John drew a triangle with side lengths of 5, 12 and 13. His friend, Bryan, looked at it and asked John if it is a right triangle. John’s response was yes. Explain or show how John can prove to Bryan that the triangle is a right triangle

The solution for the given equation is, θ = 270°.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition stated by the equation, is known as solving an equation in mathematics. Solutions typically consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider, the given inequality

sinθ = -1

The general solution for sinθ = -1 is

θ = 270° + 360°n

But the condition is,  0° ≤ θ ≤ 360°

Hence, the solution for the given equation is, θ = 270°.

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Answer:

30$ per ft^2

Step-by-step explanation:

6.4x-2.1x=129

4.3x=129

x=30

:]

Answer:

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

The other half is:

The answer, considering both halves, is:

or

Answer:

[tex]10 \leq t \leq 20[/tex]

Step-by-step explanation:

Given absolute value inequality:

[tex]1000(-2|t-15|+30) \geq 20000[/tex]

Isolate the absolute value on one side of the equation:

[tex]\implies \dfrac{1000-2|t-15|+30)}{1000} \geq \dfrac{20000}{1000}[/tex]

[tex]\implies -2|t-15|+30 \geq 20[/tex]

[tex]\implies -2|t-15|+30-30 \geq 20-30[/tex]

[tex]\implies -2|t-15|\geq -10[/tex]

[tex]\implies \dfrac{-2|t-15|}{-2}\geq \dfrac{-10}{-2}[/tex]

[tex]\implies |t-15|\leq 5[/tex]

[tex]\textsf{Apply absolute rule:\quad {If} $|u| \leq a, \;a > 0$ \;then\; $-a \leq u \leq a$}[/tex]

[tex]\implies -5 \leq t-15\leq 5[/tex]

Solve both equations:

[tex]\begin{aligned}\underline{\sf Equation\;1} && \underline{\sf Equation\;2}\\t-15 &\geq -5 \quad & t-15& \leq 5\\t-15+15& \geq-5+15 &\qquad t-15+15& \leq 5+15\\t&\geq10 & t &\leq20\end{aligned}[/tex]

Merge the overlapping intervals:

[tex]10 \leq t \leq 20[/tex]

Answer:

The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. To find the function value for a given x, we first need to subtract 3 from x and then take the absolute value of the result. For example, if x = 5, then the function value would be f(5) = |5 - 3| = |2| = 2.

The domain of the function is the set of all possible values of x that we can plug into the function to get a real number result. In this case, the function will work for any real number value of x, so the domain of the function is the set of all real numbers, which can be written as:

Domain: (-∞, ∞)

In other words, the function f(x) = |x - 3| can be used to determine how far any real number x is away from the number 3 on the number line.

Answer:

(23x+4.2)

Step-by-step explanation:

A linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate is L(x)=-6 -4x .

What is function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Nearest integer is x =-1

Centre of linearization as x =-1

f(x)=3x2 +2x -3

f(-1)=3(-1)2 +2(-1) -3

f(-1)=-2

f(x)=3x2 +2x -3

f '(x)=6x +2

f '(-1)=6(-1) +2

f '(-1)= -4

L(x)=f(-1) + f '(-1) (x-(-1))

L(x)=-2 -4(x+1)

L(x)=-2 -4x -4

L(x)=-6 -4x

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Using trigonometric relations we will see that:

a =  5*√3

b = 5

The correct option is the one you marked.

For a right triangle with a known hypotenuse H and a known angle x, we can use the trigonometric relations:

cos(x)= (adjacent cathetus)/h

sin(x) = (opposite cathetus)/h

Here the hypotenuse measures 10 units, and the known angle is x = 30°.

The adjacent cathetus to that angle is a, so we can write:

cos(30°) = a/10

a = cos(30°)*10  = 10*√3/2 = 5*√3

And b is the opposite cathetus:

sin(30°) = b/10

b = 10*sin(30°) = 5

Then the correct option is the one you marked.

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The upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6 is 10.1913798 and 10.19913798.

What is upper and lower sums?

Using rectangles that are both enscribed in and circumscribed by a curve, we may approximate the area under a curve. The total area of the rectangles that are inscribed is the lower sum, while the total area of the rectangles that are circumscribed is the higher sum.

[tex]$n=6: \quad \Delta x=\frac{2 \pi}{6}$[/tex]

[tex]\begin{aligned}& \text { Lower sum }=\frac{2 \pi}{6}\left[f(-\overline{4})+f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)\right] \\& c_6=\frac{2 \pi}{6}[1+1.5+1.8660256+2+1.8660254+1.5] \\& c_6=10.1913798\end{aligned}[/tex]

upper sum:

[tex]\begin{aligned}& =\frac{2 \pi}{6}\left[f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)+f(\pi)\right] \\R_6 & =\frac{2 \pi}{6}[1.5+1.8660254+2+1.8660254+1.5+1] \\R_6 & =10.1913798]\end{aligned}[/tex]

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Answer:

Step-by-step explanation:

This in standard form (Ax + By = C.) In order to make this slope-intercept form, you need to isolate y.

y = -1.5x + 2.75

y=mx + b is slope intercept, where m is the slope and b is the y-intercept.

In this case, -1.5 is the slope and 2.75 is the y-intercept.

Hope this helps!!

By using the concept of factorization and compound interest, it can be calculated that-

1a) f(2) = 0

 b) f(x) = (x - 2)(x + 6)(x + 3)

2)   Miguel must initially invest 497118.23

What is factorization and compound interest?

Factorization is the reduction of an algebraic expression into two or more algebraic expressions of smaller degree

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

1) a) f(x) = x³+7 x²-36

      f(2) =  2³+7(2)²-36

      f(2) = 36 - 36 = 0

  b) Since f(2) = 0, (x - 2) is a factor of f(x)

      f(x) =  x²(x - 2) + 9x(x - 2) + 18(x - 2)

      f(x) = (x - 2)(x² + 9x + 18)

      f(x) = (x - 2)(x² + 6x + 3x + 18)

      f(x) = (x - 2){x(x + 6) + 3(x + 6)}

      f(x) = (x - 2)(x + 6)(x + 3)

  c) Let the principal be $p

      Rate = 3%

      Time = 4 years

      [tex]560000 = p(1 + \frac{3}{200})^{4 \times 2}\\\\560000 = p(\frac{203}{200})^8\\\\\\p = 560000 \times (\frac{200}{203})^8\\\\p = 497118.23[/tex]

      Miguel must initially invest 497118.23

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Answer:

x>9

Step-by-step explanation:

2x-5>13

2x>13+5

2x>18

x>18/2

x>9

Answer:

x > 9

Step-by-step explanation:

To find the solution to this inequality we need to follow these steps:

2x - 5 > 13

2x > 18 (-5 will be eliminated by +5 on the left side while 13 will be 18 when 5 added to it)

x > 9

[tex]3^x=(-27)^{-6} \\ \\ 3^x=(-3^3)^{-6} \\ \\ 3^x=(3^3)^{-6} \\ \\ 3^x=3^{-18} \\ \\ \boxed{x=-18}[/tex]

Answer:

Step-by-step explanation:

exponential

The median cost of the market research surveys is $900 so option (a) is correct.

Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.

As per the given surveys,

Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900.

Write the surveys in the increasing format as

$175,$850,$900,$1250,$1350

The median will be the middle value thus $900 will be correct.

Hence "The median price of the surveys for market research is $900".

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Answer:

B. x = 0 and x = 5

Step-by-step explanation:

The zeros of this function are x = 0 and x=5

_________________

Have a great day!

Based on the study, the researcher may develop a hypothesis that smoking is associated with an increased risk of depression.

An explanation that is put up for a phenomena or a group of facts is called a hypothesis. It is a speculative explanation that needs more testing and improvement because it is supported only by a small body of data. A hypothesis is not a tested theory, but rather a point of departure for more research. A hypothesis is examined in scientific study by testing and observationit. The purpose of hypothesis testing is to evaluate the likelihood that the suggested explanation is accurate and to spot any discrepancies or holes in the available data. The act of testing and improving hypotheses is a crucial component of the scientific method since it ensures that scientific ideas are supported by reliable data.

How to solve?

This hypothesis can then be tested through further research, such as conducting a larger study with more participants, or conducting experiments to evaluate the potential mechanisms by which smoking may affect the development of depression.

The researcher may also use statistical methods to analyze the data collected from the study, in order to determine the significance of the relationship between smoking and depression.

If the hypothesis is supported by the evidence, the researcher may conclude that smoking is a risk factor for depression, and may recommend interventions or preventative measures to reduce the risk of depression among smokers.

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Answer:

8x4=32

Step-by-step explanation:

I hope I helped you

If P is the minimum number of tests to achieve full statement coverage for f(x) and Q is the minimum number of tests to achieve full branch coverage for f(x), then (P,Q) =(3, 4)

Branch coverage: During program testing, every branch in a statement must be run at least once.

Coverage of the statement:

This means that during testing, every statement in the computer code must be run at least once.

All of the statements must be executed in order to obtain complete statement coverage.

Statement coverage is calculated as (statement executions divided by total statement executions).

To obtain complete statement coverage in the code above, two test cases are necessary.

Case 1: If the if condition is satisfied,

{

int res=0;

if(m<0) {res=n-m;}

return res;

}

These commands will be carried out.

Case 2: All remaining statements will also be put into effect when the other two cases of else do. Full statement coverage is attained after three tests.

Branch coverage: It includes both true and false situations and is decision-based.

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The optimal binary search tree for the given frequency is attached below.

Binary search tree:

Binary search tree refers the value of left node must be smaller than the parent node, and the value of right node must be greater than the parent node.

Given,

Here we have to plot  the optimal binary search tree for the following words, where the frequency of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).

In order to plot the binary search tree, we have to do the following steps,

Then we get the binary search tree like the following.

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Step-by-step explanation:

this is a college question ?

oh, my dear ...

we start at -426 ft.

swimming upwards reduces depth by adding hight.

so,

-426 + 212 = -214 ft

basically the same method is used as if we would subtract 212 from 426.

so, the diver is currently at -214 ft (214 ft below the surface).

Answer: y=-7

Step-by-step explanation:

Answer: y=-7

Step-by-step explanation:

Answer:

x=1   y=6

Step-by-step explanation:

???

Answer:

the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).

Step-by-step explanation:

A point (x,y) falls on a line where the constant of proportionality is k if y is equal to k times x. In other words, the equation for the line is y = kx.

Given this, we can determine which of the given points fall on a line where the constant of proportionality is k by evaluating whether the y-coordinate of each point is equal to k times the x-coordinate.

For example, if k = 2, then the point (6,8) falls on the line y = 2x because 8 is equal to 2 times 6. Similarly, the point (3,2) falls on the line y = 2x because 2 is equal to 2 times 3.

On the other hand, the point (6,4) does not fall on the line y = 2x because 4 is not equal to 2 times 6.

Therefore, the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).

Note that if k is not specified, then any of the given points could potentially fall on a line where the constant of proportionality is k, depending on the value of k.

3/2 part of the garden is planted by both the sisters.

A division is a process of splitting a specific amount into equal parts.

Given,

Jane's family divided up their garden so that 2/3 of garden will have vegetables.

Jane and her sister will plant2/3 of the vegetable portion of the garden

2/3 is the vegetable portion

In this vegetable portion 2/3 part is of the vegetable portion of the garden

3/2/2/3

3/2×3/2

6/4

3/2

Hence, 3/2 part of the garden is planted by both the sisters.

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a) The exponential function that models the population in t years after 2000 is of: P(t) = 14300(1.06)^t.

b) The estimate for the population in 2008 is of: 22792.

Considering it's standard format, the increasing exponential function is defined as follows:

P(t) = P(0)(1 + r)^t.

In which the parameters of the function are defined as follows:

Hence the values of these parameters are given as follows:

P(0) = 14300, r = 0.06.

Thus the function is given by:

P(t) = 14300(1.06)^t.

2008 is eight years after 2000, thus the estimate is P(8), which is obtained as follows:

P(8) = 14300 x (1.06)^8 = 22792.

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The expression that is a factor of the polynomial x³ + 2x² - 9x - 18 is (x + 2).

Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

For example x² - 4 can be broken as (x - 2) and (x + 2).

Therefore, the expression that factor the polynomial x³ + 2x² - 9x - 18 is as follows:

Therefore,

x³ + 2x² - 9x - 18 = (x - 3)(x² + 5x + 6)

Let's break (x² + 5x + 6) down

x² + 5x + 6

x² + 2x + 3x + 6

x(x + 2) + 3(x + 2)

(x + 3)(x + 2)

Therefore, the factors are (x + 3)(x + 2) and (x - 3)

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Answer:

The answer is C, (x+2).

Answer:

Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10

wut do i have to find

Step-by-step explanation: