Use the Distributive Property to find 6(14 + 7).
F 91
G 126
H 42
J 56

Answer:

\(\huge\boxed{1)\ n=-7}\\\boxed{2)\ n=2}\)

Step-by-step explanation:

\(1)\\-4(n-7)+4n=-8-3(n-5)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-4)(n)+(-4)(-7)+4n=-8+(-3)(n)+(-3)(-5)\\\\-4n+28+4n=-8-3n+15\\\\\text{combine like terms}\\\\(-4n+4n)+28=-3n+(-8+15)\\\\28=-3n+7\\\\\text{subtract 7 from both sides}\\\\28-7=-3n+7-7\\\\21=-3n\\\\\text{divide both sides by (-3)}\\\\\dfrac{21}{-3}=\dfrac{-3n}{-3}\\\\-7=n\to\boxed{n=-7}\)

\(2)\\4(-8n+10)+4(4n-4)=-6n+2n\\\\\text{use the distributive property}\\\\(4)(-8n)+(4)(10)+(4)(4n)+(4)(-4)=-6n+2n\\\\-32n+40+16n-16=-6n+2n\\\\\text{combine like terms}\\\\(-32n+16n)+(40-16)=(-6n+2n)\\\\-16n+24=-4n\\\\\text{add}\ 16n\ \text{to both sides}\\\\-16n+16n+24=-4n+16n\\\\24=12n\\\\\text{divide both sides by 12}\\\\\dfrac{24}{12}=\dfrac{12n}{12}\\\\2=n\to\boxed{n=2}\)

Answer:

1) n = - 7       2) n = 2

Step-by-step explanation:

1)

-4(n-7)+4n=-8-3(n-5)  Let's multiply it out

-4*n - 4* (-7) + 4n = - 8 - 3*n -3 * (- 5)

-4n + 28 + 4n = - 8 -3n +15     Combine like terms

-4n + 4n + 28 = -8 + 15 - 3n

28 = 7 - 3n  Subtract 7 from each side

28 - 7 = 7 - 7 - 3n

21 = - 3n  Divide each side by -3

21 / -3 = - 3n / -3     -3 cancels on the right

21 / -3 = n

- 7 = n

2)

4(-8n+10)+4(4n-4)= -6n+2n Multiply it out

4 * - 8n + 4 * 10 + 4 * 4n + 4 * (-4) = - 6n + 2n

- 32n + 40 + 16n - 16 = - 6n + 2n  Combine like terms

- 32n + 16n + 40 - 16 = - 6n + 2n

- 16n + 24 = - 4n   Add 16n to each side

- 16n + 16n + 24 = - 4n + 16n

24 = 12n  Divide each side by 12

24/12 = 12n/12      12 cancels on the right

24/12 = n

2 = n

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

Answer:

c

basically you add male (x) and female (y) together and get 127, there are 23 more male athletes (x) so to get the same amount of make and female you need to add 23 to female (y) so the answer will be c.

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Mr. Welsh

has a stating production of

f(1)=70

from the statement

He has determined that the production of eggs will increase each year to be the square of 60 eggs less than the previous year

previous year =fn

then

where

f(1)=70

then the correct answer is

option C

Answer:

A) 13, 10, 16

Step-by-step explanation:

The Triangle Inequality Theorem will help you solve this question. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The options that are given are:

Lets solve each one to figure out if they could be the lengths of a triangle.

A) 13, 10, 16.

We can write three inequalities to see if the lengths are true.

13 + 10 > 16

10 + 16 > 13

13+ 16 > 10

Solve each one.

23 > 16

26 > 13

29 > 10

According to the information above, the set of numbers from option A does  fit the Triangle Inequality Theorem. Therefore, they are possible lengths.

B) 1, 2, 3

Write three inequalities:

1 + 2 > 3

2 + 3 > 1

3+ 1 > 2

Solve each.

3 > 3

5 > 1

4 > 2

As you see, only two lengths fit the theorem, but the third side (3 > 3) does not. This set of lengths is not a possible set for a triangle.

C) 5.2, 11, 4.9

Write three inequalities:

5.2 + 11  > 4.9

4.9 + 11 > 5.2

5.2 + 4.9 > 11

Solve each.

16.2 > 4.9

15.9 > 5.2

10.1 > 11

As you see, only two sides lengths can repsent the lengths of a triangle but the third does not, so its not a possible set of lengths for a triangle.

D) 208, 9, 219

Write three inequalities:

208 + 9 > 219

219 + 9 > 208

208+ 219 > 9

Solve each.

217 > 219

228 > 208

427 > 9

Although two lengths fit the theorem, one length does not, so this a not a possible set of lengths.

In summary, only one set of lengths is possible for a triangle, with is A.

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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The cost of polishing the floor of the square hall is ₹2343.75

The Side of Square Hall = 12.5 m

The cost of polishing the floor per meter sq. = ₹ 15

We have to find the cost of polishing the floor.

First we will calculate the area of floor of the square hall.

Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units, with the standard unit being square meters (\(m^{2}\)).

Area of square=\((12.5)^2\)

Area of square =\(12.5 \times 12.5\)

Area of square =156.25

The area of the floor of Square Hall is 156.25 \(\mathrm{~m}^2$\)

Per square meter cost of polishing the floor is ₹15,

To find the cost of polishing the floor of the square hall of area 156.25 sq. m, simply multiply 15 by the area of the floor of the square hall.

Therefore, the cost of polishing,

=15×156025

=2343.75

Therefore, the cost of polishing is ₹2343.75.

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Find the cost of polishing the floor of a square hall at the rate of 15 per meter sq, if each side of the hall is 12.5 m.​

Answer:

c

Step-by-step explanation:

44

mark as brainlist......

Answer:

I think it will be C but sure it will be C hope that helps

The area of the surface generated by revolving the curve y = 6x about the x-axis is 0.

To find the area of the surface generated by revolving the curve y = 6x about the x-axis, we can use the formula for the surface area of revolution:

A = 2π∫[a,b] y√(1 + (dy/dx)²) dx

In this case, the curve y = 6x is a straight line, so the derivative dy/dx is a constant. Let's find the derivative:

dy/dx = d(6x)/dx = 6

Now we can substitute the values into the formula for surface area:

A = 2π∫[a,b] y√(1 + (dy/dx)²) dx

= 2π∫[a,b] 6x√(1 + 6²) dx

= 2π∫[a,b] 6x√(1 + 36) dx

= 2π∫[a,b] 6x√37 dx

The limits of integration [a, b] depend on the range of x values for which the curve y = 6x is defined. Since the given condition is 0 < x, the curve is defined for x > 0. Therefore, the limits of integration will be [0, c] where c is the x-coordinate of the point where the curve intersects the x-axis.

To find the x-coordinate where y = 6x intersects the x-axis, we set y = 0:

0 = 6x

x = 0

So the limits of integration are [0, c]. To find the value of c, we substitute y = 6x into the equation of the x-axis, which is y = 0:

0 = 6x

x = 0

Therefore, the value of c is 0.

Now we can rewrite the integral with the limits of integration:

A = 2π∫[0, 0] 6x√37 dx

Since the limits of integration are the same, the integral evaluates to zero:

A = 2π(0) = 0

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Answer:

3,384

Step-by-step explanation:

So this is a classic multiplication problem. If each patron has 6 books, and there's 564 patrons, you multiply:

564 x 6 = 3,384

hope this helps:D

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

By examining the connection between natural selection and evolution, Darwin's theory of evolution is examined. Controlling natural selection in an interactive population will help you achieve this. Each species displays.

For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Evolution and Natural Selection A species' members do not all resemble one another. Each species displays. For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

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Answer:

27/2 would be your answer.

Step-by-step explanation:

9/1 ÷2/3

Change to mutiplication after you flip 2/3 to 3/2..

9/1×3/2

27/1×2

27/2

9 ÷ 2/3 = 27/2

We will need 100 more samples to make the margin error of 0.3 .

acc to our question-

Hence, We will need 100 more samples to make the margin error of 0.3 .

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If there were no count variable, the complexity of the size() method for the linked implementation of a list would be O(n).

How complicated is the size?

Since the linked list's length cannot be stored in a count variable, we must traverse the list from head to tail to get its size.

To obtain the size for n nodes, we will traverse all n nodes. As a result, the time complexity is O (n).

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The position vector r (with components x1, x2, x3) and any vector v can be expressed as r = x1*i + x2*j + x3*k and v = a*i + b*j + c*k, respectively.

The dot product of two vectors is defined as the sum of the products of their corresponding components. Therefore, the dot product of r and v can be calculated as:

r · v = (x1*i + x2*j + x3*k) · (a*i + b*j + c*k)

     = (x1*a) + (x2*b) + (x3*c)

Here, we multiplied the corresponding components and summed them up. The dot product represents the scalar projection of one vector onto the other, which indicates the magnitude of one vector in the direction of the other.

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===================================================

Explanation:

let's find the prime factorization for each value. If the value is prime, then just move onto the next value

2 = 2 ... already prime, nothing needed to do here

3 = 3

4 = 2*2

5 = 5

6 = 2*3

8 = 2*2*2

9 = 3*3

10 = 2*5

The list of prime factors that show up are: {2, 3, 5}

We have '2' show up at most 3 times, the prime '3' show up at most 2 times, and the prime '5' show up at most 1 time.

This means 2^3*3^2*5 = 360 is the LCM of the list {2,3,4,5,6,8,9,10}

Any multiple of 360 will also be a common multiple of the original list of values.

Multiples of 360: {360, 720, 1080, ...}

We see that 1080 is the smallest 4-digit multiple of 360.

The Law of detachment states that if m then n and m is true then q is true.

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

The Law of detachment states that if m then n and m is true then q is true.

We have,

If two angles are complementary, then the sum of their measures is 90°.

This is in the form of,

If M then N and if M is true then N must be true.

So,

If two angles are complementary, then the two angles' sum is 90 degrees.

If the two angles are m∠E and m∠F.

m∠E + m∠F = 90

Thus,

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

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Answer:

1 1/2 inches on a map is 18 miles in real life.

Step-by-step explanation:

1 in. = 12 miles

1 1/2 in. = X

1 1/2 x 12 = 18

1 1/2 inches on a map is 18 miles in real life.

The sales trend Sales = 181.00 + 2t where t= time in quarters, beginning in Q1 2014The seasonal factors for the four quarters are i.e: {0.9, 1.1, 1.2, 0.8}

To find the seasonalized forecast for Q2 of 2017, the following steps must be followed:

Step 1: Calculate trend for the Q2 of 2017 t = 3.25

Step 2: Determine seasonal factor for Q2 which is 1.1 since it's the second quarter

Step 3: Multiply trend and seasonal factors to get seasonalized trend for Q2 = (181 + 2(3.25)) * 1.1 = 198.95

Step 4: Therefore, the seasonalized forecast for Q2 of 2017 is 198.95.

Therefore, we have Sales = 181.00 + 2t where t is the time in quarters, starting from Q1 2014. In other words, t = 1 for Q1 2014, t = 2 for Q2 2014, and so on.

In addition, we have seasonal factors for each quarter, i.e, {0.9, 1.1, 1.2, 0.8}.

To calculate the seasonalized forecast for Q2 of 2017, we need to follow the following steps:

Step 1: Calculate trend for the Q2 of 2017t = 3.25 [since there are 13 quarters between Q1 2014 and Q2 2017.

The 13th quarter corresponds to Q2 2017. So, t = 13. Therefore, t = 2 + 4(13 - 1) = 3.25]

Step 2: Determine the seasonal factor for Q2 of 2017

The seasonal factor for Q2 of 2017 = seasonal factor for the second quarter = 1.1

Step 3: Multiply trend and seasonal factors to get seasonalized trend for Q2

Therefore, seasonalized trend for Q2 of 2017 = (181 + 2(3.25)) * 1.1 = 198.95Step 4:

Therefore, the seasonalized forecast for Q2 of 2017 is 198.95.

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The distance of the jot air balloon to ground is 21.62 ft.

Here, we have,

In triangle ACB:

tan36° = x/y

x  = y tan36°

In triangle ADB:

tan25° = x/y + 12

x  = y+12 * tan25°

Therefore equating both equations gives:

y tan36°  =  y+12 * tan25°

y tan36°  =  y tan25° + 12tan25°

so, we get,

y = 21.50 ft

Therefore x = 21.50*tan(36) = 15.62 ft

The distance of the jot air balloon to ground = 15.62 + 6 = 21.62 ft

Hence, The distance of the jot air balloon to ground is 21.62 ft.

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The equation of a line passing through the point (4, 1) with a gradient of 3 is,  y = 3x - 11.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line that passes through the point (4,1) and has a gradient of 3.

We know the equation of a line in slope-intercept form is y = mx + b.

∴ The equation of a line passing through the point (4, 1) with a gradient of 3 is,

1 = 3(4) + b.

b = 1 - 12.

b = - 11.

∴ y = 3x - 11.

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In the given definitions, there are several difficulties and violations of the rules for definition by genus and difference. These include ambiguity, lack of specificity, and the inclusion of irrelevant information.

The rules being violated include the requirement for clear and concise definitions, inclusion of essential characteristics, and avoiding irrelevant or subjective statements.

12. The definition of a raincoat as an outer garment of plastic that repels water is too broad. It lacks specificity regarding the material and construction of the raincoat, as not all raincoats are made of plastic. Additionally, the use of "outer garment" is subjective and does not provide a clear distinction from other types of clothing.

13. The definition of a hazard as anything that is dangerous is too broad and subjective. It fails to provide a specific category or characteristics that define what qualifies as a hazard. The definition should include specific criteria or conditions that identify a hazard, such as the potential to cause harm or risk to safety.

14. The definition of sneezing as emitting wind audibly by the nose is too narrow and lacks clarity. It excludes other aspects of sneezing, such as the involuntary reflex and the expulsion of air through the mouth. The definition should encompass the essential characteristics of sneezing, including the reflexive nature and expulsion of air to clear the nasal passages.

15. The definition of a bore as a person who talks when you want him to listen is subjective and relies on personal preference. It does not provide objective criteria or essential characteristics to define a bore. A more appropriate definition would focus on the tendency to dominate conversations or disregard the interest or input of others.

In conclusion, these definitions violate the rules for definition by genus and difference by lacking specificity, including irrelevant information, and relying on subjective or ambiguous criteria. Clear and concise definitions should be based on essential characteristics and avoid personal opinions or subjective judgments.

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Answer:

l think the answer is 024 inches because it has to division

Step-by-step explanation:

just divide both sides by 3.14 yes

The radius of the circle is 12 inches.

Radius is the distance from the center of the circle to any point on its circumference, which means the line segment that connects the center of a circle to any point on its circumference is called the radius.

Given that the circumference of a circle is 75 inches we need to find the radius,

So,

C = π × diameter

75 = 3.14 × d

d = 23.88

∵ d = 2r

∴ r = 23.88/2

r = 11.94

r ≈ 12

Hence the radius of the circle is 12 inches.

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Answer :  1) the result of the integration is x^3 + x^2 + x + C, where C is the constant of integration, 2) the result of the integration is (1/4) * (sin(3x) + (1/3) * sin(9x)) + C, where C is the constant of integration.

1. ∫(3x^2 + 2x + 1) dx:

To integrate this polynomial function, we can use the power rule of integration. The power rule states that for a term of the form ax^n, the integral is (a/(n+1)) * x^(n+1).

∫(3x^2 + 2x + 1) dx = (3/3) * x^3 + (2/2) * x^2 + x + C

                   = x^3 + x^2 + x + C

So, the result of the integration is x^3 + x^2 + x + C, where C is the constant of integration.

2. ∫[cos(x) sin(sin(x))] dx:

This integral involves nested trigonometric functions. Unfortunately, there isn't a simple closed form for the integral of this function. It can be expressed using special functions such as the Fresnel integral or elliptic integrals, but those are more advanced topics.

So, the integral of cos(x) sin(sin(x)) cannot be evaluated in a simple closed form.

3. ∫[8^|cos(x) – sin(x)|] dx:

To evaluate this integral, we need to consider the absolute value expression. Let's break down the integral based on the sign of the expression inside the absolute value.

When cos(x) - sin(x) ≥ 0 (i.e., cos(x) ≥ sin(x)), the absolute value is not needed.

∫[8^(cos(x) - sin(x))] dx = ∫[8^(cos(x)) * 8^(-sin(x))] dx

Using the property a^m * a^n = a^(m+n), we can rewrite the integral as:

∫[8^(cos(x)) * 8^(-sin(x))] dx = ∫[8^(cos(x)) / 8^(sin(x))] dx

Using the property (a^m)/(a^n) = a^(m-n), we can simplify further:

∫[8^(cos(x)) / 8^(sin(x))] dx = ∫[8^(cos(x) - sin(x))] dx

                             = ∫[8^(cos(x) - sin(x))] dx

When sin(x) - cos(x) ≥ 0 (i.e., sin(x) ≥ cos(x)), the expression inside the absolute value becomes -(cos(x) - sin(x)).

∫[8^(cos(x) - sin(x))] dx = ∫[8^(-(cos(x) - sin(x)))] dx

                          = ∫[1/8^(cos(x) - sin(x))] dx

Combining the two cases:

∫[8^|cos(x) – sin(x)|] dx = ∫[8^(cos(x) - sin(x))] dx + ∫[1/8^(cos(x) - sin(x))] dx

Solving these integrals requires numerical methods or approximations.

4. ∫[|x^4 – 2x^3 + 2x^2 – 4x|] dx:

To integrate this absolute value function, we need to consider the intervals where the expression inside the absolute value is positive and negative.

When x^4 - 2x^3 + 2x^2 - 4x ≥ 0 (i.e., x^4 - 2x^3 + 2x^2 - 4x ≥ 0), the absolute value is not needed.

∫[|x^4 - 2x^3 + 2x^2 - 4x|] dx = ∫[x^4 -

2x^3 + 2x^2 - 4x] dx

Integrating this polynomial function:

∫[x^4 - 2x^3 + 2x^2 - 4x] dx = (1/5) * x^5 - (1/2) * x^4 + (2/3) * x^3 - 2x^2 + C

When x^4 - 2x^3 + 2x^2 - 4x < 0 (i.e., x^4 - 2x^3 + 2x^2 - 4x < 0), the expression inside the absolute value changes sign.

∫[|x^4 - 2x^3 + 2x^2 - 4x|] dx = -∫[x^4 - 2x^3 + 2x^2 - 4x] dx

Integrating this polynomial function:

-∫[x^4 - 2x^3 + 2x^2 - 4x] dx = -(1/5) * x^5 + (1/2) * x^4 - (2/3) * x^3 + 2x^2 + C

So, depending on the sign of x^4 - 2x^3 + 2x^2 - 4x, we have two cases for the integration.

5. ∫[cos^(3)(3x)] dx:

This integral involves the cosine function raised to the power of 3. To evaluate it, we can use the power-reducing formula:

cos^(3)(3x) = (1/4) * (3cos(3x) + cos(9x))

Now, we can integrate each term separately:

∫[cos^(3)(3x)] dx = (1/4) * ∫[(3cos(3x) + cos(9x))] dx

                 = (1/4) * (3∫[cos(3x)] dx + ∫[cos(9x)] dx)

                 = (1/4) * (3 * (1/3) * sin(3x) + (1/9) * sin(9x)) + C

                 = (1/4) * (sin(3x) + (1/3) * sin(9x)) + C

So, the result of the integration is (1/4) * (sin(3x) + (1/3) * sin(9x)) + C, where C is the constant of integration.

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The lifter would need to perform approximately 27 reps of lifting a 16-lb barbell through a distance of 1.1 ft to work off 150 C.

To answer this question, we need to know the amount of work done in each rep of the lift. Work is defined as force multiplied by distance, so the work done in lifting the 16-lb barbell through a distance of 1.1 ft is:

Work = Force x Distance
Work = 16 lb x 1.1 ft
Work = 17.6 ft-lb

Now we can calculate the number of reps required to work off 150 C. One calorie is equivalent to 4.184 joules of energy, so 150 C is equal to:

150 C x 4.184 J/C = 627.6 J

We can convert this to foot-pounds of work by dividing by the conversion factor of 1.3558:

627.6 J / 1.3558 ft-lb/J = 463.3 ft-lb

To work off 463.3 ft-lb of energy, the lifter would need to perform:

463.3 ft-lb / 17.6 ft-lb/rep = 26.3 reps (rounded up to the nearest whole number)

Therefore, the lifter would need to perform approximately 27 reps of lifting a 16-lb barbell through a distance of 1.1 ft to work off 150 C.

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