simplify 11/16 - 11/12​

Answer:

h(x) = 10x

Step-by-step explanation:

given:

f(x) = 3x-1 and g(x)= 4x-2

h(x) = 2 f(x) + g(x)

= 2 (3x+1) + (4x-2)

= 6x + 2 + 4x - 2

= 10x

The question revolves around combining functions in mathematics. To solve for h(x) when h(x) is equal to 2f(x) + g(x), we substitute f(x) and g(x) values into the equation for h(x) and simplify the resulting expression. Our calculated function h(x) = 10x - 4.

This is a question about combining function operations. We have been given two functions f(x) = 3x-1 and g(x) = 4x-2, and asked to find h(x) = 2f(x) + g(x).

To solve it, we must substitute f(x) and g(x) into our equation for h(x):

So, the function h(x) when h(x) is = 2f(x) + g(x) is h(x) = 10x - 4.

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Answer:

The number of children attending = 324

The number of adults attending  = 176.

Step-by-step explanation:

Here, the total number of people attending = 500

Let us assume the umber of children attending the breakfast = m

So, the number of adults attending the breakfast = 500 - m

Cost of ticket for each children  = $12.95

So, the cost of m children's tickets = m x ( Cost of 1 children ticket)

=  m x ( $12.95)  = 12.95 m .... (1)

Cost of ticket for each adult  = $17.95

So, the cost of (500 -m)  adults's tickets

= (500 - m) x ( Cost of 1 adult ticket)    = (500 -m) x ( $17.95)  

 = 8,975 - 17.95 m     .... (2)

Now, the total earnings from the total ticket sold = $7355

So, The earning from ( Adult's + children's tickets)  = $7355

⇒  12.95 m  +  8,975 - 17.95 m = $7355

or, - 5 m = 7355 - 8975 =   -1620

or, m = 1620/5 = 324

⇒  m =324

Hence the number of children attending =  m = 324

The number of adults attending = 500 - m = 500 - 324 = 176.

Final answer:

There were 176 adults and 324 children present.

Explanation:

We are given the prices of adult and child tickets, as well as the total revenue and number of people. By setting up two equations, we can solve for the number of adults and children. Let's define adults as A and children as C.

From the given information, we can set up the following equations:

The total revenue from the tickets is $7355: 17.95A + 12.95C = 7355

We can use the substitution or elimination method to solve these equations. If we express C from the first equation as C = 500 - A and substitute it into the second equation, we get:

17.95A + 12.95(500 - A) = 7355

Which simplifies to:

17.95A + 6475 - 12.95A = 7355

Combining like terms, we get:

5A = 880

Thus:

A = 176

Substituting A back into the equation for C, we have:

C = 500 - 176 = 324

Therefore, there were 176 adults and 324 children at the Disney breakfast event.

Answer:

[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]

Step-by-step explanation:

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex]

Adding and Subtracting 1 to the Numerator

[tex]\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx[/tex]

Dividing Numerator seperately by [tex]x^{4} - 1[/tex]

[tex]\int 1 + \frac{1}{x^{4}-1 }\, dx[/tex]

Here integral of 1 is x +c1 (where c1 is constant of integration

[tex]x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx[/tex]----------------------------------(1)

We apply method of partial fractions to perform the integral

[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)}[/tex] = [tex]\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}[/tex]------------------------------------------(2)

[tex]\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}[/tex]

1 = [tex]A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)[/tex]-------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = [tex]\frac{1}{4}[/tex]

1 = B(-1-1)(1+1)

B = [tex]-\frac{1}{4}[/tex]

1 = C(i-1)(i+1)

C = [tex]-\frac{1}{2}[/tex]

Substituting A, B, C in equation (2)

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }[/tex]

On integration

Here [tex]\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx[/tex]

[tex]\int\frac{x^{4}}{x^{4} -1}dx[/tex] = [tex]\frac{1}{4} ln(x-1)[/tex] - [tex]\frac{1}{4} ln(x+1)[/tex] - [tex]\frac{1}{2} arctanx[/tex] + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

[tex]x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2[/tex]

Here c1 + c2 can be added to another and written as c

Therefore,

[tex]\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c[/tex]

Answer:

The speed of River's mom drove for 10 miles distance is 0.234 mph.

The speed of  River's mom drove for 25 miles is 10.234 mph.

Step-by-step explanation:

Given as :

The first distance cover by River's mom = 10 miles

The rate of speed = x mph

The second distance cover by river's mom = 25 miles

The rate of speed = x + 10 mph

The total driving time = 45 min

Now, According to question

[tex]Time = \frac{Distance}{Speed}[/tex]

So, [tex]45 =  \frac{10}{x}+\frac{25}{x+10}[/tex]

Now dividing by 5 on both side we get;

[tex]9=\frac{2}{x}+\frac{5}{x+10}\\\\9= \frac{2(x+10)+5x}{x(x+10)}\\\\9= \frac{2x+20+5x}{x^2+10x}\\\\9(x^2+10x)= 7x+20\\9x^2+90x-7x-20=0\\9x^2+83x-20=0[/tex]

Solving this quadratic equation we get;

[tex]x=\frac{-b\±\sqrt{4ac}}{2a}[/tex]

[tex]x=\frac{-83\±\sqrt{4\times9 \times 20}}{2\times 9}\\\\x= \frac{-83\±\sqrt{720}}{18}\\ \\x= \frac{-83+87.22}{18} \ \ \ or \ \ x = \frac{-83-87.22}{18}\\\\x= 0.234 \ \ \ or\ \ \ \ x= - 9.4567[/tex]

Since speed cannot be in negative hence we will consider x= 0.234

So, The speed for 10 miles distance = x = 0.234 mph

and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph

Hence The speed of River's mom drove for 10 miles distance is 0.234 mph

and The speed of  River's mom drove for 25 miles is 10.234 mph  

Answewell 6 divided by 2 is great than 1 its 3 if this helps?

Step-by-step explanation:

The question presents an inequality, A/6 > 1. Solving this inequality yields A > 6, meaning any number greater than 6 will satisfy this equation.

The equation given in the question is A divided by 6 is greater than 1. This can be written in mathematical terms as A/6 > 1.

To find which numbers could represent A, you have to solve this inequality. As a first step, you can multiply both sides of the inequality by 6 to isolate A. This gives us A > 6 * 1, which simplifies to A > 6.

Therefore, any number greater than 6 should satisfy the inequality A/6 > 1.

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All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon

The final price of the computer after both discounts is T(x) = 0.9x - 150

We have been given that all computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is:

P(x) = x - 0.1x

P(x) = 0.9x  

The function that gives the price, C, if only a $150 coupon is used is:

C(x) = x - 150  

We need to choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon.

So, we have to formulate a function to combine both the discounts.

The price after 10% discount is 0.9x and the price after $150 coupon is x-150.

So, the composite function that gives the final sale price after 10% discount followed by $150 is given as follows:

Let the final price be denoted as T(x)

Therefore,

T(x) = original price - 10% discount - $150 coupon

T(x) = x - 10% of x -150

T(x) = x - 0.1x - 150

T(x) = 0.9x -150

Hence the final price of the computer after both discounts is T(x) = 0.9x-150

Answer:

A

570

Step-by-step explanation:

got it correct

Answer:

x = -9

Step-by-step explanation:

the equation is 2^4x = 8^x - 3.

therefore 2^4x = 2^3(x-3)

since both have powers of 2

therefore

4x = 3(x-3)

4x = 3x - 9

4x -3x = -9

x = -9

Answer:

D) 2^4x=2^3x-9

Step-by-step explanation:

took quiz

Answer:

B. 4

Step-by-step explanation:

The degree of the polynomial (the exponent of the highest term) is the total number of roots (including imaginary roots).

The degree of this polynomial is 4, so there are 4 roots.

Answer:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Step-by-step explanation:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Answer:

The answers are below:

Step-by-step explanation:

Answer 1: Attachment.

Answer 2: Line A is parallel to line B.

Answer 3: Line Z is a Traversal.

Answer 4:

[tex]\angle 3 \ and \ \angle 5\ and\\ \angle 4 \ and \ \angle 6\\[/tex] are the same side interior angles.

Answer 5:

[tex]\angle 3 \ and \ \angle 6\ and\\ \angle 4 \ and \ \angle 5\\[/tex] are the alternate interior angles.

Answer 6:

[tex]\angle 3 \ and \ \angle 7\ and\\ \angle 4 \ and \ \angle 8\\[/tex][tex]\angle 6 \ and \ \angle 1\ and\\ \angle 5 \ and \ \angle 2\\[/tex] are corresponding pair angles.

Answer 7:

[tex]\angle 8 \ and \ \angle 2\ and\\ \angle 7 \ and \ \angle 1\\[/tex]are the alternate exterior pair angles.

Answer:

dividing the number by what?

Answer:

6/10

Step-by-step explanation:

Answer:

the ratio as a fraction is 6

10

Answer:

Average rate of change= 3

Step-by-step explanation:

Recall the definition of average rate of change of a function [tex]f(x)[/tex] in an interval [tex][a,b][/tex]:

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

In your case:

[tex]f(x) = 3x+4[/tex], and the interval  [tex][a,b][/tex] i  [tex][2,6][/tex], therefore:

Average rate of change = [tex]\frac{f(6)-f(2)}{6-2}=\frac{f(6)-f(2)}{4}[/tex]

Now we evaluate the function at the two requested points:

[tex]f(x)=3x+4\\f(6)=3(6)+4=18+4=22\\f(2)=3(2)+4=6+4=10[/tex], then [tex]f(6)-f(2)=22-10=12[/tex]

So finally the Average rate of change is: [tex]\frac{f(6)-f(2)}{6-2}=\frac{12}{4} =3[/tex]

David is 16 years old.

Alisa is 4 years old.

Answer:

y = 12x

Step-by-step explanation:

The graph shown on the coordinate plane passes through the points (0,0) and (2,24).

The equation of the line passing through the origin is

[tex]y=mx[/tex]

To find m substitute coordinates of point (2,24):

[tex]24=2m\\ \\m=12[/tex]

So, the equation of proportioanl relationship is

[tex]y=12x[/tex]

1. The graph shows straight line passing through the origin, so this graph represents the proportional relationship.

2. The equation [tex]y=12x[/tex] determines proportional relationship, because 12 is the coefficient of direct proportionality and you can determine y for every given x multiplying by this coefficient of proportionality.

Answer:

y = 12

Step-by-step explanation:

slope = rise/run

slope = 24/2

slope = 12

y-intercept = starts at (0,0)

equation = y = mx + b

equation = y = 12x + 0

Answer:

0

Step-by-step explanation:

0/5 is 0

Anything divided by zero is zero.

Answer:

Your answer:0/5 =0

Step-by-step explanation:Learned it in school... can you please mark me brainliest?!?

Answer:

x = 4

Step-by-step explanation:

6x - 8 = 4x

Bringing all the x's to one side and the whole number to the other,

6x - 4x = 8

2x = 8

Therefore, x = 4

Answer:

6x-8=4x

Bring over 4x to the other side of the equation

2x-8=0

2x=8

x=4

Answer: 10

Step-by-step explanation:

m divided by 10 = 1 so m is 10

n divided by 10 = 4 so n is 40

m + n is equal to 40 + 10 which is 50.

Divide 50 by 5 and you get 10!

Answer:

180.5

Step-by-step explanation:

2z=361

z=361/2=180.5

Answer:

Angle = 135°

Supplement of the Angle = 45°

Step-by-step explanation:

The complement of an angle, say "x", would be 90 minus that angle:

90 - x

The supplement of an angle, say "y", would be 180 minus that angle:

180 - y

Since we have 1 angle, let it be "x", and that angle is 3 TIMES the SUPPLEMENT of that angle, we can write:

x = 3(180 - x)

Now, we solve for the angle x:

[tex]x = 3(180 - x)\\x = 540 - 3x\\x + 3x = 540\\4x = 540\\x = \frac{540}{4}\\x=135[/tex]

So, the angle is 135°

The supplement of the angle is  180 - 135 = 45°

The measure of the smaller angle is 45 degrees, and the larger angle, which is three times the size of the smaller one, measures 135 degrees.

The subject of this question falls under the branch of Mathematics, specifically geometry. The question deals with supplementary angles, which are pairs of angles that add up to 180 degrees.

Let's denote the smaller angle as 'x.' According to the problem, the larger angle is three times the size of the smaller, thus it is 3x. Because these are supplementary angles, they add up to form 180 degrees. So, we can create this equation: x + 3x = 180.

By simplifying and solving for x, we get: 4x = 180, hence x = 45 degrees. Therefore, the larger angle, which is three times the smaller, is 3*45 = 135 degrees.

In conclusion, the measure of the smaller angle is 45 degrees while the larger angle measures 135 degrees.

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Answer:

r=121/148 or r=0.81756

Step-by-step explanation:

-30=1/4-37r

37r=1/4-(-30)

37r=1/4+30

37r=1/4+120/4

37r=121/4

r=(121/4)/37

r=(121/4)(1/37)

r=121/148

Answer: 20%

Step-by-step explanation: if u want it on a decimal, here :0.2

hope this helps u :)

Answer:  The second one is not clarified give us the full clarification please....

Step-by-step explanation:

Let's evaluate the two inequalities:

1. 9g - 6 > 12g + 1

Subtracting 9g from both sides gives:

-6 > 3g + 1

Subtracting 1 from both sides gives:

-7 > 3g

Dividing both sides by -3 (and flipping the inequality sign) gives:

g < 7/3

1. 4 > + 8

This inequality is not correct, as it is missing a term on the right-hand side. It should be something like:

4 > x + 8

Subtracting 8 from both sides gives:

-4 > x

Without more information, we can't determine the value of x.

Please clarify or provide more context for the second inequality!

Answer:

7,326.64

Step-by-step explanation:

20 is 1/10 times as great as 200.

A number that satisfies this equation is 26

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc.

Given here the number 6,257.11 , here the digit 2 is in the 100th place hence it is equivalent to 200 and 1/10 th of 200 is 20 . Thus any number with its tenth place with digit 2 is acceptable and 26 is one such number.

Hence, the number is  26

Learn more about decimal numbers here:

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Answer:

probably answer c

Step-by-step explanation:

Answer: 9/20

Step-by-step explanation:

9/10 is given as the fraction of the crates filled with animals , 1/2 of this fraction holds dog , that is

1/2 of 9/10

= 1/2 x 9/10

= 9/20

Therefore the fraction of the total number of crates holding dog is 9/20

Answer:

Step-by-step explanation:

A 40 percent

Answer: (A)

(40%)

Step-by-step explanation:

By making an equation, we can get this answer. Let's say "what percent" is wp.

20 is wp of 50

20=wp(50)

20=50wp

wp=2/5

wp=40% (A)

Answer:

The sum of the first 5 terms of the series is 77.

Step-by-step explanation:

1. Let's review the information provided to us for solving the sum of the first 5 terms of the series:

1st term = 7

2nd term = - 14

3rd term = 28

4th term = - 56

2. Let's solve the sum of the first 5 terms of the series:

Aₙ = Aₙ₋₁ * -2 ; A₁ = 7

A₁ = 7

A₂ = A₁ * -2 = 7 * - 2 = - 14

A₃ = A₂ * - 2 = -14 * - 2 = 28

A₄ = A₃ * - 2 = 28 * - 2 = - 56

A₅ = A₄ * - 2 = -56 * - 2 = 112

Sum of the first 5 terms of the series = 7 - 14 + 28 - 56 + 112

Sum of the first 5 terms of the series = 77

Answer:

9

Step-by-step explanation:

Length: a

Width: b

ab = 54

a = b + 3

=> (b + 3)b = 54

=> b^2 + 3b = 54

=> b^2 + 3b - 54= 0

=> (b - 6)(b + 9)

=> b = 6 AND b = -9

Rectangular's sides > 0 => b = 6

Hope it's helpful :)

Answer:

x=-1, y=-9. (-1, -9).

Step-by-step explanation:

y=3x-6

x=2x+1

----------

x-2x=1

-x=1

x=-1

--------

y=3(-1)-6=-3-6=-9