Apply the 45°-45°-90° Triangle Theorem to find the length of the hypotenuse of the triangle

If the length of each leg of the triangle is 15√2 in, what is the length of the hypotenuse(c)?

There would be approximately \(1.79 \times 10^{135\) bacteria after 7 hours. This

number is extremely large and is beyond the capacity of most calculators

to handle.

After 30 minutes (0.5 hours), each bacterium will undergo fission and

become two bacteria. Therefore, the number of bacteria will double after

every 30 minutes.

In 7 hours, there are 7 x 2 x 2 x 2 x 2 x 2 x 2 = 7 x 2^6 = 448 bacterial

cycles.

So, the final number of bacteria would be:

\(500 \times 2^{448} = 1.79 \times 10^{135\)

Therefore, there would be approximately 1.79 x 10^135 bacteria after 7

hours.

This number is extremely large and is beyond the capacity of most

calculators to handle.

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The slope intercept form of the line that passes through the point (1, 9) and has the slope 2 is y = 2x + 7.

The slope intercept form of the line is:

y - y₁ = m (x - x₁)

Given that the point that the line passes through is: (1, 9)

The slope of the line is: m = 2

Substitute the values in the equation, we get;

y - 9 = 2 ( x - 1)

y - 9 = 2x - 2

y = 2x + 7

Therefore, we get that, the slope intercept form of the line that passes through the point (1, 9) and has the slope 2 is y = 2x + 7.

So, the numbers that would be in the blanks would be 2 and 7, respectively.

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Answer:

The rate of change is 2 feet per second.

The acres of vacant land that the county have now will be 144 acres.

Since 36% has been used, the remaining percentage will be:

= 1 - 36%

= 64%

Therefore, the acres of vacant land that the county has now will be:

= 64% × 225

= 64/100 × 225

= 0.64 × 225

= 144

Therefore, the acres of vacant land that the county have now will be 144 acres.

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Answer:

15 is larger than -4

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

15 ÷ (-4) = -3.75

The radius of the circular fountain is approximately 17 feet.

The formula for the volume of a circular fountain is given by V = πr^2h, where V is the volume, r is the radius, and h is the depth. In this case, we are given that the depth of the fountain is 3 feet and the volume is 1800 cubic feet. So we can plug in these values into the formula and solve for r as follows:

1800 = πr^2(3)

Simplifying this equation, we get:

r^2 = 600/π

Taking the square root of both sides, we get:

r = sqrt(600/π)

Using a calculator to approximate the value of sqrt(600/π), we get:

r ≈ 17

Therefore, the radius of the circular fountain is approximately 17 feet when rounded to the nearest whole number.

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Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The total displacement is 50 km

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

A car moved 30 km in the North- East direction, then moved 40 km due north.

This can be drawn as,

                                    B   Final point

                                     /  |

                                   /    |  (40 km)

                                /       |

                          A /          |

     Starting point    (30 km)

Displacement is the distance of AB.

Applying the Pythagorean theorem.

AB² = 40² + 30² = 1600 + 900 = 2500

AB = √2500 = 50

Thus,

The total displacement is 50 km

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The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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The Stokes approximation and Oseen approximation are methods used to determine the motion of fluid particles in a fluid dynamics problem.

The Stokes approximation applies to slow-moving fluid particles, where viscous forces are dominant, while the Oseen approximation applies to higher velocities, where convective forces are dominant..Oseen approximation: In this approximation, the equations governing the motion of fluid particles account for the convective forces in addition to the viscous forces.

This approximation is valid at moderate Reynolds numbers and is used when the viscous forces are still strong but not as dominant as in the Stokes approximation. The velocity of the fluid decreases less rapidly than in the Stokes approximation, and the approximation is valid for Reynolds numbers greater than one .The difference between the results of the two approximations lies in their range of applicability and the accuracy of their results.

The significance of the difference between the two approximations lies in their application to real-world problems. In fluid dynamics, it is essential to have accurate approximations to predict the behavior of fluid particles accurately. Therefore, choosing the appropriate approximation for the specific problem is critical. knowing the range of applicability of each approximation can help in determining the parameters for the problem.

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To graph the equation y = (1/2)x, we can plot points on a coordinate plane and connect them to create a straight line. Here's how to do it:

1. Choose some x-values to evaluate the equation. Let's select a range of x-values, such as -10, -5, 0, 5, and 10.

2. Substitute each x-value into the equation to find the corresponding y-values. For example:

  - For x = -10, y = (1/2)(-10) = -5

  - For x = -5, y = (1/2)(-5) = -2.5

  - For x = 0, y = (1/2)(0) = 0

  - For x = 5, y = (1/2)(5) = 2.5

  - For x = 10, y = (1/2)(10) = 5

3. Plot the points (x, y) on a graph. In this case, the points would be:

  (-10, -5), (-5, -2.5), (0, 0), (5, 2.5), (10, 5)

4. Connect the plotted points with a straight line. The line should pass through all the points.

The resulting graph is a straight line with a slope of 1/2, passing through the origin (0, 0), and extending infinitely in both directions.

Here is a rough sketch of the graph:

```

   |      

6  |         .

   |       .

5  |     .

   |   .

4  | .  

   |

3  |   .

   |

2  |     .

   |      

1  |       .

   |      

0  -----------------------

  -10 -5  0  5  10

```

Note: The above graph is a visual representation and may not be to scale. The line should pass through the plotted points accurately.

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Answer:

390 cm

Step-by-step explanation:

How to find Volume

Width x Height x Length

=Volume

--

6.5 x 12 x 5 = 390

390 cm

--

The other side of the triangle by using Pythagoras theorem is 15 cm.

Given that,

The triangle has an hypothesis 25cm, adjacent is 20 cm and opposite is x cm.

We have to find the other side by using Pythagorean theorem.

The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.

c²=a²+b²

25²=20²+x²

625=400+x²

x²=625-400

x²=225

Square root on both sides.

x=√225

x=15.

Therefore, The other side of the triangle by using Pythagoras theorem is 15 cm.

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Answer:

160

Step-by-step explanation:

How many 3/16 are in 30.

30 ÷ 3/16

160

the probability that he drove the small car is 0.890 (option A).

Using Bayes' theorem to solve the problem given, let us represent the following events:

A: Friend drives the small carB: Friend drives the large carC: Friend is on timeGiven that three-quarters of the time he drives the small car and one-quarter of the time he drives the large car, we can calculate the prior probabilities:

P(A) = 3/4 and P(B) = 1/4.

Also, given that he usually has little trouble parking with probability 0.9 when driving the small car and is on time with probability 0.6 when driving the large car, we can calculate the likelihoods:

P(C|A) = 0.9 and P(C|B) = 0.6

Using Bayes' theorem, we can calculate the posterior probability of driving the small car given that he was on time on a particular morning:

P(A|C) = P(C|A) * P(A) / (P(C|A) * P(A) + P(C|B) * P(B))= 0.9 * 3/4 / (0.9 * 3/4 + 0.6 * 1/4) = 0.890

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Answer:

C

Step-by-step explanation:

Rectangle base, tiny triangle sides, but rectangle top

Answer: 5 hours/week

They will have to work 5 hours/week to get their amount equal.

An equation is the statement of equality between two expressions consisting of variables and/or numbers.

Given that, Alexa gets $100 every week from her parents and earns $25 per hour tutoring. Jenna gets $150 from her parents every week and earns $15 per hour baby-sitting.

Let the number of hours they work be n, then according to question,

100 + 25n = 150 + 15n

10n = 50

n = 5

Hence, They will have to work 5 hours/week to get their amount equal.

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Answer: Given the molar masses of the reactants and products, we can calculate the number of moles of KCl produced from 180 g.

First, convert the mass of KCl to moles:

180 g / 74.55 g/mol = 2.41 moles

Next, we can use the mole ratio between KCl and KClO3 from the chemical equation to determine the number of moles of KClO3 decomposed:

2.41 moles KCl / 1 mole KClO3 = 2.41 moles KClO3

Finally, we can convert the number of moles of KClO3 to mass using its molar mass:

2.41 moles * 122.5 g/mol = 295.4875 g

Therefore, the mass of potassium chlorate decomposed was 295.4875 g.

Step-by-step explanation:

Answer:

40km/h

Step-by-step explanation:

Speed = Distance/Time

Speed = 60/1.5

Speed = 40km/h

The equation 2(x² + 2) = 3x has no real solutions.

The quadratic equation 2(x² + 2) = 3x can be solved using the quadratic formula. By substituting the coefficients into the formula, we can find the solutions for x.

To solve the equation 2(x² + 2) = 3x using the quadratic formula, we first rewrite the equation in standard quadratic form: 2x² + 4 - 3x = 0. The equation is now in the form ax² + bx + c = 0, with a = 2, b = -3, and c = 4.
Next, we substitute these values into the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Plugging in the values, we have x = (-(-3) ± √((-3)² - 4(2)(4))) / (2(2)).
Simplifying further, we get x = (3 ± √(9 - 32)) / 4. Since the discriminant (b² - 4ac) is negative (-23 in this case), the quadratic equation has no real solutions. Hence, there are no real values for x that satisfy the equation.
Therefore, the equation 2(x² + 2) = 3x has no real solutions.

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We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

-10-(-4)

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Using slope formula, change in y (3) over change in x (2) is 3/2. So the equation would be y=3/2x.

Answer:    54

--------------------

Answer:

4/11

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 1 - -3)/(7 - -4)

     = (1+3)/(7+4)

    = 4/11

Answer:

x = 6 units

Step-by-step explanation:

For θ = 30°, Perpendicular is 3. Hypotenuse is x.

We can use trigonometry to find x.

\(\sin(30)=\dfrac{P}{H}\)

\(\sin(30)=\dfrac{3}{x}\\\\x=\dfrac{3}{\sin(30)}\\\\x=6\)

So, the value of x is equal to 6 units.

Answer:10

Step-by-step explanation:

14 ft to 21 ft = 2 ft to 3 ft

The event that the card is a queen, denoted as e, and the event that the card is a heart, denoted by f, are not independent.

Independent events are events where the occurrence or outcome of one event does not affect or influence the occurrence or outcome of another event. In other words, the outcome of one event has no effect on the probability of the other event happening. For example, flipping a coin and rolling a dice are independent events, because the outcome of one event (e.g., heads on a coin flip) does not affect the outcome of the other event (e.g., rolling a six on a dice).

The event "the card is a queen" reduces the number of cards in the deck, while the event "the card is a heart" also reduces the number of cards in the deck. The intersection of these two events, "the card is a queen of hearts," is a smaller set of cards than either event individually, so these events are dependent.

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Answer:

1.8 cm to nearest tenth.

Step-by-step explanation:

The unmarked angle = 180 - 105 - 15 = 60.

By the Sine Law:

2 / sin105 = a/ sin 60

a = 2 sin 60 / sin 105

  = 1.793