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Explain how you can identify the opposite and adjacent sides of a right triangle and explain how these can change in any given triangle. Use a diagram to support your explanation.

The perimeter of the triangle is the sum of the lengths of its sides, which is: 12.24

Explanation:

To show that the given points form an isosceles right angled triangle, we first need to find the lengths of the sides of the triangle using the distance formula.

Let the given points be A(4, 9, 6), B(-1, 6, 6), and C(0, 7, 10).

The distance between points A and B is given by:

AB = sqrt((4 - (-1))^2 + (9 - 6)^2 + (6 - 6)^2) = sqrt(5^2 + 3^2 + 0^2) = sqrt(34)

The distance between points A and C is given by:

AC = sqrt((4 - 0)^2 + (9 - 7)^2 + (6 - 10)^2) = sqrt(4^2 + 2^2 + 4^2) = 2*sqrt(6)

The distance between points B and C is given by:

BC = sqrt((-1 - 0)^2 + (6 - 7)^2 + (6 - 10)^2) = sqrt(1^2 + 1^2 + 4^2) = sqrt(18)

Now, we can see that the triangle ABC is not isosceles since all three sides have different lengths.

To check if the triangle is right-angled, we can use the Pythagorean theorem. If the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

Here, the longest side is AC with length 2*sqrt(6), so we need to check if:

AC^2 = AB^2 + BC^2

4*6 = 34 + 18

24 = 52

This equation is not true, so the triangle ABC is not a right-angled triangle.

Therefore, the given points do not form an isosceles right angled triangle.

The perimeter of the triangle is the sum of the lengths of its sides, which is:

AB + AC + BC = sqrt(34) + 2*sqrt(6) + sqrt(18) ≈ 12.24

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Answer:  assuming g(x) is the inverse of f(x)

domain of g(x) = range of f(x)

range of g(x) = domain of f(x)

Answer:

12.7

Step-by-step explanation:

Answer: Area for trapezoid= 1/2(4+5×1)=4.5 m

Area of triangle= Iam not exactly sure

hope this helped you a bit

Step-by-step explanation:

Siddhu's actual roll number is 660.

First, let's break down the information we have:

- Arsha's roll number is 616.
- The digits at the ones place and tens place of the sum of place values of 6 in Arsha's number need to be exchanged to find Siddhu's roll number.

Step 1: Determine the place values of the digit 6 in Arsha's roll number (616):
- The first 6 is in the hundreds place (600).
- The second 6 is in the ones place (6).

Step 2: Add the place values of the two 6s:
- 600 + 6 = 606.

Step 3: Exchange the digits at the ones place and tens place of the sum:
- The ones place digit is 6, and the tens place digit is 0.
- Exchanging these digits gives us the number 660.

Therefore, Siddhu's actual roll number is 660.

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When one zero of 3x³ 4x² - 28x - 16 is 4, another zero will be C. -2.

It should be noted that to find the other zeros of the polynomial, we can use polynomial long division or synthetic division to factorize it.

Therefore, we have factored the polynomial as:

3x³ + 4x² - 28x - 16 = (x - 4)(3x² + 16x + 32)

The discriminant is negative, so the roots are complex conjugates:

x = (-16 ± 8i*✓(2)) / 6

x = (-8 ± 4i*✓(2)) / 3

Therefore, the other zeros of the polynomial are:

x = -2, (-8 + 4i*✓(2)) / 3, (-8 - 4i*✓(2)) / 3.

So the answer is option C: -2.

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0.2a can be expressed as 0.2x, where x is the value of the variable.

To calculate the value of 0.2a in terms of x, we first need to understand what the variable a is representing. Let's assume that a is equal to some value x. Then, we can write 0.2a as 0.2x. This means that 0.2a is equal to 0.2 times the value of x, or 0.2x. To calculate the numerical value of 0.2x, we can simply multiply 0.2 by the value of x. For example, if x is equal to 5, then 0.2x is equal to 1, since 0.2 times 5 is 1. Similarly, if x is equal to 10, then 0.2x is equal to 2, since 0.2 times 10 is 2.

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Answer:

2

Step-by-step explanation:

Answer:

52 degrees

Step-by-step explanation:

the triangle has to equal 180 to be a perfect triangle so you would add 64+64=128 then subtract that from 180 to get 52.

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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1) The statement of Lin is correct.

2) (a) When scale factor, k = 9, area of the new triangle = 8100 square inches

(b) When k = 3/4, area of the new triangle = 56.25 square inches.

Given that,

A triangle has area 100 square inches.

It's dilated by a factor of k = 0.25.

When the triangle is dilated by a scale factor of k, then, each of the base and height is dilated by the scale factor of k.

So new area of the triangle after the dilation with the original triangle having base = b and height = h is,

Area of new triangle = 1/2 (kb)(kh) = k² (1/2 bh) = k² × Area of original triangle

Here original area = 100 square inches.

k = 0.25

New area = (0.25)² 100 = 6.25 square inches

So the correct statement is that of Lin.

Mai may found the new area by just multiplying the scale factor with 100, instead of taking the square of the scale factor. That is why she got 25 square inches as the new area.

2) (a) When k = 9,

Area of the new triangle = 9² (100) = 8100 square inches

(b) When k = 3/4

Area of the new triangle = (3/4)² (100) = 56.25 square inches

Hence the areas are found.

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To assess the effect of class attendance on student performance, you could conduct a regression analysis with attendance as the independent variable and student performance as the dependent variable.

The coefficients obtained from the analysis would provide information on the relationship between attendance and performance. For instance, if the coefficient for attendance is positive, it would suggest that as attendance increases, so does student performance. The values of 0, 1, 2, and 3 in the question may represent different levels of attendance, which could be used to determine the specific effect of attending more or fewer classes on student performance.
Based on your question, it seems you are interested in the relationship between class attendance and student performance. Here's an answer incorporating the terms you provided:

Class attendance can be a significant factor in student performance. As attendance increases (represented by the values 0, 1, 2, 3, with 0 being no attendance and 3 being full attendance), there is a likelihood that student performance will improve. This is because attending class allows students to engage with the material, participate in discussions, and receive guidance from teachers.

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Answer:

2/5

Step-by-step explanation:

24/60= 2/5 (If divided by 12)

Answer:

4 1/6 or 4 2/12 pounds

Step-by-step explanation:

Using Trigonometric ratios, we can conclude the length of the indicated side is 12.70m.

It can be solved using Trigonometric ratios and Pythagoras theorem

Firstly using Trigonometric ratios

Using Sinθ,

Sinθ = perpendicular / hypotenuse(h)

Sin 39 = 8 / h

0.63 = 8 / h

h = 8 / 0.63

h = 12.70

∴ The length of indicated side is 12.70m

Secondly, using Pythagoras theorem,

(hypotenuse)² = (Altitude)² + (Base)²

⇒ (H)² = 8² + 10²

⇒ (H)² = 64 + 100

⇒ (H)² = 164

⇒ H = √164

⇒ H = 12.80

∴ The length of indicated side is 12.80m

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A jug holds 10 pints of milk. If each child gets one cup of milk, it can serve 20 children. To determine how many children can be served with the 10 pints of milk, we need to convert pints to cups and divide the total amount of milk by the amount each child will receive.

1. Convert 10 pints to cups:
Since there are 2 cups in a pint, we can multiply 10 pints by 2 to get the total number of cups.
10 pints x 2 cups/pint = 20 cups of milk.
2. Divide the total cups of milk by the amount each child will receive:
Since each child gets one cup of milk, we can divide the total cups of milk by 1 to find the number of children that can be served.
20 cups ÷ 1 cup/child = 20 children.
Therefore, the jug of milk can serve 20 children if each child receives one cup of milk.

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Answer:

\(\sqrt{74}\) units

Step-by-step explanation:

Hi there!

We can use the Pythagorean theorem to solve this question:

\(a^2+b^2=c^2\) where a and b are the two legs and c is the hypotenuse

Plug in the two legs 5 and 7 and solve for c, the hypotenuse:

\(5^2+7^2=c^2\\25+49=c^2\\74=c^2\\c=\sqrt{74}\)

Therefore, the length of the hypotenuse in radical form is \(\sqrt{74}\) units.

I hope this helps!

Answer:

Step-by-step explanation:

The area of a rectangle is length time width.

A=LW

In this case,

A=32x^2+12

W=4x

Solve for L

L=A/W

Substitute

L=(32x^2+12)/4x

L=(8x^2+3)/x

The arc length is equal to the measure of the arc in radians only if the radius of the circle is 1 unit, for all the other circles this is false.

For a circle of radius R, if we have an arc defined by an angle of θ radians, then the length of that arc is:

L = R*θ

Particularly, the length is equal to the measure in radians only if the radius of the circle is R = 1:

L = 1*θ

So the statement is only true for the unit circle but is false for every other circle.

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Answer:

Step-by-step explanation:

The slope for the given situation will be $2.96. 5.92/2 = $2.96 per meal

Answer:

B

Step-by-step explanation:

x = -5

Put in -5 for x, and expand:

-40(k-x) = -40(k+5)

B. -40(k+5)

Answer:

Milky way galaxy

Step-by-step explanation:

Mark me branliest please<3

The conditional probability that the bottom card is the king of diamonds given that the bottom card is a red card is 1/26.

We need to find the conditional probability that the bottom card is the king of diamonds given that the bottom card is a red card.

So, we can use the conditional probability formula, which states that:

Conditional probability of an event A given that an event B has occurred is defined as

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

Here, we let A be the event that the bottom card is the king of diamonds, and B be the event that the bottom card is a red card.

We know that a deck of cards contains 52 cards, 26 are red, and 2 of them are the king of diamonds.

So:

P(B) = probability of a red card

      = 26/52

      = 1/2P(A and B)

      = probability of both events A and B occurring together

      = 1/52 (since there is only one king of diamonds at the bottom of the deck and it can be red or black)

Therefore, P(A|B) = P(A and B)/P(B)

                             = (1/52) / (1/2)

                             = 1/26

The conditional probability that the bottom card is the king of diamonds given that the bottom card is a red card is 1/26.

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The expression 1/(4n) satisfies the pattern observed in the sequence, and it represents the nth term of the given sequence.

To find an expression for the nth term of the given sequence, let's examine the pattern and identify the relationship between the terms.

The sequence starts with 1/4, followed by 1/8, 1/12, and 1/16. Looking closely, we can observe that each term in the sequence is the reciprocal of a multiple of 4.

Let's express the sequence in terms of the pattern we observed:

1/4 can be written as 1/(4*1),

1/8 can be written as 1/(4*2),

1/12 can be written as 1/(4*3),

1/16 can be written as 1/(4*4).

We can see that each term in the sequence can be expressed as 1 divided by the product of 4 and the corresponding term number.

Therefore, the nth term of the sequence can be written as 1/(4n).

Let's verify this expression with a few terms:

For n = 1, the first term would be 1/(4*1) = 1/4, which matches the first term of the sequence.

For n = 2, the second term would be 1/(4*2) = 1/8, which matches the second term of the sequence.

For n = 3, the third term would be 1/(4*3) = 1/12, which matches the third term of the sequence.

For n = 4, the fourth term would be 1/(4*4) = 1/16, which matches the fourth term of the sequence.

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The term that completes the blank and fits the description is an array

From the question, we understand that:

The term that fits the above highlights is array

Hence, the complete statement is:

array can hold multiple values within a single variable and is defined by having values between square brackets.

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