Pythagorean Theorem• Create a real-world problem involving threelengths that form a right triangle• Give the measurement of the "legs", then solvefor the missing side

Knowing that

- The number of classified documents has increased linearly.

- In 2001 there were 8.2 million documents.

- In 2005 there were 17.4 million documents.

- The variable "n" represents the number of documents (in millions) labeled as classified.

- The variable "t" represents the number of years since 2000.

The Slope-Intercept Form of the equation of a line is:

Where "m" is the slope and "b" is the y-intercept.

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

Where these two points are on the line:

In this case, you know these two points:

Then, you can substitute values into the formula and find the slope of the line:

Now you know that the form of the equation is:

In order to find "b", you need to:

- Choose one of the points on the line:

- Identify the value of each variable. Notice that:

- Substitute those values of "n" and "t", and the slope into the equation:

- Solve for "b":

Therefore the equation of the Linear Model is:

Hence, the answer is: Option D.

The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10

Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.

Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.

If the graph passes through the points (0, 0) and (2, 10), hence:

h - 10 = [(10 - 0)/(2 - 0)](t - 0)

h - 10 = 5(t)

h = 5t + 10

The graph is given as h = 5t + 10

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[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]

Answer:

[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]

[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]9\sqrt{56x^7y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 56 as 4·14:

[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 4 as 2²:

[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Simplify:

[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]

Rewrite ⁷/₂ as 3 + ¹/₂

[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]

Rearrange:

[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]

Given expression:

[tex]7\sqrt{32}-6\sqrt{72}[/tex]

Rewrite 32 as 16·2 and 72 as 36·2:

[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]

Rewrite 16 as 4² and 36 as 6²:

[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]

Simplify:

[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]

[tex]\implies -8\sqrt{2}[/tex]

The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333

Let x = number of tornados

n = 14

p = 0.03

There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03

Consequently, we may determine the probability using the binomial distribution.

Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)

Using Excel:

P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333

Be aware that the default Excel command to find binomial probabilities that are less than or equal is  "=BINOMDIST(x, n, p, 1)"

Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.

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Every column have 7 bricks

There are 8 columns,

Then there are

8x7 = 56 bricks + another 7 bricks = 63 bricks

Divide now 63 between 10

63/10 = 6 tens + 3 ones

ANSWER IS

6 TENS 3 ONES

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

Explanation:

A = probability of picking a 7

A = 1/4 since one card is labeled "7" out of four cards total

B = probability of picking an odd number

B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.

C = A*B = probability events A and B happen

C = (1/4)*(1/2)

C = 1/8

This only works when we put the first card back, which means each event is independent.

we have the expression

Multiply in cross

Simplify

z^2-4=(z+2)(z-2) -----> difference of squares

z^2+z-12=(z+4)(z-3)

substitute in the above expression

Simplify

Answer:

linear

Step-by-step explanation:

y+4x=0

-4x   -4x

=y=-4x+0

it is in the y=mx+b form so it is linear

Answer:

B. radio stations stopped advertising

Answer:

As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.

Step-by-step explanation:

In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.

Answer:

Step-by-step explanation:

square kilometre (km 2): 1,000,000    hectare: 10,000

Unit: Area in m 2                                   square meter: SI Unit

There exist more distinctions and classifications for different types of

trapezoids, but their areas are still calculated in the same manner using the

following equation: area = b 1 + b 2 2 × h where b1 and b2 are the bases. h is the height, or perpendicular distance between the bases The Farmer and his Daughter – Ramping Endeavors

Answer:

the transformation matt can from A

Answer:

what graph?

Step-by-step explanation:

By the knowledge on absolute values, functional theory and rigid transformations and given that the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.

here, we have,

According to the image attached herein,

the function f(x) is an absolute value and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of the function is conserved.

There, we can define the function g(x) as follows:

g(x) = f(x - k), for k > 0     (1)

By the knowledge on absolute values, functional theory and rigid transformations

and given that

the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

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Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:

This is the base of the parallelogram.

The height of each triangle is the radius of the circle, therefore:

The area of the parallelogram is the product of the base and the height.

So the base is pi*r;

The height is r;

The area is pi*r².

let x is the random variable that represents the speed of car.

probability that x is higher than 100 :

for x=100:

so,

probability =total area - area of the left of (z=1)

and the area of the left of z=1 is 0.8413 (from normal distribution)

The measures of the frequency distribution is;

(A) Range = 7

(B) Mean = 29

(C) Mode = 12

(D) Median = 29

(E) Variance = 7.612

(F) Standard Deviation = 2.759

A) The range of a frequency distribution is;

Range = Highest Value - Lowest Value

Thus;

Range = 32 - 25

Range = 7

B) Mean is expressed as;

x' = ∑fx/∑f

x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]

x' = 928/32

x' = 29

C) Mode is the value with the highest frequency and so in this case;

Mode = 12

D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29

E) Variance = 7.612

F) The standard deviation is;

σ = √Variance

σ = 2.759

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The intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Increased or decreased functions are two categories of functions. Consequently, a function increases when the y-values grow, while a function decreases when the y-values decrease.

The graph indicates the y-values increase in the x-intervals from -∞  to 0 and from 3.5 to ∞. You can express that a function is increasing in the following ways using interval notation:  (-∞, 0) U (3.5, ∞).

The graph, on the other hand, is decreasing: (0, 3.5)

Hence, the intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

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Solution

The mean of the internal body temperature of the 12 abducted aliens is given by;

The solutions will be (x-2)(x+1), (3x+5)(5x+2) and (x+1)(x-1) respectively using factorization.

A number or other mathematical object is factorized or factored in mathematics by writing it as the product of numerous factors, typically smaller or simpler things of the same kind.

18) 8x³-8x²-16x = 0

Taking 8x common we get,

8x(x²-x-2) = 0

x²-x-2 = 0×8x

x²-(2-1)x-2 = 0

x²-2x+x-2 = 0

x(x-2)+1(x-2) = 0

(x-2)(x+1) = 0

Hence, the factors are (x-2)(x+1).

19) 15x³+31x²+10x = 0

Taking x as common as we get,

x(15x²+31x+10) = 0

Factorize 15x²+31x+10=0

15x²+(25+6)x+10=0

15x²+25x+6x+10=0

5x(3x+5)+2(3x+5)=0

(3x+5)(5x+2)=0

Hence the factors are (3x+5)(5x+2).

20) x³-x=0

Taking x as common as we get,

x(x²-1)=0

x²-1=0

(x+1)(x-1)=0

Hence the factors are (x+1)(x-1).

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According to the solving the  Polynomial  Standard Form of the given equation is :

3x^2-7x-17.

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

f(x)= x-7

g(x)= 3x^2-7x-10

f(x)= x-7 by substituting in the value of  g into f.

f(3x^2-7x-10) =  (3x^2-7x-10)-7

                     = 3x^2-7x-17

According to the solving the slandered form of the given equation is :

3x^2-7x-17

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Recall that:

Let Victoria's speed be v.

Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.

Hence the time of journey upstream is given by:

And the time of journey downstream is given by:

Since the time of journey upstream is the same as the time of journey downstream, it follows that:

Therefore, Victoria's speed is 46 mph

If  an automatic machine inserts mixed vegetables into a plastic bag.  the probability of selecting four packages that are underweight is: 0.000000390625

Probability can be defined as the tendency or likelihood that an event will happen.

We would be making use of multiplication rule to determine the probabiliy that four packages are underweight.

Given :

Underweight = 2.5 % or 0.025

Hence,

Now let find the probability that  P (all four underweight) :

P(all four underweight) = ( 0.025 ) ( 0.025 ) ( 0.025 ) ( 0.025 )

P(all four underweight) = 0.000000390625

Therefore we can conclude that the probability is  0.000000390625.

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Answer:

-7 - 26i

Step-by-step explanation:

(5+2i)(-3 - 4i)

take this and distribute them to each other

-15 -20i -6i -8i^2

then combine like terms

-15-26i-8i^2

i^2 is always equal to -1, so replace i^2 with -1 in the problem

-15-26i-8(-1)

now solve

-15-26i+8

now combine like terms and you have your answer

-7-26i

Answer:

[tex]y=\frac{6}{5}(x-5)[/tex]

Step-by-step explanation:

Use point-slope form.

The domain will be x ≥ 3 for f(x)=√x-3 and g(x)=1-x².

In case a function f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the domain of f. there are some conditions to be checked such as denominators cannot equal 0, radicands of even roots can't have a negative value, logarithms can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x)  since it's a polynomial function its domain had to be real numbers, whereas for f(x) is all positive and real numbers.

for the given  condition (f•g)(x)

=> (f•g)(x)= f(x)*g(x)

=> (f•g)(x) = √(x-3) * (1 - x²)

=>(f•g)(x) = √(x-3)-x²(√x-3)

So the domain for (f•g)(x) will be all positive real numbers x≥3 x ∈ [3,∞)

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first we writte the information they are giving to us:

For company A:

initial fee = $90

rent per mile = $2

For combany B:

initial fee = $50

rent per mile = $3

Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)

And for company B:

Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B

and finaly we can solve for n

so if they drive for 40 miles the will pay the same

The ways to translate the figure include:

It doesn't change its orientation.

It also doesn't change its size or shape.

When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.

When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.

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Answer:

y + 4 = -6 (x - 8)

Step-by-step explanation:

Change the equation to the slope intercept form for a line

x - 6y 5 = 0  Add 5 to both sides

x - 6y = 5  Subtract x from both sides

-6y = -x + 5  Divide both sides by -6

y = [tex]\frac{1}{6}[/tex] c  - [tex]\frac{5}{-6}[/tex]  Your slope is [tex]\frac{1}{6}[/tex]

A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]

y - -4) -6(x-8)

y + 4= -6 (x -8)

Given h(x), find h(4x) as shown below

Answer

SOLUTION

Problem Statement

The question gives us an expression to simplify and we are to simplify by finding the product. We are also asked to find the degree of the polynomial as well

Method

We simply need to expand the bracket to solve this question. But the degree of the polynomial is gotten by assessing which term in the final expression has the highest power. If the expression has a term with its highest power being 3, then the degree of the polynomial is 3.

With this information, let us begin solving.

Implementation

1. Expanding the expression:

Expanding the polynomial, we have:

2. Degree of the polynomial:

From the above result, we can see that the highest degree of n in all the terms is 3, therefore, the degree of the polynomial is 3

Final answer