A basketball player is 15 ft horizontally from the center of the basket, which is 10 ft off the ground. At what angle should the player aim the ball if it is thrown from a height of 8.2 ft with a speed of 29 ft/s ?

Final answer:

The number of commercial orbital launches is 18, and the number of noncommercial orbital launches is 55.

Explanation:

Let's assume that the number of commercial orbital launches is represented by x. According to the problem statement, the number of noncommercial orbital launches is more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches would be 3x + 1.

Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation:

x + (3x + 1) = 73

Combining like terms, we get:

4x + 1 = 73

Subtracting 1 from both sides, we get:

4x = 72

Dividing both sides by 4, we get:

x = 18

Therefore, there were 18 commercial orbital launches and 55 noncommercial orbital launches.

The number of commercial orbital launches is 24, and the number of noncommercial orbital launches is 49.

Let's assume that the number of commercial orbital launches is represented by 'x'. According to the question, the number of noncommercial orbital launches is one more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches can be represented by '3x + 1'.

Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation 'x + (3x + 1) = 73' to represent the total launches. Solving this equation will give us the values of 'x' and '3x + 1', which represent the number of commercial and noncommercial orbital launches, respectively.

By solving the equation, we find that 'x = 24' and '3x + 1 = 73 - 24 = 49'.

Consider the function

f(x) = [tex]\frac{x-3}{x-4}[/tex]

Domain of the function = All real numbers except , x≠4 .

[tex]y=\frac{x-3}{x-4} \\\\ xy - 4y = x-3 \\\\ x y -x= 4 y-3\\\\ x=\frac{4 y-3}{y-1}[/tex]

Range = All real numbers except , y≠1 .

Horizontal Asymptote= Since the degree of numerator and denominator of rational function  is same , So Divide coefficient of x in numerator by divide coefficient of x in denominator.

So Horizontal Asymptote , is : y=1

To get vertical asymptote, put

Denominator =0

x-4=0

x=4 , is vertical asymptote.

Domain = All real numbers except vertical Asymptote

Range = All real numbers except Horizontal Asymptote

Final answer:

The vertical asymptotes of a rational function can be found by determining the roots of the polynomial in the denominator, while the horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches infinity. The asymptotes are closely related to the function's domain and range.

Explanation:

Vertical asymptotes of a rational function can be determined by finding the roots of the polynomial in the denominator. Each root corresponds to a vertical asymptote. For example, if the polynomial has a factor of (x - 2), then there is a vertical asymptote at x = 2.

On the other hand, horizontal asymptotes of a rational function can be found by analyzing the behavior of the function as x approaches positive or negative infinity. If the leading terms of the numerator and denominator have the same degree, then the function will have a horizontal asymptote. For instance, if the leading terms are both x^2, then the horizontal asymptote will be y = 0.

The domain of the function is the set of all valid inputs, while the range is the set of possible outputs. The vertical asymptotes and the behavior of the function as x approaches infinity are closely related to the domain, while the horizontal asymptotes are related to the range.

Answer:

-37260

Step-by-step explanation:

did it in my head

Answer:

Two rational solutions.  This is the right answer

Step-by-step explanation:

Answer:

Answer:

16 miles per gallon

Step-by-step explanation:

Answer:

Option A is correct

the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is [tex]\frac{5\sqrt{11}} {11}[/tex]

Explanation:

Given expression is, [tex]\frac{5}{ \sqrt{11}}[/tex]

Multiply and divide by the denominator by [tex]\sqrt{11}[/tex] in the given expression, we have,

[tex]\frac{5}{\sqrt{11}} \times \frac{\sqrt{11}} { \sqrt{11}}[/tex]

or

[tex]\frac{5 \cdot \sqrt{11}} {\sqrt{11} \cdot \sqrt{11}}[/tex]

use : [tex]\sqrt{a}\cdot\sqrt{a}=(\sqrt{a} )^2 = a[/tex]

then;

[tex]\frac{5\sqrt{11}} { (\sqrt{11})^2} =\frac{5\sqrt{11}} {11}[/tex]

Therefore, the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is, [tex]\frac{5\sqrt{11}} {11}[/tex]

Answer: x=6 and y=3

Step-by-step explanation:

4x - 7y = 3 -------(1)

x - 7y = -15 ------(2)

equation(1) - equation (2)

3x = 18

Divide bothside by 3

x = 18/3

x= 6

also, multiply equation (2) by 4

4x - 28y = -60--------------(3)

subtract equation(3) from equation(1)

21y = 63

divide bothside by 21

y = 63/21

y = 3

By setting up a system of linear equations based on the shopper's purchases and solving it, we found that the cost of each T-shirt is $20, and the cost of each pair of pants is $12.

To find out how much each T-shirt and each pair of pants cost based on the shopper's purchases, we can set up a system of linear equations. Let's denote the cost of a T-shirt as T and the cost of a pair of pants as P.

The two purchases give us these equations:

8T + 5P = $220

5T + 1P = $112

Next, we use a method such as substitution or elimination to solve these simultaneous equations. If we multiply the second equation by 5, we get:

5(5T + 1P) = 5($112)

25T + 5P = $560

Now subtract the first equation from this result:

25T + 5P - (8T + 5P) = $560 - $220

17T = $340

T = $20

Now that we know the cost of a T-shirt, we can substitute T in one of the original equations to find P:

5T + P = $112

5($20) + P = $112

$100 + P = $112

P = $12

So, a T-shirt costs $20 and a pair of pants costs $12.

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Answer: 11.50

Step-by-step explanation:

6$ to get in+ rides=$

11(rides)*.50(price of rides)=5.50

5.50+6=$11.50

Answer:

Option 4th is correct

[tex]2 \cdot (x-4)(x+4)[/tex]

Step-by-step explanation:

Using difference of square:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

GCF is the largest number that divide the given polynomial or expression.

Given the expression:

[tex]2x^2-32[/tex]

We have to completely factor the expression.

GCF of [tex]2x^2[/tex] and 32 is, 2

then;

[tex]2 \cdot (x^2-16)[/tex]

Using difference of square

[tex]2 \cdot (x-4)(x+4)[/tex]

therefore, the completely factor of [tex]2x^2-32[/tex] is, [tex]2 \cdot (x-4)(x+4)[/tex]

Answer:

D.  2(x + 4)(x − 4)

Step-by-step explanation:

Final answer:

The inequality |2x + 4| > 8 is resolved by considering the inside expression being greater than 8 and less than -8, which leads to x > 2 and x < -6. The proper representation on a number line is with open circles on -6 and 2, shading away from these points, indicating the range of solutions.

Explanation:

To solve the absolute value inequality |2x + 4| > 8, we must consider the two scenarios that could make the inequality true: when (2x + 4) is greater than 8 and when -(2x + 4) is less than -8. Absolute values denote the distance from zero, so they are never negative. Since the inequality is strict (indicated by '>'), we will use open circles in the graph.

First, let's consider when the expression inside the absolute value is positive:

2x + 4 > 8

2x > 4

x > 2
This scenario corresponds to all x-values greater than 2.

Now for the negative scenario:

-(2x + 4) > 8

-2x - 4 > 8

-2x > 12

x < -6
This scenario corresponds to all x-values less than -6.

The correct graph of the solution set on a number line would have open circles on -6 and 2, with shading going in opposite directions away from these points, indicating all the numbers greater than 2 and all the numbers less than -6 satisfy the original inequality.

Based on this, the third choice is correct: A number line with open circles on negative 6 and 2, shading going in the opposite directions.

Answer:

Step-by-step explanation:

A. The given equation is:

[tex](x-2)(2x+3)[/tex]

simplifying this,

[tex]2x^{2}-4x+3x-6[/tex]

[tex]2x^{2}-x-6[/tex]

Option A is correct

B. The given equation is:

[tex](3x+2)(4x-3)[/tex]

simplifying this,

[tex]12x^{2}+8x-9x-6[/tex]

[tex]12x^{2}-x-6[/tex]

Option D is correct.

C. The given equation is:

[tex](4p-2)(p-4)[/tex]

simplifying this,

[tex]4p^2-2p-16p+8[/tex]

[tex]4p^2-18p+8[/tex]

Option B is correct.

D. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. Then,

Surface area of cylinder=[tex]2r^{2}+2rh[/tex]

=[tex]2r(r+h)[/tex]

=[tex]2(3x-2)(3x-2+x+3)[/tex]

=[tex]2(3x-2)(4x+1)[/tex]

=[tex]2(12x^{2}-8x+3x-2)[/tex]

=[tex]24x^{2}-10x-4[/tex]

Therefore, Surface area of cylinder=[tex]24x^{2}-10x-4[/tex] sq units

The two types of exponential functions are:

Exponential Growth: exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.

Exponential Decay: exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.

The two types of exponential functions are:

Exponential Growth: In an exponential growth function, the base (often denoted by "a") is greater than 1.

As the input (x) increases, the output (y) grows at an increasing rate, creating a steep upward curve on the graph.

The general form of an exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.

Exponential Decay: In an exponential decay function, the base (often denoted by "a") is between 0 and 1 (exclusive).

As the input (x) increases, the output (y) decreases at an increasing rate, creating a steep downward curve on the graph.

The general form of an exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.

Both types of exponential functions show rapid growth or decay patterns, and their graphs exhibit a characteristic curve that is continuous and smooth.

The difference lies in the behavior of the output (y) concerning the input (x).

In exponential growth, the output increases exponentially with increasing input, while in exponential decay, the output decreases exponentially as the input increases.

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Answer:

37.7

Step-by-step explanation: K12

Answer:

The highest Y-intercept would be f(x)

The expression for the distance between the points (2, 5) and (-4, 8) is the square root of 45 or 3√5, which is approximately 6.708.

The expression that gives the distance between the points (2, 5) and (-4, 8) is found using the distance formula which is derived from the Pythagorean theorem. The formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are coordinates of the two points.

To find the distance between (2, 5) and (-4, 8), substitute x1=2, y1=5, x2=-4, and y2=8 into the formula:

√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √45

The distance is therefore the square root of 45, which can be simplified to 3√5 (approximately 6.708).

Final answer:

The distance between the points (2, 5) and (-4, 8) is calculated using the distance formula, resulting in 3√(5) units.

Explanation:

The distance between the points (2, 5) and (-4, 8) can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given values, the distance d can be calculated as follows:

√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √(45) = 3√(5)

Therefore, the distance between the points (2, 5) and (-4, 8) is 3√(5) units.