + 113° = 180°

m∠BAC  = 180°- 113°

m∠BAC = 67°

Then,

Measure of arc BEC = 2 × m∠BAC

Measure of arc BEC = 2 × 67°

Measure of arc BEC = 134°

Hence, the measure of arc BEC is 134°

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Answer:

21

Step-by-step explanation:

Using proportions, it is found that the ratios are given as follows:

a) 9:196.

b) 27:2744.

c) 3:14.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The scale factor is of 3:14, hence:

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