find the conditional probability that x is greater than 2 6 given that x is less than or equal to 1 2 .

The derivative of f(x) is

[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].

The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.

In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.

The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].

Combining these terms together, the derivative of f(x) is

[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].

This answer is the derivative of the given function. This is how the function changes as its input changes.

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The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is  [tex]-5\pi x^{\pi -1}[/tex]+  [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.

The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.

The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾

To calculate the derivative of the given function, we begin by applying the power rule to each term.

The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].

The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].

The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].

Therefore, the derivative of the given function

f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is  [tex]-5\pi x^{\pi -1}[/tex]+  [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].

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Question:

Compute the derivative of the given function.

f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]

​

Using simple division we know that the acceleration per second is 11.54 m/s.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

The division is a mathematical process that includes dividing a sum into groups of equal size.

For instance, "12 divided by 4" translates to "12 shared into 4 equal groups," which would be 3 in our example.

So, to find the acceleration per second:

We need to perform division as follows:

= 27.7/2.4

= 11.54

Therefore, using simple division we know that the acceleration per second is 11.54 m/s.

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Answer: tens

Step-by-step explanation:

The value of error term E(x,y) = 8x^2 - 8x - 56.

The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:

f(x,y) - f(a,b) = L(x,y) + E(x,y)

where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).

In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).

First, we need to calculate f(-1,-7):

f(-1,-7) = 8(-1)^2 - 8(-7) = 56

Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):

∇f(-1,-7) = (16,-8)

The linear function L(x,y) is given by:

L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)

where · denotes the dot product.

Substituting the values, we get:

L(x,y) = 56 + (16,-8) · (x+1, y+7)

= 56 + 16(x+1) - 8(y+7)

= 8x - 8y

Finally, we can calculate the error term E(x,y) as:

E(x,y) = f(x,y) - L(x,y) - f(-1,-7)

= 8x^2 - 8y - (8x - 8y) - 56

= 8x^2 - 8x - 56

Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.

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The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12

The slope of a graph is the derivative of the graph at that point.

Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).

To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.

So,  f(x) = 3x² + 7

Differentiating with respect to x,we have

df(x)/dx = d(3x² + 7)/dx

= d3x²/dx + d7/dx

= 6x + 0

= 6x

dy/dx = f'(x) = 6x

At (-2, 19), we have x = -2.

So, the slope f'(x) = 6x

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

= -12

So, the slope is -12.

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Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

Step-by-step explanation:

the volume of container B is Travers from A to B.

so, the volume of the empty space in A is exactly the volume of container B.

the volume of a cylinder is

base area × height = pi×r² × height.

the reside is as always half of the diameter.

r = 8/2 = 4 ft

the volume of the empty space in A = the volume of container B =

= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈

≈ 1,005.3 ft³

Using differentiation, the area of the triangle is decreasing at the given time.

The formula for the area of a triangle is:

A = (1/2)bh

where b is the base and h is the height.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]

Substituting the given values, we get:

[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]

Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.

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The balance of the account after the seventh deposit can be calculated using the formula below:

A = P (1 + r/n)ⁿ

where:

A = the balance of the account

P = The initial deposit of $800

r = the interest rate of 5%

n = the number of times the interest is compounded annually

n = 1

Therefore, the balance of the account after the seventh deposit is:

A = 800 (1 + 0.05/1)⁷

A = 800 (1.05)⁷

A = 800 (1.4176875)

A = 1128.54

Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.

We can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams for standard deviation of 0.13 gram.

A normal distribution is a symmetric, bell-shaped continuous probability distribution that is defined by its mean and standard deviation. The majority of the data in a normal distribution is located close to the mean, and the number of data points decreases as you deviate from the mean in either direction. Because many real-world events, like human height or test scores, have a tendency to follow a normal distribution, the normal distribution is frequently utilised in statistics. A helpful technique for determining the range of values within a normal distribution based on the mean and standard deviation is the empirical rule, commonly known as the 68-95-99.7 rule.

Given that, the mean of 3.30 grams and standard deviation of 0.13 gram.

Using the empirical formula the range that falls in 95% is associated to two standard deviations.

Mean + 2 standard deviations = 3.30 + 2(0.13) = 3.56 grams

Mean - 2 standard deviations = 3.30 - 2(0.13) = 3.04 grams

Hence, we can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams.

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Alberto's statement is flawed because all squares can be called rectangles, but not vice versa

Alberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.

While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.

A square is a special type of rectangle with all sides equal in length.

Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).

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The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.

Martin features a spinner with four compartments marked A, B, C, and D.

To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.

Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

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Answer:

Step-by-step explanation:

Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.

We set up synthetic division as follows:

-1 | 1 -3 16 20

| -1 4 -20

|_____________

1 -4 20 0

The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:

x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))

= (4 ± sqrt(-64)) / 2

= 2 ± 2i√2

Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.

The fig's right side of total surface = 42yds.

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

According to our question-

(17+17+8)yds

42yds

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The statement " the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables" is true because  continuity correction is used to adjust for the discrepancy between continuous and discrete variables when approximating a discrete distribution

The continuity correction is used when approximating a discrete distribution, such as the binomial distribution, with a continuous distribution, such as the normal distribution. The normal distribution assumes continuous variables, while the binomial distribution uses discrete variables.

The continuity correction helps to account for the fact that the normal distribution is continuous, whereas the binomial distribution is not. It adjusts the boundaries of the intervals used in the approximation, to better reflect the underlying discrete nature of the data.

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Step-by-step explanation:

1. 2/10

2.3/15

3.4/20

4. 5/25

5.6/30

6.7/35

It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.

X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.

X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.

Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.

Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.

The expected value of X is E[X] = np = 35(20/50) = 14.

The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.

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Answer:

-8: (-4, -3]

-7: (-3, -1]

(-5, -1]: (-5, -1]

(-4, -1]: (-4, -1]

[-3, 1]: [-3, 1]

(2, 1): (1, 2]

Answer:

its reflection

Step-by-step explanation:

a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Answer:

It is Reflection. Check if it is in the list.

Step-by-step explanation:

See Venn diagram below

i. The total height of the tent including the spire is 150 m.

ii. The length of the side of the tent  x is 132.7 m.

Trigonometric functions are required functions in determining either the unknown angle of length of the sides of a triangle.

Considering the given question, we have;

a. To determine the total height of the tent, let its height from the ground to the top of the tent be represented by x. Then:

Tan θ = opposite/ adjacent

Tan 42.7 = h/ 97.5

h = 0.9228*97.5

  = 89.97

h = 90 m

The total height of the tent including the spire = 90 + 60

                                           = 150 m

b. To determine the length of the side of the tent x, we have:

Cos θ = adjacent/ hypotenuse

Cos 42.7 = 97.5/ x

x = 97.5/ 0.7349

  = 132.67

The length of the side of the tent x is 132.7 m.

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The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.

To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.

To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.

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--The question is incomplete, answering to the question below--

"find the midpoint of a line and arc using straight edge-compass-construction method"

The value of the constant c that makes the following function are c = 0.

Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).

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Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.

A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.

27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.

28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.

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Complete Question:

The value of PF1 + PF2 equals to 10 for any point P on curve ellipse of equation 16x^2 + 25y^2 = 400. So, the correct answer is B).

We can start by finding the coordinates of the point P on curve of the ellipse. We can write the equation of the ellipse as:

16x^2 + 25y^2 = 400

Dividing both sides by 400, we get:

x^2/25 + y^2/16 = 1

So, the center of the ellipse is at the origin (0,0) and the semi-axes are a=5 and b=4.

Let the coordinates of point P be (x,y). Then, we can use the distance formula to find the distances PF1 and PF2:

PF1 = sqrt((x-3)^2 + y^2)

PF2 = sqrt((x+3)^2 + y^2)

Therefore, PF1 + PF2 = sqrt((x-3)^2 + y^2) + sqrt((x+3)^2 + y^2)

We can use the property that the sum of the distances from any point on an ellipse to its two foci is constant, and is equal to 2a, where a is the semi-major axis. So, we have:

PF1 + PF2 = 2a = 2(5) = 10

Therefore, PF1 + PF2 equals to 10 for any point P on the ellipse 16x^2 + 25y^2 = 400. So, the correct option is B).

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Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:

A = B + 0.2B

Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:

A = 1.2B

Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:

(B lebih kecil dari A) / A x 100%

Substitusikan nilai A = 1.2B dan kita dapatkan:

(B lebih kecil dari 1.2B) / 1.2B x 100%

Maka:

0.2B / 1.2B x 100%

= 0.1667 x 100%

= 16.67%

Jadi, B adalah 16.67% lebih kecil dari A.

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The result of the cross breeding between the heterozygous and homozygous pea plant is  the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).

When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).

The possible combinations of alleles that the offspring can inherit from their parents are:

Gg x gg

Therefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

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Answer:

the question is incomplete, so I looked for similar questions:

There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.

the answer = 3 x 4 x 2 = 24 possible combinations

Explanation:

for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich

since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24

If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.

For this question's answer, there are 2 x 5 = 10 lunch specials are possible.

The number of lunch specials possible are 10.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

We are given that;

Number of sandwiches=2

Number of drinks=5

Now,

To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.

Number of sandwich choices = 2

Number of drink choices = 5

Total number of lunch specials = 2 x 5 = 10

Therefore, by combinations and permutations there are 10 possible lunch specials.

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If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.

Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:

P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)

By the principle of inclusion-exclusion, we can write:

P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.

This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.

In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.

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Step-by-step explanation:

Set it up as a ratio:

14 is to (14 +6)   as   21 is to  ?

14/20 = 21/?

? = 21 * 20 / 14 = 30 units

Step-by-step explanation:

For RIGHT triangles, using S-O-H-C-A-H-T-O-A

A sinA= cosB         yes   12/13 = 12/13

B. sinA=tanB          no      12 /13   not equal to  5/12

C. sinB= tanA         no       5/13   not equal to  12/5

D. sinB= cosB         no        5/13   not equal to 12/13

A) sinA= cοsB statement is true. Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A.

A triangle is a twο-dimensiοnal geοmetric shape that cοnsists οf three straight line segments, called sides, that cοnnect three nοn-cοllinear pοints, called vertices.

Based οn the given image, the fοllοwing statements are true:

1. The triangle is a right triangle, which means that οne οf the angles is a right angle (90 degrees).

2. The side οppοsite the right angle is called the hypοtenuse, which is the lοngest side οf the triangle. In this case, it is the side that is labeled "c".

3. The οther twο sides οf the triangle are called legs. In this case, they are labelled "a" and "b".

4. The Pythagοrean theοrem applies tο this triangle, which states that the sum οf the squares οf the lengths οf the legs is equal tο the square οf the length οf the hypοtenuse. In οther wοrds,  [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A

A sinA= cοsB         yes     12/13 = 12/13

B. sinA=tanB          nο       12 /13   nοt equal tο  5/12

C. sinB= tanA         nο       5/13   nοt equal tο  12/5

D. sinB= cοsB         nο       5/13   nοt equal tο 12/13.

To learn more about triangle from given link:

https://brainly.com/question/2773823

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Complete Question:

In  Δ ABC , angle C is right Angle

Which Statement must be True?

A sinA= cosB

B. sinA=tanB

C. sinB= tanA

D. sinB= cosB