Practice: Describe the similarities and differences between the following
equations.
y = -6x and y = -6x + 3

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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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:

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:

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:

A

Step-by-step explanation:

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

So, the answer is A.

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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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:

x = -0.01685

(Is the equation written correctly?  This feels like a very unfortunate number)

Step-by-step explanation:

(2x+5/60-95x-3/30=3/2

2x+(5/60)-95x-(3/30)=3/2

2*(2x+(5/60)-95x-(3/30))=3     [Multiply both sides by 2]

4x+(10/60)-190x-(6/30))=3      

(2/30)-186x-(6/30))=3              [Simplify]

-186x-(4/30)=3

-186x=3+(4/30)

-186x=(90/30)+(4/30)

x = (94/30)/(-186)

x = -0.01685

Answer:

3. Completing the Square

4. 0, 1, or 2

Step-by-step explanation:

Hello!

a) Graphing

Graphing is a useful method as it lays the answer out in front of you. Once you graph the parabola, you simply take the intersections of the graph and x-axis as your x-intercepts. Therefore, it is a method.

b) Factoring

Factoring can be used to find x-intercepts, and after factoring, you can set each factor to 0 and solve for x, which are the x-intercepts. This method is also called the Zero Product Property.

c) Quadratic Formula

The quadratic formula is meant to solve for the x-intercepts, as the formula uses values of the coefficients to isolate x and solve for it.

Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

Plugging in the values of a, b, and c give you the solutions for x.

d) Completing the Square

Completing the square CAN be used to find the x-intercepts, but not directly so. It is used to convert standard form into a different form, known as the vertex form. It is meant so find the vertex, not the x-intercepts.

Therefore, Completing the Square is NOT a method to find the x-intercepts.

The number and types of solutions depend on the discriminant of the quadratic (the part under the square root in the QF).

Types of roots:

That means that a quadratic equation can have 0, 1, or 2 roots.

Answer:

Completing the square and 2, 1, and 0.

Step-by-step explanation:

Person above is correct!!

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:

Hey there :) The answer is 0.25 minutes.

Step-by-step explanation:

1 minute = 60 seconds

So, 15 ÷ 60 = 0.25 minutes

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

Answer:

27.2

Step-by-step explanation:

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

Answer:

I have just wrote answers

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:

2.094 x 10¹⁰ I have to add more words soo

Answer:

I'm assuming that it is 4:1

Step-by-step explanation:

Answer:

y<7

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer: y < 7

Step-by-step explanation:

We can assume that the less than sign is an equals sign and use algebra to isolate y.

[tex]5y+1-1 < 36-1\\ 5y < 35\\\frac{5y}{5} < \frac{35}{5}\\ y < 7[/tex]

We first subtracted 1 from both sides to get rid of the +1.

Then we divided both sides by 5 to isolate y.

The ordered pairs from the options given that is from the table is: D. (6,5).

An ordered pair is written in the form, (x, y). The first number in the bracket is the x-value on the table, and the second number is its corresponding y-value form the table.

From the table given, the ordered pairs are: (3, 4), (4, 4), (5, 2), and (6, 5).

The number pair from the table from the given options is: D. (6,5).

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The variation equation is p = kr^2

The variables are give as:

Pressure = P

Radius= r

The direct variation from p to the square of r is represented as:

[tex]p\ \alpha\ r^2[/tex]

Express as an equation

p = kr^2

Where k represents the constant of variation

Hence, the variation equation is p = kr^2

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Answer:

The correct answer is the 3rd option

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

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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Answer:

B

Step-by-step explanation:

area = 10x^2 + 20x

base = 20x

10x^2 + 20x = 0.5(20x)(height)

10x^2 + 20x = 10x(height)

(10x^2 + 20x) / 10x = height

[tex]\frac{10x^2 + 20x}{10x} = \frac{10x + 20}{10} = \frac{x + 2}{1} = x + 2[/tex]

The answer is B

Answer:

B

Step-by-step explanation:

when a square pyramid is cross sectioned the shape that will appear is the same as that of the base

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

Using translation concepts, the change of f(x) = x to g(x) = x - 90 can be described as follows:

The base graph has been shifted down 90 units.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) - 90, that is, the base graph was shifted down 90 units.

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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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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

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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The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}

The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}

The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.

The graph of f(x)= x^2 is given

We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2

The Graph of 3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=12

x=-1 g(x)=3

x=0 g(x)=0

x=1 g(x)=3

x=2 g(x)=12

The Graph of -3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=-12

x=-1 g(x)= -3

x=0 g(x)=0

x=1 g(x)= -3

x=2 g(x)=-12

Domain of g(x) is R and it's range is {y∈R / y≥0}

Domain of h(x) is R and it's range is {y∈R / y ≤0}

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