Find the distance between A and C. Simplify completely.

To find the time it takes for the object to hit the ground, we can solve the quadratic equation -16t^2 + 1600 = 0 using the quadratic formula. The positive solution to this equation gives us the time in seconds. Therefore, the object will take √102400/32 seconds to hit the ground.

To find the time it takes for the object to hit the ground, we need to solve the equation -16t^2 + 1600 = 0. This is a quadratic equation, so we can use the quadratic formula. Plugging in the values, we get t = (-b ± √(b^2 - 4ac))/(2a). In this case, a = -16, b = 0, and c = 1600. Plugging in these values, we get t = (± √(0 - 4(-16)(1600)))/(2(-16)). Simplifying the equation further, we get t = (± √(0 + 102400))/(32). This gives us two possible values for t: t = √102400/32 and t = -√102400/32. Since time cannot be negative in this context, we can discard the negative solution. Therefore, the object will take √102400/32 seconds to hit the ground.

The discriminant of the given polynomial is 0, indicating one real root.

The discriminant of a quadratic equation is a value that can be used to determine the nature of the solutions (roots) of the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation.

In the given polynomial, the coefficients are a = 4, b = -20, and c = 25. Plugging these values into the formula, we get: (-20)^2 - 4(4)(25) = 400 - 400 = 0.

Since the discriminant is equal to zero, the polynomial has one real root.

The answer is

20.7 ft/s

Without the specific function that calculates the object's downward speed on Earth, it is not possible to estimate the impact speed on Mars even with knowing the vertical compression factor.

Estimating Impact Speed on Mars

The question asks us to estimate how fast a rover would hit the surface of Mars after bouncing 15 ft in height, with the Mars function being compressed vertically by a factor of about 2/3 compared to the function used on Earth. Although the specific Earth function isn't provided, we can still proceed with a general understanding. To find this, we would normally use the Earth function for speed and multiply the result by 2/3 to adjust for Mars' weaker gravity. However, since we are only given the option to select an answer, no calculation can be performed without the Earth function. Therefore, it's not possible to provide a confident answer to this question.

V=1/3bh
324=1/3(9)* h
324=3h
h=324/3
h=108

height is 108cm

Answer: 12 cm

The other guy that answered didn't do it correctly, he didn't find the height. You have to do:

1/3 (9 • 9) (x) = 324

1/3 • 81x = 324

27x = 324

x = 12

Trust me, I just finished my quiz and got ths answer right.

The most appropriate statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis, specifically a Pearson correlation coefficient.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Correlation coefficient test measures the strength and direction of the linear relationship between two continuous variables, which is suitable for examining the relationship between temperature and the number of ice cream cones sold.

Additionally, a scatterplot could be used to visually assess the relationship between the two variables before conducting the statistical test.

Hence, statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis

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Answer: Dilation is a transformation that proportionally reduces or enlarges a figure.

Step-by-step explanation:

It stretches or shrinks the actual figure. It produces similar figures.

Since the corresponding sides of similar figures are in proportion.

⇒ It proportionally reduces or enlarges a figure.

Hence, A dilation is a transformation that proportionally reduces or enlarges a figure.

Final answer:

A scale transformation or dilation is a linear transformation that proportionally enlarges or reduces a figure, maintaining the proportional size relationships within the figure.

Explanation:

A transformation that proportionally reduces or enlarges a figure is known as a scale transformation or dilation. In such a transformation, lines are transformed into lines, and parallel lines remain parallel, consistent with the requirement for a transformation to be linear. This is important because it maintains the proportionality of the figure, meaning the size relationship of the parts of a figure to each other and to the whole figure remains constant, even though the overall size changes. Dilation can be characterized by a scale factor, which dictates how much larger or smaller the figure will become. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure reduces in size.

Answer:

Angles are 34.59°, 85.08° and 60.33°

Step-by-step explanation:

Let ABC is a triangle, ( that show the dog park)

In which,

AB = 150 feet

BC = 98 feet

CA = 172 feet,

By the cosine law,

[tex]BC^2=AB^2+AC^2-2(AB)(AC)cos A[/tex]

[tex]2(AB)(AC)cos A=AB^2+AC^2-BC^2[/tex]

[tex]\implies cos A=\frac{AB^2+AC^2-BC^2}{2(AB)(AC)}-----(1)[/tex]

Similarly,

[tex]\implies cos B=\frac{AB^2+BC^2-AC^2}{2(AB)(BC)}-----(2)[/tex]

[tex]\implies cos C=\frac{BC^2+AC^2-AB^2}{2(BC)(AC)}-----(3)[/tex]

By substituting the values in equation (1),

[tex]cos A=\frac{150^2+172^2-98^2}{2\times 150\times 172}[/tex]

[tex]=\frac{22500+29584-9604}{51600}[/tex]

[tex]=\frac{42480}{51600}[/tex]

[tex]\approx 0.8233[/tex]

[tex]\implies m\angle A\approx 34.59^{\circ}[/tex]

Similarly,

From equation (2) and (3),

m∠B ≈ 85.0°, m∠C ≈ 60.33°

20+0.15x = 35+0.10x

0.15x=15+0.10x

0.05x=15

x= 15/0.05

x= 300minutes

check:

300*.015 = 45+20=65

300*0.10 = 30 + 35 = 65

they equal

 so number of minutes would be 300

Answer:

the input (x) values of the relation

Step-by-step explanation:

(a) No, The output (y) values of the relation are called Range. So it is the wrong option.

(b) Yes, the input (x) values of the relation are called Domain. Thus, it is the correct option.

(c) No, it is not a definition of Domain. Thus, this is an incorrect option.

(d) No, it is not a definition of Domain. It is called the cartesian point. Thus it is also an incorrect option.

Further,

The Domain is the all possible input values of a function that gives defined values.  

The Range is the all defined output values that we get from a function (or y).

83 x 6 = 498

 all six of her scores need to equal at least 498 for an 83 average

83 + 84 + 93 + 77 + 85 = 422

498-422 = 76

 she needs a 76

If they have a remainder of 4 when divided by six the sequence of terms are: 6n+4

42≤6n+4≤92

subtract 4 from both ends

 38≤6n≤88

divide both ends by 6

 6.3≤n≤14.6

since n must be an integer...

7≤n≤14 so the number of integers is:

14-7+1=8 

they are 6n+4 for n=[7,14]...46,52,58,64,70,76,82,88

There are 8 integers between 42 and 92, inclusive, that have a remainder of 4 when divided by 6. These integers can be expressed in the form of 6n + 4 and can be found by incrementally adding 6, starting from the smallest integer greater than 42 that meets this condition.

To find how many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6, we need to identify the numbers that fit the condition. These numbers are of the form 6n + 4, where n is an integer. Starting with the smallest number greater than 42 that fits the condition, which is 46 (as 6*7 + 4 = 46), we can find the next by adding 6 to get 52, then 58, and so on, up until we reach the largest number less than or equal to 92 that fits the condition, which is 88 (as 6*14 + 4 = 88).

To find the total count, we calculate (88 - 46) / 6 + 1 = 42 / 6 + 1 = 7 + 1 = 8. Therefore, there are 8 numbers between 42 and 92 that have a remainder of 4 when divided by 6.

Keywords:

Polynomial, classify, degree, greatest exponent

For this case we have the following polynomial: [tex]Q (x) = 3x ^ 2 + x-6[/tex], we must classify the polynomial according to its degree. For this, we must bear in mind, that by definition, a polynomial is of the form:

[tex]P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]

Where:

a, b, c, d, e, f: They are the coefficients of the polynomial

n, n-1,3,2,1,0: They are the exponents. This polynomial is of degree "n", because "n" is the largest exponent.

x: It is the variable

Thus, [tex]Q(x) = 3x ^ 2 + x-6[/tex]is of degree "2" because "2" is the largest exponent.

Answer:  

It is a quadratic polynomial

Option C

The correct classification for this polynomial is C. quadratic.

The polynomial 3x^2 + x - 6 is classified by its degree, a fundamental characteristic of polynomials determined by the highest power of the variable 'x.'

In this case, the highest power is 2, making it a quadratic polynomial. Quadratic polynomials represent a U-shaped graph when plotted, often described as a parabola.

They play a significant role in various areas of mathematics, science, and engineering, serving as fundamental models for various real-world phenomena.

Quadratic equations are commonly encountered in physics, engineering, economics, and other fields, making them essential for solving problems and making predictions. Thus, the correct classification for this polynomial is C. quadratic.

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The sine of negative eleven pi divided by twelve is -0.5.

To find the sine of negative eleven pi divided by twelve, we need to determine the exact value of this trigonometric function. The sine function represents the ratio between the length of the side opposite the angle and the hypotenuse in a right triangle. In this case, the angle is negative, which means it lies on the negative y-axis. Remember that the unit circle can help us determine the values of trigonometric functions for any angle. By mapping the angle on the unit circle, we can see that -11π/12 is equivalent to -330 degrees. Since the sine function has a period of 360 degrees, we can find the reference angle by subtracting 360 degrees. So, the reference angle is 30 degrees (360 - 330).The sine of 30 degrees is 0.5. However, the angle is negative, so the sine function is negative. Therefore, the exact value of sine of -11π/12 is -0.5.

Final Answer:

The exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

Explanation:

To find the sine of an angle that is not one of the commonly known angles, such as [tex]\(-\frac{11\pi}{12}\)[/tex], we can use sine sum and difference identities. In this case, we know the sine of [tex]\(-\frac{\pi}{12}\)[/tex] is not a standard angle, but we can express it as a sum or difference of angles like [tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{\pi}{3}\)[/tex] whose sines we do know.

The sum identity for sine is:
[tex]\[\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)\][/tex]

We can express the angle [tex]\(-\frac{11\pi}{12}\)[/tex] as the sum of two angles for which we do know the sine and cosine values, for example,[tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{2\pi}{3}\)[/tex] because:
[tex]\[-\frac{11\pi}{12} = -\frac{3\pi}{4} - \frac{2\pi}{3}\][/tex]
Using the sum identity for sine, we can find the sine value as follows:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \sin\left(-\frac{3\pi}{4}\right)\cos\left(-\frac{2\pi}{3}\right) + \cos\left(-\frac{3\pi}{4}\right)\sin\left(-\frac{2\pi}{3}\right)\][/tex]

Now, let's find the values of sine and cosine for these angles.
[tex]\(\sin\left(-\frac{3\pi}{4}\right) = -\sin\left(\frac{3\pi}{4}\right) = -\sin\left(\frac{\pi}{2} + \frac{\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex]since sine is an odd function.

[tex]\(\cos\left(-\frac{2\pi}{3}\right) = \cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}\)[/tex] since cosine is an even function.

[tex]\(\cos\left(-\frac{3\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex] since cosine is an even function.

[tex]\(\sin\left(-\frac{2\pi}{3}\right) = -\sin\left(\frac{2\pi}{3}\right) = -\frac{\sqrt{3}}{2}\)[/tex] since sine is an odd function.

Substitute these trigonometric values into the sum identity:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{1}{2}\right) + \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{\sqrt{3}}{2}\right)\][/tex]

Simplify the expression:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\][/tex]
Combine the terms with a common denominator:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

Therefore, the exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]

Answer:

(-2, 18) and (8, 38)

Step-by-step explanation:

First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.

So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.

Credit: AoPs

To find h(-12), substitute -12 into the function h(x)=2x²-2. The value of h(-12) is 286.

To find h(-12), we substitute -12 into the function h(x)=2x²-2:

h(-12) = 2(-12)² - 2

h(-12) = 2(144) - 2

h(-12) = 288 - 2

h(-12) = 286

Therefore, h(-12) is equal to 286.

Final answer:

To calculate the percent uncertainty in the volume of a spherical beach ball when the radius is uncertain, you multiply the square of the radius by four (surface area), by the uncertainty in the radius, and then compare this value to the total volume. The percent uncertainty is found to be approximately 2.62%.

Explanation:

To determine the percent uncertainty in the volume of a spherical beach ball with a radius of 2.86 1 0.09 meters, one must first calculate the volume's uncertainty, then relate this to the total volume, and finally convert this relationship into a percentage.

The formula for the volume of a sphere is [tex]V = (4/3)\pi(r^3)[/tex]. Since volume is proportional to the cube of the radius, any uncertainty in the radius dramatically affects the volume uncertainty. Using a function for the volume V(r) and applying the approximation for small changes in r, we have:

[tex]V = (4/3)\pi(r^2))(r)[/tex]

For a radius of 2.86 meters and an uncertainty of 0.09 meters, the uncertainty V in volume is 170 [tex]cm^3[/tex]. The volume is approximately V = [tex](4/3)(3.14)(2.86^3)[/tex] = 6538 [tex]cm^3[/tex]. Therefore, the volume expressed with its uncertainty is [tex]6500 \pm170[/tex] [tex]cm^3,[/tex] rounded to avoid false precision.

To find the percent uncertainty:

Convert the uncertainty to the same units as the ball's volume if needed (here both are in cm^3).

Divide the uncertainty by the volume: (170/6500) x 100%.

The percent uncertainty is approximately 2.62%.

Answer:0

Step-by-step explanation:

A right triangle can have at most one obtuse angle since it already contains one right angle, and the sum of its angles must be 180 degrees according to geometrical axioms.

The question asks about the maximum number of obtuse angles that can be contained in a right triangle. In a right triangle, one angle is 90 degrees by definition, which is a right angle. According to Theorem 20, the sum of the angles of a triangle is two right angles, which equals 180 degrees. Having an obtuse angle, which is greater than 90 degrees, combined with a 90 degree angle, would exceed 180 degrees when the third angle is added, and this is not possible in a plane geometric figure. Therefore, a right triangle cannot have more than one right angle. As such, the option with the maximum number of obtuse angles a right triangle can contain is:

Answer: B) 1

Answer: 3/5 is the probability that person's skin cleared up given that they used the medication.

Step-by-step explanation:

let S represents skin cleared and M represents medicine used.

According to the given Venn diagram,

P(S) = 40

P(M)= 50

[tex]P(M\cap S) = 30[/tex]

Thus by the definition of conditional probability,

If it is given that the skin is cleared then the probability that persons used the medicine,

P(M/S)=[tex]\frac{P(M\cap S)}{P(S)}[/tex]=30/50= 3/5.

P(M/S)=3/5.

The probability that the person's skin will clear up given that they used the medication is:

This refers to the likelihood of an event to occur based on certain conditions.

If we want to find the probability about whether the skin will clear up is:

We would assign S to represent the skin

M to represent medicine

Hence,

P(MnS) = 30

Using the conditional probability rule,

P9M/S)= P(MnS)/P(S) = 30/50

=3/5

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