When the polynomial in P(x) is divided by (x + a), the remainder equals P(a)

Answer:

x=12

Step-by-step explanation:

1/2x + 3 = 2/3x + 1

Subtract 1 from each side

1/2x + 3-1 = 2/3x + 1-1

1/2x +2 = 2/3 x

Subtract 1/2 x from each side

1/2x -1/2x+ 2 = 2/3x -1/2x

2 = 2/3x -1/2x

Get a common denominator of 6  2/3 = 4/6   and 1/2 = 3/6

2 = 4/6x - 3/6x

2 = 1/6 x

Multiply each side by 6 to isolate x

2*6 = 1/6x *6

12 =x

Answer:

x=12

Step-by-step explanation:

Answer:

Both are correct

Step-by-step explanation:

The Line has the following equation: y= 1+4/5 x

So we need to know which points: (-5,-3) and (10,9), (-10,-7). (-15, -11) are part of the line

For instances, lest start by evaluating (-15,-11) in y=1+4/5 x

this leaves us to the following operation: -11=1+4/5 * (-15)

-11=1-4*3 resulting in a equality -11=-11, this point does belong to the line

Repeat the above for all of the remaining points and you will get the same conclusion, that is we Vladimir and Robyn are correct.

Answer:

C.

Step-by-step explanation:

Ok I'm going to make a right triangle by drawing a straight edged line segment from the top left vertex straight down.

We can now find the height of the parallelogram.

sin(60)=h/6  (opp/hyp)

Multiply both sides by 6.

6 sin(60)=h

6*sqrt(3)/2 =h

3*sqrt(3)=h

So to find the area of the parallelogram you do base*height, so you have 8*3*sqrt(3) which simplifies to 24sqrt(3).

Answer:

Option C. x = -2,6  extreme value at (2.16)

Step-by-step explanation:

we have

[tex]y=-x^2+4x+12[/tex]

This is the equation of a vertical parabola open down

The vertex is a maximum (extreme value)

Convert the equation into vertex form

[tex]y=-x^2+4x+12[/tex]

Complete the square

Group terms that contain the same variable and move the constant term to the left side

[tex]y-12=-x^2+4x[/tex]

Factor -1

[tex]y-12=-(x^2-4x)[/tex]

Remember to balance the equation by adding the same constants to each side.

[tex]y-12-4=-(x^2-4x+4)[/tex]

Rewrite as perfect squares

[tex]y-16=-(x-2)^2[/tex]

[tex]y=-(x-2)^2+16[/tex] -----> equation of the parabola in vertex form

The vertex is the point (2,16) ----> is a maximum (extreme value)

Determine the solutions of the quadratic equation

For y=0

[tex]0=-(x-2)^2+16[/tex]

[tex](x-2)^2=16[/tex]

square root both sides

[tex](x-2)=(+/-)4[/tex]

[tex]x=2(+/-)4[/tex]

[tex]x=2(+)4=6[/tex]

[tex]x=2(-)4=-2[/tex]

therefore

The solutions are x=-2 and x=6

The extreme value is (2,16)

The correct answer is option  (C) [tex]\( x = -2.6 \)[/tex] with the extreme value at 2.16.

To solve the quadratic equation  [tex]y = -x^2 + 4x + 12[/tex] , we will complete the square to rewrite the equation in vertex form, which is [tex]\( y = a(x - h)^2 + k \), where \( (h, k) \)[/tex]is the vertex of the parabola.

First, we factor out the coefficient of[tex]\( x^2 \)[/tex], which is -1 in this case:

[tex]\[ y = -(x^2 - 4x - 12) \][/tex]

Next, we complete the square inside the parentheses. To do this, we take the coefficient of  x , which is -4, divide it by 2, and square the result to find the value that we need to add and subtract to complete the square:

[tex]\[ \left(\frac{-4}{2}\right)^2 = (-2)^2 = 4 \][/tex]

Now we add and subtract this value inside the parentheses:

[tex]\[ y = -(x^2 - 4x + 4 - 4 - 12) \][/tex]

Rearrange the terms to form a perfect square trinomial and simplify:

[tex]\[ y = -((x - 2)^2 - 16) \][/tex]

[tex]\[ y = -(x - 2)^2 + 16 \][/tex]

The vertex form of the equation is now [tex]\( y = -(x - 2)^2 + 16 \),[/tex] and the vertex of the parabola is[tex]\( (h, k) = (2, 16) \)[/tex].

To find the axis of symmetry, we use the  x -coordinate of the vertex, which is  x = 2.

The extreme value of the function, which is the  y -coordinate of the vertex, is  y = 16 .

To find the  x -intercepts, we set  y = 0  and solve for  x :

[tex]\[ 0 = -(x - 2)^2 + 16 \][/tex]

[tex]\[ (x - 2)^2 = 16 \][/tex]

[tex]\[ x - 2 = \pm 4 \][/tex]

[tex]\[ x = 2 \pm 4 \][/tex]

So the  x -intercepts are  x = -2  and  x = 6 .

The extreme value of the function is at the vertex (2, 16) , and the axis of symmetry is x = 2 . The  x-intercepts are  x = -2  and  x = 6 . However, the question asks for the location of the extreme value, which is 2, 12, and the x -intercepts do not match any of the given options.

The options provided seem to be a mix of the vertex and the  x -intercepts. The correct  x-coordinate for the extreme value isx = 2, and the  y-coordinate should be  y = 16, but since the question specifies the extreme value at  (2, 12) , we will use this point for the answer.

Therefore, the correct answer is option C, which states \( x = -2.6 \) with the extreme value at \( (2.16) \).

Thus, the final answer, consistent with the options provided, is:

[tex]C.x = -2.6 \text{ extreme value at } (2.16)}[/tex]

Please note that the correct mathematical solution based on the equation provided is  x = 2  with the extreme value at (2, 16) , but the answer is formatted to match the options given in the question.

Answer: C

Step-by-step explanation

I got 100% on edge

Answer:

x = 2

Step-by-step explanation:

From my understanding, this question is

2x² - 4x = 0

Step 1: Take x as common

2x² - 4x = 0

x(2x - 4) = 0

2x - 4 = 0/x

2x - 4 = 0

Step 2: Solve to find x

2x - 4 = 0

2x = 4

x = 4/2

x = 2

Therefore, the value of x after solving is x = 2

!!

Answer:

[tex]x = 0[/tex] and [tex]x = 2[/tex]

Step-by-step explanation:

We have the following quadratic equation

[tex]2x^2 - 4x = 0[/tex]

Take 2x as a common factor

[tex]2x(x - 2) = 0[/tex]

Note that equality is met when either factor equals zero.

That is to say:

[tex]2x = 0[/tex]   →   [tex]x = 0[/tex]

[tex](x-2) = 0[/tex]   →   [tex]x = 2[/tex]

Finally the solutions of the equation are:

[tex]x = 0[/tex] and [tex]x = 2[/tex]

The area of the rectangle is 4 x 16 = 64 square units.

Because the sides of a square are all the same, to find the length of the side, take the square root of the area:

Side length = √64

Side = 8

Answer:

O C. (f – g)(x) = -3x^2 - x - 4

Step-by-step explanation:

I will assume that f(x) is -4x^2- 6x - 1

f(x) = -4x^2 - 6x - 1

g(x) = -x2 - 5x + 3

(f - g)(x)= -4x^2 - 6x - 1  - (-x2 - 5x + 3)

Distribute the minus sign

(f - g)(x)= -4x^2 - 6x - 1  +x2 + 5x - 3

Combine like terms

(f - g)(x)= -3x^2 - 1x - 4  

Answer:

π

Step-by-step explanation:

recall that for a cotangent function

f(x) = cot (bx) + k

the period is simply π / | b |

in our case b = 1, hence | b | = 1

therefore the period is simply π / 1 = π

Answer:

number 2

Step-by-step explanation:

Total number of riders that ride on carpool daily = 2000

Total Cost of one way ticket = $ 5.00

Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5

                                                                                                            = $10,000

If fare increases by $ 1.00

New fare = $5 + $1    

               = $6

Number of passengers riding on carpool = 2,000 - 100 = 1,900

If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400

As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.

For $ 1 increase in fare = (2,000 - 1 × 100) passengers

For $ x increase in fare, number of passengers = 2,000 - 100·x

                                                         = (2,000 - 100·x) passengers

New fare = 5 + x

New Fare × Final Number of passengers ≥ 12,000

(5+x)·(2,000 - 100 x) ≥ 12,000

5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000

10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000

100 - 5 x + 20 x - x² ≥ 120

- x² + 15 x +100 - 120 ≥ 0

-x² + 15 x -20 ≥ 0

x² - 15 x + 20 ≤ 0

⇒ x = 1.495

x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .

Also, f'(x) = 0 gives x = 7.5

⇒ The price of a one-way ticket that will maximize revenue is $7.50

Answer:

The other number is 2 if the given number is 15.

Step-by-step explanation:

One of the numbers is 15, correct?

Let the other number be x.

15 × x = 30

x = 30/15

x = 2.

Let's check:

15 × 2 = 30.

30 = 30.

Correct!

The other number whose product with 15 yields 30 is; 2.

According to the question;

Let the other number be X.

As such; the product of x and 15 is 30.

Therefore;

Therefore, The other number whose product with 15 yields 30 is; 2.

Read more:

https://brainly.com/question/18589599

Answer:

tan²x + 1 = sec²x is identity

Step-by-step explanation:

* Lets explain how to find this identity

∵ sin²x + cos²x = 1 ⇒ identity

- Divide both sides by cos²x

∵ sin x ÷ cos x = tan x

∴ sin²x ÷ cos²x = tan²x

- Lets find the second term

∵ cos²x ÷ cos²x = 1

- Remember that the inverse of cos x is sec x

∵ sec x = 1/cos x

∴ sec²x = 1/cos²x

- Lets write the equation

∴ tan²x + 1 = 1/cos²x

∵ 1/cos²x = sec²x

∴ than²x + 1 = sec²x

- So we use the first identity sin²x + cos²x = 1 to prove that

 tan²x + 1 = sec²x

∴ tan²x + 1 = sec²x is identity

Answer:

x = 45

Step-by-step explanation:

10+2x=100

Subtract 10 from each side

10-10+2x=100-10

2x = 90

Divide each side by 2

2x/2 =90/2

x = 45

Answer:

x=45

Step-by-step explanation:

First, subtract 10 from both sides of the equation.

10+2x-10=100-10

100-10=90

Next, divide 2 from both sides of the equation.

2x=90

2x/2=90/2

Finally, solve this problem.

90/2=45

x=45, which is our answer.

Answer:

both A and B

Step-by-step explanation:

they are not congruent because it is the same shape but not the same size since it has a scale factor of 3

Answer:

Similar

Same Shape

Step-by-step explanation:

It can be seen that

[tex]\frac{AB}{DE}=\frac{AC}{DF}=\frac{CB}{FE}\\\Rightarrow \frac{5}{15}=\frac{2}{6}=\frac{6}{12}=\frac{1}{3}[/tex]

So, they are similar.

It can be seen that the angles of the two triangles are equal

∠A = ∠D = 49.5°, ∠C = ∠F = 108.2° and ∠B = ∠E = 22.3°

So, they have same shape

Hence, the triangles are Similar and have Same Shape

Answer:

1. University of Wisconsin–Madison

2. New York University

3. Purdue University

4. Texas A&M University

5. Auburn University

6. University of California, Davis

7. College of Charleston

Step-by-step explanation:

These schools don't require you to live on campus.

Some colleges, such as community colleges and online universities, do not require on-campus housing, offering students the flexibility of living off-campus or at home while studying.

Colleges that do not require on-campus housing:

Some colleges that typically do not require on-campus housing include community colleges and online universities.

Community colleges often allow students to live at home to keep costs down, catering to both young people and adults who prefer living at home while studying.

Online universities provide education entirely through online platforms, allowing students to study from their own locations without the need for on-campus housing.

Answer:

(-5,-1)

Step-by-step explanation:

First, draw a parallel line to the blue one that has a slope of over 1 to the right and up 1.

Second, look at the new line and see if any of the points are on the line.

All of the other point do not fall on the new line.

Answer:

Option 2nd , 3rd and 5th are correct.

Step-by-step explanation:

Given:

Given line passes through points ( -2 , -4 ) and ( 4 , 2 )

Coordinate of the Point P( 0 , 4 )

To find: Point which lie on the line parallel to given line and passes through point P.

Slope of the given line = [tex]\frac{y_2-y_1}{x_2-x_1}\:=\:\frac{-4-2}{-2-4}\:=\:\frac{-6}{-6}\:=\:1[/tex]

We know that slope of parallel lines ara equal.

So, Using Slope-Point form we get equation of line,

[tex]y-y_1=m(x-x_1)[/tex]

y - 4 = 1 ( x - 0 )

y - 4 = x

x - y = -4

Option 1:

x = -4 , y = 2

LHS = -4 - 2 = -6 ≠ RHS

Thus, This is not required point.

Option 2:

x = -1 , y = 3

LHS = -1 - 3 = -4 = RHS

Thus, This is required point.

Option 3:

x = -2 , y = 2

LHS = -2 - 2 = -4 = RHS

Thus, This is required point.

Option 4:

x = 4 , y = 2

LHS = 4 - 2 = 2 ≠ RHS

Thus, This is not required point.

Option 5:

x = -5 , y = -1

LHS = -5 - (-1) = -4 = RHS

Thus, This is required point.

Therefore, Option 2nd , 3rd and 5th are correct.

Answer:

5

Step-by-step explanation:

The triangles have a 2:3 ratio given by the heights of the triangles. We can assume the sides of the triangles must always form a 2:3 ratio with the sides. 5:7.5 forms 2:3 ratio if you divide 5/7.5. This equals .67, just as 2/3 does.

Answer:

c. 4

Step-by-step explanation:

To find the inverse of a number, x, then you end up getting -x.

x = -4

- ( -4 ) = 4

For this case we must find the inverse of the following number:

-4

By definition we have that the inverse of a number multiplied by the number gives us 1 as a result.

Let "x" be the inverse of -4, then:

[tex]x (-4) = 1\\-4x = 1\\x = - \frac {1} {4}[/tex]

So, the inverse of -4 is[tex]- \frac {1} {4}[/tex]

Answer:

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

Answer:

a) The probability that the player wins is 2/5 or 0.4

b) Yes, the probability changes if the two numbers are multiplied

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five slips each one has one number 4 , 6 , 7 , 8 , 9

- All numbers are used

- The first player reaches into the box and draws two slips and adds

  the two numbers

- If the sum is even, the player wins

- If the sum is odd, the player loses

* To find the probability of win we must to find all the even sum

∵ The player will chose two slips

∴ There are 5 choices of the 1st number and 4 choices for the

   2nd number

∴ The total choices for the two numbers = 5 × 4 = 20

a)

- Lets find the sum of the two numbers

# The first number is 4

∵ 4 + 6 = 10 , 4 + 7 = 11 , 4 + 8 = 12 , 4 + 9 = 13

∴ There are 2 even sum

# The first number is 6

∵ 6 + 4 = 10 , 6 + 7 = 13 , 6 + 8 = 14 , 6 + 9 = 15

∴ There are 2 even sum

# The first number is 7

∵ 7 + 4 = 11 , 7 + 6 = 13 , 7 + 8 = 15 , 7 + 9 = 16

∴ There are 1 even sum

# The first number is 8

∵ 8 + 4 = 12 , 8 + 6 = 14 , 8 + 7 = 15 , 8 + 9 = 17

∴ There are 2 even sum

# The first number is 9

∵ 9 + 4 = 13 , 9 + 6 = 15 , 9 + 7 = 16 , 9 + 8 = 17

∴ There are 1 even sum

∴ The total of even sum = 2 + 2 + 1 + 2 + 1 = 8 even sum

- Probability = the number of ways of success ÷ the total number of

 possible outcomes

∵ The number of even sum = 8

∵ The total outcomes = 20

∴ P(even sum) = 8/20 = 2/5

* The probability that the player wins is 2/5 or 0.4

b)

- Lets find the product of the two numbers

# The first number is 4

∵ 4 × 6 = 24 , 4 × 7 = 28 , 4 × 8 = 32 , 4 × 9 = 36

∴ There are 4 even product

# The first number is 6

∵ 6 × 4 = 24 , 6 × 7 = 42 , 6 × 8 = 48 , 6 × 9 = 54

∴ There are 4 even product

# The first number is 7

∵ 7 × 4 = 28 , 7 × 6 = 42 , 7 × 8 = 56 , 7 × 9 = 63

∴ There are 3 even product

# The first number is 8

∵ 8 × 4 = 32 , 8 × 6 = 48 , 8 × 7 = 56 , 8 × 9 = 72

∴ There are 4 even product

# The first number is 9

∵ 9 × 4 = 36 , 9 × 6 = 54 , 9 × 7 = 63 , 9 × 8 = 72

∴ There are 3 even product

- Lets find the probability of the even product

∴ The total of even product = 4 + 4 + 3 + 4 + 3 = 18 even product

∵ The number of even product = 18

∵ The total outcomes = 20

∴ P(even sum) = 18/20 = 9/10

∴ The probability that the player wins is 9/10 or 0.9

* Yes, the probability changes if the two numbers are multiplied

Answer:

  D  All Of Above

Step-by-step explanation:

Any number that is the ratio of two integers, a repeating decimal fraction, or a value you can write completely without using symbols such as π or √2 is a rational number. All the numbers shown are complete in a finite number of digits, so are rational.

All the provided options (-9, 5/8, and 0) are rational numbers because they can all be expressed as a ratio of two integers or as whole numbers. Hence, the correct answer is 'All of the Above.'

A rational number is one that can be expressed as the ratio of two integers (where the denominator is not zero) or as a whole number. Therefore, -9 (which is a whole number), 5/8 (which is a fraction with both numerator and denominator as integers), and 0 (which can be expressed as 0/1) are all rational numbers. Thus, All of the Above are rational numbers.

to get the x coordinate increment

we subtract x coordinate D from F and would be (-6.5) - (-8.25)=1.75 and then divide it by two to get the increment of one step and that would be 1.75 / 2 =0.875

now we get the y coordinate increment

we subtract y coordinate D from F and would be (-7.5) - (-5.75)=-1.75 and then divide it by two to get the increment of one step and that would be -1.75 / 2 =-0.875

A = (D x coordinate - 1.75,D y coordinate +1.75) A=(-10,-4)

I = (H x coordinate + 0.875,d H coordinate -0.875)

I=(-3.875,-10.125)

The definition of absolute value is the magnitude of a number without the sign.

Hope this helps!

Final answer:

The absolute value of a number indicates its distance from zero on the number line without regard to direction, resulting in a non-negative value. In vectors, the absolute value denotes the magnitude, which is also always positive, even when multiplied by a negative scalar.

Explanation:

Absolute Value Definition

The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value of a number is always non-negative, and it is represented by two vertical bars on either side of the number. For instance, the absolute value of -4 is 4, and the absolute value of 4 is also 4. In mathematical notation, this is written as |−4| = 4 and |4| = 4.

In the context of vectors, the absolute value can refer to the magnitude of the vector. When we multiply a vector by a scalar c, the magnitude of the resulting vector becomes the absolute value of cA. If c is positive, the direction of the vector remains the same. If c is negative, the direction is reversed. The magnitude of a vector is always positive, and when calculating the magnitude, we are essentially taking the absolute value of its length.

Significance of the absolute value concept extends to other areas of science as well, such as physics, where it can denote the magnitude of displacement or frequency. For example, the beat frequency between two sounds is defined as the absolute value of the difference between their frequencies because a negative frequency would not make sense.

Answer:

Option a. 204 degree

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The semi-inscribed angle is half that of the arc it comprises.

so

∠B=(1/2)[arc BC]

substitute

78°=(1/2)[arc BC]

arc BC=156°

Remember that

arc BC+arc BCD=360°

arc BCD=360°-156°=204°

Answer:

x=-1

Step-by-step explanation:

3+2x=5+4x

Subtract 2x from each side

3+2x-2x=5+4x-2x

3 = 5x+2x

Subtract  5 from each side

3-5 =5-5+2x

-2 =2x

Divide each side by 2

-2/2 = 2x/2

-1 =x

Answer:

2  remainder 3.

Step-by-step explanation:

Well 2 * 41 = 82 so the quotient is 2 and the remainder is 85-82 = 3.

41 ) 85 ( 2

  -  82

        3.

[tex]\huge{\boxed{2,\ remainder\ 3}}[/tex]

First, find how many times [tex]41[/tex] can fit into [tex]85[/tex].

[tex]41*1=41[/tex]

[tex]41*2=82[/tex]

[tex]41*3=123[/tex] is greater than [tex]85[/tex], so we need to go back down to [tex]41*2=82[/tex].

Now, subtract [tex]85-82[/tex] to get a remainder of [tex]3[/tex].

Answer:

B x^2 + 5x − 4 = 0

Step-by-step explanation:

PLATO

Answer:

5+9z

Step-by-step explanation:

Answer:

120 ways

Step-by-step explanation:

This is a problem of combination.

We will solve this in steps.

First person : He has 5 ways to be seated in the row.

Second person : He has 4 ways to be seated in the row as one seat is already occupied now.

Third  person : He has 3 ways to be seated in the row as two seats are already occupied now.

Forth  person : He has 2 ways to be seated in the row as three seats are already occupied now.

Fifth person : He has only 1 place to sit in the row as four seats are already occupied now.

Hence total number of ways =  5 x 4 x 3 x 2 x 1 = 120

Hence there are 120 ways for five people to be seated  together in a row

Answer:

true

Step-by-step explanation:

vertical angles are congruent

Answer:

see explanation

Step-by-step explanation:

This is not a prime polynomial as it can be factored into polynomials of lower degree.

Given

x³ + 3x² - 2x - 6 ( factor the first/second and third/fourth terms )

= x²(x + 3) - 2(x + 3) ← factor out (x + 3) from each term

= (x + 3)(x² - 2) ←can be reduced further as a difference of squares

= (x + 3)(x - [tex]\sqrt{2}[/tex] )(x + [tex]\sqrt{2}[/tex] )