Use the parabola tool to graph the quadratic function f(x)=3x^2+6x-24

The correct statement regarding the proportional relationships is given as follows:

D. The first bucket will be completely filled 11 minutes before the second bucket.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

For the first bucket, the equation is given as follows:

y = 0.4x.

Meaning that 0.4 gallons are inserted each minute, hence the time to insert 2 gallons is given as follows:

2/0.4 = 5 minutes.

For the second bucket, the constant is taken from the graph as follows:

k = 0.5/4

k = 0.125.

Hence the time is given as follows:

2/0.125 = 16 minutes.

Hence the difference is of:

16 - 5 = 11 minutes.

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The absolute increase from the younger group to the older group is 59.9% - 14.3% = 45.6%. Rounding to the nearest point, the answer is 46 points.

The absolute increase is the difference between two values, regardless of the direction of change. In this case, we want to find the absolute increase in the percentage of people who vote from the younger group (20-25 years old) to the older group (60-65 years old).

To find the absolute increase, we subtract the percentage of people who vote in the younger group from the percentage of people who vote in the older group, taking the absolute value of the result.

So, the absolute increase in the percentage of people who vote from the younger group to the older group is:

|59.9% - 14.3%| = 45.6%

This means that the percentage of people who vote in the older group is 46 percentage points higher than the percentage of people who vote in the younger group.

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The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units. Option C is a correct choice.

To find the coordinates of the center of the circle and the length of the radius, we need to rewrite the equation of the circle in standard form, which is (x - h)² + (y - k)² = r². Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius.

Given equation: x² + y² - x - 2y - 1 = 0

To convert it into standard form, we complete the square for the x and y terms separately.

Rearranging the equation:

x² - x + y² - 2y = 1

Completing the square for x:

(x² - x + 1/4) + (y² - 2y) = 1 + 1/4

Completing the square for y:

(x² - x + 1/4) + (y² - 2y + 1) = 1 + 1/4 + 1

Simplifying:

(x - 1/2)² + (y - 1)² = 9/4

Comparing it with the standard form, we can see that:

Center coordinates: (1/2, 1)

Radius: √(9/4) = 3/2 = 1.5 units

Therefore, the correct answer is C. The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units.
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Question -

A circle is defined by the equation given below. x² + y² - x - 2y - 1 = 0 What are the coordinates for the center of the circle and the length of the radius?

A. (-1,-1), 2 units −1),

B. (- 1/2 ,1), 4 units

C. (1/2 , 1), 2 units

D. (-1/2 ,-1), 4 units

a) Value of K is Option 3. 98.83%

b) It takes Option 2. 183 bounces for the ball to bounce back to a height of less than 3 inches (1/4 of a foot).

a) To determine k, we can use the formula for the nth term of a geometric sequence:

[tex]a_n[/tex] = [tex]a_1[/tex] * [tex]r^{(n-1)}[/tex]

where a_1 is the initial term, r is the common ratio, and n is the term number.

We know that [tex]a_1[/tex] = 10 feet and [tex]a_5[/tex] = 9.04 feet, so we can set up the equation:

[tex]a_5[/tex] = [tex]a_1[/tex] * [tex]r^{(5-1)}[/tex]

9.04 = 10 * [tex]k^4[/tex]

Solving for k, we get:

k = [tex](9.04/10)^{(1/4)}[/tex] = 0.9883 or 98.83%

Therefore, the answer is (Option 3) 98.83%.

b) We can use the formula for the nth term of a geometric sequence again to find the height of the ball after the nth bounce:

[tex]a_n[/tex] = 10 * [tex]k^{(n-1)}[/tex]

We want to find the smallest n such that a_n < 1/4 foot, or 0.25 feet. Substituting k = 0.9883, we get:

10 * [tex]0.9883^{(n-1)}[/tex] < 0.25

Solving for n, we get:

n > log(0.25/10) / log(0.9883) + 1

n > 183.3

Since n must be a whole number, the smallest n that satisfies this inequality is n = 184. Therefore, it takes 183 bounces for the ball to bounce back to a height of less than 3 inches (Option 2).

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1. The best equation for circle A is (x + 4)² + (y + 2)² = 9. Option D

2. The equation of the circle with coordinates (1, 1) (1, 11) is (x - 1)² + (y - 6)² = 25. Option A

1. For the equation of circle A, we can pick out the coordinates we see.

Circle A has its midpoint at (-4, -2) and its edges at (-4, 1) and (-4, -5).

The equation of a circle in a plane is (x - h)² + (y - k)² = r²

the circle has a radius of 3 units (from -2 to 1 or from -2 to -5)

(x - (-4))² + (y - (-2))² = 3²

when we simplify, it becomes (x + 4)² + (y + 2)² = 9

2. The equation of a circle with diameter AB. A (1, 1), B(1, 11) is

h = (x₁ + x₂)/2 ⇒(1 + 1)/2 = 1

k = (y₁ + y₂)/2⇒ (1 + 11)/2 = 6

the center of the circle is at (1, 6).

A and B which are (1, 1) and (1, 11), it's clear that the diameter is 10 units (11 - 1). Thus, the radius is 5 units.

(x - h)² + (y - k)² = r²

Substituting the obtained values we get

(x - 1)² + (y - 6)² = 5²

which becomes

(x - 1)² + (y - 6)² = 25

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Answer:

  C.  18/48 and 21/56

Step-by-step explanation:

You want to identify pairs of ratios that are proportional.

Ratios are proportional when they have the same value. We can check whether the values are the same by reducing each ratio to lowest terms.

The attached calculator display shows the proportional ratios are ...

  18/48 and 21/56 . . . . choice C

__

Additional comment

Both of these reduce to 3/8. You can remove a factor of 6 from the numbers of the first ratio, and a factor of 7 from the numbers of the second ratio to reduce both of them to 3/8.

<95141404393>

Answer: C.  18/48 and 21/56

Step-by-step explanation:  Hope it helps

If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.

option C.

When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.

If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.

In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.

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Answer:

Step-by-step explanation:

1. The figure  is a rectangular prism.

Formula: V = lwh

Given: 13 ft x 7ft x 9 ft

Substitute the values to the formula and solve.

V = lwh

V = 13ft(7ft)(9ft)

V = 819 ft³

2. The given figure is a triangular prism. Notice that the base forms a right triangle.

Formula: V = 1/2bhl

Given:

b = 9m

h = 12m

l = 16 m

Substitute the given values to the formula and solve.

V = 1/2(9m)(12m)(16m)

V = 864 m³

3. This is a cylinder

Formula: V = πr²h

Given:

r = 11 yd

h = 26 yd

Solve:

V = π (11yd)²(26yd)

V = 9883.45 yd³

4. The figure is a rectangular prism.

Formula: V = lwh

Given dimensions: 9m x 9m x 13.5m

Solve:

V = 9m(9m)(13.5m)

V = 1093.5 m³

5. The figure is a triangular prism

Formula: V = 1/2bhl

Given:

b = 15yd

h = 13 yd

l = 24 yd

Solve:

V = 1/2 (15yd)(13yd)(24yd)

V = 2340 yd³

Answer:

I would go with 900 but I’m not for sure

Step-by-step explanation:

The  Linear function is y equals negative one third times x plus 1

A linear function is a function that has a constant rate of change, meaning that as one variable (usually x) increases or decreases by a certain amount, the other variable (usually y) also changes by a constant amount.

Out of the four given equations, the only one that represents a linear function is the third one:

y equals negative one third times x plus 1

This is because the equation has a constant rate of change of -1/3 for any change in x. For example, if we increase x by 3, y will decrease by 1 (because 3*(-1/3) = -1). Similarly, if we decrease x by 3, y will increase by 1. This constant rate of change is what makes the equation represent a straight line when graphed.

The other three equations do not represent linear functions.

The first equation, x = 3, is not a function at all because there are multiple possible y values for the given x value of 3.

The second equation, y = 3x2, is a quadratic function because it contains an x2 term, which means that the rate of change of y with respect to x is not constant.

The fourth equation, 3x - 4 = 7, is a linear equation but not a function because for any given x, there is only one corresponding value of y. However, when the equation is solved for y, it becomes y = 3x - 3, which represents a linear function with a constant rate of change of 3.

The  linear function is y equals negative one third times x plus 1

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The coefficient of a²b² in the expansion of (2a - b)⁴ is 24

From the question, we have the following parameters that can be used in our computation:

(2a - b)⁴

When the expression is expanded, we have

(2a-b)⁴ = (2a-b)(2a-b)(2a-b)(2a-b)

So, we have

(2a-b)⁴ = 16a⁴ - 32a³b + 24a²b² - 8ab³ +b⁴

Consider an expression ax where the variable is x

The coefficient of the variable in the expression is a

Using the above as a guide, we have the following:

The coefficient of a²b² in the expansion is 24

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The height of the triangle must increase by 4.29 feet so that the area would increase by 1.2 square feet.

To calculate the area of a triangle, you can use the formula presented as follows:

[tex]\sf Area = \huge \text(\dfrac{1}{2}\huge \text) \times base \times height[/tex]

In which the parameters are given as follows:

Considering the triangle that has a base of 14 feet and a height of 6 feet, the area of the triangle is given as follows:

[tex]\sf A = 0.5 \times 14 \times 6[/tex]

[tex]\sf A = 42 \ square \ feet.[/tex]

An increase of 1.2 square feet would lead to an area of 43.2 square feet, hence the height would be of:

[tex]\sf 4.2h = 43.2[/tex]

[tex]\sf h = \dfrac{43.2}{4.2}[/tex]

[tex]\sf h = 10.29 \ feet[/tex].

Then the increase in the height would be of:

[tex]\sf 10.29 - 6 = 4.29 \ feet[/tex].

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The value of the expression "A- 2--0.5x47" is 25.5.

Using the order of operations (PEMDAS) we first simplify the multiplication before subtracting from 2:

2 - (-0.5 x 47)

= 2 - (-23.5)

When subtracting a negative number, we can think of it as adding the positive value. Therefore, we can rewrite the expression as:

2 + 23.5

= 25.5

Therefore, the value of the expression "A- 2--0.5x47" is 25.5.

In conclusion, to determine whether a given value is a solution to an equation, we need to know what the equation is. However, given an expression, we can simplify it and then substitute a value for the variable to determine whether it is a solution.

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Question

which value is a solution  A- 2-( -0.5x47)

The probability that at least six hamburgers are contaminated in a random sample of 10 hamburgers is approximately 0.2 or 20%

We can approach this problem using the binomial distribution, where:

n = 10 (the sample size)

p = 0.25 (the probability of a hamburger being contaminated)

q = 1 - p = 0.75 (the probability of a hamburger not being contaminated)

We want to find the probability that at least six hamburgers are contaminated, which can be expressed as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + ... + P(X = 10)

where X is the number of contaminated hamburgers in the sample.

Using the binomial probability formula, we can calculate each individual probability:

P(X = b) = (n choose b) x pᵇ x q⁽ⁿ⁻ᵇ⁾

where (n choose k) represents the number of ways to choose k items from a set of n items, and is calculated as:

(n choose k) = n! / (k! x (n-k)!)

Using a calculator or software, we can find each individual probability and sum them up to get the total probability:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= (10 choose 6) x 0.25⁶ x 0.75⁴ + (10 choose 7) x 0.25⁷ x 0.75³ + (10 choose 8) x 0.25⁸ x 0.75² + (10 choose 9) x 0.25⁹ x 0.75¹ + (10 choose 10) x 0.25¹⁰ x 0.75⁰

= 0.0197

= 0.02

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Answer:

Corresponding angles is the answer to your question

Answer: 9" x 10" x 11" = 990 cubic inches.

990 cubic inches / 5 minutes = 198 cubic inches per minute

22" x 23" x 33" = 16698 cubic inches

16698/198 = 84 and 1/3 minutes

1 hour 24 minutes and 20 seconds

Answer:

2553(base 7) = 969(base 10)

Step-by-step explanation:

3 in units place means 3.

5 in the 7's place means 5 × 7 = 35

5 in the 7²'s place means 5 × 7² = 5 × 49 = 245

2 in the 7³'s place means 2 × 7³ = 2 × 343 = 686

3 + 35 + 245 + 686 = 969

The other solution to the equation x³ + 3x² - x = |x-1| is approximately x~ = -2.6.

1. Start by plotting the graphs of both sides of the equation on a graphing calculator.

2. The left side of the equation, x³ + 3x² - x, can be plotted as a curve.

3. The right side of the equation, |x-1|, can be plotted as a V-shaped graph with the vertex at (1, 0).

4. Find the intersection points of the two graphs.

5. By observing the graph, it can be seen that the two given solutions, a~ = -0.7 and b~ = 0.5, are present.

6. Identify the other solution, which is the third intersection point.

7. Determine the approximate x-coordinate of the third intersection point by reading the value from the graph.

8. Round the obtained x-coordinate to the nearest tenth.

9. The other solution is approximately x~ = -2.6.

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Answer: Trust me I don't know either

Step-by-step explanation:

For asking questions about whatever in life I guess

The limit as n approaches infinity of ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) is 6.

To evaluate the limit as n approaches infinity of the expression ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵), we can simplify it using algebraic manipulations.

Let's expand the numerator and denominator using the binomial:

Numerator:

((n+1)⁶-(n-1)⁶) = [n⁶ + 6n⁵ + 15n⁴ + 20n³ + 15n² + 6n + 1] - [n⁶ - 6n⁵ + 15n⁴ - 20n³ + 15n² - 6n + 1]

= 12n⁵ + 40n³ + 12n

Denominator:

((n+1)⁵+(n-1)⁵) = [n⁵ + 5n⁴ + 10n³ + 10n² + 5n + 1] + [n⁵ - 5n⁴ + 10n³ - 10n² + 5n - 1]

= 2n⁵ + 20n³ + 2n

Now, let's simplify the expression by canceling out common terms:

((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) = (12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)

As n approaches infinity, we can see that the highest power of n in the numerator and denominator is n⁵.

We can divide all terms by n⁵ to determine the limit:

lim(n→∞) [(12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)]

= lim(n→∞) [(12 + 40/n² + 12/n⁴) / (2 + 20/n² + 2/n⁴)]

= 12/2

= 6

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Amount of ice cream can the cone hold is, 9.8 inches³

We have to given that;

An ice cream cone has a height of 6 inches and a diameter of 2.5 inches.

Hence, We get;

Radius of cone = 2.5 / 2 = 1.25 inches

Since, We know that;

Volume of cone is,

V = πr²h/3

v = 3.14 × 1.25² × 6 / 3

V = 9.8 inches³

Hence, Amount of ice cream can the cone hold is, 9.8 inches³

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The additional reason will be JK/PQ = KL/QR.

Option C is correct.

Given that are two triangles, ΔJKL and ΔPQR, where ∠K ≅ ∠Q, we need to determine a reason to show ΔJKL and ΔPQR are similar,

So, we know that the similar triangles have congruent corresponding angles and corresponding sides are in equal ratio,

So, from the options if we take JK/PQ = KL/QR we can prove that the triangles are similar by SAS rule.

Hence the option C is correct.

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The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.

Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:

|A| = 150

|B| = 770

|A ∪ B| = 900

We want to find |C| and |A ∩ B| (which is the number of youths using both).

Using the inclusion-exclusion principle, we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

900 = 150 + 770 - |A ∩ B|

|A ∩ B| = 20

So, 20 youths use both iPhone and Samsung.

To find the number of youths who use neither, we can use the fact that:

|A ∪ B ∪ C| = 1100

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Plugging in the values we know, we get:

1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200

Since the number of youths using both is 20, we have:

|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0

So, we can simplify the equation to:

|C| = 200

Therefore, 200 youths use neither iPhone nor Samsung.

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Answer:

[tex]\\[/tex]

Step-by-step explanation:

In the first year, the trainers will be worth 80% of their original value, which is:

[tex]\rm\implies{£100 \times 0.8 = £80}[/tex]

[tex]\\[/tex]

In the second year, they will be worth 80% of their value after the first year:

[tex]\rm\implies{£80 \times 0.8 = \boxed{\boxed{\sf{\:\:\:\green{£64}\:\:\:}}}}[/tex]

[tex]\\[/tex]

[tex]\\[/tex]

[tex]\therefore[/tex] The trainers will be worth £64 in 2 years' time.

Step-by-step explanation:

One complete revolution is one circumference

circumference of a circle is found using the formula  circumf = pi * d

so    308 m = pi * d   or

                  308 m / pi = diameter = 98 m   (a VERY large bicycle wheel!)

Answer:

Step-by-step explanation:

No

for it to be a right angle triangle the longest side would have to be the square root of 8 squared plus 11 squared which is 13.6

answer

no Pythagorean theorem doesnt work

steps

8²+11² should equal 17²

BUT

121+64=185

17²=289

Answer:

BC is 32 cm

Step-by-step explanation:

The probability of drawing an orange marble and a blue marble without replacement is:P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

The probability of drawing an orange marble and a blue marble without replacement, we need to consider the total number of marbles and the number of desired outcomes.

Let's assume we have a bag of marbles containing both orange and blue marbles. The total number of marbles in the bag is not given, so we'll consider it as an unknown value, denoted as N.

First, we need to calculate the probability of drawing an orange marble on the first draw. Since there is no replacement, the probability of drawing an orange marble on the first draw is given by the ratio of the number of orange marbles to the total number of marbles:

P(Orange on first draw) = Number of orange marbles / Total number of marbles

Next, after the first marble is drawn, the bag will contain one less marble, and the number of orange marbles and blue marbles will change accordingly. Assuming we drew an orange marble on the first draw, the number of orange marbles will decrease by 1, and the total number of marbles will decrease by 1.

Now, we need to calculate the probability of drawing a blue marble on the second draw, given that an orange marble was drawn on the first draw. The probability is calculated as:

P(Blue on second draw | Orange on first draw) = Number of blue marbles / Total number of marbles after the first draw

Since there is no replacement, the total number of marbles after the first draw is N - 1.

Finally, to find the probability of drawing an orange marble and a blue marble without replacement, we multiply the probabilities of the two events:

P(Orange and Blue without replacement) = P(Orange on first draw) * P(Blue on second draw | Orange on first draw)

To simplify the calculation, we can substitute the given values:

P(Orange on first draw) = 3/10 (assuming there are 3 orange marbles out of 10 marbles in total)

P(Blue on second draw | Orange on first draw) = (N - 4) / (N - 1) (assuming there are N - 4 blue marbles left in the bag after drawing an orange marble)

Therefore, the probability of drawing an orange marble and a blue marble without replacement is:

P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

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To calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.

One way to extend the maxHP for levels beyond 60 is to use the same formula that was used to calculate the maxXP for levels 1-60, but with the appropriate values plugged in.

The formula for the maxHP for a given level can be approximated as:

maxHP = baseHP x  (1 + level/5)²

where baseHP is the starting HP for level 1 (in this case, it's 330).

To extend the maxHP for levels 61-70, you can simply plug in the appropriate level values into the formula and calculate the corresponding maxHP values.

For example, to find the maxHP for level 61, you would plug in level = 61:

maxHP = 330 x (1 + 61/5)²

maxHP ≈ 2619.9

Similarly, you can calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.

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The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:

Calculating the absolute change:

Absolute change = Final value - Initial value

= 57.7 pounds - 67.8 pounds

= -10.1 pounds

Step 2: Calculate the relative change:

Relative change = (Absolute change / Initial value) * 100

= (-10.1 pounds / 67.8 pounds) * 100

≈ -14.9%

The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

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