HELP which postulate proves these triangles are congruent??

Therefore, when x = 3, y = 3/4.

Given that y varies directly with x, we can express this relationship as:y = kxwhere k is the constant of proportionality. To find the value of k, we can use the given information

:y = kx => 4 = k(16) => k = 4/16 => k = 1/4

So, we have:y = (1/4)xNow, we can use this relationship to find y when

x = 3:y = (1/4)x => y = (1/4)(3) => y = 3/4

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The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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The calculated value of the probability of B is (c) 0.25

From the question, we have the following parameters that can be used in our computation:

P(A or B) = 0.3

P(A and B) = 0.2

P(A/B) =0.8

First, we have

P(A/B) = P(A and B)/P(B)

Substitute the known values in the above equation, so, we have the following representation

0.2/P(B) = 0.8

So, we have

P(B) = 0.2/0.8

Evaluate

P(B) = 0.25

Hence, the probability of B is 0.25

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The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

[tex]o = a=9[/tex]

The side labelled "f" is the hypotenuse of the triangle. Therefore:

[tex]f= 2a = 2 \cdot 9=18[/tex]

Therefore:

The value of 'n' is 18 in the given equation 8n - 5 = 139.

We have to find the value of 'n'.

To do so, we need to solve the given equation.

Let us see how we can solve the given equation.8n - 5 = 139

We need to find the value of 'n'.

Let us bring the constant term to the right side by adding 5 to both the sides of the equation.8n - 5 + 5 = 139 + 5On simplifying, we get8n = 144Now, we need to isolate 'n' to find its value.

To do so, we divide both the sides by 8.8n/8 = 144/8On simplifying, we get n = 18

Therefore, the value of 'n' is 18.

Hence, the value of 'n' is 18 in the given equation 8n - 5 = 139.

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Part A: The function is nonlinear.

Part B: We determined the function to be nonlinear because the corresponding y-values do not change by a constant rate as the x-values increase, indicating a lack of a linear relationship.

Part A: The given function is nonlinear.

Part B: To determine whether the function is linear or nonlinear, we need to examine the relationship between the x-values and the corresponding y-values in the table.

In a linear function, there is a constant rate of change between the x and y values.

This means that for every increase in x by a fixed amount, the corresponding y value will change by a constant amount.

If we look at the x-values in the given table (2, 3, 4), we can see that they are increasing by a fixed amount of 1 each time.

However, when we examine the corresponding y-values (20, 10, 40), we don't see a constant rate of change.

The y-values are not changing by the same amount for each increase in x.

For instance, when x increases from 2 to 3, the y-value decreases from 20 to 10.

This indicates a non-linear relationship as the change in y is not constant for each unit increase in x.

Additionally, when x increases from 3 to 4, the y-value jumps significantly from 10 to 40, which further confirms the nonlinear nature of the function.

Based on these observations, we can conclude that the given function is nonlinear.

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Answer:

13.4 ft

Step-by-step explanation:

[Note: See attached image to go along with explanation]

To solve this problem, we will use the Law of Cosines.

[tex]c^{2}=a^{2}+b^{2}-2ab(cosC)[/tex]

[tex]C^{2}=12^{2}+6^{2}-2(12)(6)(cos90)\\C^{2}=144+36-144(0)\\C^{2}=180\\C=\sqrt{180} \\C=13.41640786[/tex]

So, the distance from the top of the tree to the tip of the shadow is 13.4 ft long.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

Base=11.5cm

Step-by-step explanation:

Area of parallelogram = Base x Height
460/40=11.5
hope this helps

Answer:

To expand the expression (x + 3y)^4, we can use the binomial theorem. The general formula for expanding (a + b)^n is:

(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n

In this case, a = x and b = 3y, and n = 4. Let's expand the expression:

(x + 3y)^4 = C(4, 0) * x^4 * (3y)^0 + C(4, 1) * x^3 * (3y)^1 + C(4, 2) * x^2 * (3y)^2 + C(4, 3) * x^1 * (3y)^3 + C(4, 4) * x^0 * (3y)^4

Now, let's calculate the coefficients for each term:

C(4, 0) = 1

C(4, 1) = 4

C(4, 2) = 6

C(4, 3) = 4

C(4, 4) = 1

Substituting these coefficients back into the expanded expression:

(x + 3y)^4 = 1 * x^4 * 3^0 + 4 * x^3 * 3^1 + 6 * x^2 * 3^2 + 4 * x^1 * 3^3 + 1 * x^0 * 3^4

Simplifying further:

(x + 3y)^4 = x^4 + 12x^3y + 54x^2y^2 + 108xy^3 + 81y^4

Therefore, the expanded form of (x + 3y)^4 is x^4 + 12x^3y + 54x^2y^2 + 108xy^3 + 81y^4.

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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The remainder is 5 + c, which means that the expression P(x) = [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex] divided by (x + 1) results in a quotient of[tex]5x^3 + 2x^2 - 4x + 4[/tex] and a remainder of 5 + c.

To divide the polynomial P(x) = [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex] by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    [tex]5x^3 + 2x^2 - 4x + 4[/tex]

_______________________

x + 1 | [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex]

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              [tex]5x^3(x + 1)[/tex]

     _______________________

x + 1 | [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex]

- ([tex]5x^3 + 5x^2)[/tex]

This leaves us with a new polynomial:[tex]2x^3 - 7x^2 - 3x + c[/tex]. We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              [tex]5x^3(x + 1) + 2x^2(x + 1)[/tex]

     _______________________

x + 1 | [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex]

-[tex](5x^3 + 5x^2)[/tex]

_______________________

[tex]2x^2 - 3x + c[/tex]

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               [tex]5x^3(x + 1) + 2x^2(x + 1)[/tex]

     _______________________

x + 1 | [tex]5x^4 + 7x^3 - 2x^2 - 3x + c[/tex]

- [tex](5x^3 + 5x^2)[/tex]

_______________________

[tex]2x^2 - 3x + c[/tex]

-[tex](2x^2 + 2x)[/tex]

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Your teacher made a mistake. The order of multiplication matters. AB is not the same as BA in matrix multiplication.

Matrix D is 2 x 2 while matrix n is 1 x 2. A vector is a special case of a matrix.

Notice how the inner dimensions marked in bold do not match up

This would mean the matrix product [tex]D \ \cdot \ \stackrel{\to}{n}[/tex] is not possible.

I have a feeling your teacher meant to say [tex]\stackrel{\to}{n} \ \cdot \ D[/tex] instead of [tex]D \ \cdot \ \stackrel{\to}{n}[/tex]

Swap the two sets of matrix dimensions to notice the inner values in bold matching up

This match tells us that [tex]\stackrel{\to}{n} \ \cdot \ D[/tex] is possible.

We'll apply the dot product of n with the first column of D to get:

-2*(-3) + (-1)*4 = 2

This result goes in the first box.

Apply the dot product of n with the second column of D to get:

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

This is the result of the second box.

Therefore,

[tex]\stackrel{\to}{n} \ \cdot \ D = \big < 2, -1\big >[/tex]

The approximate volume of the cylinder is approximately 552.64 cubic centimeters (cm³).

To calculate the approximate volume of a cylinder, we can use the formula V = πr²h, where V represents the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

Given that the radius (r) of the cylinder is 4 cm and the height (h) is 11 cm, we can substitute these values into the formula to find the volume.

V = 3.14 [tex]\times[/tex] (4 cm)² [tex]\times[/tex] 11 cm

V = 3.14 [tex]\times[/tex] 16 cm² [tex]\times[/tex] 11 cm

V = 3.14 [tex]\times[/tex] 176 cm³

V ≈ 552.64 cm³

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A intersect b = b intersect a because the order of the sets does not matter when taking their intersection.

The intersection of two sets A and B is the collection of elements that are in both A and B. Mathematically, this is written as A ∩ B = {x ∈ A : x ∈ B}. The order of the sets does not matter, so A ∩ B = B ∩ A.

For example, let A = {1, 2, 3} and B = {2, 3, 4}. Then, A ∩ B = {2, 3} and B ∩ A = {2, 3}. As you can see, the intersection of A and B is the same as the intersection of B and A, regardless of the order of the sets.

In other words, the intersection of two sets is the collection of elements that are in both sets, and the order of the sets does not affect which elements are in the intersection. So, A intersect b and b intersect a will always be the same set.

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Answer:

x=5

Step-by-step explanation:

2x+11=6x-9

4x=20

x=5

Answer:

Step-by-step explanation:

Because all the angles of the triangle are the same, all the sides are the same. This means that the side that equals 2x+11 is the same length as the side that equals 6x-9. The next step is to make an equation out of these expressions. Because we know they are equal to the same amount, we can write 2x+11=6x-9. The step after that is to separate the variables into one side so we subtract 2x from both sides, and we get 11=4x-9. After that we have to get all the non variables onto one side so we add 9. This gets us the equation 20=4x so we divide 20 by 4 to get 5=x

Therefore the answer to this question is: the variable x equals 5.

The reflection of the rectangle over the line y = x will map the rectangle onto itself.

Therefore, the correct answer is "D. None of the above."

To determine the line over which the reflection of the rectangle will map the rectangle onto itself, we need to analyze the properties of the rectangle and the transformation of reflection.

A reflection is a transformation that flips an object over a line called the line of reflection.

In order for the reflection to map the rectangle onto itself, the line of reflection must pass through the midpoint of each side of the rectangle.

Let's consider the options given:

A. y = 0: This is the x-axis.

If the rectangle is reflected over the x-axis, the image will be upside down, not mapping the rectangle onto itself.

B. y = -2: This is a horizontal line parallel to the x-axis.

Reflecting the rectangle over this line will not map the rectangle onto itself.

C. y = x: This is a diagonal line with a slope of 1.

Reflecting the rectangle over this line will not preserve its shape and proportions, so it will not map the rectangle onto itself.

D. y = 2x: This is a diagonal line with a slope of 2.

Reflecting the rectangle over this line will also not preserve its shape and proportions, so it will not map the rectangle onto itself.

Based on the options provided, none of the given lines will map the rectangle onto itself.

Therefore, the correct answer is "D. None of the above."

It's important to note that without further information about the properties and dimensions of the rectangle, it is not possible to determine the exact line of reflection that will map the rectangle onto itself.

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The volume of the solid obtained by rotating the region bonded bt the given curves about the specified line is (19/2)π.

To find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis, we can use the method of cylindrical shells.

The region is bounded by the curves y = 2 - (1/2)x, y = 0, x = 1, and x = 2.

First, we need to determine the limits of integration for x. The region extends from x = 1 to x = 2.

Consider an infinitesimally thin vertical strip at a given x-value. The height of the strip is the difference between the upper curve y = 2 - (1/2)x and the lower curve y = 0, which is simply y = 2 - (1/2)x.

The circumference of the shell is 2πr, where r is the distance from the x-axis to the x-value.

The volume of each shell is V = 2π(2 - (1/2)x)dx.

To find the total volume, we integrate this expression from x = 1 to x = 2:

V = ∫[1,2] 2π(2 - (1/2)x)dx.

Evaluating this integral gives the volume as (19/2)π.

The correct answer is (19/2)π.

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"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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Answer:

a. The theoretical probability of rolling a 5 on a fair 6-sided die is 1/6. This is because there are six equally likely outcomes (numbers 1 through 6), and only one of them is a 5.

b. To find the experimental probability of rolling a 5, we need to count the actual occurrences of 5 in the 30 rolls and divide it by the total number of rolls. Let's say the number of times a 5 was rolled was 6. Then the experimental probability would be 6/30, which simplifies to 1/5.

c. The probabilities found in parts (a) and (b) are different because theoretical probability is based on the assumption of an idealized, fair die where all outcomes have equal likelihood. On the other hand, experimental probability is based on the actual outcomes observed in a specific set of trials. In real-world situations, the experimental probability may differ from the theoretical probability due to factors like chance, sampling error, or variations in the way the die is rolled.

Note: It would really mean the world to me if I received a special thanks from anyone viewing!!!

Answer:

[tex]\textsf{a)} \quad \dfrac{1}{6}[/tex]

[tex]\textsf{b)} \quad \dfrac{1}{5}[/tex]

c)  See below.

Step-by-step explanation:

Theoretical probability refers to the likelihood of an event occurring based on assumptions, rather than observed data. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.

For a fair 6-sided die, the theoretical probability of rolling a 5 can be calculated by dividing the number of favorable outcomes (rolling a 5) by the total number of possible outcomes (the numbers 1 to 6):

[tex]\sf P(X=5)=\dfrac{1}{6}[/tex]

[tex]\hrulefill[/tex]

Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly). It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment.

From the given table, we can see that a 5 was rolled 6 times in a trial of 30 rolls. Therefore, the experimental probability of rolling a 5 can be calculated by dividing the recorded number of times a 5 was rolled (6 times) by the total number of trials (30):

[tex]\sf P(X=5)=\dfrac{6}{30}=\dfrac{1}{5}[/tex]

[tex]\hrulefill[/tex]

The probabilities found in parts (a) and (b) are different because the theoretical probability is based on mathematical calculations and assumes that the die is fair, with all outcomes equally likely. On the other hand, the experimental probability is obtained through actual observations and can be influenced by various factors such as chance variations, sample size, or possible biases. In this case, the experimental probability is slightly higher than the theoretical probability due to chance fluctuations in the small sample size of 30 rolls. With more rolls, the experimental probability would tend to converge towards the theoretical probability.

The population proportion is approximately 0.301, the mean of the sampling distribution is 0.301, and the standard deviation of the sampling distribution is approximately 0.045 when the sample size is n=100 students.

To find the population proportion, mean, and standard deviation of the sampling distribution for samples of size n=100 students, we can use the information provided.

Population Proportion:

The population proportion is calculated by dividing the number of students who watch more than 2 hours of television (245) by the total number of students (812).

Population Proportion = 245 / 812 ≈ 0.301

Mean of the Sampling Distribution:

The mean of the sampling distribution is equal to the population proportion.

Mean of Sampling Distribution = 0.301

Standard Deviation of the Sampling Distribution:

The standard deviation of the sampling distribution can be determined using the formula:

Standard Deviation of Sampling Distribution = √[(p * (1 - p)) / n]

where p is the population proportion and n is the sample size.

Standard Deviation of Sampling Distribution = √[(0.301 * (1 - 0.301)) / 100] ≈ 0.045

Therefore, the population proportion is approximately 0.301, the mean of the sampling distribution is 0.301, and the standard deviation of the sampling distribution is approximately 0.045 when the sample size is n=100 students.

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Question

A study by doctors of children attending a certain elementary school finds that, of 812 students, 245 watch more than 2 hours of television each day. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=100 students. Round all answers to 3 decimal places.

Therefore, the height of the kite from the ground is 184.97 ft (rounded to 3 decimal places).

Let us solve the given problem,Given data,The string of the kite is 375 ft longThe angle made by the kite with a horizontal line is 50°The bottom end of the string is 5.5 ft off the groundLet's assume the kite is at point A and the bottom end of the string is at point B.

AB represents the string of the kite and AC is perpendicular to the ground.So, we have to find the height of point A from the ground.To solve this problem, we have to break the given angle of 50° into two parts such that we get a right-angled triangle.

This is because we need to use trigonometric ratios in order to solve the problem.

As per the given figure, we can see that ∠EAB = 90° - ∠BAD = 90° - (50°/2) = 65°Now, we can calculate the height of point A from point C.So, in right-angled ΔABC,

an 65° = height AB / 5.5 ft

=> AB = 5.5 tan 65° = 20.04 ft

Now, we can find the height of point A by calculating BC.In right-angled ΔABC, cos 65° = BC / 375 ft

=> BC = 375 cos 65° = 164.93 ft

So, the height of the kite from the ground is given as:height of point A = height of point C + height AB=> height of point

A = 0 + 20.04 ft + 164.93 ft= 184.97 ft

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Answer:

To simulate one trial of this situation using a random number table, we can follow these steps:Step 1: Assign the digits 00-04 to represent packages not delivered on time and 05-99 to represent packages delivered on time.Step 2: Generate a two-digit random number from the random number table.Step 3: If the generated number falls between 00 and 04, count it as a package not delivered on time. If the generated number falls between 05 and 99, count it as a package delivered on time.Step 4: Repeat steps 2 and 3 until we get a package not delivered on time.The correct option is: Read two-digit numbers. Count the number of packages that are needed in order to find one that was not delivered on time.

Step-by-step explanation:

The x-intercepts are at (1, 0) and (1/3, 0), so we plot these Points on the x-axis. The turning point is at (2/3, -5/9), so we plot this point on the graph as well.

The given function is 7(x) = 3x^2 - 4x + 1.To find the y-intercept of the given function, we must put x = 0 in the given function. Therefore,7(0) = 3(0)^2 - 4(0) + 1 ⇒ y = 1

So, the y-intercept is (0, 1).To find the x-intercepts of the given function, we must put y = 0 in the given function. Therefore,7(x) = 3x^2 - 4x + 1 ⇒ 3x^2 - 4x + 1 = 0

Using the quadratic formula, we get:$$x = \frac{4 \pm \sqrt{{(-4)}^2 - 4 \times 3 \times 1}}{2 \times 3} = \frac{4 \pm \sqrt{16 - 12}}{6} = \frac{4 \pm 2}{6}$$x = 1 or x = 1/3.So, the x-intercepts are (1, 0) and (1/3, 0).

Now, we can calculate the turning point by using the formula :$$x = \frac{-b}{2a}$$where a and b are the coefficients of the x^2 and x terms, respectively. Here, a = 3 and b = -4.

Therefore,$$x = \frac{-(-4)}{2 \times 3} = \frac{2}{3}$$Now, to find the corresponding y-coordinate of the turning point, we can substitute x = 2/3 in the given function, so:7(x) = 3x^2 - 4x + 1⇒ 7(2/3) = 3(2/3)^2 - 4(2/3) + 1⇒ y = -5/9So, the turning point is at (2/3, -5/9).

Now, we can sketch the graph using the information we have found:

The y-intercept is at (0, 1), so we plot this point on the y-axis. The x-intercepts are at (1, 0) and (1/3, 0), so we plot these points on the x-axis. The turning point is at (2/3, -5/9), so we plot this point on the graph as well.

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Answer:

5520 cubic cm

Step-by-step explanation:

The first step you have to complete in order to get the solution is to calculate the surface area of the two isosceles triangles. The formula for calculating a triangle is (hxb)/2. This makes the equation (40x18)/2, which equals 360. Because we have two of them, we multiply the answer by 2, which means the surface area of the two triangles totals 720. Next, we calculate the two big rectangles in the shape. The formula for calculating a rectangle is hxw which, in this case, makes 41x48. This equals 1968, and because we have two of them, this equals 3936. Next, we have to calculate the smaller rectangle, which is 18 by 48 feet which equals 864. Finally, we have to add these totals together, which creates the equation 720+3936+864, which equals 5520.

The length of side AB is 11.44, and the length of side BC is 8.32 in triangle ABC. Option D.

To determine the lengths of sides AB and BC in triangle ABC, we can use the concept of similarity between triangles. When two triangles are similar, their corresponding sides are proportional.

Given that triangle ABC is similar to triangle DEF, we can set up the following proportions:

AB/DE = BC/EF = AC/DF

We are given the lengths of DE, EF, FD, and AC. Plugging in the values, we have:

AB/8.8 = BC/6.4 = 7.93/6.1

Simplifying the proportion, we have:

AB = (8.8 * 7.93) / 6.1 ≈ 11.44

BC = (6.4 * 7.93) / 6.1 ≈ 8.32

Therefore, the length of side AB is approximately 11.44, and the length of side BC is approximately 8.32 in triangle ABC.

These values are obtained by using the concept of similarity and the given lengths of the corresponding sides of the two triangles. The proportions allow us to find the lengths of unknown sides by comparing them to the known sides of the similar triangles. So Option D is correct.

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Answer:

(y - 12)/3.

Step-by-step explanation:

To solve for x in the equation 3(x + 2) = y - 6, we need to isolate x on one side of the equation.

First, we will distribute the 3 to the expression inside the parentheses:

3x + 6 = y - 6

Next, we will isolate the x term by subtracting 6 from both sides:

3x = y - 12

Finally, we will solve for x by dividing both sides by 3:

x = (y - 12)/3

Therefore, the solution for x in terms of y is x = (y - 12)/3.

Answer:

therefore x = y-4

Step-by-step explanation:

[tex]3(x + 2) = y - 6 \\ 3x + 6 = y - 6 \\ 3x = y - 6 - 6 \\ 3x = y - 12 \\ \frac{3x}{3} = \frac{y - 12}{3} \\ x = y - 4[/tex]

The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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3-√11 must also be a root of f(x).

If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3+√11, then its complex conjugates must also be roots of f(x). The complex conjugate of 3+√11 is 3-√11.

Therefore, 3-√11 must also be a root of f(x).

Complex conjugates always occur in pairs, so if one complex number is a root, its conjugate is also a root.

Since the polynomial function has rational coefficients, the roots will either be rational or come in conjugate pairs.

In this case, the root 3-√11 is the conjugate of the given root 3+√11, making it a valid root of f(x). Thus, 3-√11 must also be a root of f(x).

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Answer:

39 or 39(unit)^2

Step-by-step explanation:

Area of the shape = area of the triange RMV + area of rectangle VEDR

triangle area = (base × height)/2

(6×3)/2 = 9

rectangle area = base × height

5 × 6 = 30

30+9=39

Polynomial word problems are those word problems in which one is supposed to convert the given sentences into an algebraic equation which can be further solved by finding the roots of the equation or by using the factor theorem, or other techniques used to find the solutions of a polynomial. Solving polynomial word problems involves understanding and following a set of steps as follows:

Step 1: Read and re-read the word problem carefully to understand what is required to be found.

Step 2: Identify the unknowns in the problem and assign a variable to it.

Step 3: Write the equation using the knowns, unknowns, and other data provided in the question

Step 4: Solve the equation by using the appropriate technique to find the roots of the equation.

Step 5: Verify the solution by substituting the values in the original equation. If the left-hand side of the equation is equal to the right-hand side of the equation, the solution is correct. If not, the solution is incorrect. Here is an example of a polynomial word problem:Suppose the perimeter of a rectangular plot of land is 600 meters, and its length is 4 times its width. What is the length and width of the rectangular plot?

Step 1: The problem requires finding the length and width of the rectangular plot.

Step 2: Assign a variable. Let the width of the rectangular plot be x meters. Then its length would be 4x meters.

Step 3: Write the equation. As the perimeter of the plot is 600 meters, we know that 2l + 2w = 600. Substituting l = 4x, we get

,2(4x) + 2x = 600 => 8x + 2x = 600 => 10x = 600 => x = 60 meters.

Therefore, the width of the rectangular plot is 60 meters, and the length is 4x = 240 meters.Step 4: Verify the solution. Substituting the value of x and 4x in the equation,

we get:

2(240) + 2(60) = 600 => 480 + 120 = 600.

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