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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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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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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

Solution

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

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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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

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

Answer:

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

Step-by-step explanation:

Use point-slope form.

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.

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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.

Answer:

26

Step-by-step explanation:

PEMDAS

8 + 2 = 10

6 - 4 = 2

10 x 2 = 20

2 x 3 = 6

20 + 6 = 26

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:

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

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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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

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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Two parallel lines has the same slope.

The given line:

Is written in the form y=mx+b where m is the slope.

The slope is 8

To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:

Slope is -1/8 (it is not parallel to given line)

_______________

Slope is 1/8 (it is not parallel to given line)

________________

Slope is -8 (it is not parallel to given line)

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

Hello!

What is a slope-intercept line:

 [tex]y = mx + b[/tex]

            [tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]

           ==> value of y-intercept is '-2'

Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]

Hope that helps!

Answer: y=-2/3x-2

Step-by-step explanation:

1) Draw a triangle from one point to the next point.

For this example, I will use (-3,0) and (0,-2).

You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.

2) Find the y-intercept

Looking at the graph, you can find that the y-intercept is (0,-2).

3) Fill in the y=mx+b

y=-2/3x-2

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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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.

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

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

Answer:

the transformation matt can from A

Answer:

Q is greater than P by 291

Step-by-step explanation:

The terms of these Arithmetic Sequences are odd natural numbers, because their common difference is 2

And, sum of 'n' odd natural numbers starting from 1 = n²

P = 99² - (1) = 9800

Q = 101² - (1 + 3 + 5) = 10192

Q - P = 291

Answers:

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]

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Explanation:

We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]

Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]

I skipped steps in solving so let me know if you need to see them.

Keep in mind that cosine is negative in quadrant 2

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Once you've determined cosine, divide sine over cosine to get tangent

[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]

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To determine cosecant, we apply the reciprocal to sine.

[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]

Similarly, secant is the reciprocal of cosine

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]

Depending on your teacher, rationalizing the denominator may be optional.

Lastly, cotangent is the reciprocal of tangent

[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]

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Side notes:

Sine and cosecant are the only things positive in Q2

Everything else (cosine, tangent, secant, cotangent) are negative in Q2.