Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles
A = 59°, a = 13, b = 14

The factorized expression using difference of squares is as follows,

9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

Difference of Squares

Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares,  a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.

Factorization Using Difference of Squares

Given expression is,

36a⁴b¹⁰ - 81a¹⁶b²⁰

= (6a²b⁵)² - (9a⁸b¹⁰)²

Using square of differences, we have

a² - b² = (a + b) (a - b)

Here, a = 6a²b⁵ and b = 9a⁸b¹⁰

Thus, we get,

(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)

Further Factorization

We can take out 3 common from both the bracket terms after applying difference of squares

3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

Further, we can take out a²b⁵ as common from both the bracket terms

= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

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Andrew should make 6 bookcase and 12 tv stand to maximize his profut $1560.

Given that 18 pieces of furniture is made and the materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00 and he has $600.00 to spend on materials. He makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand.

Let x represent the number of book case and let y represent number of tv stand.

Total number of book case and total number of tv stand is x+y≤18     ......(1)

Total amount of book case and total amount of tv stand is 20x+40y≤600   ......(2)

minimum amount of book case is x≥0 and minimum amount of tv stand is y≥0.

Now, solve the inequality (1) by converting it into equality and substituting x=0 and y=0, we get

x+y=18

When x=0 then

0+y=18

y=18

When y=0 then

x+0=18

x=18

Now, solve the inequality (2) by converting it into equality and substituting x=0 and y=0, we get

20x+40y=600

When x=0 then

20(0)+40y=600

40y=600

y=15

when y=0 then

20x+40(0)=600

20x=600

x=30

Further, we will grph the inequalities and we get feasible region and taking boundary point from graph.

From the graph the vertices of the feasible region is (0,0),(6,12),(0,15) and (18,0)

Further, we will find the maximization profit for the equation Z=60x+100y

When (x,y)=(0,0) then

Z=60(0)+100(0)

Z=0

When (x,y)=(6,12) then

Z=60(6)+12(100)

Z=360+1200

Z=1560

When (x,y)=(0,15) then

Z=60(0)+12(15)

Z=0+1500

Z=1500

When (x,y)=(18,0) then

Z=60(18)+100(0)

Z=1080

Hence, maximum profit is $1560 when andrew should build 6 bookcase and 12 tv stand.

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Answer:

5a(a - 2)

2(a^2 - 4)

(x + 5)(x - 5)

(x - 4)(x^2 + 4x + 16)

(a - 3)(a - 2)

(x^2 + x + 1)(x^2 - x - 1)

Step-by-step explanation:

5a^2 - 10a     factor out GCF

5a(a - 2)

2a^2 - 8      factor out GCF

2(a^2 - 4)

x^2 - 25     difference of squares

(x + 5)(x - 5)

x^3 - 64      difference of cubes

(x - 4)(x^2 + 4x + 16)

a^2 - 5a + 6      factors of 6 that add to -5

a^2 - 2a - 3a + 6

a(a - 2) - 3(a - 2)

(a - 3)(a - 2)

x^4 - x^2 - 2x - 1      group last three terms

x^4 + (-x^2 - 2x - 1)

x^4 - (x^2 + 2x + 1)        factors of 1 that add to 2

x^4 - (x + 1)(x + 1)

x^4 - (x + 1)^2         difference of squares

(x^2 + (x + 1))(x^2 - (x + 1))        simplify

(x^2 + x + 1)(x^2 - x - 1)

Answer:

I'm assuming that it is 4:1

Step-by-step explanation:

Answer:

I have just wrote answers

Answer:

A

Step-by-step explanation:

By the triangle inequality theorem, 5<AC<23.

So, the answer is A.

Answer:

(4, -3)

Step-by-step explanation:

y = f(x -5) means y = f(x) shifted 5 units to the right. So the minimum point would shift 5 units to the right as well.

Answer:

47.25

Step-by-step explanation:

8.89 is about 9.

So, we have 9(5.25)=9(5)+9(0.25)=45+2.25=47.25

The following equation represents the function g in function notation,

g(x) = 3x - 14 [Option (A)]

Definition of a Function

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.

Given equation is,

y -3x = -14

⇒ y = -14 + 3x

or y = 3x - 14

Here, y stands for or represents the function g(x) which is a function of independent variable x.

Thus, the correct function notation is as follows,

g(x) = 3x - 14

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Answer:

2.094 x 10¹⁰ I have to add more words soo

The inverse proportionality expression is y =40/x

If the variable y is inversely proportional to x, this is expressed as;

y = k/x

where

k is the constant of proportionality

If y = 5 and x = 8. then;

5 = k/8

k = 5 * 8

k = 40

Determine the inverse proportionality

Recall that y = k/x

y = 40/x

Hence the inverse proportionality expression is y =40/x

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Step-by-step explanation:

what is the best definition of luminous

The terms that are possible on the domain of a sequence are given as follows:

13, 25, 60.

A sequence is a list containing numbers, that may be related or not. It has a 1st term, 2nd term, and so on until the nth term.

The domain is the indexes of the terms, which starts at one and goes until n, hence the possible numbers are:

13, 25, 60.

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Answer:

V = 15 in.³

Step-by-step explanation:

The original cylinder has radius r and height h.

V = πr²h

Its volume is 30 in.³, so

πr²h = 30 in.³

The new cylinder has radius (1/2)r and height 2h.

Its volume is

V = π(r/2)²(2h)

V = πr² × 2h/4

V = πr²h/2

πr²h is the volume of the original cylinder, and it is 30 in.³.

V = 30 in.³/2

V = 15 in.³

The length of the third side of the triangle is 4. 33

We have the length of the two sides to be;

2 and 5

If the angle between them is 60 degrees, then the third side is the opposite side

To find the opposite side, we use the sin ratio, which is

sin 60 = opposite/hypotenuse

sin 60 = x/ 5

Cross multiply

sin 60 × 5 = x

x = 0. 8660 × 5

x = 4. 33

Thus, the length of the third side of the triangle is 4. 33

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Answer:

(2x-5)(2x-5), 81 meters

Step-by-step explanation:

All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)

Using this equation we can plug in 7 for x:

(2(7)-5)(2(7)-5) =

(14-5)(14-5) =

9*9 = 81

Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

To do this, we make use of 1.50% interest rate

Here, we have:

Initial, a= 625

Rate, r = 1.5%

The exponential growth equation is

A(t) = a * (1 + r)^t

So, we have:

A(t) = 625 * (1 + 1.5%)^t

Evaluate

A(t) = 625 * 1.015^t

Hence, the exponential growth equation is A(t) = 625 * 1.015^t

Here, t = 25.

So, we have:

A(25) = 625 * 1.015^25

Evaluate

A(25) = 906.84

Hence, the value in 25 years is $906.84

#Investment A

a = 625

r = 1.5%

t = 5

So, we have:

A(5) = 625 * 1.015^5

Evaluate

A(5) = 673.3

#Investment B

a = 625

r = 5%

t = 1

So, we have:

A(1) = 625 * 1.5^1

Evaluate

A(1) = 937.5

By comparison, 937.5 is greater than 673.3

Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

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The equation becomes of the pressure is   P = 90 + 10 sin(π/36(t +4 ))

By observation the sine function should be of form P=  90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.

At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg

Substituting it in the equation we get,

100 = 90 + 10 sin(ω(t − c))

10 = 10  sin(ω(14 − c))

1 = sin(ω(14 − c))

ω(14 − c) = π/2                           -1)

At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg

80 = 90 + 10 sin(ω(t − c))

-10 = 10 sin(ω(2 − c))

3π/2 = ω(2 − c)                           -2)

dividing 2) with 1) we get

3 = (14 − c) /(2 − c)  

6 - 3c = 14 - c

2c = -8

c = - 4

Substituting the value of c in 1) we get,

ω(14 − (-4)) = π/2

ω18 =  π/2

ω = π/36

Thus the equation becomes  P = 90 + 10 sin(π/36(t +4 ))

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Answer:

17

Step-by-step explanation:

x+3x+x-7=78

5x-7=78

5x=78+7

5x=85

x=85/5

x=17

Answer:

The three numbers are 17, 10 and 51.

Step-by-step explanation:

Let the first, second, and third numbers be [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] respectively.

• From the question, we know:

sum of the numbers is 78.

∴ [tex]x + y + z = 78[/tex]   ----------(1st equation)

Let's express both [tex]x[/tex] and  [tex]z[/tex] in terms of [tex]\bf y[/tex] :

• We know that:

the third number is 3 times the first.

∴ [tex]z = 3x[/tex]

⇒ [tex]x = \frac{z}{3}[/tex]     ----------(2nd equation)

• We also know that:

the first number is 7 more than the second.

∴ [tex]\boxed{x = 7 + y}[/tex]

Substituting  [tex]x = \frac{z}{3}[/tex]  (from 2nd equation)

⇒ [tex]\frac{z}{3} = 7 + y[/tex]

⇒ [tex]\boxed{z = 21 + 3y}[/tex]

• We can now substitute  [tex]x = 7 + y[/tex]  and  [tex]z = 21 + 3y[/tex]  into the first equation:

[tex]x + y + z = 78[/tex]

⇒ [tex](7 + y) + y + (21 + 3y) = 78[/tex]

⇒ [tex]5y + 28 = 78[/tex]

⇒ [tex]5y = 50[/tex]

⇒ [tex]y = \bf 10[/tex]

∴ [tex]x = 7 + 10\\[/tex]

⇒ [tex]x = \bf 17[/tex]

[tex]z = 21 + 3(10)[/tex]

⇒ [tex]z = \bf 51[/tex]

∴ The three numbers are 17, 10 and 51.

Answer:

C

Step-by-step explanation:

The average is the total of the scores divided by 5.  

128 x 5 Gives us the total scores of 640.  I know that one bowler had a score of 160.  I will subtract that from the total of 640.  640-160 = 480.  Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120

Answer:

  (c)  y = -3x +6

Step-by-step explanation:

The equation can be written in slope-intercept form when we know the slope and the y-intercept.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . where m is the slope and b is the y-intercept

The y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...

The line goes down to the right. This is a negative slope, eliminating choice B.

The equation of the line is y = -3x +6.

__

Additional comment

The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...

  m = rise/run = -6/2 = -3

Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is

  y =-3x +6

98.3, 94.1, 89.9, 85.7 (Arithmetic)

1, 0, -1, 0 (Neither)

1.75, 3.5, 7, 14 (Geometric)

-1, 1, -1, 1..... (Geometric)

An arithmetic sequence has a common difference

A geometric sequence has a common ratio

Considering the given sequences one after the other:

For 98.3, 94.1, 89.9, 85.7,..........

The common difference, d = 94.1 - 98.3 = -4.2

Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence

For 1, 0, -1, 0......

The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence

For 1.75, 3.5, 7, 14,.....

The common ratio = 3/1.75 = 2

Therefore, it is a geometric sequnec

For -1, 1, -1, 1.....

The common ratio = 1/-1 = -1

It is a geometric sequence

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The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.

A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.

We are asked what shape is formed.

From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.

Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.

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Answer:

Step-by-step explanation:

Heart Shaped

The statement when a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed is True.

Appeal occur when a person convicted of a crime want another court to reverse a decisions or to examine and re-check the judgement or outcome of a trial court outcome because the convicted person was not satisfied with the outcome or the result  of the trial court .

Hence, the statement is true because an offender  that was convicted of a crime can tend to files an  appeal with a higher court or appellate court so as to examine the trial court's decisions.

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Answer:

The volume of the cylinder is smaller than the rectangular prism.

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

If 5/6 = 180

lets find what 1/6 equals

To do this lets divide 180 by 5 to find 1/6

[tex]\frac{180}{5} =36[/tex]

Therefore, 1/6 = 36

We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.

Anyways, we can check our answer by doing:

36*5 = 216 then taking 5/6 of 216, which should equal 180

[tex]216*\frac{5}{6} =180[/tex]

Therefore, we know 36 is the correct answer

The expression that represents the volume of the composite figure is: 1/3(8)(6)(6) + (8)(6)(4).

The volume for the given composite figure = volume of the rectangular pyramid + volume of rectangular prism.

= 1/3(l)(w)(h) + (l)(w)(h)

Thus, with the given dimensions, plug in the values to get the expression represents the volume of the composite figure:

Volume = 1/3(8)(6)(6) + (8)(6)(4)

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The tabular values can be used to derive the formula relationship between x and P which gives the percentage commission of Zachary as 1%

From the above table, we have;

Where;

y = The fixed percentage commission Zachary makes

b = Zachary's base pay

Therefore;

Subtracting equation (1) from (2), gives;

110 - 105 = (3500 - 3000) × y + b - b = 0

5 = 500•y

y = 5/500 = 0.01 = 1%

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Answer:

27.2

Step-by-step explanation:

V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth

Shyam travel total  [tex]10km 317m[/tex]  distance ,when he travelled  [tex]8 km 52 m[/tex]  by bus and [tex]2 km 265 m[/tex]  by car .

How to find the total distance travel by Shyam ?

Shyam travelled distance by bus [tex]=8 km 52 m[/tex]

Shyam travelled distance by car [tex]=2 km 265 m[/tex]

Total distance travelled by shyam is

Total distance= distance travelled by car + distance travelled by bus

Total distance

[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]

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