A polynomial has one root that equals 5 - 7i. Name one other root of this
polynomial.

The surface area of the prism is 224 ft².

Having identical endpoints in three dimensions, a prism is a solid object. This combination consists of flat faces, identical bases, and equal cross-sections.

We are given a figure of a prism having a square base.

We know that

Surface Area of Prism (A) = 2a² + 4ah

We are given the following information:

a = 4 ft

h = 12 ft

On substituting these values in the formula, we get

⇒A = 2(4)² + 4(4)(12)

⇒A = 2(16) + (16)(12)

⇒A = 32 + 192

⇒A = 224 ft²

Hence, the surface area of the prism is 224 ft².

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Since there are multiple questions so the question answered above is attached below

25-9x² can be expressed in factor form as (5+3x)(5-3x)

An expression is combination of variables, numbers and operators.

The given expression is 25-9x²

We have to factor it completely

We have an identity that a²-b²=(a+b)(a-b)

25-9x² can be written as 5²-(3x)²

Now apply the identity

(5+3x)(5-3x)

Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)

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As a result, the length of the second rectangle is 22.5 inches.

Every square is also a rectangle because a square is a parallelogram with all particular corners at right angles. Yet not all rectangles are squares; for a rectangle to be a square, all of its sides must be the same length.

We can infer that the two rectangles may have a similar shape but differ in size because we can see how similar they are to one another.

By using the fact that the ratio of the adjacent angles of two comparable rectangles is the same, we can determine the length of the following rectangle.

Let x be the second rectangle's length. Then we can establish a ratio:

9/6 = x/15

We can cross-multiply to find x:

9 x 15 = 6 × x

135 = 6x

x = 22.5

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Answer: 1030.301 rounded is $1,030

Step-by-step explanation:

1000(1+.01)^3=1030.301

You multiply your initial amount by 1 and add your percent after you convert it to a decimal by moving your point two paces to the left. If you're withdrawing, you subtract your decimal. Everything is them raised to the power of 3. You then can multiply it on paper, my teacher lets us use calculators though to ensure we don't get an incorrect answer.

The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

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For the arithmetic sequence:

f(n) = f(1) + (n - 1)*4

Where the first term of the sequence is f(1) = 2

are:

f(1) = 2

f(2) =  6

f(3) = 10

f(4) =  14

f(5) =  18

We want to write the first five terms of a sequence, so first let's define the sequence.

We can define an arithmetic sequence with the recursive formula:

f(n) = f(n) + 4

And the explicit formula.

f(n) = f(1) + (n - 1)*4

Where we can define the first term of the sequence as f(1) = 2

Then the first five terms are:

f(1) = 2

f(2) = 2 + 4 = 6

f(3) = 6 + 4 = 10

f(4) = 10 + 4 = 14

f(5) = 14 + 4 = 18

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Answer:

I CAN NOT SEE THAT OML

Step-by-step explanation:

If the VAT in South Africa is 15%, then selling price of the laptop after the VAT is R4830 .

The cost price of the laptop before the VAT is R4200,

The VAT percent on goods and services is = 15%,

In order to calculate the selling price of the laptop that costs R4200 before VAT is added at 15% in South Africa, we can use the following formula:

⇒ Selling Price = Cost Price + (Cost Price × VAT )

Substituting the values,

We get,

⇒ Selling Price = R4200 + (R4200 × 0.15)

⇒ Selling Price = R4200 + R630

⇒ Selling Price = R4830

Therefore, the selling price of the laptop, including 15% VAT, will be R4830.

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The value of the angles of the parallelogram are 72 degree and 108 degree.

A quadrilateral with the opposing sides parallel is known as a parallelogram. It has numerous crucial traits, including:

A parallelogram has equal-length opposite sides. A parallelogram has opposite angles that are equally sized. A parallelogram's diagonals cut each other in half. A parallelogram is divided into four equal-sized triangles by its diagonals. A parallelogram's internal angles add up to 360 degrees. A parallelogram is classified as a rectangle if it also contains four right angles, making it a rectangle-shaped parallelogram.

Let us suppose the smaller angle = x.

The other angle is thus x + 36.

In a parallelogram the opposite angles are equal thus:

x + x + x + 36 + x + 36 = 360

4x + 72 = 360

4x = 288

x = 72

The value of x + 36 = 72 + 36 = 108

Hence, the value of the angles of the parallelogram are 72 degree and 108 degree.

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According to the information, the mathematical expression with which the problem is solved is 8x < 672.

To find the expression that solves this problem we must take into account that it is an inequality. So we must use the symbols greater than > or less than <. Additionally, we must read the information in the statement to identify how it goes to the inequality.

According to the above, there are less than 84 students who answered that they had never bought online (x). Then the expression would start like this:

Subsequently, they do not say that x equals one eighth of the total number of students. Then the expression would be modified like this:

Finally, if we simplify this expression, it would look like this:

So, that would be the expression of this inequality.

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Answer:

Mei and Ming both improved their yards by planting rose bushes and ivy they bought from the same store. Mei spent $36 on 3 rose bushes and 1 pot of ivy, while Ming spent $168 on 9 rose bushes and 8 pots of ivy. The cost of one rose bush and one pot of ivy would be $21, since the cost of one rose bush is $7 and one pot of ivy is $14

Step-by-step explanation:

Answer:

56.14

Step-by-step explanation:

673.36/12

The missing degrees in the circle are 260 degrees.

What is circle ?

A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.

To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.

In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.

Therefore, we can set up the following equation:

100 + x = 360

To solve for x, we can subtract 100 from both sides:

x = 260

Therefore, the missing degrees in the circle are 260 degrees.

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Answer:

Triangle A is not a scale drawing

Triangle B is a scale drawing

Triangle C is not a scale drawing

They are relatively prime.

Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,

they must have no common factors other than 1,

so they are relatively prime.

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Using the leg rule and the Pythagorean theorem, we have:

x = 4

y ≈ 4.5

The leg rule that can be use to solve the missing measures of the right triangle is given as:

hypotenuse/leg = leg/part

We have the following:

Hypotenuse = 9

Leg = 6

Part = x

Plug in the values:

9/6 = 6/x

9x = 36

x = 36/9

x = 4

Use the Pythagorean theorem to find y:

y = √(6² - 4²)

y ≈ 4.5

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Answer:

8.50667 or approximately 8.51 feet per second

Step-by-step explanation:

The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.

The region that contains the solution to the system is region B

Given the following system of inequalities

y ≤ x - 2

y ≥ 1/4x - 4

Next, we analyze each of the inequalities expressions

Inequality 1: y ≤ x - 2

Inequality 2: y ≥ 1/4x - 4

Using the above as a guide, we have the following:

This means that the intersection regionn contains the solution

This is represented by the region (b)

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The ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The given inequality is y > 3x + 4. To check which ordered pair is not a solution of this inequality, we need to substitute the values of x and y from each ordered pair into the inequality and check whether the inequality holds or not.

Checking the ordered pairs one by one, we have:

(2, 12): y = 12 and x = 2, so 12 > 3(2) + 4 is true. Therefore, (2, 12) is a solution of the inequality.

(0, 5): y = 5 and x = 0, so 5 > 3(0) + 4 is true. Therefore, (0, 5) is a solution of the inequality.

(-2, 1): y = 1 and x = -2, so 1 > 3(-2) + 4 is false. Therefore, (-2, 1) is not a solution of the inequality.

(1, 7): y = 7 and x = 1, so 7 > 3(1) + 4 is true. Therefore, (1, 7) is a solution of the inequality.

Therefore, the ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).

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For the given equation of the height the appropriate domain for this situation is 0 ≤ t ≤ 6.

The collection of all feasible input values that are appropriate for the circumstance being represented is known as the domain. In this instance, the domain stands for the range of time values relevant to the height of the football following a kick. The domain helps to avoid absurd or impossible outcomes by ensuring that the function is only evaluated for legitimate inputs.

The ball with follow a parabolic path, thus the maximum height is attained at:

t = -b/2a

Substituting the values we have:

t = -96/(-32) = 3 seconds.

The ball will then follow the downward path and will take an additional 3 seconds to reach the ground.

Thus, the total time taken will be 3 + 3 = 6 seconds.

Also, the ball initially starts from rest at 0 seconds.

Hence, the domain of the situation will be represented as 0 ≤ t ≤ 6.

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In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.

How is area determined?

The length of the other leg of the right triangle can be determined using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where the hypotenuse is c and the triangle's legs are a and b.

We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:

[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]

[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]

Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:

[tex](1/2) * Base * Height = Area[/tex]

We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:

Area: (1/2) * 4 feet * 4 square feet (3)

= 8sqrt(3) square feet

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The value of v is 8.83.

A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.

To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:

6(v-8) = 5

Then add 8 to both sides to get rid of the variable in the denominator:

6v - 48 = 5

Finally, add 48 to both sides to isolate the variable v:

6v = 53

Finally, divide both sides by 6 to solve for v:

v = 53/6 = 8.83

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Answer: 56 inches

Step-by-step explanation:

To find the length of each side, use Pythagorean's Theorem, a² + b² = c²

Note the bottom sides are the same length and the top two are the same length.

Bottom sides:

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

Top sides:

9² + 12² = c²

81 + 144 = c²

225 = c²

15 = c

Add it all together

13 + 13 + 15 + 15 = 56

The perimeter is 56 inches.

Hope this helps!

The radian measure of 180 degrees is [tex]\pi \\[/tex] radians.

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

We are given that;

Radius=5units

Radian=180 degrees

Now,

The arc length of a circle is given by the formula:

arc length = (r * theta)

where r is the radius of the circle and theta is the angle in radians subtended by the arc at the center of the circle.

We know that the radius of the circle is 5 units, and we want to find the radian measure of an arc that subtends an angle of 180 degrees.

Since 180 degrees is half of a full circle, the arc length of this arc will be half of the circumference of the circle:

arc length = (1/2) * 2 * pi * r

          = pi * r

Plugging in r = 5, we get:

arc length = pi * 5 = 5pi

Now we can use the formula for arc length to find the radian measure of the arc:

arc length = r * theta

5pi = 5 * theta

theta = pi

Therefore, by the arc length the answer will be [tex]\pi[/tex] radians.

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The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).

To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).

Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.

(-(5)/(2)) | 20  44  -17  -5
         |______________

Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.

(-(5)/(2)) | 20  44  -17  -5
         |     -50
         |______________
         | 20

Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.

(-(5)/(2)) | 20  44  -17  -5
         |     -50   3   10
         |______________
         | 20  -6  -14   5

Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).

Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).

f(x) = 20x^(3)+44x^(2)-17x-5

= (4x+1)(5x-1)(x+5)

Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).

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For two vectors to be orthogonal, their dot product should be zero.

(a) The dot product of u and v is k+21k=22k. For u and v to be orthogonal, 22k=0, which means k=0.

(b) The dot product of u and v is -2k^2+5k^2+k^2=4k^2. For u and v to be orthogonal, 4k^2=0, which means k=0.

Therefore, in both cases, the vectors are orthogonal when k=0.

Let AB and AC be vectors joining the points A(0,-1), B(1,-2), and C(4,1), respectively. Then,

AB = (1-0, -2-(-1)) = (1,-1)

AC = (4-0, 1-(-1)) = (4,2)

The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).

(a) Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(4) + (-1)(2))/sqrt(2^2+1^2 * 4^2+2^2) = 2/3

Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (4(1) + 2(-1))/sqrt(4^2+2^2 * 2^2+1^2) = 1/3

Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(3) + (-1)(-1))/sqrt(2^2+1^2 * 2^2+1^2) = 5/9

(b) Let AB and BC be vectors joining the points A(3,0,2), B(4,3,0), and C(8,1,-1), respectively. Then,

AB = (4-3, 3-0, 0-2) = (1, 3, -2)

BC = (8-4, 1-3, -1-0) = (4, -2, -1)

AC = (8-3, 1-0, -1-2) = (5, 1, -3)

The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).

Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(5) + 3(1) + (-2)(-3))/sqrt(1^2+3^2+(-2)^2 * 5^2+1^2+(-3)^2) = 0

Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (5(1) + 1(3) + (-3)(-2))/sqrt(5^2+1^2+(-3)^2 * 1^2+3^2+(-2)^2) = -7/9

Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(4) + (

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Answer:

Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).

Step-by-step explanation:

Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).

Answer:15 because it is connected to the line

Step-by-step explanation:

The time is takes to manufacture the piece after two improvements is 28 minutes

From the question, we are to calculate how long it takes to manufacture a metal piece

First, we need to find the new time taken to manufacture the metal piece after the two improvements.

The first improvement reduces the time by 8%. This means that the new time is:

32 - (8% of 32)

= 32 - 2.56

= 29.44 minutes

The second improvement reduces the time by 5%. This means that the new time is:

29.44 - (5% of 29)

= 29.44 - 1.45

= 27.99 minutes

We can round this to the nearest minute, which gives us 28 minutes.

Hence, it takes 28 minutes to manufacture the metal piece.

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