is x + 3 a factor of f(x)=x^4+6x^3+5x^2-15x-2

Answer: 2

Step-by-step explanation:

The slope of the line is

[tex]\frac{-2-1}{0-9}=\frac{1}{3}[/tex]

So, the equation of the line is [tex]y=\frac{1}{3}x-2[/tex].

Substituting in x=12,

[tex]y=\frac{1}{3}(12)-2=2[/tex]

The domain and range is  [-4, 4] and [0, 4]

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

x² + y² = 16

y = √16 - x²

For domain under root should not be negative quantity,

16 - x²≥0

16≥x²

So, x≤4 or x≥4

Thus, the domain is  [-4, 4]

Range:

y is maximum at x=0, y=4

y is minimum at x=4, y=0

Thus, range = [0, 4]

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Answer:

y + 2 = 5/3(x - 4)

Step-by-step explanation:

Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)

It looks like this:

y - Y = m(x - X)

The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.

y - -2 = m(x - 4)

Fill in the slope for the m.

y - -2 = 5/3(x - 4)

Simplify if possible.

y + 2 = 5/3 (x - 4)

On the base of visual inspection , it can be said that the Group A has an average lower than the Group B

It is the simple form of data visualization , in which the frequency of a data is marked as dots on x and y axis.

The dot plot is given for two groups of 30 people , who go to painting class.

It has been asked that which group most likely has a lower mean age of painting students .

On the base of visual inspection , it can be said that the Group A has an average lower than the Group B

It can be said so as the dots are highest at the age of 19 in Group A , and the whole distribution lies between 9 to 19 age of people ,

while in Group B the age of the people is wide distributed and therefore the average age will be more ,

By calculation it is proved that the average age of Group A is 15.967

and the average age of Group B is 19.7.

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Answer:

Read books, watch documentaries, exercise, anything that benefits your body and mind

Step-by-step explanation:

The turning point of the parabola is (64, -43)

Turning point is that point on a parabolic curve in which the gradient of the curve changes value.

It is also the point on the curve in which the curve starts rising or falling.

Analysis:

[tex]27(x-64)^{2}[/tex] + 43

27(x-64)(x-64) + 43

27([tex]x^{2}[/tex] -64x -64x +4096) + 43

27[tex]x^{2}[/tex] -3456x +110592 +43

27[tex]x^{2}[/tex] -3456x +110635

at turning point dy/dx = 0

dy/dx = 54x - 3456

54x - 3456 = 0

54x = 3456

x = 3456/54 = 64

To find the value of y at x = 64

27[tex](64)^{2}[/tex] -3456(64) +110635

110592 - 221184 +110635 = -43

Therefore the turning point of the parabola is (64, -43)

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Answer:

This could be described by the stock market. Suppose you had stock of tesla that went up then flat then down

Step-by-step explanation:

you went for a walk : you started at home, walked away, first slower, then a little bit faster, stayed a little bit first at one place, then started walking back home, stayed a really short time at a second place and finally walked back home.

Based on the weight of the pig and the age in days, the function notation would be w = f (d).

The function will take the form of:

y = f(x)

y will be the weight and x will be the age of the pig in days.

The function would therefore be:

w = f (d)

In conclusion, the function notation to express the pig's weight is w = f (d).

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The value of x is 3

The given parameters are:

Length = 10cm

width = 2cm

Height = x

The surface area is calculated as;

Area = 2 *(lw + lh + wh)

So, we have:

2 * (10 * 2 + 2x + 10x) = 112

Evaluate the like terms and divide by 2

20 + 12x = 56

Subtract 20 from both sides

12x = 36

Divide by 12

x = 3

hence, the value of x is 3

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Answer: -5

Step-by-step explanation:

When x = 8, y = -5.

Two or more triangles are said to be congruent if and only if they have equal lengths of sides and equal measures of angles.

Thus, the required proof is as shown below:

   STATEMENTS                                             REASONS

1. ΔABC and ΔDEC with AB ≅ DE;

  BC ≅ EC; <1 ≅ <2                                          Given

2. <1 and < ABC; < 2 and <DEC are sup     Sum of angles on a straight line

3. <ABC ≅ <DEC                                Congruent angles of similar triangles

4. ∴ΔABC ≅ ΔDEC                              Side-Angle-Side (SAS) postulate

5. ∴<ACB ≅ <DCE                                         CPCTC postulate

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Answer:

5x+8

Step-by-step explanation:

The from is the key word

That means the second term is first

6x^2 -2x +6 - (6x^2 -7x -2)

Distribute the minus sign

6x^2 -2x +6 - 6x^2 +7x +2

Combine like terms

5x+8

Step-by-step explanation:

♦ Solution ♦ :-

Given Information :

The ratio of heights of the two girls = 5:7

Assumption

Consider their height be 5X cm and 7X cm

The height of the first girl = 5X cm

But According to the condition mentioned in given problem

The height of the first girl = 192 cm

=> 5X = 192

=> X = 192/5

=> X = 38.4

Therefore, X = 38.4 cm

Now the height of the second girl = 7X cm

=> 7 × 38.4 cm

=> 268.8 cm

♦ Alternative Method♦ :-

The ratio of the heights of the two girls = 5:7

The height of the first girl = 192 cm

Assume that the height of the second girl = X cm

Therefore, 5:7= 192:X

=> 5/7 = 192/X

=> 5X = 7×192

=> X = (7×192)/5

=> X = 7× 38.4

=> x = 268.8 cm

♦ Answer ♦ :-

The height of the second girl is 268.7 cm

Answer: Being connected means greater opportunities to learn from each other, mine each other's wisdom, and help each other thrive. Connecting. By being more closely interconnected, each member of the community is able to enjoy a wider, richer network of resources, wisdom, connections, and support.

The solution which can be used to fill in both blanks in the table is; (6,7).

It follows from the task content that the system given has been simplified to the point that;

3x = 18

x = 18/3 = 6.

Hence, the value of y can be evaluated as follows;

2y - x = 8. where (x=6.

2y = 8+6

y = 14/2 = 7.

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The expression that is equivalent to the given complex fraction is; (-2y+5x) / (3x - 2y)

The given algebraic sentence can be rewritten as;

((-2/x) + (5/y))/((3/y) - (2/x))

The LCM is xy and as such when we put it in the denominators of each fraction, we have:

((-2y + 5x)/xy)/((3x - 2y)/xy)

Putting 'xy' in the numerator and denominator of the whole fraction:

(-2y + 5x)/(3x - 2y)

The final expression we have is (-2y + 5x)/(3x - 2y)

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Answer:

its A -2y+5x ÷ 3x-2y

Step-by-step explanation:

Edge 2022

Answer:

A is x - 4n / 3, B is 6k + 9n, C is 11k + 16n

Step-by-step explanation:

Pretty simple, you are adding the algebra grids, or substituting variables and making out an equation.

Solving for B: 4k + 6n + 2k + 3n = 6k + 9n

Solving for A: (2k + 3n) + x = 5k + 7n = x - 4n / 3

Solving for C: 6k + 9n + 5k + 7n = 11k + 16n

The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.

It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.

It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.

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The expression is defined for all the real values except x = -y , y = -x.

An expression is a mathematical statement consisting of constants , variables and mathematical operators.

The expression given in the question is 1/(x +y)

An expression f(x) is undefined when the denominator = 0

f(x) = 1/(x +y)

For the denominator to be zero,

x = -y

or y = -x

So the expression is defined for all the real values except x = -y , y = -x

It can be written as

E = {x ∈ R ∧ x ≠ -y} or

E = {y ∈ R ∧ y ≠ -x}

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The quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x+6[/tex] is (x-2_.

Given the polynomial [tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x+6[/tex] and the first expression or polynomial is divided by second.

Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.

To find the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by  , we have to divide the expression first.

We know that ,

Divident=Divisor*Quotient+remainder

[tex]x^{3}+3x^{2} -4x-12[/tex]=[tex]x^{2} +5x-6[/tex]*(x-2)-12

If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).

Hence the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x-6[/tex] is (x-2).

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Question is incomplete as the given expressions are incomplete as they should be like this:

[tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x-6[/tex].

Answer:  D)  union

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

Explanation:

Let's solve the first inequality for x.

4x-5 ≥ 3

4x ≥ 3+5

4x ≥ 8

x ≥ 8/4

x ≥ 2

Now solve the other inequality

5 - x > 8

5 > 8+x

8+x < 5

x < 5-8

x < -3

The two solutions we get are x < -3 or x ≥ 2

These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.

Either x is smaller than -3, OR it is 2 or larger

I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.

Answer:

The simplest ratio would be 5:3

Step-by-step explanation:

Both 10 and 6 can be divided by 2.

They turn into 5 and 3.

Since you can't make 5 and 3 any smaller, this will be the answer.

5:3

Hope this helped! :D

The 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.

Given that the perimeter of the triangle is 44 cm.

Let us consider a side 's' which is 4 cm shorter than the second side.

That means the second side is 4 cm longer than s, hence the second side is s+4 cm in length.

We also have that the side of length s is of length twice as long as the third side.

Hence, the length of the third side is half that of s so, it is of length s/2.

Hence, at the end 44=s+(s+4)+(s/2)=s(2+1/2)+4

⇒ s(5/2)=40

⇒ s=8*2=16

So, the 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.

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No, it isn't true that blending problems arise when one must decide which of two or more ingredients is to be chosen to provide a product.

Given sentence "Blending problems ...............................supply a product."

We have to answer whether the given sentence is true or false.

We can say that the given sentence is fake. the sole objective functions allowed for applied math problems maximizing profits and minimizing costs.

Blinding problems are a typical application of mixed integer applied mathematics. They involve blending several resources or materials to make one or more products similar to a requirement. Mixed integer linear programs are linear problems during which some variables are required to require integer values.

Hence the given statement is fake regarding arise of blending problems.

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Question is incomplete because it should includes:

State whether the statement is true or false.

The value of x that will satisfy the equation is x=-1.

We have given that,

[tex]\left|x-1\right|=\left|x+3\right|[/tex]

We have to solve the above inequality

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

Find the positive and negative intervals

[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]

Solve the inequality for each interval

[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]

[tex]\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=-1[/tex]

Therefore we get,

[tex]x=-1[/tex]

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Answer:

B The vertex is at (2,2)

Or could possibly be

C the axis of symmetry is x=2

Step-by-step explanation:

first we need to find the length of CD, so that we can use Pythagoras to find AC.

to get CD we use again Pythagoras. there is a smaller right-angled triangle on top of the BCD rectangle.

so, AD = 11 = 4 + 7

7 = the vertical leg of the upper right-angled triangle.

the horizontal leg is congruent to CD and is

sqrt(16² - 7²) = sqrt(256 - 49) = sqrt(207).

AC² = sqrt(207)² + 11² = 207 + 121 = 328

AC = sqrt(328) = 18.11077028... cm ≈ 18.1 cm

The domain of the function f(x)= [tex]\sqrt{x-2}[/tex]is all numbers greater than or up to 2.

Given Function f(x)=[tex]\sqrt{x-2}[/tex]

We have to search out the domain of the function f(x)=[tex]\sqrt{x-2}[/tex]

Domain is that the value of x which we put within the function to induce the various values and range is that the value which we get after putting the worth.

f(x)=[tex]\sqrt{x-2}[/tex]

put the function =0

squaring either side we get

x-2=0

x=2

So the domain of the function f(x)=[tex]\sqrt{x-2}[/tex] is [2,∞) because we are able to put all values greater than 2 within the function.

Hence the domain of the function is [2,∞).

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