Factor completely 12a^3d^2 – 6ad^3

(625 • (a4)) + 22b4

54a4 + 22b4

Final result :

625a4 + 4b4

Answer: x + y = 180²

Step-by-step explanation:

A linear pair is a pair of adjacent, supplementary angles.

Adjacent means next to each other.

Supplementary means that the measures of the two angles add up to equal 180 degrees.

Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.

Answer:

The parent cubic function has been vertically stretched by a factor of 4.

Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]

Answer: Option B

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Graph 1

Part (a)

The function is increasing when x > 0. The function is decreasing when x < 0.

The function is never constant

An increasing portion is when the graph goes uphill when moving left to right. A decreasing portion goes in the opposite direction: it goes downhill when moving left to right.

The reason why the function is never constant is because there aren't any flat horizontal sections. Such sections are when x changes but y does not. No such sections occur.

------------------------

Graph 1

Part (b)

Domain = set of all real numbers

Range = set of y values such that [tex]y \ge 0[/tex]

The domain is the set of all real numbers because we can plug in any value for x without any restriction. There are no division by zero errors to worry about, or square roots of negative numbers to worry about either.

The range is the set of nonnegative numbers as the graph indicates. The lowest y gets is y = 0.

------------------------

Graph 1

Part (c)

The function is even

The function f(x) = 1.6x^12 is an even function due to the even number exponent. For any polynomial, as long as the exponents are all even, then the function itself is even. If all the exponents were odd, then the function would be odd. This applies to polynomials only. A power function is a specific type of polynomial.

Note in the graph, we have y axis symmetry. The mirror line is vertical and placed along the y axis. This is a visual trait of any even function.

We could use algebra to show that f(-x) = f(x) like so

f(x) = 1.6x^12

f(-x) = 1.6(-x)^12

f(-x) = 1.6x^12

The third step is possible because (-x)^12 = x^12 for all real numbers x. It's similar to how (-x)^2 = x^2. You could think of it like (-1)^2 = (1)^2

============================================================

Graph 2

Part (a)

The function is decreasing when x < 0 and when x > 0

The function is never increasing

The function is never constant

In other words, the function is decreasing over the entire domain (see part b). The only time it's not decreasing is when x = 0.

The function is decreasing because the curve is going downhill when moving to the right. You can think of it like a roller coaster of sorts.

At no point of this curve goes uphill when moving to the right. Therefore, it is never increasing. The same idea applies to flat horizontal sections, so there are no constant intervals either.

------------------------

Graph 2

Part (b)

Domain: x is any real number but [tex]x \ne 0[/tex]

Range: y is any real number but [tex]y \ne 0[/tex]

Explanation: If we tried plugging x = 0 into the function, we get a division by zero error. This doesn't happen with any other number. Therefore, the set of allowed inputs is any number but 0.

The range is a similar story. There's no way to get y = 0 as an output.

If we plugged y = 0 into the equation, then we'd get this

y = 17x^(-3)

0 = 17/(x^3)

There's no way to have the right hand side turn into 0. The numerator is 17 and won't change. Only the denominator changes. We can't have the denominator be 0.  

------------------------

Graph 2

Part (c)

The function is odd

We can prove this by showing that f(-x) = -f(x)

f(x) = 17x^(-3)

f(-x) = 17(-x)^(-3)

f(-x) = 17* ( -(x)^(-3) )

f(-x) = -17x^(-3)

f(-x) = -f(x)

This is true for nearly all real numbers x, except we can't have x = 0.

Graphic 1:

(A) If f(x) = 1.6x ¹², then f '(x) = 19.2x ¹¹. Both f '(x) and x have the same sign, which means

• for -∞ < x < 0, we have f '(x) < 0, so that f(x) is decreasing on this interval

• for 0 < x < ∞, we have f '(x) > 0, so f(x) is increasing on this interval

f(x) is not constant anywhere on its domain.

(B) Speaking of domain, since f(x) is a polynomial (albeit only one term), it has

• a domain of all real numbers

• a range of {y ∈ ℝ : y = f(x) and y ≥ 0} (in other words, all real numbers y such that y = 1.6x ¹² and y is non-negative)

(C) This function is even, since

f(-x) = 1.6 (-x)¹² = (-1)¹² × 1.6x ¹² = 1.6x ¹² = f(x)

Graphic 2:

(A) Now if f(x) = 17/x ³, then f '(x) = -51/x ⁴. Because x ⁴ ≥ 0 for all x, this means f '(x) < 0 everywhere, except at x = 0. So f(x) is decreasing for (-∞ < x < 0) U (0 < x < ∞).

(B) f(x) has

• a domain of {x ∈ ℝ : x ≠ 0} (or all non-zero real numbers)

• a range of {y ∈ ℝ : y = f(x) and y ≠ 0} (also all non-zero reals)

(C) This function is odd:

f(-x) = 17/(-x)³ = 1/(-1)³ × 17/x ³ = -17/x ³ = -f(x)

Answer:

V = 2143.57 cm^3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

The diameter is 16 so the radius is 1/2 of the diameter or 8

V = 4/3 ( 3.14) (8)^3

V =2143.57333

Rounding to the nearest hundredth

V = 2143.57 cm^3

Answer:

2143.57 cm^3

Step-by-step explanation:

V = 4/3 * 3.14 * r^3

r = 1/2 * 16 = 8

So V = 4/3 * 3.14 * 8^3

= 2143.57 cm^3.

Answer: Therefore 100 student tickets were sold

Step-by-step explanation:

Let the number of student tickets be x

So adult tickets = 390 - x

ATQ

4.5(x) + 6(390-x) = 2190

4.5x + 2340 - 6x = 2190

-1.5x + 2340 = 2190

-1.5x = 2190-2340

-1.5x = -150

x = -150/-1.5

x = 100

Therefore 100 student tickets were sold

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Answer:

[tex]5x + 2 = 100 \\ 5x = 100 - 2 \\ 5x = 98 \\ x = \frac{98}{5} \\ x = 19.6[/tex]

Answer: the answer would be x because that's the actual variable in the question then if 19.6 was not an option

Step-by-step explanation:

选项 (d)

option (d)

!!!!!!!!!

Answer:

Area of rectangle = 2H² - 5H

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

Length =2H - 5

To write the algebraic expression to model the area of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = L * H

Where;

Substituting the values into the formula, we have;

Area of rectangle = (2H - 5)*H

Area of rectangle = 2H² - 5H

Answer:

√5/121

Step-by-step explanation:

formula: a^½=√a

(⁵/¹²¹)^½=√⁵/¹²¹

Answer:

x = 1/x - 2

Step-by-step explanation:

Answer:

Point-slope form: y-4=2(x+1)

Slope intercept form: y=2x+6

I hope this helps!

Answer:

[tex]y-4=2(x+1)[/tex]

Step-by-step explanation:

Point-slope form is equal to

[tex]y-y_1=m(x-x_1)[/tex]

where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:

[tex]4-2=m(-1-(-2))[/tex]

We can simplify negative one minus negative two as positive 1.

[tex]4-2=m(1)[/tex]

4 minus 2 is 2, so m times 1 is 2. That means m is 2.

Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:

[tex]y-4=2(x+1)[/tex]

Answer:

1.572

Step-by-step explanation:

For a standard normal distribution,

P(z > c) = 0.058

To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;

Using technology or table,

Zscore equivalent to P(Z > c) = 0.058 is 1.572

Hence, c = 1.572

Answer:

Step-by-step explanation:

I am assuming i is the imaginary number:

Factor:

(3 + i)x - (4-2i) = 0.

In order for this to equal 0, x must be equal to 1-i.

I don't want to be reported to so take my word for it.

Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.

Using BTS he properties, find the unit's digit of the cube of each of the following numbers

Answer:

1 ???????

Step-by-step explanation:

Answer:

224π in^2

Step-by-step explanation:

Just plug in the values,

Surface area=2πr(h+r) [Factoring]

r=7in

h=9in

2πr(h+r)=2π*7(9+7)=14π(16)=224π in^2

Answer:

3003 ways

Step-by-step explanation:

(7+8)C5

= 15C5

= 15!/(5!10!)

= 3003

Answer:

-3x² - 2x - 54

Step-by-step explanation:

(-7²-x-5)-(3x²+x)

-7² - x - 5 - 3x² - x

-49 - x - 5 - 3x² - x

-3x² - x - x - 49 - 5

-3x² - 2x - 54

Answer:3 and 4

Step-by-step explanation:

Answer:

D.√85

Step-by-step explanation:

We can find the distance between two points using the distance between two points formula

Distance between two points formula:

d = √(x2 - x1)² + (y2 - y1)²

Where the x and y values are derived from the given points

We are given the two points (-2,7) and (7,9)

Using these points let's define the variables ( variables are x1, x2, y1, and y2)

Remember points are written as follows (x,y)

The x value of the first point is -2 so x1 = -2

The x value of the second point is 7 so x2 = 7

The y value of the first point is 7 so y1 = 7

The y value of the second point is 9 so y2 = 9

Now that we have defined each variable let's find the distance between the two points

We can do this by substituting the values into the formula

Formula: d = √(x2 - x1)² + (y2 - y1)²

Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9

Substitute values in formula

d = √(7 - (-2))² + (9 - 7)²

Evaluation:

The two negative signs cancel out on 7-(-2) and it changes to +7

d = √ (7+2)² + (9-7)²

Add 7+2 and subtract 9 and 7

d = √ (9)² + (2)²

Simplify exponents 9² = 81 and 2² = 4

We then have d = √ 81 + 4

Finally we add 81 and 4

We get that the distance between the two points is √85

Answer:

62.8

Step-by-step explanation:

Area of sector=(pi*r^2)*(theta/360)

Area of sector=(pi*100)*(72/360)=62.8

The area of the shaded sector AOB in terms of π is 20π units squared.

The area of a sector can be described as follows;

area of sector = ∅ / 360 × πr²

where

Therefore,

r = 10 units

∅ = 72°

Hence,

area of the sector = 72° / 360° × π10²

area of the sector = 7200 / 360 π

area of the sector = 20π units²

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Answer:

True negative numbers are considered as diseased individual. So, the true negative numbers will increase

Step-by-step explanation:

True negative numbers are considered as diseased individual. So, the true negative numbers will increase.

Answer:

8.7 feet

Step-by-step explanation:

Use the square area formula, a = s², where s is the side length of the square.

Plug in the area and solve for s:

a = s²

75 = s²

√75 = s

8.7 = s

So, to the nearest tenth of a foot, the height is 8.7 feet

Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 185}{32}[/tex]

[tex]Z = -2.66[/tex]

[tex]Z = -2.66[/tex] has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]

5 parachutes, which means that [tex]n = 5[/tex]

This probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Answer:

See attachment for graph

Step-by-step explanation:

Given

[tex]f(x) = \left[\begin{array}{cc}-1&x<-1\\0&-1\le x \le -1\\1&x>1\end{array}\right[/tex]

Required

The graph of the step function

Before plotting the graph, it should be noted that:

[tex]\le[/tex] and [tex]\ge[/tex] use closed circle at its end

[tex]<[/tex] and [tex]>[/tex] use open circle at its end

So, we have:

[tex]f(x) = -1,\ \ \ \ x < -1[/tex]

The line stops at -1 with an open circle      

[tex]f(x) = 0,\ \ \ \ -1 \le x \le 1[/tex]

The line starts at - 1 and stops at -1 with a closed circle at both ends

[tex]f(x) = 1,\ \ \ \ x > 1[/tex]

The line starts at 1 with an open circle

The options are not complete, so I will plot the graph myself.

See attachment for graph

Answer:

option A

Step-by-step explanation:

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