first combine like terms in 3/4a + 8 - 1/4a - 2

The zeros of the polynomial function f(x) are:

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

To find the complex zeros of the given polynomial function f(x), we can use the fact that every polynomial with complex coefficients has at least one complex zero.

First, we can use the Rational Zeros Theorem to find any rational zeros. The possible rational zeros are of the form p/q, where p is a factor of the constant term 45 and q is a factor of the leading coefficient 2. Therefore, the possible rational zeros are ±1, ±3/2, ±5, ±9/2, ±15, and ±45/2. We can test each of these values using synthetic division or long division to see if they are actually zeros of the polynomial.

Using long division, we find that x=−1 and x=−3/2 are zeros of the polynomial. Therefore, we can factor out (x+1) and (x+3/2) from the polynomial to get:

f(x) = (x+1)(x+3/2)(2x^3+8x^2+14x+30)

Next, we can use the quadratic formula to find the zeros of the cubic factor 2x^3+8x^2+14x+30. The quadratic formula gives:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = 8, and c = 15. Plugging in these values, we get:

x = (-8 ± sqrt(8^2 - 4(2)(15))) / 4

= (-8 ± 2i) / 4

= -2 ± i/2

These are the exact values of the complex zeros of the polynomial function.

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Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.

To solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.

So the length of the metal strip available for the 12 holes is:

3414 - 2 - 2 = 3410 inches

Dividing this length by the number of holes gives us:

3410 ÷ 12 = 284.166666... inches

To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:

284.166666... ÷ 11 = 25.833333...

Rounding this to the nearest hundredth of an inch, we get:

25.83 inches (to the nearest hundredth)

Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.

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The weighted average price index is 171, which means that the average price of the components in Year 2 was 171% of their average price in Year 1.

To compute the weighted average of relatives, we need to find the weighted average of the ratio of the prices of each component in Year 2 to Year 1. Let's call this ratio the "relative price".

Relative price for component A = Po Year 2 / Po Year 1 = 6.00 / 3.00 = 2.00

Relative price for component B = Pn Year 2 / Pn Year 1 = 8.50 / 6.80 = 1.25

Relative price for component C = Pn Year 2 / Po Year 1 = 17.68 / 20.80 = 0.85

Next, we'll find the weighted average of the relatives by summing the product of each relative price and its corresponding standard weight, and dividing by the sum of the standard weights.

Weighted average of relatives = (2.00 * 16 + 1.25 * 6 + 0.85 * 2) / (16 + 6 + 2)

= (32 + 7.5 + 1.7) / 24

= 41.2 / 24

= 1.71

The weighted average of relatives is 1.71, which means that the average price of the components increased by 71% from Year 1 to Year 2.

To compute the weighted average price index, we'll use the weighted average of relatives as a reference point and multiply it by 100.

Weighted average price index = Weighted average of relatives * 100

= 1.71 * 100

= 171

Therefore the weighted average price index is 171, which means that the average price of the components in Year 2 was 171% of their average price in Year 1.

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Answer:

6%

Step-by-step explanation:

percent of change formula = difference between new and original values divided by original value, then multiply by 100 to get a percent

(159 - 150) / 150 = 9/150

9/150 = .06 = 6%

Answer:

To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:

distance = speed * time

Rearranging the formula, we get:

time = distance / speed

Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.

Now we can plug in the values for distance and speed into the formula:

time = 30 feet / 58.8 fps

time = 0.5104 seconds

Rounding to the nearest second, we get:

time = 0.51 seconds

So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.

Step-by-step explanation:

The value of x for the given circle will be going to be 50°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr

where r is the radius of the circle.

Angles of Intersecting Chords Theorem

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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The difference in cost between a one-line ad and a four-line ad is $14.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find how much Ben paid in sales tax, we need to first calculate the amount of the sales tax.

The sales tax is 9.5% of the purchase price of the car, which can be expressed as a decimal by dividing by 100:

Sales tax rate = 9.5% = 0.095

To find the amount of sales tax, we can multiply the purchase price by the sales tax rate

Sales tax = 0.095 x $25,500 = $2,422.50

Therefore, Ben paid $2,422.50 in sales tax.

The cost of an ad in a local paper is given by the piecewise function:

c(x) = 40, for x ≤ 5 (one-line ad)

c(x) = 40 + 7(x - 4), for x > 5 (four-line ad)

To find the difference in cost between a one-line ad and a four-line ad, we can subtract the cost of a one-line ad from the cost of a four-line ad:

c(6) - c(1) = (40 + 7(6 - 4)) - 40 = 14

Therefore, the difference in cost between a one-line ad and a four-line ad is $14.

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To find the mean (average) of a set of numbers, you add up all the numbers and then divide by the number of items in the set.

Mean = (79g + 88g + 116g + 109g + 93g) / 5

Mean = (475g) / 5

Mean = 95g

So, the mean of the set of numbers is 95g.

The value of mean of the data set is,

⇒ Mean = 97 g

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Data set is,

79g, 88g, 116g, 109g, 93g

Now, We get;

The mean of data set is,

⇒ Mean = 79g + 88g + 116g + 109g + 93g / 5

⇒ Mean = 485g / 5

⇒ Mean = 97 g

Thus, The value of mean of the data set is,

⇒ Mean = 97 g

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Answer:

Simplifying

-27 = 19 + -2x

Solving

-27 = 19 + -2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2x' to each side of the equation.

-27 + 2x = 19 + -2x + 2x

Combine like terms: -2x + 2x = 0

-27 + 2x = 19 + 0

-27 + 2x = 19

Add '27' to each side of the equation.

-27 + 27 + 2x = 19 + 27

Combine like terms: -27 + 27 = 0

0 + 2x = 19 + 27

2x = 19 + 27

Combine like terms: 19 + 27 = 46

2x = 46

Divide each side by '2'.

x = 23

Simplifying

x = 23

The percentage of gratuity paid is 20%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount for the bill = $50

Amount paid = $60

The amount of gratuity.

= 60 - 50

= $10

Now,

The percentage of gratuity.

= 10/50 x 100

= 20%

Thus,

The percentage of gratuity is 20%.

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Step-by-step explanation:

Since every single mile it descends the same amount (which is 500ft), that means it's linear, so we'll use that they gave us, the h(x) = mx+b

To find m, we use the following equation

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

to find b, we have to find out the starting point. luckily they gave it to us, which is 4,000ft. B = 4000

Now every 500 feet, we go down 1 mile

Which means at 1000 feet, we go down 2 miles

500 and 1000 can be our y1 and y2

1 and 2 can be our x1 and x2

[tex] \frac{1000 - 500}{2 - 1} = \frac{500}{1} = 500 = m[/tex]

Now that we have our m and b, we just put it together

[tex]h(x) = - 500x + 4000[/tex]

A negative was placed before the 500 because they are descending, not ascending.

Answer:

Step-by-step explanation:

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we can use points A(4, 5) and B(9, 7):

slope = (7 - 5) / (9 - 4) = 2 / 5

So, the slope of line AB is 2/5.

The volume of the rectangular pyramid is 64 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

V = (l)(b)(h) / 3

V = (6)(8)(4) / 3

V = 192 / 3

V = 64 cubic feet.

Hence, the volume of the rectangular pyramid is 64 cubic feet.

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The correct question is:

The reasons for (1) and (2) are added below

One reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.

One reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.

This means that the candle's height is bounded and cannot continue to decrease linearly forever.

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Using logarithm expressing log b100 in terms of x and y is logb100 = 2y + x

The logarithm of a number x to base a written as logₐy is such that when a is raised to the power of x,it equals y.

Since

We desire to express logb100 in terms of x and y.

So, we proceed as follows.

We have logb100, re-writing this, we have

logb100 = logb(25 × 2)

Now, applying the addition law of logarithm which states that

logab = loga + logb.

So, we have that

logb100 = logb(25 × 2)

logb100 = logb25 + logb2

= logb5² + logb2

Now applying the power rule of logarithm which states that logaⁿ = nloga

So,

logb100 = logb5² + logb2

= 2logb5 + logb2

= 2y + x

So, logb100 = 2y + x

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The area of the parallelogram that is shown above would be = 9 yd².

A parallelogram is defined as the quadrilateral that has four sides whose sides are also parallel to each other.

The formula that can be used to calculate the area of the parallelogram = base × height ( diagonal)

The base = 4½ yd

height = 2 yd (diagonal)

Area = 4½× 2 = 9yd².

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Answer: undefined

Step-by-step explanation: can’t raise a negative number to a integer exponent

Answer:

9^1 has a power of 1.  it evaluates to 9

Step-by-step explanation:

The coordinates of the fourth vertex D = (3,−1.5).

A parallelogram has the following property AB=DC

AB=OB−OA=(3,3)−(1,5)=(2,−2)

DC=OC−OD=(8,3)−(a,b)=(2,−2)

OD=OC−DC=(8,3)−(2,−2)=(6,5)

Turn them into vectors. Position vector of point d

should be 6,5

To get the 2nd point, just do AD=BC

BC=OC−OB=(8,3)−(3,3)=(5,0)

AD=OD−OA=(a,b)−(1,5)=(5,0)

OD=OA−AD=(1,5)−(5,0)=(−4,5)

As long as the shape has four sides and two of them are parallel, and you know the length, this should work. For instance, a trapezium where AB=2DC/2CD:

A=(0,0),B=(2,0),C=(2,−1.5),D=(a,b)

AB=(2,0)DC=(2,−1.5)−(a,b)=12(2,0)(a,b)=(1,−1.5)

OR

AB=(2,0)CD=(a,b)−(2,−1.5)=12(2,0)(a,b)=(3,−1.5)

Thus, The coordinates of the fourth vertex D = (3,−1.5).

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The option B is a linear function. The solution has been obtained by using the properties of a linear function.

What is a linear function?

A function is referred to as linear if it can be represented on a graph as a straight line. Typically, the highest degree of this polynomial function is 1 or 0. Despite the fact that linear functions can be expressed in both calculus and linear algebra.

We are given four functions.

It is clearly visible that option A is not a linear function because the degree of the function is 2.

Option B is a linear function because we obtain a straight line on the graph.

Also, option C is not a linear function because the degree of the function is greater than 1.

Similarly, option D is also not a linear function because it's graph is not a straight line.

Hence, option B is a linear function.

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The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.

The new coordinates of B will be:

x-coordinate: 4 x (-2) = -8

y-coordinate: 4 x (-1) = -4

So the new vertex B' is (-8, -4).

The new coordinates of C will be:

x-coordinate: 4 x (2) = 8

y-coordinate: 4 x (-2) = -8

So the new vertex C' is (8, -8).

The new coordinates of D will be:

x-coordinate: 4(1) = 4

y-coordinate: 4(2) = 8

So the new vertex D' is (4, 8).

Therefore, the image of the resultant figure is given in the image below.

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The required value of the trigonometric function is sin (α - β) = - 10.96/15.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric ratios are given in the question, as follows:

sin α = -2/5 and cos β = -1/3

So cos α = √1 - (-2/5)² = √(1 - 4/25) = √21/5

And sin β = √1  - (-1/3)² = √(1 - 1/9) = √8/3

We have to determine the value of sin (α - β).

According to trigonometric identity,

sin (α - β) =  sinα cos β - cos α sin β

Substitute the values of sin α = -2/5 and cos β = -1/3,

sin (α - β) = (-2/5)( -1/3) - (√21/5)(√8/3)

sin (α - β) = 2/15 - (√21×8)/15

sin (α - β) = 2/15 - (√168)/15

sin (α - β) = 2/15 - 12.96/15

sin (α - β) = - 10.96/15

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The measure that changes the most is the mean and the new value is 74.33°

If a value of 71° is changed to 93°, we have:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

Mean = (58+ 61+ 93+77+ 91+ 100+ 105+ 102 + 95 + 82+ 66+ 57)/12 = 74.33°

To find the median, arrange the data in order of size and pick the middle number. That is:

57, 58, 61, 66, 77, 82, 91, 93, 95, 100, 102, 105

Median = (82+91)/2 = 86.5°

Range = 105 - 57 = 48°

IQR = 97.5 - 63.5 = 34°

Therefore, the measure that changes the most is the mean and the new value is 74.33°

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Answer: it is 86.5 i got the answer correct on test trust me i want to help you guys out.

Step-by-step explanation:

The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.

In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.

Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.

Options;

A. -0.28

B. -0.82

C. -4/5

D. -1/5

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The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of the wood necessary to frame the outside of the railing will be given as,

l² = 32² + 36²

l² = 1,024 + 1,296

l² = 2,320

I = 48.167 inches

The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

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1) the rule for the graph is y=3x+3

2) the rule for the graph is y=4x+10

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

1)  slope, m = change in y/change in x = 3/1 = 3

y-intercept = b = 3  

A line's slope intercept form is y=mx+b

Thus, the rule for the graph is y=3x+3

2)  slope, m = change in y/change in x = 4/1 = 4

y-intercept = b = 10

A line's slope intercept form is y=mx+b

Thus, the rule for the graph is y=4x+10

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