Find the value of this triangle!

The solutions to the quadratic function are x = 0 and x = 4, with the negative answer first.

We can use the values of the points given in the table to form a system of equations that will allow us to find the coefficients of the quadratic function.

Let's assume that the quadratic function is of the form:

\(y = ax^2 + bx + c\)

Using the points (-2,0), (0,1), and (2,0), we can form three equations:

0 = 4a - 2b + c (equation 1)

1 = c (equation 2)

0 = 4a + 2b + c (equation 3)

Simplifying equations 1 and 3 by eliminating c, we get:

4a - 2b = -c (equation 1')

4a + 2b = -c (equation 3')

Adding equations 1' and 3', we get:

8a = -2c

c = -4a

Substituting c = -4a into equation 2, we get:

1 = -4a

a = -1/4

Substituting a = -1/4 into equation 1', we get:

-1 + 2b = 1

b = 1

Therefore, the quadratic function is:

\(y = -1/4 x^2 + x - 0\)

To find the solutions to the quadratic, we need to solve for x when y = 0:

\(0 = -1/4 x^2 + x\)

0 = x(-1/4 x + 1)

x = 0 or x = 4

Therefore, the solutions to the quadratic are x = 0 and x = 4, with the negative answer first.

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The area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints is approximately 0.6345. The area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and left endpoints is approximately 0.7595.

To estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints, we first divide the interval [1, 2] into four equal intervals. The width of each interval is (2 - 1)/4 = 1/4. The right endpoints of the intervals are 1, 5/4, 3/2, and 7/4. The height of each rectangle is f(x) evaluated at the right endpoint of the interval. The height of the first rectangle is f(1) = 1, the height of the second rectangle is f(5/4) = 4/5, the height of the third rectangle is f(3/2) = 2/3, and the height of the fourth rectangle is f(7/4) = 4/7. The area of each rectangle is its height times its width. The total area of the four rectangles is 1/4 + 4/5 + 2/3 + 4/7 = 0.6345.

To estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and left endpoints, we first divide the interval [1, 2] into four equal intervals. The width of each interval is (2 - 1)/4 = 1/4. The left endpoints of the intervals are 1, 3/4, 1/2, and 5/4. The height of each rectangle is f(x) evaluated at the left endpoint of the interval. The height of the first rectangle is f(1) = 1, the height of the second rectangle is f(3/4) = 4/3, the height of the third rectangle is f(1/2) = 2, and the height of the fourth rectangle is f(5/4) = 4/5. The area of each rectangle is its height times its width. The total area of the four rectangles is 1/4 + 4/3 + 2 + 4/5 = 0.7595.

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The area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints is approximately 0.6345. The area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and left endpoints is approximately 0.7595.

To estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints, we first divide the interval [1, 2] into four equal intervals. The width of each interval is (2 - 1)/4 = 1/4. The right endpoints of the intervals are 1, 5/4, 3/2, and 7/4. The height of each rectangle is f(x) evaluated at the right endpoint of the interval. The height of the first rectangle is f(1) = 1, the height of the second rectangle is f(5/4) = 4/5, the height of the third rectangle is f(3/2) = 2/3, and the height of the fourth rectangle is f(7/4) = 4/7. The area of each rectangle is its height times its width. The total area of the four rectangles is 1/4 + 4/5 + 2/3 + 4/7 = 0.6345.

To estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and left endpoints, we first divide the interval [1, 2] into four equal intervals. The width of each interval is (2 - 1)/4 = 1/4. The left endpoints of the intervals are 1, 3/4, 1/2, and 5/4. The height of each rectangle is f(x) evaluated at the left endpoint of the interval. The height of the first rectangle is f(1) = 1, the height of the second rectangle is f(3/4) = 4/3, the height of the third rectangle is f(1/2) = 2, and the height of the fourth rectangle is f(5/4) = 4/5. The area of each rectangle is its height times its width. The total area of the four rectangles is 1/4 + 4/3 + 2 + 4/5 = 0.7595.

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The total distance from the library to the school is 1,020,000 centimeters (1.02 x 10^6 cm), and the distance from the school to home is 480,000 centimeters (4.8 x 10^5 cm).

To find the total distance from the library to the school, we add the distance from the library to home (unknown) and the distance from home to the school (540,000 cm):

Total distance = Distance from library to home + Distance from home to school

Total distance = x + 540,000 cm

Given that the distance from home to school is 480,000 cm, we can substitute it into the equation:

Total distance = x + 480,000 cm + 540,000 cm

Total distance = x + 1,020,000 cm

Therefore, the total distance from the library to the school is 1,020,000 centimeters (1.02 x 10^6 cm).

Similarly, the distance from the school to home is given as 480,000 centimeters (4.8 x 10^5 cm).

It's important to note that the unknown distance from the library to home is represented by 'x' in this explanation, and its value is not provided in the question.

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Answer:

36°; 108°

Step-by-step explanation:

The measure of each interior angle of a regular pentagon is 108°.a) Two consecutive radii are joined to form an angle. The sum of these two angles is equal to 360° as a full rotation. Therefore, each angle formed by two consecutive radii measures (360°/5)/2 = 36°.b) A radius and a side of the polygon form an isosceles triangle with two base angles of equal measure. The sum of the angles of this triangle is 180°. Therefore, the measure of the angle formed by a radius and a side is (180° - 108°)/2 = 36°. Thus, the angle formed by the radius and the side plus two consecutive radii angles equals 180°. Hence, the angle formed by a radius and a side measures (180° - 36° - 36°) = 108°.Therefore, the measures of the angles formed by two consecutive radii and a radius, and a side of the polygon are 36° and 108°, respectively. Thus, the answer is 36°; 108°.

Answer:

\(y=2\)

Step-by-step explanation:

Standard form is y=mx+b, where m=slope and b=y-intercept

I really hope this helps :-)

\(-noorati\)

If n is a positive integer, and a and b are integers relatively prime to n such that (ordₙ(a), ordₙ(b)) = 1, then ordₙ(ab) = ordₙ(a) * ordₙ(b).

Let n be a positive integer, and let a and b be integers relatively prime to n such that (ordₙ(a), ordₙ(b)) = 1. We want to prove that ordₙ(ab) = ordₙ(a) * ordₙ(b).

First, let's denote ordₙ(a) as k and ordₙ(b) as m. This means aᵏ ≡ 1 (mod n) and bᵐ ≡ 1 (mod n).

Now, let's consider the order of ab modulo n. We want to find the smallest positive integer t such that (ab)ᵗ ≡ 1 (mod n).

Expanding (ab)ᵗ, we have (ab)ᵗ = aᵗ * bᵗ.

Since aᵏ ≡ 1 (mod n) and bᵐ ≡ 1 (mod n), we can rewrite aᵗ and bᵗ as (aᵏ)ᵗ⁄ᵏ and (bᵐ)ᵗ⁄ᵐ, respectively.

(aᵏ)ᵗ⁄ᵏ = (aᵗ)ᵏ⁄ᵏ ≡ 1ᵏ ≡ 1 (mod n)

(bᵐ)ᵗ⁄ᵐ = (bᵗ)ᵐ⁄ᵐ ≡ 1ᵐ ≡ 1 (mod n)

Therefore, we have (ab)ᵗ ≡ 1 (mod n), which implies that ordₙ(ab) divides t.

Since k is the smallest positive integer such that aᵏ ≡ 1 (mod n) and m is the smallest positive integer such that bᵐ ≡ 1 (mod n), it follows that ordₙ(a) divides t and ordₙ(b) divides t.

As a result, ordₙ(a) * ordₙ(b) divides t, satisfying the definition of the order.

Hence, we have shown that ordₙ(ab) = ordₙ(a) * ordₙ(b).

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the chi-square value corresponding to a sample size of 17 and a confidence level of 98 percent is 31.410.

To find the chi-square value corresponding to a sample size of 17 and a confidence level of 98 percent, we need to look up the critical value of the chi-square distribution.

The chi-square distribution is determined by the degrees of freedom, which in this case is equal to the sample size minus 1. Since the sample size is 17, the degrees of freedom will be 17 - 1 = 16.

To find the chi-square value at a 98 percent confidence level, we need to determine the critical value associated with an alpha level of 0.02 (since the confidence level is 98 percent, the remaining 2 percent is split into two tails, each with a probability of 1 percent or 0.01).

Using a chi-square distribution table or a statistical calculator, the critical chi-square value with 16 degrees of freedom and an alpha level of 0.02 is approximately 31.410.

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Answer:

press d

Step-by-step explanation:

Answer:

6x = - 21

Step-by-step explanation:

Given

3x - 7 = 5x ( subtract 3x from both sides )

- 7 = 2x

Then

6x = 3 × 2x = 3 × - 7 = - 21

Answer:

2

Step-by-step explanation:

Answer:

7×=5 ×=5/7

Step-by-step explanation:

Answer:

circumference= 192

Step-by-step explanation:

\(\frac{angle}{360}=\frac{arc}{circumference}\)

\(\frac{30}{360}=\frac{16}{circumference}\)

30(circumference)= 16(360)

30(circumference)= 5760

circumference= 192

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

꧁. ꧂

Step-by-step explanation:

꧁. ꧂꧁. ꧂

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

8

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

Step-by-step explanation:

First Let's know how to find the mean;

The mean is the same as the average value in a data set.

Solve;

3+4+5+7+10+12+15=56

Count; 3,4,5,7,10,12,15​=7

Now divide..

56/7 = 8

Hence, Mean of the given date is 8.

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

~[RevyBreeze]~

two sides are equal means isosceles triangle which means 2 angles are equal, and sum of all angles are = 180, so add 2 angles, subtract them from 180 and u get 3rd angle.

61 + 61 = 122

180-122= 58

x = 58

Answer:

-6.3

Step-by-step explanation:

You can do it on calculator.

Answer:

-15(4) or -4(15) or 15(-4)

Step-by-step explanation:

As long as you stick with the same variables, you can change their position in the equation or change both of their signs. This should give you the same answer.

Let's say your equation was -2(6). This means you must multiply -2 and 6. This should give you -12. You could also phrase it as 2(-6) or -6(2) or 6(-2). They all give you -12 as a result.

Answer:

(-1)(15+15+15+15)

(-15)+ (-15)+ (-15)+ (-15)

Step-by-step explanation:

Answer:

6000

Convert 8 and 10 to a decimal

8=0.8

10=0.1

0.1*0.8=0.8

4800/0.8=6000

Step-by-step explanation:

Hope this helps! =D

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An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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Answer:

Y = 4

Step-by-step explanation:

The probability at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

To determine the probability that at least 7 of the puppies will be male, we will have to use the binomial probability formula.

P(X ≥ k) = 1 - P(X < k)

where X is the number of male puppies, P is the probability of a puppy being male and k is the minimum number of male puppies required.

We can solve this problem by finding the probability that 0, 1, 2, 3, 4, 5, or 6 of the puppies are male, and then subtracting that probability from 1. We use the binomial distribution formula to find each of these individual probabilities.

P(X=k) = nCk * pk * (1-p)n-k

where n is the total number of puppies, p is the probability of a puppy being male (0.5), k is the number of male puppies, and nCk is the number of ways to choose k puppies out of n puppies. We'll use a calculator to compute each probability:

P(X < 7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

P(X = 0) = 11C0 * 0.5⁰ * (1-0.5)¹¹ = 0.00048828125

P(X = 1) = 11C1 * 0.5¹ * (1-0.5)¹⁰ = 0.00537109375

P(X = 2) = 11C2 * 0.5² * (1-0.5)⁹ = 0.03295898438

P(X = 3) = 11C3 * 0.5³ * (1-0.5)⁸ = 0.1171875

P(X = 4) = 11C4 * 0.5⁴ * (1-0.5)⁷ = 0.24609375

P(X = 5) = 11C5 * 0.5⁵ * (1-0.5)⁶ = 0.35595703125

P(X = 6) = 11C6 * 0.5⁶ * (1-0.5)⁵ = 0.32421875

P(X < 7) = 0.00048828125 + 0.00537109375 + 0.03295898438 + 0.1171875 + 0.24609375 + 0.35595703125 + 0.32421875 = 1 - P(X < 7) = 1 - 1.08184814453 = -0.08184814453 ≈ 0.0805

Therefore, the probability that at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

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There are 2 rearrangements of abcd in which no two adjacent letters are also adjacent letters in the alphabet.

What is letter arrangements?

A sorting technique that allows the person to arrange alphabets as conditioned according to the question. Then total arrangements are calculated to know the result.

According to the given question:

Using XXXX as stencil for letters arrangement

We can't put B in either of the middle positions, as there would only be the far end at which to put both A and C and we can't put two things in one slot. That is, XBXX would require A and C to both be in the red X in order to avoid putting them next to B...can't do that, so B can't go in the middle.

Similarly, we can't put C in either of the middle positions, as there would only be the far end at which to put both B and D and we can't put two things in one slot.

So, B and C must go on the ends.

BXXC can only be filled in as BDAC.

CXXB can only be filled in as CADB.

Hence there are 2 such arrangements.

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Since the terms oscillate but do not approach one single value, the sequence appears to diverge

To find the first n terms of the sequence with the given terms a1 = 1, a2 = 2, and the rule for n ≥ 2, \(an = 1/2((an-1)(an-2))\), let's use n = 30.

1. Start with the given terms: a1 = 1 and a2 = 2.
2. Use the formula to find the next terms, up to n = 30.

It's important to calculate some of the terms in the sequence to determine if it converges or diverges. However, due to the character limit, I can't list all 30 terms here. Nevertheless, let's calculate the first few terms:

⇒ \(a_{3}= \frac{1}{2} ((a_{3})(a_{3})\)

= \(= \frac{1}{2} ((2)(1))\)

= 1
⇒\(= a_{4}= \frac{1}{2} ((a_{3})(a_{2}))\)

= \(\frac{1}{2} ((1)(2))\)

= 1
⇒\(a_{5}= \frac{1}{2} ((a_{4}) (a_{3}))\)

\(=\frac{1}{2} ((1)(1))\)

= 0.5

By examining the terms of the sequence, we can see that they oscillate but do not approach one single value. Therefore, the sequence appears to diverge.

Since the terms oscillate but do not approach one single value, the sequence appears to diverge.

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