What is the factored form of the polynomial?
x2 - 12x + 27?
(x + 4)(x+3)
(x - 4)(x + 3)
(x + 9)(x + 3)
(x-9)(x - 3)

Answer:

[tex](x+4)^2-1[/tex]

Step-by-step explanation:

We need to evaluate gOf. This basically means that we substitute the value of f(x) (i.e.; x+4) into g(x) in place of x.

[tex]g(x)=x^2-1\\f(x)=x+4\\\therefore gof(x) = g(f(x))=g(x+4)=(x+4)^2-1[/tex]

Answer:

768

Step-by-step explanation:

3 x (-2^8) = 768

Answer:

if cone is on there then it'd be cone but it may also be a cylinder

Step-by-step explanation:

i dont know the list of objects so i cant guarantee this

Answer:

Equidistant is your answer.

Step-by-step explanation:

Hope i have helped you!

Answer:

x = 5; the slope is undefined

Step-by-step explanation:

A line perpendicular to the x-axis is a vertical line.

In a vertical line, every point has a different y-coordinate and the same x-coordinate. Since you want a line that is vertical and passes through the point (5, -3), then every point on the line must have x-coordinate 5 no matter what its y-coordinate is. The slope of a vertical line is undefined.

Answer: The equation is x = 5; the slope is undefined

Answer:

+- square root of x+36

Step-by-step explanation:

f(x) = x^2 -36

y = x^2 -36

Exchange x and y

x = y^2 -36

Solve for y

Add 36 to each side

x+36 = y^2 -36+36

x+36 = y^2

Take the square root of each side

±sqrt(x+36) = y

±sqrt(x+36) = f^-1(x)

Answer:

90

Step-by-step explanation:

x/18=5

x=18*5

=90

Answer:

90

Step-by-step explanation:

Quotient means division

Is means equals

Let n = number

n/18 = 5

Multiply each side by 18

n/18 * 18 = 5*18

n = 90

The number is 90

Answer:

  b.  (x, y, z) = (-8, 10, -6)

Step-by-step explanation:

The easiest way to do this one is to try the answers to see which works.

  2(-8) +4(10) +3(-6) = -16 +40 -18 = 6

  5(-8) +8(10) +6(-6) = -40 +80 -36 = 4

  4(-8) +5(10) +2(-6) = -32 +50 -12 = 6

The answers of choice B work in the given equations.

___

In case you don't have answers to select from, you generally solve this sort of problem using elimination. You can also use Cramer's rule, a graphing calculator, an on-line equation solving tool, or any of a variety of other methods.

Here, we can find the variable x by subtracting twice the first equation from the second:

  (5x +8y +6z) -2(2x +4y +3z) = (4) -2(6)

  x = -8

This is sufficient to identify the correct answer choice.

We can substitute this into the last two equations to get ...

  -40 +8y +6z = 4 . . . . 8y +6z = 44

  -32 +5y +2z = 6 . . . . 5y +2z = 38

Subtracting the first of these from 3 times the second gives ...

  3(5y +2z) -(8y +6z) = 3(38) -(44)

  7y = 70 . . . . . . . simplify

  y = 10 . . . . . . . . divide by 7

Substituting this into the second of the above equations, we have ...

  5(10) +2z = 38

  25 +z = 19 . . . . . . divide by 2

  z = -6 . . . . . . . . . . subtract 25

_____

The choice of the combinations to use to eliminate variables can be ad hoc (as here), or it can be made according to some rules (as in Gaussian elimination).

My personal choice for solving systems like this is to use the matrix functions of a graphing calculator.

Answer:

40 MPH (Miles Per Hour)

Step-by-step explanation:

Well i will put it in simple terms. Put 2/3 into a decimal point, which for this fraction is 0.66666666667 (the 6 is infinite basically). Then you multiply it by 60, because you know it goes in that distance in one minute and 60 minutes makes a hour, which equals 40. So the answer is 40 MPH.

40 miles per hour.

To determine how many miles per hour a bird is flying when it covers 2/3 of a mile per minute, we can follow a simple conversion. Since there are 60 minutes in an hour, we need to multiply 2/3 by 60.

Let's do the calculation:

(2/3 mile/minute) times 60 minutes/hour = 40 miles/hour

This means that when a bird flies 2/3 of a mile per minute, it is equivalent to flying at a speed of 40 miles per hour.

Answer:

1

Step-by-step explanation:

You gave me slope intercept form, but typically the number paired with x is the slope. Because there is no number, the slope is 1.

Answer:

m = 1

Step-by-step explanation:

y = x -3  and y = mx + b are the same thing

Since you have mx and x as the same thing, then m = 1 (for which slope is m)

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0.86

The hundredths place is the second digit after the decimal point.  It is the 6 in this case.

Since the next digit (3) is 4 or less, the hundredths place stays the same and the rest is basically just cut off, leaving 0.86.

If the next digit (3) were 5 or more, the hundredths place would have gone up 1 (to 7) and the rest would have been cut off, giving a final result of 0.87

The decimal numeral system is the most widely used system for representing both integer and non-integer values. When 0.8637 is rounded to the nearest hundredth​ the number will be 0.86.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is Hindu–Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system.

A decimal number is rounded off based on its preceding number if the preceding number is greater than 5 then the number is rounded off to the next number, but if it's not, then the number is left in the same way.

Therefore, when 0.8637 is rounded to the nearest hundredth​ the number will become,

0.8637 ≈ 0.86

Hence, when 0.86 is rounded to the nearest hundredth​ the number will be 0.86.

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Answer:

8

Step-by-step explanation:

The union of the 2 sets are the elements in set A and B

A = { 1, 2, 3, 4, 5, 7 } and B = {3, 4, 8, 9 }

A ∪ B = { 1, 2, 3, 4, 5, 7, 8, 9 }

Note 3 and 4 are not repeated

number of elements in A ∪ B  = 8

Answer:

See below,

Step-by-step explanation:

2x > 50

Dividing both sides by 2:

x > 25 which is Graph C  (because the red line is to the right of 25).

x + 6 < 32

x < 32 - 6

x < 26  which is Graph B .

Ques 1)

The first inequality is given by:

                  [tex]2x>50[/tex]

on dividing both side of the inequality by 2 we obtain:

               [tex]x>25[/tex]

i.e. the solution set is the set of all the real values which are strictly greater than 25.

i.e. the shaded region is to the tight of 25 and there will be a open circle at 25 (Since the inequality is strict inequality )

i.e. the solution set is: (25,∞)

Hence, the graph which represents the inequality 2x>50 is: Graph C.

Ques 2)

The second inequality is given by:

             [tex]x+6<32[/tex]

on subtracting both side of the inequality by 6 we get:

                 [tex]x+6-6<32-6\\\\i.e.\\\\x+0<26\\\\i.e.\\\\x<26[/tex]

This means that the solution set is the set of all the real values which are strictly less than 26.

i.e. the shaded region is to the left of 26 and there will be a open circle at 26 ( since the inequality is strict)

i.e. the solution set is: (-∞,26)

The graph which represents the inequality x+6<32 is:  Graph B

let x = a number

difference means that its subtraction

twice a number is 2x

so the equation should be

2x-5=3

add 5 to both sides

2x=8

divide both sides by 2

x=4

Answer:

86

Step-by-step explanation:

To evaluate f(- 9) substitute x = - 9 into f(x)

f(- 9) = (- 9)² + 5 = 81 + 5 = 86

The correct answer is not listed in the provided options. f(-9) is found by substituting -9 into the function f(x) = x² + 5, giving us (-9)² + 5, which results in 86. The provided options do not include the correct answer, suggesting there may be a mistake.

To find f(-9) when f(x) = x² + 5, we simply substitute -9 for x in the function and calculate the result.

Step-by-Step Solution:

Replace every x in the function with -9: f(-9) = (-9)² + 5.

Calculate the square of -9: (-9)² = 81.

Add 5 to the result: 81 + 5 = 86.

Thus, f(-9) = 86.

The correct answer is not listed in the provided options, so there might be a typo in the original function or the options given.

Answer: 17.49 = L  or  17 1/2 = L

Step-by-step explanation:

a = L x W

55 = L x 3 1/7

55 ÷ 3 1/7   3 1/7 ÷ 3 1/7

17.49 = L

     or

17 1/2 = L

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To find the length of a rectangle with an area of 55 square feet and a width of 3 1/7 feet, you divide the area by the width after converting the mixed number to an improper fraction. Length = 55 / (22/7), which simplifies to 17.5 feet.

To find the length of the rectangle when the area is 55 square feet and the width is 3 1/7 feet, you can use the formula for the area of a rectangle, which is Area = Length × Width. You will first need to convert the width to an improper fraction, where 3 1/7 feet is 22/7 feet. Then, use the area to find the length:

Area = Length × Width

55 = Length × (22/7)

To find the Length, divide both sides by the width: Length = 55 / (22/7)

Multiply by the reciprocal of the width: Length = 55 × (7/22)

Simplify to find the Length: Length = 55/22 × 7

Length = 2.5 × 7

Length = 17.5 feet

Therefore, the length of the rectangle is 17.5 feet.

I would think 168

Because 84×2= 168

The measure of an arc is twice the measure of the angle that intercepted it.

Answer:

False

Step-by-step explanation:

The area is found by multiply length with width.

6 & 1 works (interchangeable with either length or width), because:

6 x 1 = 6

Therefore, False is your answer.

~

Answer:

correct answer is false

hope this helps :)

Answer:

12.54 square miles

Step-by-step explanation:

Area of Parallelogram = Base x Height

In this case, Base = 3.3 mi and Height = 3.8 mi

Hence,

Area = 3.3 x 3.8 = 12.54 square miles

Increasing means the plane was rising.

The linear increasing interval would be:

Jireh flew his crop duster from the ground to an altitude of 3,500 feet.

Answer:

A

Step-by-step explanation:

The answer is A as the height starts at 36 and decreases by 9 inches vertically every 12 inches it goes down horizontally.

If you turn this into an equation, you get y = -(9/12)x+36.

Then, you simplify this to y = -(3/4)x+36, which is A.

The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is [tex]y = -\frac{3}{4} x \ + \ 36[/tex]. (Option A).

The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is calculated as follows;

The general equation of a line;

y = mx + c

where;

If the stairs decreases by 9 inches vertically every 12 inches it goes down horizontally, then the slope becomes;

m = (0 - 9)/(12 - 0)

m = - 3/4

The y - intercept becomes the initial vertical height = 36

The equation that models the problem becomes;

[tex]y = -\frac{3}{4} x \ + \ 36[/tex]

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Answer

D, 12m

Step-by-step explanation:

Answer:

12 m

Step-by-step explanation:

Area of a triangle is:

A = ½ bh

Given that h = b - 5 and A = 42:

42 = ½ b (b - 5)

84 = b² - 5b

0 = b² - 5b - 84

0 = (b + 7) (b - 12)

b = -7, 12

The length of the base can't be negative, so b = 12 m.

Answer:

Option A

Step-by-step explanation:

We can try to factorize all the options one by one.

For A:

[tex]x^{2} +5x-4\\=> x^{2}+4x+x-4\\=>x(x+4)+1(x-4)[/tex]

We can see that the quadratic expression cannot be solved by factorization as the factors at the end of factorization are not equal in both brackets. So Option A is the correct answer for the given question.

Moreover we can also note that all the other quadratic expressions can be factorized ..

Answer:

x2 + 5x − 4 = 0

Step-by-step explanation:

The steps to solve the inequality 3b + 8 ≥ 14 involve subtracting 8, then dividing by 3 to find b ≥ 2.

To solve the inequality 3b + 8 ≥ 14:

Subtract 8 from both sides: 3b + 8 - 8 ≥ 14 - 8, which simplifies to 3b ≥ 6.

Divide by 3 to isolate b: 3b/3 ≥ 6/3, giving you b ≥ 2.

Therefore, the solution to the inequality is b ≥ 2, indicating that b must be greater than or equal to 2.

Answer:

3x

Step-by-step explanation:

-(x-1) +5 = 2(x+3) - c

C is the unknown term

Distribute the negative sign and the 2

-x+1 +5 = 2x+6 -c

Combine like terms

-x+6 = 2x +6-c

Solve for c

Add x to each side

-x+x +6 = 2x+x +6-c

6 = 3x+6 -c

Add c to each side

6+c = 3x +6 -c+c

c+6 = 3x+6

Subtract 6 from each side

c+6-6 = 3x+6-6

c = 3x

When c = 3x, the two sides of the equation are equal, and the solutions are infinite.

Answer: [tex]3x[/tex]

Step-by-step explanation:

Let be "z" the missing term:

[tex]-(x-1)+5=2(x+3)-z[/tex]

For the system to have infinite number of solutions, [tex]2(x+3)-z[/tex] must be equal to [tex]-(x-1)+5[/tex].

Now you must solve for "z". Apply Distributive property:

[tex]-x+1+5=2x+6-z[/tex]

Add the like terms on the left side:

[tex]-x+6=2x+6-z[/tex]

Now you need to subtract [tex]2x[/tex] and 6 from both sides of the equation and finally you can multiply both sides by -1. Then:

[tex]-x+6-2x-6=2x+6-z-2x-6\\\\(-1)-3x=-z(-1)\\\\z=3x[/tex]

Answer:

Step-by-step explanation:

We could multiply the first equation by -3 and, separately, multiply the second equation by 4.  The result would be:

-12x - 15y = -21

12x  - 8y = -48

the x terms now cancel.  The result is:

- 15y = -21

- 8y = -48

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

-23y = -69, or y = 3.  If y = 3, then 3x - 2y = -12 becomes:

3x - 2(3) = -12, or

3x - 6 = -12, or    3x = -6, and so x = -2.

The solution is (-2, 3).

Answer:

In the slot for 4x + 5y = 7 is -3. Which makes -21.

In the slot for 3x-2y=-12 is 4. Which makes -48.

Step-by-step explanation:

When you add the -21 and -48 you get -69.

The solution is (-2, 3)

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Answer:

Option (B) 4 = 2x - 3

Step-by-step explanation:

Let distance travel by Marcus be "x" miles

Then, according to question

Distanced travelled by Jenney will be

twice of "x" minus 3.

Distance travelled by Jenny = 2x - 3.

Also, it is given that Jenny has travelled 4 miles.

then, 4 = 2x - 3. So, here option (B) is the correct option.

Answer:

B

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The equation of the fourth side of the considered parallelogram is y = 2x + 10

Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.

Since given parallel line has equation [tex]y = 2x + 2[/tex], thus its slope is 2 and thus, the slope of the needed line is 2 too.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx + c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

A parallelogram is a four sided polygon, whose opposite sides are parallel to each other.

The slopes of y = 0 and y = 2 is same. (being 0)

Therefore the fourth side would've same slope as that of y = 2x.

The slope of y = 2x is 2 (the coefficient of x)

Thus, the equation of fourth side would be:

y = 2x + c for some real number c

Let we find the coordinates of four vertices. These are intersections of the equations of the adjacent sides.

Intersection of y = 0:

Putting y = 0 gives 0 = 2x, or x = 0

Thus, the intersection is on (0,0)

Putting y = 0 gives 0 = 2x + c, or x = -c/2

Thus, the intersection is on (-c/2, 0)

Intersection of y = 2:

Putting y = 2 gives 2 = 2x, or x = 1
Thus, the intersection is on (1,2)

Putting y = 2 gives 2 = 2x + c, or x = (2-c)/2

Thus, the intersection is on ((2-c)/2, 2)

Thus, the four vertices' coordinates are:

(0,0), (1,2), (-c/2, 0), and ( (2-c)/2, 0)

Let we name these points, as:

A(0,0), B(-c/2, 0),  C( (2-c)/2, 2) and D(1,2),

AB is line y = 0 (known from the y-coordinates of A and B)

Similarly, CD is line y = 2 (known from the y-coordinates of C and D)

AD and BC are parallel. (these are going to be other pair of parallel sides).

The length of AD is:

[tex]\sqrt{(1-0)^2 + (2-0)^2} = \sqrt{5} \: \rm units[/tex]

A parallelogram has its parallel sides of equal length.

Thus, length of BC is of √5 units too.

Since this parallelogram has two side lengths of 5 units, adn as AD and BC are not those sides, so we must have:

|AB| = |CD| = 5 units.

Length of AB is:

[tex]|AB| = \sqrt{(-c/2 - 0)^2 + (0 - 0)^2 } = c/2 = 5\\c = 10[/tex]

Thus, the equation of the fourth line is:

[tex]y = 2x + 10[/tex]

The graph of the considered parallelogram is given below.

Thus, the equation of the fourth side of the considered parallelogram is y = 2x + 10

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Answer:

y intercept = 5

Step-by-step explanation:

f(x)=5•(1/6)^x

The y intercept is when x =0

Let x =0

f(0)=5•(1/6)^0      

= 5* 1     = 5

The y intercept is 5

If the question is

f(x)=5•(1/6)x

although I have never seen the question written this way

The y intercept is when x =0

Let x =0

f(0)=5•(1/6)0      

= 5* 0     = 0

The y intercept is 0