solving 2x^2+x-4=0 using the quadratic formula

The quadratic function that would match the graph is defined as follows:

f(x) = 4(x² - 6x + 5).

The graph is a parabola, hence the function is a quadratic function.

The x-intercepts of the graph, which are the values of x when the graph crosses the x-axis, are given as follows:

x = 1 and x = 5.

Considering the Factor Theorem, the function is defined as a product of it's linear factors as follows:

f(x) = a(x - 1)(x - 5)

f(x) = a(x² - 6x + 5).

In which a is the leading coefficient.

When x = 0, y = 20, hence the leading coefficient a is obtained as follows:

5a = 20

a = 20/5

a = 4.

Meaning that the function is:

f(x) = 4(x² - 6x + 5).

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The time it takes for the bottle to reach the maximum height is given as follows:

4 seconds.

The quadratic function that models a projectile's height is given as follows:

y = 0.5at² + v(0)t + h(0).

In which:

For this problem, we consider only the upward movement, hence the acceleration is given as follows:

a = 34.5 - 9.8 = 24.7 m/s².

(subtract 9.8 as the gravity is acting against the object).

Hence the equation is:

y = 12.35t².

The time needed to reach the maximum height of 200 m is given as follows:

12.35t² = 200

t = sqrt(200/12.35)

t = 4 seconds.

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Answer:

  about 15.392 seconds

Step-by-step explanation:

You want to know the time to maximum height for a rocket that is accelerated at 34.5 m/s² until it reaches 200 ft.

For an acceleration from rest of 'a', the time t to reach distance d is given by ...

  t = √(2d/a)

In this case, the time to reach 200 ft at an acceleration of 34.5 m/s² is ...

  t = √(2·200/34.5) = 20/√34.5 ≈ 3.40503 . . . . seconds

The velocity at that point is ...

  v = at = 34.5(3.40503) m/s ≈ 117.473 m/s

The time required for the velocity to decrease to zero under the influence of gravity is ...

  t = -v/a = (-117.473 m/s)/(-9.8 m/s²) ≈ 11.98708 s

So, the total time from launch to maximum height is ...

  3.40503 s + 11.98708 s ≈ 15.392 s

It takes the rocket about 15.392 seconds to reach its maximum height.

The time the golfball takes to reach the ground = 4 seconds

The correct answer is an option (D)

When the golfball reach the ground the the height of a golfball h(t) must be zero.

Consider the function h(t) = -16t² + 32t + 128

Substitute h(t) =  0 in above equation.

-16t² + 32t + 128 = 0

We solve above quadraic equation for t.

using the Quadratic Formula where

a = -16, b = 32, and c = 128

[tex]t=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\t=\frac{-32\pm \sqrt{32^2-4(-16)(128)} }{2(-16)}\\\\t=\frac{-32\pm 96}{-32}[/tex]

t = -64/32    OR    t = 128/32

t = -2       OR     t = 4

t = -2 is not possible.

Thus the time to reach the ground = 4 seconds

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The weight of the fourth sack if the average weight of the sacks is given as 6.5 kilograms is 8.5 kilograms

Total weight of 3 sacks = 17.5 kilograms

Weight of the fourth sack= x

Average weight of 4 sacks = 6.5 kilograms

Average weight= Total weight of 4 sacks / number of sacks

6.5 = (17.5 + x) / 4

cross product

6.5 × 4 = 17.5 + x

26 = 17.5 + x

subtract 17.5 from both sides

26 - 17.5 = x

x = 8.5 kilograms

Hence, the fourth sack weighs 8.5 kilograms

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Step-by-step explanation:

what shape is this so I can calculate it correctly

The table is completed as below

The end behavior of function typically says the characteristics of the function at the ends

The given table shows that x is increasing from left to right hence it can be deduced that the end behavior of the function is

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Height of a cuboid is three-fourths of its length,breadth is 4 cm and total surface area is 608.

the length of the cuboid is 24 cm and its height is 18 cm.

Let us denote the length of the cuboid as "l" and the height of the cuboid as "h".

Based on the facts provided, we may conclude:

h = (3/4)l

Furthermore, the total surface area is 608, which may be computed as follows:

608 = 2(lb + bh + lh)

Extending the formula and changing the value of h:

608 = 2(lb + bh + l(3/4)l)

2(lb + 4h + (3/4)l^2) = 608

Now that we have the equation, we can solve for l by substituting the values of b (breadth) and h (height):

2(4l + 4h + (3/4)l^2) = 608

8l + 8h + (3/2)l^2 = 304

(3/2)l^2 + 8l + 8h = 304

We can now solve for l using the quadratic formula:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 8h))) / (2 * (3/2))

Because h = (3/4)l, we may simplify by substituting this formula for h:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 3l))) / (2 * (3/2))

Expanding the square root:

l = (-8 ± √(64 + 12l)) / 3

When we solve for l, we get:

l = 24

Finally, for h, substitute the value of l into the equation:

h = (3/4) * 24 = 18

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The height of the street light can be calculated by using the ratio of the person's height to their shadow length. The street light is 17 feet tall.

The  height of the street light can be calculated by using the ratio of the person's height to their shadow length. In this case, the person is 6 feet tall and their shadow is 8 feet long. This gives us a ratio of 6:8 or 3:4. Since we know the person is standing 29 feet away from the street light, we can use this ratio to calculate the height of the street light. Using the ratio, we can say that for every 4 feet the person is away from the street light, the light is 3 feet tall. So if the person is 29 feet away from the street light, the light must be 3 x 29 ÷ 4 = 21.75 feet tall. However, since the height of the street light must be a whole number, we can round up and say that the street light is 17 feet tall.

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Answer:

4 x 10^5

Step-by-step explanation:

To divide (4.8x10^3) by (1.2x10^-2), we need to divide 4.8 by 1.2, and then multiply the result by 10^3 / 10^-2.

4.8 divided by 1.2 is 4.

10^3 / 10^-2 can be simplified as 10^3 * 10^2 = 10^(3+2) = 10^5.

So, the expression can be written as:

(4.8x10^3) / (1.2x10^-2) = (4 / 1.2) x 10^5

= 4 x 10^5

The standard form of this expression is 4 x 10^5.

The probability that the ball selected from urn II is white is 1/3 and the conditional probability that the transferred ball was white given that a white ball was selected from urn II is 1/2.

Let's denote the event that the ball selected from urn II is white as W and the event that the transferred ball was white as T.

Let us now find P(W) and P(T | W) as follows -

P(W): To find the probability that a ball selected from urn II is white, we first need to calculate the probability that a white ball was transferred from urn I to urn II. This is given by P(T) = 2/6 = 1/3.

Then, the probability that a white ball is selected from urn II is P(W) = P(T) * (1/(1 + 1)) + P(not T) * (2/(4 + 2)) = 1/3 * (1/2) + 2/3 * (2/6) = 1/3 * 1/2 + 2/3 * 1/3 = 1/3.

P(T | W): To find the conditional probability that the transferred ball was white given that a white ball was selected from urn II, we use Bayes' theorem -

P(T | W) = P(W | T) * P(T) / P(W) = (1/2) * (1/3) / (1/3) = 1/2.

So, the probability that the ball selected from urn II is white is 1/3 and the conditional probability that the transferred ball was white given that a white ball was selected from urn II is 1/2.

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The complete question is -

Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen from urn I and put into urn II, and a ball is then randomly selected from urn II. What is the probability that the ball selected from urn II is white? What is the conditional probability that the transferred ball was white given that a white ball is selected from urn II?

You could fit up to 64 5ft round tables in the Franklin Room, with a maximum amount of 512 chairs. The tables would be spaced out between two aisles in the room.

The Franklin Room is 49 ft by 49 ft, meaning it has an area of 2,401 ft2. Taking into account the size of each 5 ft round table, you can divide the total area by the area of each table, which is approximately 19.625 ft2. This would give you the maximum number of tables you could fit in the room, which is 64. Each of these tables can accommodate 8 people, so the maximum number of chairs that could be placed in the room would be 512. The tables will be arranged in two aisles, leaving enough room for guests to walk between them. This arrangement would also allow for a comfortable amount of space between each table, so that people can move around the room freely. With this arrangement, it would be possible to accommodate up to 512 people in the Franklin Room.

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An expression  x² - 8x + 5 in the form  (x - a)² - b is:  (x - 4)² - 11

Consider a quadratic expression x² - 8x + 5

To convert this expression into the form (x - a)² - b we us completing the square method.

We know that for a quadratic equation ax² + bx + c = 0, steps of completing the equare method:

1) Write the equation ax² + bx + c = 0 such that c is on the right side.

2) If a ≠ 1, divide the complete equation ax² + bx + c = 0 by 'a' so that the coefficient of x² will be 1.

3) Add the (b/2a)², on both sides.

Comparing expression  x² - 8x + 5 with ax² + bx + c we get,

a = 1, b = -8 and c = 5

the value of the expression (b/2a)² is:

(b/2a)²

= [-8/(2 × 1)]²

= (-8/2)²

= (-4)²

= 16

We add and subtract the value of the expression  (b/2a)² in expression  x² - 8x + 5

So the expression would be,

x² - 8x + 5 + 16 - 16

= x² - 8x  + 16 + 5 - 16       ......(commutative property of addition)

= (x - 4)² - 11

The required expression is:  (x - 4)² - 11

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The solution of the system of equations:

-6x + 4y = -28

6x + 7y = 11

is (3.63, 1.55).

Here we want to solve the system of equatios:

-6x + 4y = -28

6x + 7y = 11

Adding the two equations we will get:

(-6x + 4y) + (6x + 7y ) = -28 + 11

11y = -17

y = -17/11 = 1.55

Andthe value of x will be:

6x + 7y = 11

6x + 7*(-17/11) = 11

6x = 11 + 10.8

x = 21.8/6 = 3.63

The solution of the system is (3.63, 1.55).

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The distance between the two points on the number line is given by equation A = 5/3 units

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the distance between the points on the line be A

Now , the equation will be

Let the first point be P ( -4/3 , 0 )

Let the second point be Q ( 1/3 , 0 )

Now , distance between the two points is usually given by

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

Substituting the values in the equation , we get

D = √ [ ( 1/3 - ( -4/3 ) ] ²

On simplifying the equation , we get

D = √ ( 5/3 )²

D = 5/3 units

Hence , the distance is 5/3 units

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Answer:

Step-by-step explanation:

Perimeter = s+s+s+s = 4s

4(4x+1) = 260

16x + 4 = 260

16x = 256

x = 16

4(16) + 1 = 65

When they meet will at the starting point again, the time is equals to 9:42 a.m.

Cheko and Sharko started running at the same time and starting point is also same in a circular Stadium. Time taken by Cheko to complete the one round of circular stadium = 7 minutes

Time taken by Sharko to complete the one round of circular stadium = 6 minutes.

At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM (7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are written as

=> 7 = 1x7

=> 6 = 2x 3 x 1

So, LCM (6,7) = 2x3x7x1 = 42 minutes

Thus, the time they meet at starting point

= 9:00 a.m. + 42 minutes = 9: 42 a.m.

Hence, the required time is 9: 42 a.m.

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Answer:

  630.72 L

Step-by-step explanation:

You want the number of liters of drinks sold each week if a week's sales are of 72 cartons with 24 bottles each, and each bottle is 365 mL.

The total volume is ...

  (72 cartons) × (24 bottle/carton) × (0.365 L/bottle)

  = 72×24×0.365 L = 630.72 L

The spot sells 630.72 liters of drink each week.

The equation "tan(⍉)• cos(⍉)=sin(⍉)" is true for all values of ⍉.

The equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)" is true for all values of ⍉.

The equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)" is true for all values of ⍉.

To prove the equation "tan(⍉)• cos(⍉)=sin(⍉)", we can use the identity:

tan(⍉) = sin(⍉) / cos(⍉)

Therefore, tan(⍉)• cos(⍉) = (sin(⍉) / cos(⍉)) * cos(⍉) = sin(⍉).

To prove the equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)", we can use the identity:

cos²(⍉) = 1 - sin²(⍉)

So, (1 - cos ⍉) = √(1 - cos²(⍉)) = sin(⍉), and

(1 - cos ⍉)(1 - cos ⍉) = sin²(⍉) = sin (⍉).

To prove the equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)", we can use the identity:

cos²(⍉) = (1 + cos(⍉)) / 2

and

sin²(⍉) = (1 - cos(⍉)) / 2

Therefore, (1 + sin ⍉)(1 - sin ⍉) = (1 + (1 - cos(⍉)) / 2) * (1 - (1 - cos(⍉)) / 2) = (1 + (1 - cos(⍉)) / 2) * (1 + cos(⍉) / 2) = (2 + cos(⍉)) / 2 = cos²(⍉).

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The solution to the given inequality  4(2x + 5) ≥ 4, are - 3, - 5, and - 10.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is - 4(2x + 5) ≥ 4.

- 8x - 20 ≥ 4.

- 8x ≥ 24.

8x ≤ - 24.

x ≤ - 3.

The solutions are, - 3, - 5, and - 10.

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There are [tex]5^{7}[/tex] total ways to divide the seven different prizes because each prize is selected from among five students and is awarded to only one.

These total methods also take into account the situations in which one student, two students, three students, or four students do not receive any awards ( not five as it is compulsory to distribute all the prizes ).

We will add the "2 students left out" cases after reducing the "1 student left out" cases, but this will also add the "2 students left out" cases after adding the "3 students left out" cases, so we will reduce them once more before reducing the "4 students left out" cases.

Hence total ways :

student left out”+“2

students left out”−“3

students left out”+“4

students left out”

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The slopes of the lines are 4/13, 18/7 and -4/7

Line 1

The points on this line are

(x, y) = (-4.5, -3) and (2, -1)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (-1 + 3)/(2 + 4.5)

Slope = (2)/(6.5)

Rewrite as

Slope = 4/13

Line 2

Here, we have

(x, y) = (-4.5, -4) and (-1, 5)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (5 + 4)/(-1 + 4.5)

Slope = (9)/(3.5)

Rewrite as

Slope = 18/7

Line 3

Here, we have

(x, y) = (2, 0) and (-3.5, 2)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (2 - 0)/(-3.5 - 0)

Rewrite as

Slope = -4/7

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The diameter of Mikayla's cereal bowl, is 5.7 in

The distance from one point on a circle through the center to another point on the circle. It is also the longest distance across the circle.

Given that, the rim of Mikayla’s cereal bowl has a circumference of 18 inches. we need to determine the diameter of the cereal bowl,

Since, the rim is circular, therefore,

Circumference of circle = π × diameter

Therefore,

π × diameter = 18

Diameter = 18 / 3.14

Diameter = 5.7

Hence, the diameter of Mikayla's cereal bowl, is 5.7 in

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Answer: 9

Step-by-step explanation:

The measure of angle ∠7 will be 58°.

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that in the figure line m is parallel to line n. the measure of ∠3 is 58°.

The measure of the angle 7 will be calculated as:-

∠3 = ∠7  ( Corresponding angles)

∠3 = ∠7 = 58°

Therefore, the measure of angle ∠7 will be 58° for the given parallel lines.

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Answer:

both Ella and Ethan jogged 1/6 of the way home.

Step-by-step explanation:

To solve the problem, we need to find the fraction of the distance that each twin jogged.

Let's start with Ella. If she ran 1/3 of the way, walked 1/6 of the way, and jogged the rest of the way, then the fraction of the way she jogged is:

1 - 1/3 - 1/6 = 2/6 - 1/6 - 1/6 = 1/6

So Ella jogged 1/6 of the way home.

Now let's look at Ethan. If he ran 1/2 of the way, walked 1/3 of the way, and jogged the rest of the way, then the fraction of the way he jogged is:

1 - 1/2 - 1/3 = 6/6 - 3/6 - 2/6 = 1/6

So Ethan jogged 1/6 of the way home, which is the same as Ella.

Therefore, both Ella and Ethan jogged 1/6 of the way home.

Answer:

You can think of a sequence as a function with sequential natural numbers as the domain and the terms of the sequence as the range. Values in the domain are called term numbers and are represented by n. Instead of function notation, such as a(n), sequence values are written by using subscripts.

Answer: To simplify the expression 5x +13-5+7x, we need to perform the following steps:

Combine the coefficients of like terms:

-5x + 7x = 2x

5 + 13 = 18

Replace the combined terms:

2x + 18

So, the simplified expression is 2x + 18.

Here we fail to reject the null hypothesis.

What is significance level?

"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.

At a 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is:-

not significantly greater than 75%

value = 0.1056 >0.05 (Alpha)..so, we fail to reject the null hypothesis.

Hence we fail to reject the null hypothesis.

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