3.11 Graded Assignment: Quadratic Equations - Part 2

The possible length is 9 centimeter because it can be isoceles triangle

Based on the table, the annual premium for a wood house in a rural area would be $2,000.

The values of the test statistic used are:

The test statistic to be used depends on the sample size and whether the sample standard deviation is known or not.

The z-test is used when the sample standard deviation is known and the sample size is greater than 30.

The t-test is used when the population standard deviation is or unknown and the sample size is less than 30.

a)  Since the sample size is less than 30 and the population standard deviation is known, we can use the one-sample z-test.

The test statistic is z = (x - μ) / (σ / √(n))

where;

Substituting the values in the formula above:

z = (195.6 - 191.6) / (19.3 / √(17))

z = 0.85

(b) The sample size is less than 30 and the population standard deviation is unknown, we therefore use the one-sample t-test.

The test statistic is t = (x - μ) / (s / √(n))

where;

Substituting the values in the formula above:

t = (195.6 - 191.6) / (18.5 / √(10))

t = 0.68

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If the cylindrical-barrel's volume is 785.4 ft³, then the radius of barrel is approximately 5 ft, so option(c) is correct.

We know that cylindrical barrel's volume  is given by formula : V = πr²h

where V represents volume, r represents radius, and h represents height of the cylinder.

In this case, we know that the volume of barrel is 785.4 ft³ and the height is 10 ft.

Substituting these values and π ≈ 3.14, into the Volume-formula,

We get,

785.4 = 3.14 × r² × (10);

785.4/31.4 = r²,

r = √(785.4/31.4),

r ≈ 5 ft

Therefore, the radius of the barrel is (c) 5 feet.

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As asked in the question, 48.2% is equivalent to the fraction 241/500.

To convert a percentage to a fractional equivalent, we divide the percentage by 100 and simplify the resulting fraction.
So, to convert 48.2% to a fraction, we divide 48.2 by 100:
48.2/100 = 0.482

This gives us the decimal equivalent of 48.2%.

To convert the decimal to a fraction, we write it over 1 and simplify it:
0.482/1 = 482/1000

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
482/1000 = (241/500)

Therefore, 48.2% is equivalent to the fraction 241/500.

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Answer: 48.7

Step-by-step explanation:

cos x=31/47

x=48.7

Answer:

Step-by-step explanation:

The obtained inequality be 5x + 9 < 4.

The given inequality is,

5x + 6 < 1

To obtain the required expression,

Add 3 in both sides of inequality

⇒5x + 6 + 3 < 1 + 3

⇒5x + 9 < 4

Hence,

The inequality which is required be

5x + 9 < 4

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Answer:

y = -5x/9 - 2/9

Step-by-step explanation:

if two lines are perpendicular to each other,

the product of their slopes are -1

(slope of f)(slope of g) = -1

(9/5)(slope of g) = -1

(slope of g) = -5/9

equation of g:

(y - (-3))/(x - 5) = -5/9

(y+3) = -5/9 * (x-5)

y = -5x/9 + 25/9 - 3

y = -5x/9 - 2/9

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

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As a result, there is no solution to the provided problem.

Trigonometry is the study of triangles, which is a branch of mathematics. It is also known colloquially as "trig." Mathematicians explore the connections between the sides and angles of triangles in trigonometry.

We're told that sec O = -1/0. Because sec O is the reciprocal of cos O, cos O must be -1/0. However, because there is no angle with an undefined cosine, we infer that there is no such angle O.

As a result, there is no solution to the provided problem.

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Answer: 16

Step-by-step explanation:

Taking the integral: f(x)=((2x)^4)/4-1^4/4

Differentiating: f'(x)=2(2x)^3

f'(1)=16

Option C is correct, the third dot plot represents the table data.

A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

The dots in the number line represents the number of hamsters

The dots above line represents the hamsters owned.

We have to find the dot plot which is represented by the table.

As we observe C dot plot, it matches with the given data in the table.

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Answer:

76% increase (approximately)

Step-by-step explanation:

21 lbs ➜ 37 lbs.

To calculate percentage increase, you must first find the difference of the final value and the starting value.

[tex]37-21=16[/tex]

Second, take the difference and divide it from the starting value.

[tex]16/21\\=0.76[/tex] (approximately)

Lastly, take the quotient and multiply it by 100.

[tex]0.76 *100\\=76[/tex]

Therefore, there was a 76% increase in weight.

At 15 years old, her height is 70 inches.

The height she will never achieve is the horizontal asymptote of the function.

To find the teenager's height, plug in x=0 into the function: f(0) = -1/0 + 2 + 68.

Since division by zero is undefined, the function is not valid at 15 years old.

The height she will approach but never achieve is the horizontal asymptote of the function.

As x approaches infinity, the -1/x term approaches 0.

Therefore, the height approaches 2+68 = 70 inches.

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Sum of the interior angles is 540°.

The value of x is 81.67°, and angle A, C, D are 121.67°, 131.67°, 86.67° respectively.

What is the sum of interior angles of a pentagon?

Sum of interior angles of pentagon = (n-2) ×180° = (5 - 2) × 180° = 540°

Where n is number of side of the polygon.

Here given that values of angle A, B, C, D, E are (x + 40°), 80°, (x + 50°), (x + 5°), 125° respectively.

So,

angle A + angle B + angle C + angle D + angle E = 540°

We are Substituting the given values and get,

(x + 40) + 80 + (x + 50) + (x + 5) + 125 = 540

Or, 3x + 295° = 540°

Or,3x = 245°

Or, x = 81.67°

Now,

angle A = x + 40° = 81.67° + 40° = 121.67°

angle C = x + 50° = 81.67° + 50° = 131.67°

angle D = x + 5° = 81.67° + 5° = 86.67°

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The composite figure has an area of 74 square centimeters.

In this question we find the representation of a composite figure formed by two rectangles, whose area has to be computed. The area formula for a rectangle is:

A = b · h

Where:

Now we proceed to determine the area of the composite figure:

A = (8 cm) · (3 cm) + (5 cm) · (2 cm) + (8 cm) · (5 cm)

A = 24 cm² + 10 cm² + 40 cm²

A = 74 cm²

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Answer: 112km

Step-by-step explanation:

SA rectangular prism = 2 (lh +wh + lw )

= 2 ((4x2)+(8x4)+(2x8))

= 2 (8+32+16)

= 2(56)

= 112km

The solution to the system of equation is (29, 75).

The given simultaneous equation is expressed as shown below:

3x-y=12 ............ 1

y=2x+17 ............ 2

We need to determine the unknown values of x and y

Substitute equation 2 into 1 to have:

3x-y=12

3x- (2x + 17) = 12

3x - 2x - 17 = 12

x - 17 = 12

x = 12 + 17

x = 29

Substitute x = 29 into equation 2;

y=2(29)+17

y = 58 + 17

y = 75

Hence the solution to the system of equation is (29, 75)

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The homeowner needs to work for roughly 3 weeks to save up for the cost of the fence.

Option B is correct.

We have the following values:

Length of walkway gate = 5 feet

Length of driveway gate = 15 feet

The total reduction in length = 5 + 15 = 20 feet

the Length of property = 150 feet

Width of property = 60 feet

Perimeter of property = 2(150 + 60) = 420 feet

We can calculate that Length of fence after subtracting gates is given as  = 420 - 20

= 400 feet

So in order to calculate the amount of time needed to save up for the fence:

we have:

Total cost after tax / Hourly wage = ?

where

Hourly wage = $30.66

Total cost after tax = $3,688.10

therefore the  amount of time  =

$3,688.10 / $30.66 = 120.14 hours

So it takes the homeowner 120.14 hours / 40 hours/week = 3.004 weeks to save up for the cost of the fence if they make $30.66/hour after taxes and are saving 100% of their income.

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The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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The equation of line B is y = 3x - 3, where line B is perpendicular to line A and passes through (0,-3).

The condition of line B is y = 3x - 3, where line B is opposite to line An and goes through (0,- 3).

Since line B is opposite to line An and they converge at point (0,- 3), the slant of line B should be the negative corresponding of the incline of line A.

To start with, we should find the slant of line A:

incline of line A = (y2 - y1)/(x2 - x1) = (- 3 - (- 2))/(0 - (- 3)) = - 1/3

Since line B is opposite to line A, the slant of line B is the negative corresponding of - 1/3:

slant of line B = - 1/(- 1/3) = 3

Presently, we can utilize the guide incline type of a direct condition toward track down the situation of line B:

y - y1 = m(x - x1)

where m is the slant and (x1,y1) is a point on the line.

Subbing m = 3 and the point (0,- 3), we get:

y - (- 3) = 3(x - 0)

Improving on the situation, we get:

y + 3 = 3x

Subsequently, the condition of line B in the structure y = mx + c is:

y = 3x - 3

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Jeff can use the Pythagorean Theorem to check if the corner of the room forms a right triangle, indicating a right angle between the walls.

Jeff can use the Pythagorean Theorem to determine if the walls form a right angle by following these steps:

1. Identify the two sides adjacent to the angle in question: the side that is 3 inches from the corner (Side A) and the side that is 4 inches from the corner (Side B).

2. Measure the distance between the two marks along the floor (Side C). This distance will act as the hypotenuse of the right triangle.

3. Apply the Pythagorean Theorem: A² + B² = C². In this case, A = 3 inches and B = 4 inches. Calculate A² + B², which equals 3² + 4² = 9 + 16 = 25.

4. Compare the calculated value (25) to the square of the measured distance (C²). If A² + B² equals C², then the walls form a right angle, and the corner is a right triangle.

5. If the values match, it confirms that the angle between the two walls is a right angle (90 degrees), meaning the corner forms a right triangle. If the values do not match, then the walls do not meet at a right angle.

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The coordinates of D' are (-1, 4) and the coordinates of F' are (-3, 2)

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

D = (3, 1)

And the vector is -4

                            3

So, we have

D' = (3 - 4, 1 + 3)

Evaluate

D' =  (-1, 4)

Here, we have the location of point F to be

F = (1, -1)

And the vector is -4

                            3

So, we have

F' = (1 - 4, -1 + 3)

Evaluate

F' = (-3, 2)

Hence, the coordinates of F' are (-3, 2)

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The equation for the parabola will be y = 0.765625(x + 5.25)^2 - 69.390625.

Let us commence with the generalized equation for a parabola:

y = a(x - h)^2 + k

where (h,k) is the vertex of the parabola.

We can now set up august system of equations by integrating the two provided points and their corresponding transformed points:

4 = a(-2 - h)^2 + k (1)

-11 = a(-6 - h)^2 + k (2)

1 = a(1 - h)^2 + k (3)

-5 = a(-3 - h)^2 + k (4)

Comprising four knowns (a, h, k), fostering a viable solution to our problem yet available.

-15 = a(-4h - 32)

Dividing both sides by -4 silences the equation to:

3.75 = ah + 8

Continuing, subtracting equation (3) from (4):

-4 = a(-2h - 12)

Divving and relying on -2 debases the outcome to:

2 = ah + 6

At this juncture, we have two equations compounding two unknowns (a and h). Determining the h value in accordance to a within these equations can be done by setting our solutions equal to each other and solving for a, giving you an answer of 0.765625.

Exploiting one of the previous expressions, we next find h=(2-6)/0.765625=-5.25. By means of various designs, any of the four initial equations come into play when searching for k. Rearranging, 4=0.765625(-2-(-5.25))^2+k, leads to k=-69.390625.

Thus, unto completion of a parabolic, these values grace your presence:

a= 0.765625

h= -5.25

k= -69.390625

And so, the alluring equation of such an inscribed parabola casts itself forthheartedly, incarnating as:

y = 0.765625(x + 5.25)^2 - 69.390625

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Answer:

A - Answered in picture

B - 17.09

Step-by-step explanation:

Answer:

C. The volume is multiplied by 8

Step-by-step explanation:

1*1*1=1

1+1=2

1+1=2

1+1=2

2*2*2=8

Answer:

in the picture

Step-by-step explanation:

we multiply the side by two and find the new volume, unfolding and calculations in the figure

Answer: N′(−9, −2), M′(−6, −1), O′(−9, −5)

Step-by-step explanation: N=S -9+7+9+23x52=N′(−9, −2), M′(−6, −1), O′(−9, −5)

By using Newton's divided difference formula, the polynomial function in x is f(x) = x⁴ - 3x³ + 5x² - 6.

In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as the following:

Next, we would determine the polynomial function in x from the given data by using Newton's divided difference formula;

xi   f(xi)     f[xi,xi+1] f[xi,...,xi+2] f[xi,...,xi+3] f[xi,...,xi+4]

-1     3          -9                6                  5                1

0    -6          15               41                 13

3    39          261            132

6    822     789

7    1611

By interpolating, the interpolation polynomial is given by:

Pₙ(x) = 3 + -9(x+1) + 6(x + 1)(x - 0) + 5(x + 1)(x - 0)(x - 3) + 1(x + 1)(x - 0)(x - 3)(x - 6)

f(x) = (x - 6)(x - 3)x(x + 1) + 5(x - 3)x(x + 1) + 6(x + 1) - 9(x + 1) + 3

f(x) = x⁴ - 3x³ + 5x² - 6

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