Solve 6 cos(4x) = 2 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas.

The expected value of the game in which you have a (1/20) chance of winning  is $1.50.  The probability of a student scoring between 75 and 89 is 0.5536. The probability of a student scoring above 85 is 0.4562.

1. To find the expected value of the game, we need to multiply the probability of each outcome by the value of that outcome and then add them together.

E(X) = (1/20)($300 + $15) + (19/20)(-$15)

E(X) = $315/20 - $285/20

E(X) = $30/20

E(X) = $1.50

So the expected value of the game is $1.50.

2. To find the probability of a student scoring between 75 and 89, we need to use the z-score formula:

z = (x - μ)/σ

For x = 75, z = (75 - 84)/9 = -1

For x = 89, z = (89 - 84)/9 = 0.56

Using a z-table, we can find the probability of a student scoring between these two z-scores:

P(-1 < z < 0.56) = P(z < 0.56) - P(z < -1)

P(-1 < z < 0.56) = 0.7123 - 0.1587

P(-1 < z < 0.56) = 0.5536

So the probability of a student scoring between 75 and 89 is 0.5536.

3. To find the probability of a student scoring above 85, we need to use the z-score formula:

z = (x - μ)/σ

For x = 85, z = (85 - 84)/9 = 0.11

Using a z-table, we can find the probability of a student scoring above this z-score:

P(z > 0.11) = 1 - P(z < 0.11)

P(z > 0.11) = 1 - 0.5438

P(z > 0.11) = 0.4562

So the probability of a student scoring above 85 is 0.4562.

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a) The appropriate hypothesis test for this situation is an independent samples t-test. The test statistic is the t-value, which is 0.824 b) the above hypothesis test, compute and comment on The effect size is 0.074,

The null hypothesis is that there is no difference in stress level between full-time and part-time volunteers, and the alternative hypothesis is that there is a difference in stress level between full-time and part-time volunteers.

The test statistic is the t-value, which is 0.824. The degrees of freedom is 529, which is calculated by adding the sample sizes of the two groups (336 + 195) and subtracting 2. The p-value is 0.411, which is greater than the significance level of 0.05.

This means that we fail to reject the null hypothesis and conclude that there is no significant difference in stress level between full-time and part-time volunteers.

b) The effect size for this hypothesis test can be calculated using Cohen's d, which is the difference between the two group means divided by the pooled standard deviation.

The effect size is 0.074, which is considered a small effect. This means that the difference in stress level between full-time and part-time volunteers is small and may not be practically significant.

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(fog)(-9) value is -9 when  f(x)=2x²-4x-15 and g(x)=x+12

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x)=2x²-4x-15 and g(x)=x+12

We need to find fog(-9)

Before that let us find fog(x)

f(g(x))=2(x+12)²-4(x+12)-15

f(g(-9))=2(-9+12)²-4(-9+12)-15

=2(3)²-4(3)-15

=18-12-15

=-9

Hence, (fog)(-9) value is -9 when  f(x)=2x²-4x-15 and g(x)=x+12

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Jose is in the quadrant 4 as his coordinates are (-2, -3).

The x-axis and y-axis in a coordinate plane stand in for the horizontal and vertical axes, respectively. Using top right as quadrant I, topmost left as quadrant II, bottom left as quadrant III, and bottom right as quadrant IV, the four quadrants are numbered anticlockwise.

The given coordinates are:

Cameron = (-3, 2)

Neveah = (2, -3),

Jude = (2,3) and

Jose is at (-2, -3).

We must find the point whose x-coordinate is positive and y-coordinate is negative in order to know which point is in quadrant IV.

Hence, Jose is in the quadrant 4 as his coordinates are (-2, -3).

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The correct equation that describes the relationship in the table is option B, which is y = x2 + 3.

An equation is a mathematical statement that expresses the relationship between two or more variables. Equations are used to solve problems and represent real-world relationships.

To understand why this is the correct equation, it is important to look at the values of x and y in the table. When x increases by one, the value of y increases by the same amount. This indicates that the relationship between x and y is one of direct proportionality, wherein the value of y is directly proportional to the value of x. This can be expressed mathematically as y = kx, where k is a constant.

We can also look at the values of x and y in the table to determine the value of k. When x increases from 2 to 3, the value of y increases from 7 to 17. This means that k = 10. This can be written as y = 10x.

The value of y when x = 0 is 3, which is the constant term. This can be written as y = 10x + 3.

Therefore, the equation that describes the relationship in the table is y = x2 + 3.

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Ben's ball lands approximately 2.5 seconds after Andrew's ball.

Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:

h(t) = -5t² + vt + h0

where;

Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:

h_max2 = 1.5h_max1

At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):

t_max1 = v₁ / (2 x 5)

t_max2 = v₂ / (2 x 5)

Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:

h_max2 = 1.5h_max1

-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)

Simplifying this equation, we get:

-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1

We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:

h(4) = -5(4)² + v1 * 4 = 0

-80 + 4v1 = 0

v1 = 80/4

v1 = 20 m/s

Solving these equations for t_max2 and v2, we get:

t_max1 = v1 / (2 x 5)

t_max1 = 20 / (2 x 5)  = 2 s

t_max2 = 1.5 * t_max1 = 3 s

v2 = 1.5 * v1 = 30 m/s

To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.

We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:

-5t² + v₂t = 0

-5t² + 30 = 0

5t² = 30

t² = 30/5

t² = 6

t = √6

t = 2.5 s

Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.

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There are 2 quart jars can he fill.

There is 4 pint jar can he fill with any leftover sauce.

Fractions are numerical values that are a part of whole.

Julian is making barbecue sauce to the can. He uses 6 cups white vinegar, 1/2 cup honey, and 1/2 cup maple syrup.

We know that

1 quarts = 4 cups

Total number of cups is;

6 + (1/2) + (1/2) = 7

The total number of jars that he can fill is;

= total number of cups/4

=7/4

=1.75

There are 2 quart jars can he fill.

There are pint jars he can fill with any leftover sauce is;

1 quart = 2 pints

So, 2 quart = 2 × 2 = 4 pints.

There is 4 pints jar can he fill with any leftover sauce.

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Draw a flower

Draw a cupcake

Draw a butterfly

Draw a tree

Draw a cartoon character

Draw a heart

Draw a cat

Draw a sun

Draw a bird

Draw a landscape

Draw a cloud

Draw a house

Draw a star

Draw a fish

Draw a snowman

Draw a rainbow

Draw a car

Draw a dog

Draw a person

Draw a fruit

Remember, practice makes perfect! So, keep practicing and exploring your creativity.

Answer: sm1 took my answer down but yes draw a cartoon character or something similar to an old school drawing try giving the character a new look something u never drawn before

Step-by-step explanation:

The expression [tex]20.x^25y^3+4x[/tex] is a polynomial of degree 25 and it is a binomial.

A polynomial is an expression made up of variables and coefficients, combined using addition, subtraction, and multiplication, with no division by a variable. In this expression, we have two terms, [tex]20.x^25y^3[/tex] and 4x, which are combined using addition.

Since the degree of a term is the sum of the exponents of its variables, the degree of the first term is 25 (the sum of the exponents of x and y), and the degree of the second term is 1 (the exponent of x). Since this is a polynomial with only two terms, it is a binomial.

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The midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \)[/tex].

To find the midpoint of a line segment, we can use the midpoint formula: [tex]\[ M=\left( \frac{x_1+x_2}{2})[/tex], [tex]\frac{y_1+y_2}{2} \right) \][/tex] where [tex]\( x_1 \)[/tex] and [tex]\( y_1 \)[/tex] are the coordinates of point [tex]\( A \)[/tex], and [tex]\( x_2 \)[/tex] and [tex]\( y_2 \)[/tex] are the coordinates of point[tex]\( B \)[/tex].

Plugging in the values from the given points, we get: [tex]\[ M=\left( \frac{4+(-6)}{2},\frac{4+(-4)}{2} \right) \][/tex]

Simplifying the fractions gives us: \[ M=\left( \frac{-2}{2},\frac{0}{2} \right) \]

Finally, we can simplify further to get our final answer:[tex]\[ M=(-1,0) \][/tex]

Therefore, the midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \).[/tex]

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Step-by-step explanation:

The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:

x = -b/2a

where a = 1 and b = 6 are the coefficients of the quadratic function.

x = -6/2(1) = -3

Substitute x = -3 into the function to find the minimum value:

f(-3) = (-3)^2 + 6(-3) + 11 = 2

Therefore, the minimum value of the function is 2.

The declaration made indicates that Mabel left a $15.80 gratuity.

Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.

The amount of the tip is:

Tip = Bill Amount x Tip Percentage

Tip = $79 x 0.2

Tip = $15.80

Therefore, the tip that Mabel left was $15.80.

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Answer:

Step-by-step explanation:

Let's use the variable "a" to represent the number of stamps Angela has.

From the problem, we know that Nicolas has 48 stamps, and that this is 2 times 5 less than the number of stamps Angela has. "2 times 5 less than the number of stamps Angela has" can be written as:

2(a - 5)

So the equation that relates the number of stamps Nicolas and Angela have is:

48 = 2(a - 5)

We can simplify this equation by first distributing the 2:

48 = 2a - 10

Then, we can add 10 to both sides of the equation:

58 = 2a

Finally, we can solve for a by dividing both sides by 2:

a = 29

Therefore, the equation we can use to find the number of stamps Angela has is:

2(a - 5) = 48

or, simplified:

a = 29

Answer:

Step-by-step explanation:

the diameter of the circle is approximately 1.2 kilometers.

We can use the formula for the area of a circle:

Area = pi x (diameter/2)^2

where pi is a constant approximately equal to 3.14, and diameter is the distance across the circle passing through its center.

We are given the area of the circle as 1.1304 square kilometers, so we can substitute this value into the formula and solve for diameter:

1.1304 = 3.14 x (d/2)^2

1.1304 = 0.785d^2

d^2 = 1.1304/0.785

d^2 = 1.440

d = sqrt(1.440)

d ≈ 1.2

Therefore, the diameter of the circle is approximately 1.2 kilometers.

Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

A graph is a picture of data that illustrates the connection between two or more factors. A graph in mathematics is typically a two-dimensional coordinate system with a horizontal x-axis and vertical y-axis (vertical). Data points are represented on a graph by points that are drawn with their x- and y-coordinates. The graph can be used to display trends, correlations, and temporal shifts as well as other patterns and connections between the variables. Graphs are used to aid in the interpretation and communication of data in a wide range of disciplines, including mathematics, science, economics, and social studies.

given

Locate the vertex: The vertex of a quadratic function is the lowest or highest spot on the graph. For the x-coordinate of the vertex, use the expression x = -b / (2a), and for the y-coordinate, use y = f(x), where f(x) is the quadratic function.

The places where the graph crosses the x-axis and the y-axis are known as the intercepts. If x = 0, then calculate f to determine the y-intercept (0).

Additional information: Plug a few x values into the function to determine the associated y values. You'll have more data points to display on the graph as a result.

Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

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The variables to use in a model depend on the type of model being developed and the problem being addressed. In general, variables are the inputs to a model that are used to predict the outputs or dependent variables.

In statistical models, the independent variables, also known as predictors or features, are chosen based on their ability to explain the variability in the dependent variable. For example, in a linear regression model, the independent variables may include factors such as age, income, education, and gender, which are thought to be related to the dependent variable, such as the likelihood of purchasing a product.

In machine learning models, the variables may include a wide range of features, such as text, images, or sensor data, that are used to make predictions or classifications. The process of selecting the most relevant features, also known as feature selection, is an important step in developing effective models that can generalize well to new data.

Ultimately, the choice of variables depends on the specific problem being addressed, and may involve a combination of domain expertise, statistical analysis, and machine learning techniques to identify the most important predictors or features.

P.S: An overview was given as your information is incomplete.

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Answer:

1.5 quarts/ounce

Step-by-step explanation:

I'll assume the question wants to know the simplified conversion factor for quarts and ounces.

((3/4)quart)/((1/2)oz))

Can be rewritten as:

(3/4)/(1/2) (quart/oz)

(3/4)/(1/2) can be written as:  (3/4)*(2/1)  [Invert the denominator and multiply]

(3/4)*(2/1) = (6/4)

(6/4) = (3/2)

(3/2) [or 1.5] quarts/ounce

Answer:

To determine whether the given triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

side a = 40 inches

side b = 75 inches

side c = 85 inches (the longest side)

Now we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

85^2 = 40^2 + 75^2

7225 = 1600 + 5625

7225 = 7225

Since the equation is true, we can conclude that the given triangle is a right triangle.

Answer: yes

Step-by-step explanation:

To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.

a^2 + b^2 = c^2

c is the hypotenuse, the longest side of a right triangle.

a and b are the legs of the right triangle.

40²+75²=85²

1600+5625=7225

7225=722

4/11

The probability of choosing a green marble followed by a brown marble is 4/11. Simple probability is the likelihood that an event occurs, and in this case the likelihood is 4/11. This is calculated by taking the total number of green marbles (4) divided by the total number of marbles in the jar (11).

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Step-by-step explanation:

so, let me retype this.

horizontal asymptote : y = 2

that means lim x going to ±infinity f(x) = 2.

vertical asymptotes :

x = 3

x = -4

that means the function must have these 2 points, where the expression leads to a division by 0 or something similar that would make the result undefined.

we got 4 functions :

A) y = x²/(x² + x - 12)

B) y = x²/(x² - x - 12)

C) y = 2x²/(x² + x - 12)

D) y = 2x²/(x² - x - 12)

so, for which ones we have y = 2 as limit when x goes against + or - infinity ?

that would be C and D.

A and B lead to x²/x² = 1 as limit for gigantic numbers.

C and D lead to 2x²/x² = 2 as limit.

remember, when x gets really, really big, the "±x - 12" part becomes irrelevant.

so, we look at C and D.

which one lead to a division by 0 at x = 3 and x = -4 ?

that would be C.

for x = 3

x² + x - 12 = 3² + 3 - 12 = 9 + 3 - 12 = 12 - 12 = 0

for x = -4

x² + x - 12 = (-4)² - 4 - 12 = 16 - 4 - 12 = 12 - 12 = 0

D with x² - x - 12 would have x = -3 and x = 4 as zeroes.

these are different asymptotes than requested.

so, C is the right answer.

The measure of the angle ∠Z will be 88°.

Geometry is the study of two-dimensional and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles. Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.

Given that the two angles are (9p + 20)° and (7p + 32 )°. The value of angle z is calculated as,

9p + 20 + 7p + 32 = 180

16p = 180 - 20 - 32

16p = 128

p = 8

The measure of the angle ∠Z will be,

9p + 20 + ∠Z= 180

72 + 20 + ∠Z= 180

∠Z = 180 - 72 - 20

∠Z = 88°

Therefore, the angle ∠Z is 88°.

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Answer:

  B  -4.5

Step-by-step explanation:

You want the solution to 2(x -9) = 9/(-1/3).

Simplifying the equation gives us ...

  2x -18 = -27

  2x = -9 . . . . . . . add 18

  x = -4.5 . . . . . . . divide by 2

The value -4.5 for x will make the equation true.

The polynomial g(x) can be written as the product of linear factors g(x) = (x - 5)(x - 1)(x + 3). Polynomial as the product of linear factors. g(x) = x3 – 3x2 + x + 5 g(x) = (x - 5)(x - 1)(x + 3) and all the zeroes of the function are x = 5, 1, and -3.

To find the zeros of a function, we need to set each factor of the polynomial to zero and solve for x. When x = 5, (x - 5) = 0, when x = 1, (x - 1) = 0, and when x = -3, (x + 3) = 0.

Therefore, the zeros of the function are x = 5, 1, and -3. We can use these zeros to graph the function, as each zero is a point on the x-axis. The graph of this function will have three x-intercepts at the given points. We can also use the zeros to find the y-intercept, which will be the constant term in the polynomial.

In this case, the constant term is 5, so the y-intercept will be (0, 5) the polynomial g(x) = (x - 5)(x - 1)(x + 3) has zeros at x = 5, 1, and -3, and a y-intercept at (0, 5).

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The maximum value of the objective function is 73 when x=4 and y=17 and minimum value  is 21 when x=1 and y=5.

To find the maximum and minimum values of the objective function F=5y−4x, we need to use the constraints given in the question and solve for x and y. The constraints are y≤4x+1, y≥−4x+5, and x≤4.

First, we need to graph the constraints to find the feasible region. The feasible region is the area on the graph where all the constraints are satisfied.

Next, we need to find the corner points of the feasible region. The corner points are where the constraints intersect. The corner points are (1, 5), (4, 17), and (4, 11).

Finally, we need to plug in the corner points into the objective function to find the maximum and minimum values.

F(1, 5) = 5(5) - 4(1) = 21
F(4, 17) = 5(17) - 4(4) = 73
F(4, 11) = 5(11) - 4(4) = 47

The maximum value of the objective function is 73 when x=4 and y=17. The minimum value of the objective function is 21 when x=1 and y=5.

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Answer:

144x^3+9

Step-by-step explanation:

First of all multiply 8x^2 and 18x then it is 144

The sine of angle C is √30/10.

Trigonometric ratios are mathematical expressions used to relate the angles and sides of a right-angled triangle.

Sine = Opposite / Hypotenuse

Cosine  = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent  

are the fundamental ratios in a right-angle triangle  

where

"Opposite" refers to the side opposite to the angle.

"Adjacent" refers to the side adjacent to the angle.

"Hypotenuse" refers to the longest side of the right-angled triangle

Here we have  

A right-angle triangle DCB  

Where DC = 10 units, CB = √70  

From trigonometric ratios,

Sin θ =  Opposite side/ Hypotenuse

Sin C = DB/CD

By the Pythagorean theorem  

=> DC² = CB² + DB²  

=> (10)² = (√70)² + DB²

=> 100 = 70 + DB²

=> DB² = 100 - 70

=> DB = √30

Sin C = √30/10

Therefore,

The sine of angle C is √30/10.

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The scenario that does not represent an impulse purchase is: Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother to do the oil change for free.

An impulse purchase is an unplanned purchase made on the spur of the moment, without much consideration or planning. In the first scenario, Melissa goes to get an oil change but then decides to have her car windows tinted for $300, which is an additional expense that she had not planned for. This is an impulse purchase.

In the second scenario, Melissa goes to get an oil change but then decides to spend $500 on new car stereo speakers, which is again an additional expense that she had not planned for. This is also an impulse purchase.

However, in the third scenario, Melissa decides to save the $60 and ask her brother to do the oil change for free. This decision does not involve any additional expense or impulse purchase. Instead, it is a planned decision to save money by getting the oil change done for free. Therefore, this scenario does not represent an impulse purchase.

Answer:

Below

Step-by-step explanation:

The last choice is not an impulse purchase.....it is not a purchase at all.

  the first two ARE impulse purchases.... she purchases something for which she initially had no intention.

The total number of participants in all the activities is represented by the expression 5.5s + 11.

The given information about the number of participants in each activity can be represented in the following table:

ActivityNumber of ParticipantsGolfing3(s-2)Snorkeling s Parasailings+14Surfing(1)/(2)(s+5)

To find the total number of participants in all the activities, we can add the number of participants in each activity:

Total number of participants = 3(s-2) + s + (s+14) + (1)/(2)(s+5)

Simplifying the expression gives:

Total number of participants = 5.5s + 11

Therefore, the total number of participants in all the activities is represented by the expression 5.5s + 11.

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(a) It is possible to form a triangle with the angle measures, 30°, 80°, 70°

It is not possible for all such triangles to be congruent.

(b) It is possible to form a triangle with the angle measures, 20°, 105°, 55°

It is not possible for all such triangles to be congruent.

(c) It is not possible to form a triangle with the side lengths, 4cm, 3cm, 8cm

(d) It is possible to form a triangle with these side lengths.

All such triangles are congruent

From the question, we are to determine if it is possible for a triangle to have the given angle measures or side lengths

(a) To determine if a triangle can have the angle measures 30°, 80°, and 70°, we add the angles together to see if they equal 180°, the total degrees of a triangle.

30° + 80° + 70° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures.

It is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(b) To determine if a triangle can have the angle measures 20°, 105°, and 55°, we add the angles together to see if they equal 180°.

20° + 105° + 55° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures. However, it is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(c) To determine if a triangle can have side lengths 4cm, 3cm, and 8cm, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

4cm + 3cm > 8cm

4cm + 8cm > 3cm

3cm + 8cm > 4cm

Since all three inequalities are not satisfied (4 + 3 = 7 is not greater than 8, which is the longest side), it is not possible to form a triangle with these side lengths.

(d) To determine if a triangle can have side lengths 8cm, 15cm, and 17cm, we apply the triangle inequality theorem.

8cm + 15cm > 17cm

8cm + 17cm > 15cm

15cm + 17cm > 8cm

Since all three inequalities are satisfied, it is possible to form a triangle with these side lengths.

All such triangles are congruent, since these side lengths satisfy the conditions for a unique triangle known as a Pythagorean triple.

Hence, the triangle with side lengths 8cm, 15cm, and 17cm is a right triangle, and all right triangles with these side lengths are congruent by the Pythagorean theorem.

Learn more on Determining if it is possible for a triangle to have the given angle measures or side lengths here: https://brainly.com/question/2969411

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