SICCA DI DO rower for and question
1. Which of these factors makes it challenging to make a fair comparison between a current NBA star and an NBA star from the 1990s?
O A. There has been a fall in three-point shots, and players tend to score fewer points now.
B. There has been a rise in three-point shots, and players tend to score more points now.
OC. Players are more likely to make free throws now, and free-throw percentages have increased.
D. Players are less likely to make free throws now, and free-throw percentages have decreased.

The equation of the parabola in the form y = a(x - r)(x - s) is y = -2(x + 2)(x + 8).

To determine the equation of the parabola in the form y = a(x - r)(x - s), we need to find the values of a, r, and s. We are given the x-intercepts and the vertex, so we can use this information to find these values.

The x-intercepts are -2 and -8, so we know that r=-2 and s=-8. The vertex is (-5,-18), so we can plug these values into the equation and solve for a:

y = a(x - r)(x - s)
-18 = a(-5 + 2)(-5 + 8)
-18 = a(-3)(3)
-18 = 9a
a = -2

So the equation of the parabola is y = -2(x + 2)(x + 8).

In standard form, this equation is y = -2x² - 20x - 32.

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(-3x + 2y + z = 0 )

The equation of the plane passing through the origin and containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) can be found by taking the cross product of the two vectors and using the resulting vector as the normal vector of the plane. The cross product of the two vectors is given by:

\( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \times \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] = \left[\begin{array}{c}(-1)(3) - (1)(0) \\ (1)(3) - (1)(1) \\ (1)(0) - (1)(-1)\end{array}\right] = \left[\begin{array}{c}-3 \\ 2 \\ 1\end{array}\right] \)

Therefore, the equation of the plane is given by:

\( -3x + 2y + z = 0 \)

This is the equation of the plane passing through the origin and containing the two given vectors.

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The equation of the circle centered at (-4,3) with radius 3 is (x + 4)^2 + (y - 3)^2 = 9. Simplifying this equation means to simplify the terms in the equation by using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse.

In this equation, the hypotenuse is the radius, which is 3, and the sides are (x + 4) and (y - 3). Substituting the values into the Pythagorean Theorem, we get (x + 4)^2 + (y-3)^2 = 9, which is the equation of the circle centered at (-4,3) with radius 3. This equation can be simplified further by factoring the terms, which yields (x + 4) (x + 4) + (y - 3) (y - 3) = 9. This is the fully simplified equation of the circle.

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The two possible values for the middle numbers in the geometric progression are +35 and -35.

We know that the three numbers form a geometric progression. Let the middle number be x:

5, x, 245

Since these numbers form a geometric progression, we know that:

x^2 = 5 * 245

So we have:

x = ± √(5 * 245)

x = ± 35

Therefore, the two possible values for the middle number are +35 and -35. To find the two possible values for the middle number in the geometric progression, we used the fact that the product of the first and third terms of a geometric progression is equal to the square of the second term.

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write the equation with both of them = 100

(3x + 50) + (2x + 15) = 100

combine like terms

5x + 65 = 100

subtract

5x = 35

x = 7

the question asks for <JTU = 2x + 15

plug in x = 7

x = 29

EDIT

Answer:

JTU = 29°

Step-by-step explanation:

I'm not sure if this is correct but I got 29°

(3x+50)° + (2x+15)° = 100°

x= 7°

(2x+15)°

((2x7)+15)° = 29°

Answer:

Step-by-step explanation:

Multiply each then divide by the first number you started off with.

Quinn has 6 dimes and 15 quarters in his pocket.

Let's use a system of two equations to represent the given information:

d + q = 21      (1)   // The number of dimes and quarters adds up to 21

10d + 25q = 435 (2)   // The total value of the coins in cents is 435

where d represents the number of dimes and q represents the number of quarters.

We can use equation (1) to solve for d in terms of q:

d = 21 - q

Substituting this expression for d into equation (2), we get:

10(21 - q) + 25q = 435

210 - 10q + 25q = 435

15q = 225

q = 15

So, Quinn has 15 quarters. Substituting this value into equation (1), we get:

d + 15 = 21

d = 6

So, Quinn has 6 dimes.

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This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n. To demonstrate the equations using induction, we need to follow three steps: the base case, the induction hypothesis, and the induction step.

1) P(n) : 2 + 4 + 6 + ⋯+ 2n= n(n+ 1), ∀ n∈ℕ.

Base case: For n = 1, the equation becomes 2 = 1(1+1), which is true.

Induction hypothesis: Assume the equation is true for n = k, that is, 2 + 4 + 6 + ⋯+ 2k= k(k+ 1).

Induction step: We need to show that the equation is also true for n = k+1. That is, 2 + 4 + 6 + ⋯+ 2k + 2(k+1)= (k+1)(k+2).

Using the induction hypothesis, we can substitute k(k+1) for 2 + 4 + 6 + ⋯+ 2k:

k(k+1) + 2(k+1) = (k+1)(k+2)

Distributing the (k+1) on the right side of the equation gives us:

k(k+1) + 2(k+1) = k(k+1) + 2(k+1)

This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.

2) ∑i^2= n(n+1)(2n+1)/6, ∀ n∈ℕ.

Base case: For n = 1, the equation becomes 1^2 = 1(1+1)(2(1)+1)/6, which simplifies to 1 = 1, which is true.

Induction hypothesis: Assume the equation is true for n = k, that is, ∑i^2= k(k+1)(2k+1)/6.

Induction step: We need to show that the equation is also true for n = k+1. That is, ∑i^2 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6.

Using the induction hypothesis, we can substitute k(k+1)(2k+1)/6 for ∑i^2:

k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6

Multiplying both sides of the equation by 6 gives us:

k(k+1)(2k+1) + 6(k+1)^2 = (k+1)(k+2)(2(k+1)+1)

Distributing the (k+1) on both sides of the equation gives us:

k(k+1)(2k+1) + 6(k+1)^2 = k(k+1)(k+2)(2k+3)

This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.

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The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.

Let D = (x, y)

Now, We know that;

The midpoint of AC = Mid-point of BD

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

3 = x + 3

x = 0

(- 3+3)/2 = (y + 2)/2

y = - 2

Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

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The Surface Area of Container is 954. 56 inch².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

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There are 1,000 ways to construct a 3-digit code if numbers can be repeated. This is because there are 10 possible numbers (0-9) for each digit, and since numbers can be repeated, each digit has 10 options. So the total number of ways to construct a 3-digit code is 10 × 10 × 10 = 1,000.

Here is a step-by-step explanation:
1. Start with the first digit. There are 10 possible numbers (0-9) that can be used for this digit.
2. Move on to the second digit. Again, there are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
3. Finally, move on to the third digit. There are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
4. Multiply the number of options for each digit together to get the total number of ways to construct a 3-digit code: 10 × 10 × 10 = 1,000.

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Answer:

35/40 = (7*5)/(8*5) = 7/8

So the Lions won 7/8 of the games they played.

2) To write a decimal equivalent to 7/8, we can divide 7 by 8 using long division:

0.875

___________

8 | 7.000

- 6.4

_______

60

-56

____

40

-40

____

0

So 7/8 is equivalent to the decimal 0.875.

To write a percent equivalent to 7/8, we can multiply the decimal equivalent by 100:

0.875 * 100 = 87.5%

So the Lions won 87.5% of the games they played.

A line intersecting at the axes (2,0)and (0,2) will not pass through (2,2).

Given, a line intersects at the axis (2,0)and (0,2)

let the line intercept be expressed as

[tex]ax+by=1[/tex] where a and b are the x & y intercept.

since the intercept points are the axis (2,0)and (0,2)

a=2 and b=2

[tex]2x+2y=1[/tex]

when the point (2,2) is considered and put in equation

2(2)+2(2)=4≠1

Therefore, point (2,2) doesn't satisfy the equation and line doesn't pass through (2,2).

From the graph also, we can say that the line passing through (2,0) and (0,2) intersecting the axes do not pass through the point (2,2).

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Answer: J. A = 12 (4⋅6).

Step-by-step explanation:

Answer: J. A = 12 (4⋅6).

This equation can be used to find the area of the triangle in the diagram because it uses the formula for the area of a triangle, which is A = 1/2 * b * h, where b is the base and h is the height. Since the triangle in the diagram has a base of 4 and a height of 6, the equation A = 12 (4⋅6) can be used to find the area.

Answer:

The diagram is not provided, so it's difficult to determine the exact dimensions of the triangle and parallelogram. However, we can make some general observations to determine which equation can be used to find the area of the triangle.

First, we know that the area of a triangle is given by the formula:

A = 1/2 * base * height

We also know that the area of a parallelogram is given by the formula:

A = base * height

In the diagram, the triangle can be formed into a parallelogram by taking one of its sides and using it as the base of the parallelogram. The height of the parallelogram is the same as the height of the triangle.

Based on these observations, we can conclude that the equation that can be used to find the area of the triangle is:

A = 1/2 * base * height

where the base is one of the sides of the triangle, and the height is the height of the parallelogram (which is the same as the height of the triangle).

None of the answer choices provided match this equation, so the correct answer is not given.

Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.

Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.

The arithmetic operations were used to arrive at the answer.

The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.

So, the total pounds of fruit bought = 0.5 + 3 = 3.5

Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits  = (x + y)

Hence, the required solution has been obtained.

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This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π.

Complete the statement. y=cos −1x means that x=cos y, for 0≤y≤π

This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π. In other words, if we know the value of x, we can use the inverse cosine function to find the angle y that has a cosine of x. This is useful for solving equations involving cosine, such as finding the angles of a triangle given the lengths of its sides.

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A graph of the resulting image after the given triangle is rotated 90° counterclockwise about the origin is shown in the image below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (9, 3) → Ordered pair A' = (-(3), 9) = (-3, 9).

Ordered pair B  = (3, 0) → Ordered pair B' = (-(0), 3) = (0, 3).

Ordered pair C  = (8, 0) → Ordered pair C' = (-(0), 8) = (0, 8).

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The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)

In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).

Plugging in these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

C(7, 3) = 7! / (3! * 4!)

C(7, 3) = 5040 / (6 * 24)

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, the man can take 35 different combinations of shirts without repetition.

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obtain the solution using the long division method

It is one of the most fundamental curvilinear geometric shapes, a cylinder has historically been thought of as a three-dimensional solid. It is considered a prism with a circle as its base in basic geometry.

the area of mathematics that focuses on the characteristics and connections between points, lines, surfaces, solids, and their higher dimensional equivalents.

We can find the solution this way,

The volume of water in the Cylinder before marbles were dropped in =

The volume of water in the Cylinder After marbles were dropped in -

Volume of marbles

So, we can write it as,

Volume of water before = Volume of water after - Volume of Marbles

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Therefore , the solution of the given problem of arithmetic mean comes out to be  option A an=3+2(n-1).

The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.

Here,

The following is the formula for the general word "an" in an arithmetic sequence:

=> a = a1 + (n - 1)d

where the first term is denoted by a1, the term number is n, and the common difference is d.

A1 = 3 and A11 = 23 are provided. To determine the common difference, we can use the method for the eleventh term:

=> a11 = a1 + (11 - 1)d

=> 23 = 3 + 10d

=>  d = 2

Inputting this number of d into the general term's formula yields the following results:

=> a = 3 + (n - 1)2

The right response is therefore: an=3+2(n-1).

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Answer:

You must be really must to answer that paper yho

Step-by-step explanation:

The equation that represents the resale value V (in dollars) of the smartphone as a function of the time t (in years) since it was purchased is:

V = 700e^(-0.2t)

Answer:

Point D is the solution to the system of equations.

Step-by-step explanation:

When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations.  Any point on a line that is defined by an equation is a solution to that equation.  For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc.  These points all lie on the line formed by that equation.  There are an infinite number of possible solutions.  If a second eqaution is added, there is now a constraint on the possible answers.  The goal is to find a point that satisfies both equations.

If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes.  So they will intersect at some point.  One may either solve mathematically using substitution, or by graphing, as was done here.  

Matematically:

y = 2x + 2

y = 1x + 3

Rearrange either equation to isolate a variable, x or y.  These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:

y = 1x + 3

2x + 2 = 1x + 3

x = 1

Now use this value of x to find y:

y = 2x + 2

y = 2*(1) + 2

y = 4

The point these two lines intersect is (1,4) and is the "solution" to this series of equations.

See the attached graph.

Radians and degrees are two units of measurement for angles. Each one has its own pros and cons, and the choice between the two largely depends on the situation and personal preference.

Radians:
Pros:
- Radians are the natural unit of measurement for angles in mathematics and physics. They are closely related to the concept of a circle, and many formulas and equations involving angles are simpler when using radians.
- Radians are unitless, which can make calculations easier and more intuitive.
Cons:
- Radians are not as familiar to most people as degrees, and can be harder to visualize and understand.
- Radians can be more difficult to work with when measuring small angles, since they use fractions or decimals instead of whole numbers.

Degrees:
Pros:
- Degrees are the most commonly used unit of measurement for angles, and are more familiar to most people.
- Degrees are easier to work with when measuring small angles, since they use whole numbers instead of fractions or decimals.
Cons:
- Degrees are not the natural unit of measurement for angles, and many formulas and equations involving angles are more complicated when using degrees.
- Degrees require the use of a special symbol (°) and are not unitless, which can make calculations more difficult and less intuitive.

Overall, the choice between radians and degrees deends on the situation and personal preference. Radians are generally more natural and simpler to work with in mathematics and physics, but degrees are more familiar and easier to visualize.

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Answer: 7.59

Step-by-step explanation: I added all of the miles he traveled up together. ( don't overthink questions like this)

Answer:

c(t) = $85 × (1.09)^t

Step-by-step explanation:

Assuming that the inflation rate remains constant at 9% per year, the cost of the athletic shoes after t years can be determined by multiplying the original cost by the inflation factor for t years, which is given by (1 + 0.09)^t, or 1.09^t. Therefore, the algebraic rule to determine the cost, c(t), of the shoes after t years is:

c(t) = $85 × 1.09^t

Simplifying the expression, we get:

c(t) = $85 × (1.09)^t

where t is the number of years after the original purchase.

The solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places

To solve the given trigonometric equation on the interval [0,2π), we need to use the quadratic formula.

First, let us rewrite the equation in terms of x:
2x^2 + 5x + 2 = 0

Next, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

Plugging in the values from the equation:
x = (-(5) ± √((5)^2 - 4(2)(2)))/(2(2))

Simplifying:
x = (-5 ± √(25 - 16))/4
x = (-5 ± √9)/4
x = (-5 ± 3)/4

This gives us two possible values for x:
x = (-5 + 3)/4 = -2/4 = -0.5
x = (-5 - 3)/4 = -8/4 = -2

Now we need to convert these values back to θ by using the inverse cosine function:
θ = cos^-1(-0.5)
θ = cos^-1(-2)

The first value, θ = cos^-1(-0.5), gives us two solutions on the interval [0,2π):
θ = 2π/3 and θ = 4π/3

The second value, θ = cos^-1(-2), does not give us any solutions on the interval [0,2π) because the cosine function only takes on values between -1 and 1.

Therefore, the solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places.

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The value of n for the given equation 3⁵. 3ⁿ = 3⁸ is n = 3.

Several rules of exponents are presented according to the capacities they possess. The following rule governs multiplication: Add the exponents while maintaining the base's consistency.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing similar bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the base constant.

The given equation is:

3⁵. 3ⁿ = 3⁸

Using the product rule for exponents we have:

3⁽⁵ ⁺ ⁿ⁾ = 3⁸

The above expression can be written as:

5 + n = 8

n = 8 - 5

n = 3

Hence, the value of n for the given expression 3⁵. 3ⁿ = 3⁸ is n = 3.

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The complete question is:

The fraction of a day that the average fire burns is given as follows:

100%.

The fraction of a day that the average fire burns is obtained applying the proportions in the context of the problem.

For the log cabin, the fraction is given as follows:

1/4.

The average fire burns four times this length, hence the length is given as follows:

4 x 1/4 = 4/4 = 1 = 100% of a day.

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