Find values for c and d that make h(x) continuous.

This theorem helps us identify unknown segment lengths while other segment lengths are known, which is helpful when trying to solve various problems involving intersecting chords inside of a circle.

Statement 1: The chords AB and CD cross at E in the circle O.

Reason 1 is obvious.

Draw in the chords CB and AD in statement two.

Second, a segment is determined by two points. To finish the figure, we draw chords CB and AD.

AED and CEB meet at E, according to statement 3.

Three: Lines that intersect create vertical angles.

Triangle CEA and Triangle AED are congruent, according to Statement 4.

Angle-Angle (AA) similarity is the fourth factor.

Conclusion 5: ED/EB = CE/AE.

Reason number five: Similar triangles' corresponding sides are proportionate.

Sixth statement: CE + ED = AE * EB.

Sixth reason: The equality's multiplication property.

By carrying out the aforementioned processes, we have demonstrated that AE * EB = CE * ED, which is the theorem saying that when two chords meet in a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

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Answer:

-24+4v

Step-by-step explanation:

8v-24-12v

-24+4v

Answer:

1/10, 3/10, 0.9

Step-by-step explanation:

Convert to decimals.

1/10 = 0.1

0.9

3/10 = 0.3

Arrange from least to greatest.

0.1, 0.3, 0.9

1/10, 3/10, 0.9

The graph has plotted and attached below

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2x + 3y <12.

Here The graph have plotted and attached below.

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\(2 + \frac{19}{30} = \frac{60 + 19}{30} = \frac{79}{30} \)

\( \frac{79}{30} = 2 \frac{19}{30} \)

Answer:

79/30

Step-by-step explanation:

the whole number is 60/30. If we add that to the already existing 19/30 we get 79/30.

Answer:

the correct answer is 1 29/42

Step-by-step explanation:

Answer:

10/21

Step-by-step explanation:

5/14×4/3 =

5 × 4 1

4 × 3=

 20/42

 20 ÷ 2

42 ÷ 2

= 10/21

Answer:

B 8.5 Pounds

Step-by-step explanation:

I hope this helps!

Answer: 8.5

Step-by-step explanation:

16 ounces is a pound

so we divide 136 by 16 and get 8.5

The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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Answer:

15.6.

Step-by-step explanation:

5-44• (-0.75) - 18 ÷ 2/3 • 0.8 + (-4/5)

= 5 + 33 - 27*0.8 - 0.8

= 5 + 33 -21.6 - 0.8

= 15.6.

The solution of the expression will be;

⇒ - 50.4

What is Mathematical expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5 - 44• (-0.75) - 18 ÷ 2/3 • 0.8 + (-4/5)​

Now,

Solve the expression as;

⇒ 5 - 44 • (-0.75) - 18 ÷ 2/3 • 0.8 + (-4/5)​

⇒ 5 - 44 • (-0.75) - 18 × 3/2 • 0.8 + (-4/5)​

⇒ 5 - 44• (-0.75) - 27 • 0.8 + (-4/5)​

⇒ 5 - 33 - 21.6 - 0.8

⇒ - 50.4

Thus, The solution of the expression will be;

⇒ - 50.4

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Answer:

4.5

Step-by-step explanation:

I just did this lesson and i just guessed, but i got it wrong and it said the answer was 4.5. basically, you multiply the fractions and the number value first,(like 1/6 X 0) and you do that to all of them. and then you add up all your answers, simplify them and put it in decimal form. and you get 4.5. hopefully that made enough sense.

As the given point is (60,-20), among the options the proportional relationship can be seen in (-30,10). As the points is just the half of the given cordinates.

Answer:

1235/2

Step-by-step explanation:

617.5=6175/10=1235/2

Answer:

£8.22

Step-by-step explanation:

9x33=£297

297-24.40=£272.60

297×4%=£11.88

297+11.88=£308.88

24.40×15%=£3.66

24.40+3.66=£28.06

308.88-28.06=280.82

280.82-272.60=£8.22

Answer: x=−1

Step-by-step explanation: hope this helps!

Answer:

b

Step-by-step explanation:

Answer: B <S

Step-by-step explanation:

Answer: The answer is $21.60

Step-by-step explanation:

Answer:

A. $21.60

Step-by-step explanation:

The intercepts of the equation 5x - 3y = -30 include the following:

x-intercept = (-6, 0).

y-intercept = (0, 10).

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

When the y-value = 0, the x-intercept can be calculated as follows;

5x - 3y = -30

5x - 3(0) = -30

5x = -30

x = -30/5

x = -6.

When the x-value = 0, the y-intercept can be calculated as follows;

5x - 3y = -30

5(0) - 3y = -30

3y = 30

y = 30/3

y = 10.

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Complete Question:

What are the intercepts of the equation 5x - 3y = -30?

Answer:

Step-by-step explanation:

Did you mean.

\( = \cot( \theta) . \sin(2 \theta) \)

\( = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )\)

\( = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } \)

\( = 2 \cos {}^{2} ( \theta) \)

\( = 2.(1 - \sin {}^{2} ( \theta) )\)

\( = 2 - 2 \sin {}^{2} ( \theta) \)

No option Solution.

Answer:

If the minimum reward is less than negative infinity, then the discounted reward can be unbounded.

Step-by-step explanation:

The following statements are true about discounted reward:

Maximizing for discounted reward does not always boil down to greedily maximizing for the immediate reward, since it takes into account the value of future rewards as well.

Discounted reward is guaranteed to be finite when the maximum reward is finite.

Discounted reward can be unbounded when the maximum reward is infinite.

Discounted reward converges to a finite value if the discount factor is less than 1 and the minimum reward possible from any state is greater than or equal to negative infinity.

However, if the minimum reward is less than negative infinity, then the discounted reward can be unbounded.

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Using limit definition of big O, we can show that (x²+1)/(x+1) is O(x) as the limit of (x²+1)/(x+1) as x approaches infinity is finite. Therefore, (x²+1)/(x+1) grows no faster than a linear function, which implies that it is O(x).

To show that (x²+1)/(x+1) is o(x), we need to prove that the limit of the ratio of the function and x as x approaches infinity is equal to 0. That is, we need to prove

lim (x²+1)/(x+1) / x as x → ∞ = 0

To evaluate this limit, we can use L'Hopital's rule. Taking the derivative of the numerator and denominator with respect to x gives

lim (2x) / 1 as x → ∞ = ∞

Since the limit of the ratio is not equal to 0, we can conclude that (x²+1)/(x+1) is not o(x). In fact, (x²+1)/(x+1) is actually O(x), which means it grows no faster than x.

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In order for a function to be considered o(x) as x approaches 0, the limit of the absolute value of the function divided by x must approach 0.

However, in this case, the limit is equal to 1, indicating that the function does not satisfy the condition for being o(x) as x approaches 0.

To prove that (x^2 + 1)/(x + 1) is o(x) as x approaches 0, we need to show that the absolute value of (x^2 + 1)/(x + 1) divided by x approaches 0 as x approaches 0.

Let's calculate the limit:

lim(x→0) |(x^2 + 1)/(x + 1) / x|

We can simplify the expression inside the absolute value by multiplying the numerator and denominator by (x - 1):

lim(x→0) |(x^2 + 1)/(x + 1) / x| = lim(x→0) |(x^2 + 1)/(x + 1) * (1/x)|

Now, we can simplify further by canceling out x terms:

lim(x→0) |(x + 1) / (x + 1)| = lim(x→0) |1| = 1

The limit is equal to 1, not 0.

Therefore, (x^2 + 1)/(x + 1) is not o(x) as x approaches 0.

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Scientific notation is nothing but a rewriting of numbers in decimal number system by multiplying them with \(10^k\) where k is a negative or positive whole number.

The claim that two situations are similar, despite major differences being ignored and only minor similarities being emphasized, is a fallacy known as false analogy.

False analogy is a logical fallacy that occurs when two situations are compared based on minor similarities while ignoring significant differences. It involves drawing an invalid or weak comparison between two unrelated or dissimilar things. In this fallacy, the person making the claim assumes that because two situations share some superficial similarities, they must be similar in all aspects. However, this overlooks the fundamental differences that make the situations distinct.

For example, if someone argues that banning the use of plastic bags in a city is similar to banning the use of cars, based solely on the fact that both involve restricting a common item, they would be committing a false analogy. While there may be minor similarities between the two situations, such as the concept of imposing restrictions, there are major differences in terms of environmental impact, necessity, and alternatives. Ignoring these significant differences leads to an invalid comparison and can result in flawed reasoning.

In conclusion, false analogy occurs when two situations are deemed similar based on minor similarities while disregarding major differences. It is essential to carefully evaluate the relevant factors and understand the nuances of each situation before drawing comparisons to ensure logical and valid arguments.

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C. Triangles A and B are similar.

To find out the similar triangles, we should check if their corresponding angles are congruent and their corresponding sides are proportional.

Triangle A angles = 67° and 23°, and the third angle must be 90° (since the angles in a triangle add up to 180°). So, we shall use the Pythagorean theorem to find the length of the third side:

\(\sqrt(13^2 - 5^2)\) = \(\sqrt144\)) = 12

So, the side lengths of Triangle A are 5, 12, and 13.

Triangle B angles = 67° and 37°, 3rd angle = 76°. We will use the Law of Sines to find the length of 3rd side:

10/sin(67°) = 20/sin(76°)

sin(76°) = (20sin(67°))/10 = 2sin(67°)

sin(76°)/sin(23°) = 2sin(67°)/sin(23°) = 2(5/13) = 10/13

So, the side lengths of Triangle B are 10, 20, and 13*(10/13) = 10.

Triangle C's side lengths 26, 23, and 24. We can use the Law of Cosines to find its angles:

cos(A) = (23² + 24² - 26²)/(22324) = 25/46

A = cos⁻¹(25/46) ≈ 56.8°

In the same way, let's find the other angles of Triangle C:

cos(B) = (24² + 26² - 23²)/(22426) ≈ 63.2°

cos(C) = (23² + 26² - 24²)/(22326) ≈ 60.0°

Triangle C's angles are ≈ 56.8°, 63.2°, and 60.0°.

Now we check the triangles that are similar:

A. Triangles A and C are not similar because they have no congruent angles or proportional sides.

Same goes to B. Triangles A, B, and C.

But C. Triangles A and B are similar because they have congruent angles of 67°.

We can check if their sides are proportional:

5/10 = 1/2

12/20 = 3/5

13/10 = 1.3

So, the sides of Triangle A are proportional to the sides of Triangle B with a ratio of 1:2:1.3.

D. Triangles B and C are not similar, have no congruent angles or proportional sides.

Therefore, triangles A and B are similar.

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The value of X in terms of a,b or c would be = 17.6

To determine the value of X in terms of a,b or c the following is carried out;

Extract the exponential values and relate them according to the exponential laws which states that multiply two exponential functions with the same base, we simply add the exponents.

Note that a,b,c are all the same as > 0

Therefore the equations are;

2x+3y = 5 ------> equation 1

3x +4y = 9 -----> equation 2

make y the subject of formula in equation 1

3y = 5-2x

y = 5-2x/3

Substitute y = 5-2x/3 into equation 2

3x + 4 ( 5-2x/3) = 9

3x + 20-8x/12= 9

3x + 20-8x = 108

3x-8x = 108-20

-5x = 88

X = 88/5

X = 17.6

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a) Calculation for the Riemann Area (2 bins)The given function is y = 5.2x² - 4.6x + 7.6.Bin width, w = (1 - 0)/2 = 0.

When the bin midpoints are 0.25 and 0.75 respectively, Riemann Sum is given as:Riemann Area (2 bins) = [f(0.25) + f(0.75)]*w=

[5.2(0.25²) - 4.6(0.25) + 7.6 + 5.2(0.75²) - 4.6(0.75) + 7.6]*0.5= 4.75375

Calculations for the Riemann Area (5 bins)Bin width, w = (1 - 0)/5 = 0.2

When the bin midpoints are 0.1, 0.3, 0.5, 0.7, and 0.9, respectively, Riemann Sum is given as:Riemann Area (5 bins) = [f(0.1) + f(0.3) + f(0.5) + f(0.7) + f(0.9)]*w= [5.2(0.1²) - 4.6(0.1) + 7.6 + 5.2(0.3²) - 4.6(0.3) + 7.6 + 5.2(0.5²) - 4.6(0.5) + 7.6 + 5.2(0.7²) - 4.6(0.7) + 7.6 + 5.2(0.9²) - 4.6(0.9) + 7.6]*0.2

= 4.8120

Calculation for the Integral Area Integral = ∫[5.2x² - 4.6x + 7.6]dx = [1.7333333333333x³ - 2.3x² + 7.6x]0 to 1

= [1.7333333333333(1)³ - 2.3(1)² + 7.6(1)] - [1.7333333333333(0)³ - 2.3(0)² + 7.6(0)]

= 7.1333333333333

Therefore, the Riemann area (2 bins) = 4.75375, the Riemann area (5 bins) = 4.8120 and the Integral area = 7.1333333333333.

b) Calculation for the Riemann Area (3 bins)The given function is y = 8.1[sin(7.6x)

Bin width, w = (0 - (-5))/3 = 5/8

When the bin midpoints are -5/3, 0, and 5/3 respectively, Riemann Sum is given as:Riemann Area (3 bins) = [f(-5/3) + f(0) + f(5/3)]*w

= [8.1sin(7.6*(-5/3)) + 8.1sin(7.6*(0)) + 8.1sin(7.6*(5/3))]*5/3

= 12.601

Calculation for the Riemann Area (8 bins)Bin width, w = (0 - (-5))/8 = 5/8

When the bin midpoints are -45/32, -35/32, -25/32, -15/32, -5/32, 5/32, 15/32, and 25/32 respectively, Riemann Sum is given as

:Riemann Area (8 bins) = [f(-45/32) + f(-35/32) + f(-25/32) + f(-15/32) + f(-5/32) + f(5/32) + f(15/32) + f(25/32)]*w

= [8.1sin(7.6*(-45/32)) + 8.1sin(7.6*(-35/32)) + 8.1sin(7.6*(-25/32)) + 8.1sin(7.6*(-15/32)) + 8.1sin(7.6*(-5/32)) + 8.

1sin(7.6*(5/32)) + 8.1sin(7.6*(15/32)) + 8.1sin(7.6*(25/32))]*5

= 12.669

Calculation for the Integral AreaIntegral = ∫[8.1sin(7.6x)]dx

= [-1.0657894736842cos(7.6x)]-5 to 0

= -1.0657894736842

cos(7.6(0)) + 1.0657894736842

cos(7.6(-5))= -1.0657894736842

cos(7.6(-5)) + 1.0657894736842= 2.130609418691

Therefore, the Riemann area (3 bins) = 12.601,

the Riemann area (8 bins) = 12.669 and

the Integral area = 2.130609418691.

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Here is a Venn diagram illustrating the relationship between the sets a, b, and c, where a is a subset of b and b is a subset of c:

     _______________

    |       c       |

    |               |

    |      _________

    |     |         |

    |     |    b    |

    |     |         |

    |     |______   |

    |            |  |

    |       a    |__|

    |_______________|

In this diagram, the set c is represented by the outer rectangle, the set b is the area inside the rectangle but outside the inner circle, and the set a is the area inside both the rectangle and the inner circle.

Since a is a subset of b, every element in a is also in b, and therefore the inner circle is entirely contained within the area representing b.

Similarly, since b is a subset of c, every element in b is also in c, and therefore the area representing b is entirely contained within the outer rectangle representing c.

This diagram shows that if a is a subset of b and b is a subset of c, then a is also a subset of c.

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Step-by-step explanation:

the correct answer is option a 6a-7

The value of r in permutation P(5, r) = 2P(6, r-1) is 11.  So, option d) is correct.

We know that the formula for the permutation of r objects taken from n distinct objects is P(n, r) = n! / (n-r)!. Using this formula, we can rewrite the given equation as:

5! / (5-r)! = 2 * 6! / (6-r+1)!

Simplifying this equation, we get:

5! / (5-r)! = 2 * 6! / (7-r)!

(5-r)! / 5! = (7-r)! / (2 * 6!)

(5-r)! / 5! = (7-r)! / 12

Since 5! = 120, we can simplify the left-hand side to:

(5-r)! / 120 = (7-r)! / 12

Multiplying both sides by 12, we get:

(5-r)! / 10 = (7-r)!

Multiplying both sides by 10, we get:

(5-r)! = 10 * (7-r)!

We can now manually try different values of r until we find one that satisfies the equation. Trying r = 3, we get:

(5-3)! = 10 * (7-3)!

2! = 10 * 4!

2 = 240

Since this is a contradiction, we can eliminate option (a) from the answer choices. Trying r = 5, we get:

(5-5)! = 10 * (7-5)!

1 = 20

Again, this is a contradiction, so we can eliminate option (b) from the answer choices. Trying r = 8, we get:

(5-8)! = 10 * (7-8)!

(-3)! = -10

Since the factorial of a negative number is undefined, this is not a valid solution, so we can eliminate option (c) from the answer choices. Therefore, the correct answer is (d) 11. Trying r = 11, we get:

(5-11)! = 10 * (7-11)!

(-6)! = 10 / 24

Simplifying the right-hand side, we get:

(-6)! = 5 / 12

Since the left-hand side is undefined for negative integers, we can eliminate this solution. Therefore, the only valid solution is r = 11, which we can confirm by checking that both sides of the equation are equal when r = 11. So, the correct answer is option (d).

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The required length of the guy wire, to the nearest foot is 15 feet.

We can use the Pythagorean theorem to solve for the length of the guy wire. The Pythagorean theorem 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.

In this case, we can consider the 7-foot pole, the 4-foot distance from the stake to the pole, and the guy wire as the sides of a right triangle. Therefore, the length of the guy wire (the hypotenuse) can be found using the formula:

c² = a² + b²

Where c is the length of the guy wire, a is the 4-foot distance from the stake to the pole, and b is the 14-foot distance from the pole to the tower. Plugging in the given values, we get:

c² = 4² + 14²

c² = 16 + 196

c² = 212

c = √212

c = 14.6

So, the length of the guy wire is approximately 14.6 feet, rounded to the nearest foot, which is 15 feet.

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Answer:

The answer for the nearest foot is 36ft long.

Step-by-step explanation:

So first we have to find the hypotenuse of the small triangle which is:

                                     \(a^{2}\)+\(b^{2}\)=  \(c^{2}\)

                                     \(7^{2}\)+\(4^{2}\)=\(c^{2}\)

                                     65 = \(c^{2}\)

                                     ±\(\sqrt{65}\)=\(\sqrt{c^{2} }\)​

                                     8.062... = c

Then we compare the small triangle to the big triangle:Compare the small triangle to the big triangle (in the photo link):

After that we set up a proportion and solve for x:Set up a proportion and solve for x which is:

                                     \(\frac{4}{18}\)=\(\frac{8.062}{x}\)

                                    \(4x\)=  145.120

                                    \(\frac{4x}{4}\)=\(\frac{145.120}{4}\)

                                   \(x=36.280\)

                                   \(x\)≈  36

The final answer is the guys wire is 36 ft long.