Simply the expression by combining the like terms:
-6j + 4 + 2j - 1

Answer:

k = -12.6

Step-by-step explanation:

Given rational polynomial:

[tex]\dfrac{x^3-2x^2+kx-12}{x-5}[/tex]

When we divide a polynomial f(x) by (x − d) the remainder is f(d).

If the remainder is zero, then (x - d) must be a factor of f(x).

If a cubic polynomial is divided by (x - d) then:

[tex]\implies (x-d)(ax^2+bx+c)[/tex]

where:

If the constant of the cubic polynomial is -12 and d = 5:

[tex]\implies -cd=-12[/tex]

[tex]\implies -5c=-12[/tex]

[tex]\implies c=2.4[/tex]

The leading coefficient of the cubic polynomial is one.  Therefore:

[tex]\implies (x-5)(x^2+bx+2.4)[/tex]

Expand and collect like terms:

[tex]\implies x^3+bx^2+2.4x-5x^2-5bx-12[/tex]

[tex]\implies x^3+(b-5)x^2+(2.4-5b)x-12[/tex]

The find the value of b, compare the coefficients of the term in x²:

[tex]\implies b-5=-2[/tex]

[tex]\implies b=3[/tex]

To find k, substitute the found value of b into the coefficient of x:

[tex]\implies k=2.4-5b[/tex]

[tex]\implies k=2.4-5(3)[/tex]

[tex]\implies k=-12.6[/tex]

Answer:

–12.6

Step-by-step explanation:

[tex] \frac{ \\ {x }^{3} - {2x}^{2} + kx - 12}{x - 5} = 0[/tex]

that means (x–5) is a factor of x³ – 2x² +kx – 12

since it resulted to zero according to the rules of zeros of polynomial.

x–5 = 0

x = 5

by substituting

f(x) = 5³ – 2(5)² + k(5) – 12 = 0

125 – 50 + 5k – 12 = 0

75 + 5k – 12 = 0

5k + 75 – 12 = 0

5k + 63 = 0

5k = –63

[tex] \frac{ \\ 5k}{5} = \frac{ - 63}{5} [/tex]

[tex]k = - 12.6 \: or \: - 12 \frac{3}{5} [/tex]

I hope I helped

Answer:

10

Step-by-step explanation:

10 is 10 units away from 0 on a number line

-9 is only 9 units away from 0 on a number line

The farthest away from 0 would be 10

Answer:The ratio 15:73 represents the ratio of 7th grade football players to total athletes.

Step-by-step explanation:

Answer: 20

Step-by-step explanation: Since it is 1/5 you multiply the 5 by 4 and get 20.

Answer:

20

Step-by-step explanation:

It is 20 because you have to multiply the denominator by the whole number.

Factors of  [tex]$$4(x-y)^3-x+y$$[/tex] are [tex]4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y[/tex] and [tex]$16 x^{16}-1$[/tex], respectively, are [tex]\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex].

Let's incrementally simplify.

[tex]$$4(x-y)^3-x+y$$[/tex]

Distribute:

[tex]$$=4 x^3+-12 x^2 y+12 x y^2+-4 y^3+-x+y$$$=4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y$[/tex]

Factor [tex]$16 x^{16}-1$[/tex]

[tex]$$\begin{aligned}& 16 x^{16}-1 \\& =\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex]

When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. Each check takes longer on average due to the larger size of our product and the larger size of the numbers we use to verify it.

To learn more about factorization refer to :

https://brainly.com/question/25829061

#SPJ1

47.925 can be written as a mixed number as 47(925/1000).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

47.925

This can be written as,

= 47925 / 1000

Now,

47925 = 47000 + 925

1000 x 47 = 47000

So,

47925/1000

= 47(925/1000)

Thus,

The mixed number is 47(925/1000)

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The combinations between the linear function g(x) = 4 · x + 1 and the quadratic function g(x) = 4 · x + 1 are f ° g (x) = 16 · x² + 44 · x + 10 and g ° f (x) = 4 · x² + 36 · x + 1, respectively.

Let be f(x) and g(x) a linear function and a quadratic function, respectively. The composition between two functions is represented below:

f ° g (x) = f [g(x)]

g ° f (x) = g [f(x)]

Where the input of the former function is substituted by the latter function. Now we proceed to find the resulting function:

f(x) = x² + 9 · x

g(x) = 4 · x + 1

f ° g (x) = (4 · x + 1)² + 9 · (4 · x + 1)

f ° g (x) = 16 · x² + 8 · x + 1 + 36 · x + 9

f ° g (x) = 16 · x² + 44 · x + 10

g ° f (x) = 4 · (x² + 9 · x) + 1

g ° f (x) = 4 · x² + 36 · x + 1

To learn more on composition of functions: https://brainly.com/question/29127818

#SPJ1

Answer: a. To find the age of a shark that is 200 centimeters long, we can set the function equal to 200 and solve for t:

L = 266 - 219e^(-0.05t)

200 = 266 - 219e^(-0.05t)

Solving this equation for t, we get t ≈ 2.11 years.

b. To find the length of a shark that is twice as old as the shark in part (a), we can substitute 2.11*2= 4.22 for t into the function:

L = 266 - 219e^(-0.05(4.22))

This will give us the length of the shark that is twice as old as the shark in part (a) in centimeters.

Answer:

≈51.55

Step-by-step explanation:

∆/360 πD = 7.2

x/360 *22/7*16= 7.2

x/360 *50/2/7= 7.2

x/360 = 63/440

x =51.54545455

≈51.55

f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

m (x-x1) = y-y1 or

y = mx + c

Where,

Straight-line gradient, or m, is the line's slope.

The Cartesian coordinate that the line crosses is x1, y1.

the constant c

The calculation of the gradient (m) between any two locations on a line

m = Δy / Δx

f (-1) = Because x = -1, the function used is

y = 2, so f (-1) = 2 C) f (-3) = Because -3 -1,

the function used is y = -x-4, so f (-3) = - (- 3) -4 f (-3) = 3-4 f (-3) = -1 f (3) Since the function employed is

= -2x + 11 and x = 3, f (3) = -2 (3) +11, f (3) = -6 + 11, and f (3) = 5.

Hence, f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.

learn more about straight-line equations click here:

https://brainly.com/question/25969846

#SPJ1

Answer:-1
2
5

Step-by-step explanation:

simple answer

The required vertex form of the given equation is y = x² - 4x  + 7.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
y = (x - 2)² + 3

Simplifying the expression,
y = x² -4x + 4 + 3   {since (a - b)² = a² + b² -2ab}

y = x² - 4x  + 7

Thus, the required vertex form of the given equation is y = x² - 4x  + 7.

Learn more about equations here:

brainly.com/question/10413253

#SPJ1

Answer:

33.33%

Step-by-step explanation:

You start with 36 eggs, and 24 are removed and fried. This means that the remaining eggs are the difference of 36 and 24:

36 - 24 = 12

There are 12 eggs left! To find the percentage of remaining eggs, write a ratio comparing the number of eggs that remain to the original amount of eggs:

[tex]\frac{12}{36}[/tex]

Now, simplify the fraction into a decimal:

12 ÷ 36 = 0.3333...

Multiply a decimal by 100 to convert it to a percentage:

0.3333... ⋅ 100 = 33.33...%

Rounded to the nearest hundredth, the percent of remaining eggs is 33.33%

The length of other side is 20.8 in the given triangle.

What is a triangle ?

triangle can be defined in which it consists of three sides and three angles and sum of all the angles is always 180 degrees .

Given in the triangle ,

AC = 27 cm

AB = 9 cm

CAB = 74 degrees

a2 = b2 + c2 – 2bc cos ∠x

a2 = 27*27 + 9*9 - 2*27*9*cos74

a2 = 529 + 81 - 486*0.27

a2 = 610-486*0.27

a2 = 610-131.22

a2 = 479

a= [tex]\sqrt{479}[/tex]

a = 20.8  (approximately)

Hence the length of other side is 20.8 in the given triangle.

To learn more about triangle from the given link.

https://brainly.com/question/2773823

#SPJ1

Answer: x=-1,y=4

Step-by-step explanation:

x + y = 3

y = x + 5

subtract x from both sides of the equation so you get

x + y = 3

-x + y = 5

use the elimination method and you'll get

2y = 8

simplify and

y = 4

now use that to get x

x + 4 = 3

x = -1

Therefore, the answer is

x = -1, y = 4

Answer:

x=-1, y=4. (-1, 4).

Step-by-step explanation:

x+y=3

y=x+5

----------

x+(x+5)=3

x+x+5=3

2x+5=3

2x=3-5

2x=-2

x=-2/2

x=-1

y=-1+5=4

Answer:

To graph the equation y = 1/2x - 4, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

In this equation, the slope is 1/2, and the y-intercept is -4. The slope represents the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis.

To graph the equation:

Plot the y-intercept, which is (-0, -4)

Using the slope, we can pick a second point on the line. The slope of 1/2 tells us that for every 2 units in the x direction, we will move 1 unit in the y direction. So we can pick a point that is 2 units to the right of the y-intercept, such as (2,0).

Connect the two points to get a straight line

The resulting graph will be a straight line that passes through the point (-0, -4) and (2, 0) and continues in both directions.

Alternatively, you can use a table of values to plot the points that belongs to the line and connect them, for example:

x | y

-2 | -5

-1 | -4.5

0 | -4

1 | -3.5

2 | -3

These are few points on the graph and with more points you can connect them and see the shape of the graph.

Step-by-step explanation:

Answer: To calculate the balance of the savings plan after 9 months with an APR of 3% and monthly payments of $200, we need to take into account the interest earned on the account.

First, we will calculate the interest earned by multiplying the principal (initial amount) by the interest rate (APR) and the number of months.

Interest = Principal * Interest Rate * Number of months

Interest = 200 * 0.03 * 9 = 54

Then, we will add the interest earned to the total amount of payments made.

Total = Principal + Interest + Payments

Total = 200 + 54 + (200 * 9) = 200 + 54 + 1800 = 2054

So the savings plan balance after 9 months with an APR of 3% and monthly payments of $200 is $2054.

Step-by-step explanation:

Question 1

[tex]11+2x+29=x+28 \\ \\ 2x+40=x+28 \\ \\ x+40=28 \\ \\ x=-12[/tex]

Question 2

A, B, E

34x56x79447886447567

The equivalent exponential equations are given as follows:

[tex]2^{4x} = 2^{3(x - 3)}[/tex]

The exponential expression for this problem is defined as follows:

[tex]2^{4x} = 8^{x - 3}[/tex]

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

[tex]8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}[/tex]

Meaning that the correct option is given by the fourth option.

More can be learned about the power of a power property at brainly.com/question/11975096

#SPJ1

Answer:

False

Step-by-step explanation:

A two-tailed test requires that the null hypothesis use the equal (=) sign. Rejection of the null can happen in either direction. (Ex. a test statistic that i either too high, or too low). Anything other than equal (Ex. the null hypothesis is either, "greater than or equal to", or, "less than or equal to"), indicates a one-tailed test.

C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span{u,v} is correct.

To show that a vector b is in Span{u,v}, one way is to determine if it can be written as a linear combination of the vectors in the set, i.e., if there exist scalars h and k such that b = hu + kv. If this is the case, the system containing the equations hu + kv = b is consistent, meaning that there exist values of h and k that make the equation true. Therefore, if the system is consistent, it can be concluded that the vector b is in Span{u,v}.

Therefore, option C is the correct answer.

To learn more about Consistency of a System

visit; brainly.com/question/29127526

#SPJ4

Answer: 5

Step-by-step explanation: To solve f(x), g(x), or f(g(x)) problems, we place the value of x in the functions with the value that we are given. This value will be f(g(5)) or g(3) or f(27). We plug in the number in the parentheses.

In this problem, we have to first plugin 5 to g(x) then plug g(5) into f(x).

First, we do g(5)=sqrt((5^2)+2). This gives us 3. Then we plug in 3 which is g(5) into f(x). This gives us f(g(5)) or f(3)=sqrt((3^3)-2) which is 5.

The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7). An equation is a proposition that has two equal sides as well as an equal sign .

what is equation ?

It is thought that a number's simplest form is represented by its smallest equivalent fraction. finding the simplest form: what to do. For shared factors, look into the numerator and denominator. Examine a fractional integer to determine if it is a prime number. An equation is a proposition that has two equal sides as well as an equal sign in the middle. In the general form of any equation, the degrees of all the variables are listed in descending order. The common representation of a system of equations is an x + b = 0. x + b y + c = 0 is the general form of a two-variable linear equation (or something similar). Identity or conditional equations are the two categories under which equations fall. An identity holds true regardless of how the variables are valued.

given

Equation substitution is another name for combining the equations. When one variable is added to another equation, this is done.

-8x - 5y = -13

-4x - 5y = 11

Let's make the second equation a one-variable-on-each-side equation.

-5y = 4x + 11

y = -4/5x - 11/5

Put this into your first equation right now.

-8x - 5(-4/5x - 11/5) = -13

Give out the -5 symbol.

-8x + 4x + 11 = -13

Stack similar phrases.

-4x + 11 = -13

-4x = -24

Divide both sides by -4 to isolate x.

x = -24/-4

x = 6

Reintroduce this to either equation now.

y = -4/5(6) - 11/5

Multiply.

y = -24/5 - 11/5

Subtract.

y = -35/5

Simplify.

y = -7

The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7).

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

P = 5x + 33 = 58

Q = R = 3x+46 = 61

Step-by-step explanation:

angles in a triangle add up to 180 degrees

the angles in an isosceles triangle that correspond to the two congruent sides (are opposite the sides) are also congruent

that means that angle R = angle Q because QP and RP are congruent

angles = 5x+33, 3x+46, 3x+46

5x+33 + 3x+ 46 + 3x+46 = 180

11x + 125 = 180

subtract 125 from both sides to isolate the x and its coefficient

11x = 55

divide both sides by 11 to find x

x = 5

P = 5x + 33 = 58

Q = R = 3x+46 = 61

Answer:

3 - 1

12 - 4

21 - 7

Step-by-step explanation:

Answer:

youd start and see that you can divide 12/3 this gives you 4 you then divide 4/4 and find 1 so he can do 3 lawns in 1 hour thus you just mutiplltiply each side by 7 so it'd be 21 and 7

Step-by-step explanation:

should look like this

3          1

12         4

21         7

Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.

In math, a % is a number or ratio that is expressed as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," and "pc." However, the percent sign "%" is frequently used to indicate it. The percentages' total quantity has no dimensions. Percentages are fundamentally fractions when the denominator is 100. Put a percent sign (%) next to a number to indicate that it is a percentage. For instance, if you successfully answer 75 out of 100 questions on a test (75/100), you get a 75%. Divide the money by the total to get percentages, then multiply the resulting number by 100. The formula (value/total) x 100% is used to calculate the percentage.

given

Francis purchases 450 plastic forks and

utilizes 315 of them, for

a percentage of 315/450*100

= 70%.

Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1