the product of two consecutive integers is 272. which quadratic equation can be used to find x, the smaller number? x2 1

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:

\(\frac{4+16a^3+23a^3}{a^2}\)

Step-by-step explanation:

Given

\(1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15\)

Required

Simplify

\(1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15\)

Collect Like Terms

\(1/a^2 + 1/a^2 + 2/a^2-3a-5a-8a+2+6+15\)

\(1/a^2 + 1/a^2 + 2/a^2-16a+23\)

Add Fractions:

\(\frac{1+1+2}{a^2} + 16a + 23\)

\(\frac{4}{a^2} + 16a + 23\)

This can be further expressed as:

\(\frac{4+16a^3+23a^3}{a^2}\)

Answer:Direction: Opens Down

Vertex:  

(

5

2

,

17

4

)

Focus:  

(

5

2

,

4

)

Axis of Symmetry:  

x

=

5

2

Directrix:  

y

=

9

2

Select a few  

x

values, and plug them into the equation to find the corresponding  

y

values. The  

x

values should be selected around the vertex.

Tap for more steps...

x

y

0

−

2

1

2

5

2

17

4

3

4

4

2

Graph the parabola using its properties and the selected points.

Direction: Opens Down

Vertex:  

(

5

2

,

17

4

)

Focus:  

(

5

2

,

4

)

Axis of Symmetry:  

x

=

5

2

Directrix:  

y

=

9

2

x

y

0

−

2

1

2

5

2

17

4

3

4

4

2

Step-by-step explanation:nn

Answer:

5km

Step-by-step explanation:

Do not let the number line fool you, instead take the numbers from teh numberline.  Because mean is the numebrs added up and divided by the number of numbers there are in the data.  If we take 4+4 (two 4s on number lines) and add 7, we get 15 and because there are 3 numbers we divide by 3 to get 5km

The minimum length of the crest vertical curve is 354.1 feet, and the minimum length of the sag curves is 493.4 feet.

In designing the crest vertical curve, several criteria need to be considered, including driver perception-reaction time, design speed, and grade changes. The design should ensure driver comfort and safety by providing adequate sight distance.

To determine the minimum length of the crest vertical curve, we consider the stopping sight distance, which includes the distance required for a driver to perceive an object, react, and come to a stop. The minimum length of the crest curve is calculated based on the formula:

Lc = (V^2) / (30(f1 - f2))

Where:

Lc = minimum length of the crest vertical curve

V = design speed (in feet per second)

f1 = gradient of the approaching grade (in decimal form)

f2 = gradient of the departing grade (in decimal form)

Given the design speed of 60 mph (or 88 ft/s), and the grade changes of +4% and -3%, we can calculate the minimum length of the crest vertical curve using the formula. The result is approximately 434 feet.

Additionally, the sag curves are designed to provide a smooth transition between the crest curve and the approaching and departing grades. The minimum lengths of the sag curves are typically equal and calculated based on the formula:

Ls = (V^2) / (60(a + g))

Where:

Ls = minimum length of the sag curves

V = design speed (in feet per second)

a = acceleration due to gravity (32.2 ft/s^2)

g = difference in grades (in decimal form)

For the given scenario, the difference in grades is 7% (4% - (-3%)), and using the formula with the design speed of 60 mph (or 88 ft/s), we can calculate the minimum lengths of the sag curves to be approximately 307 feet each.

By considering the perception-reaction time, design speed, and grade changes, the minimum lengths of the crest vertical curve and the sag curves can be determined to ensure safe and comfortable driving conditions on the two-lane highway.

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An airplane can go 4860 kilometers in 9 hours when flying against the wind. Flying with the wind, the same plane travels 4300 kilometers in 5 hours. The rate of the plane in still air is 700 km/h and the rate of the wind is 160 km/h.

Let's use "p" to represent the rate of the plane in still air and "w" to represent the rate of the wind.

When the plane is flying against the wind, the effective speed of the plane is reduced by the speed of the wind. Therefore, we can set up the following equation based on the distance and time:

4860 = (p - w) * 9

When the plane is flying with the wind, the effective speed of the plane is increased by the speed of the wind. Therefore, we can set up another equation based on the distance and time:

4300 = (p + w) * 5

We now have two equations with two unknowns. We can solve for "p" and "w" by using algebraic techniques to eliminate one of the variables. The use of substitution is one typical strategy.

From the first equation, we can rearrange it to solve for "p - w":

p - w = 540

The second equation's "p-w" can now be replaced with the following expression:

4300 = (p + w) * 5

4300 = 5p + 5w

4300 = 5(p - w + 2w) (substituting p - w = 540)

4300 = 5(p - w) + 10w

4300 = 5(540) + 10w

4300 = 2700 + 10w

1600 = 10w

w = 160

Now that we have found the value of "w", we can substitute it back into either equation to solve for "p":

p - 160 = 540

p = 700

Therefore, the rate of the plane in still air is 700 km/h, and the rate of the wind is 160 km/h.

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Answer:

10.75

Step-by-step explanation:

The cost of an adult ticket is £6 more than that of a child ticket, so will be shown by c+6.

Now, we are told that the cost of four child tickets and two adult tickets is £40.50, so we can put this in an equation and solve for c:

(c+6)+(c+6)+c+c+c+c=40.50

6c+12=40.50

6c=28.50

c=4.75

so, a childs ticket is 4.75

now to find the cost of an adult ticket you add 6,

4.75 + 6

= 10.75

Answer:

1/3

Step-by-step explanation:

So there are 12 natural numbers in total: (113 - 102) + 1

Then there are the prime numbers: 103, 107, 109, and 113

so there are 4/12 prime numbers or 1/3

Answer:

1/3

Step-by-step explanation:

We can list all the numbers from 102 to 113:

To check if each number is prime, we simply have to check divisibility by 2, 3, 5, and 7 — if any of these numbers are not divisible by those, it will have no factors lower than its square root, and will therefore be prime.

102 - composite, multiple of 2

103 - prime

104 - composite, multiple of 2

105 - composite, multiple of 5

106 - composite, multiple of 2

107 - prime

108 - composite, multiple of 2

109 - prime

110 - composite, multiple of 2

111 - composite, multiple of 3

112 - composite, multiple of

113 - prime

4/12 or 1/3 of the numbers in this list are prime.

Answer:

.

Step-by-step explanation:

Dissatisfied customers are likely to share their negative experiences with an average of 9-15 people, but with the reach of social media, their impact can be significantly amplified, potentially influencing a wider audience and damaging a salesperson's reputation and sales.

When dissatisfied with a product or service, customers are more likely to share their negative experiences with others. The exact number of people they may tell can vary, but it's often cited that dissatisfied customers will share their negative experiences with an average of 9 to 15 other people.

This number can increase significantly in the age of social media, where dissatisfied customers have the ability to reach a much larger audience through online platforms and reviews. Therefore, it's crucial for salespeople to address customer concerns and ensure customer satisfaction to prevent negative word-of-mouth and potential damage to their reputation.

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The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Answer:

6 gallons of punch, 24 quarts of punch.

Step-by-step explanation:

1. Multiply 32 and 3. That is 96.

2. Divide 96 by 16 because there are 16 cups in a gallon. The answer is 6 so they need 6 gallons of punch.

3. Multiply 6 by 4 because there are 4 quarts in a gallon. The answer is 24.

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

32 people x 3 cups = 96 cups

96 cups : 16 = 6 gallons

6 gallons x 4 = 24 quarts

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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Answer:

7 friends.....

Step-by-step explanation:

7÷2=3.5

Answer:

\(f=14\)

Step-by-step explanation:

Answer:

cocomelon . 3/5 - 4

Step-by-step explanation:

Answer:

x=\(\sqrt3\) and -\(\sqrt3\\\)

Step-by-step explanation:

the roots(zeros) are the value of x where the graph intersects the x-axis.

to find the roots:

x^2-3=0

x^2=3

x=+-\(\sqrt3\)

Answer:

–6.8

Method:

Counting backwards from –7 to –6.5

Answer:

-6.8

Step-by-step explanation:

it is 3 units from -6.5 so you can even add them

-6.5 + 3

= -6.8

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

All they do is swap the order of what is in the parentheses which means the result will stay the same, on all the other ones they changed which numbers were in the parentheses which means the result would of been different!

I hope this helps, and have a great day!

Answer:

to do this you need to Multiply 14 by 6 to satisfy the fact she has 6 times the amount of milk for 14 teaspoons of rennet

Answer:

8.5 in

Step-by-step explanation:

Area = Length × Width

153 = L × 18

L = 153÷18

L= 8.5

L= 8.5 in

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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Notice that 100 is 20 less than 120, or equivalently 2 standard deviations σ below the mean µ. So

P(x ≥ 100) = P(x ≥ µ - 2σ)

Recall the empirical rule for normal distributions (these are true for any mean µ and s.d. σ):

• P(µ - σ ≤ x ≤ µ + σ) ≈ 0.65

• P(µ - 2σ ≤ x ≤ µ + 2σ) ≈ 0.95

• P(µ - 3σ ≤ x ≤ µ + 3σ) ≈ 0.997

The probability we want is the same as

P(x ≥ µ - 2σ) = P(µ - 2σ ≤ x ≤ µ + 2σ) + P(µ + 2σ ≤ x)

or

P(x ≥ µ - 2σ) ≈ 0.95 + P(µ + 2σ ≤ x)

which is clearly some number larger than 0.95, so A must be correct.

Suppose a normal distribution has a mean of 120 and a standard deviation, P(x >= 100) is 0.975. Option A. This is further explained below.

Generally, normal distribution is simply defined as a function that displays the dispersion of numerous unknown parameters as a symmetrical bell-shaped graph.

In conclusion, based on the function

P(x ≥ µ - 2σ) ≈ 0.95 + P(µ + 2σ ≤ x)

the function P(x >= 100) is 0.975

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Answer:

x - 1/2y = 0

Step-by-step explanation:

=> x = 1/2y

=> x - 1/2y = 0

Hope it helps.

Answer:

2 buses

Step-by-step explanation:

This is quite simple, ( if I read this right). You know that there are three of the 14 students, so 14x3. Next you know there would be 25 seats on each bus, and 14x3= 42, meaning you would need 2 buses so there would be enough for all the students. If you want me to explain this in more detail just ask.

hope this helps

The figure below shows a line graph and two shaded triangles that are similar:

A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, 4, and 0, 0, and 16, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, 2 labeled as A, one leg is from 0, 0 to negative 8, 0, and the second leg is from negative 8, 0 to negative 8, 2. Another shaded right triangle is formed with the hypotenuse from negative 8, 2 to negative 12, 3 labeled as B, one leg is from negative 8, 2 to negative 12, 2, and the second leg is from negative 12, 2 to negative 12, 3.

Which statement about the slope of the line is true?

The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.

The slope from point O to point A is 4 times the slope of the line from point A to point B.

It is fraction negative 1 over 4 throughout the line.

It is −4 throughout the line

The equation that can be used to find the value of x, representing the number of children under three years, is (54 - x)32 = C.

The equation (54 - x)32 represents the number of children aged 3 to 12 years multiplied by the ticket price for that age group, which is $32. Since the total amount of money collected from tickets that day is represented by C, this equation helps calculate the revenue from children aged 3 to 12 years. By subtracting x, the number of children under three years, from the total of 54 children aged 12 and under, we get the number of children aged 3 to 12. Multiplying this by $32 gives us the revenue generated from this age group. Therefore, the equation (54 - x)32 = C can be used to find the value of x.

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Answer:

That actually depends. We don't know if i is a negative number or not. If i is a negative number, -i would be larger. If i is a positive number, -i would be smaller. It all depends on whether i or -i is negative or positive.

Hope that helps!

Step-by-step explanation:

"i" is larger 'cause positive number are always greater than negative numbers.