long division x^3 - 6x^2 + 13x -12 over x - 3

22 = 9x + 4 -3x

22 - 4 = -3x + 9x

18 = 6x

x = 18 : 6

x = 3

Answer:

[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]

Step-by-step explanation:

We are given that an expression

[tex]x^4+10x^2+25[/tex]

We have to find the factorize the expression completely over the cmplex number.

[tex](x^2+5)^2[/tex]

Using identity [tex](a+b)^2=a^2+b^2+2ab[/tex]

[tex](x^2+5)(x^2+5)[/tex]

Substitute each factor equal to zero.

[tex]x^2+5=0[/tex] ,[tex]x^2+5=0[/tex]

[tex]x^2=-5[/tex]

[tex]x=\pm \sqrt{-5}=\pm i \sqrt 5[/tex]

[tex]x=i\sqrt 5[/tex] and [tex]x=-i\sqrt 5[/tex]

[tex]x-i\sqrt 5=0[/tex] and [tex]x+i\sqrt 5=0[/tex]

The factor of second term is also same

Therefore, the factors of the   expression completely is given by

[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]

The solution to the quadratic equation is ±5i

Given the expression below:

x^4+10x^2+25 = 0

Let P = x^2

Substituting into the expression, we will have;

P^2 + 10P + 25 = 0

Factorizing the expression, we will have:

P^2 + 10P + 25 = 0

P^2 + 5P+ 5P + 25 = 0

P(P+5) + 5(P + 5) = 0

(P+5)(P+5) = 0

P = - 5 twice

Substitute into the given substitute

x^2 = -5

x = √-5

x = ±5i

Hence the solution to the quadratic equation is ±5i

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When the product of two numbers is 40 and one of the numbers is 8/15, the other number can be found by dividing 40 by 8/15, which is 937.5.

The question is asking for the other number when the product of two numbers is 40 and one of the numbers is given as 8/15. To answer this, we need to use the concept that the product of two numbers is equal to one number multiplied by the other. Therefore, to find the missing number, we need to divide 40 (the product) by the given number (8/15).

So, the calculation will look like this: 40 ÷ (8/15) = 7500/8 = 937.5.

Thus, the other number is 937.5 .

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Answer: The angle of depression is 51.34°.

Step-by-step explanation:

1. You can make the diagram shown in the figure attached. Where [tex]A[/tex] is the point where the clue is and [tex]B[/tex] is the point where Tyler is.

2. To calculate the angle of depression, which is identified in the diagram as [tex]\alpha[/tex], you can use [tex]tan^{-1}[/tex], as following:

[tex]tan^{-1}(\alpha)=\frac{3.5}{2.8}[/tex]

3. Then, you obtain the following angle of depression from the clue to the point where Tyler is:

[tex]\alpha=51.34[/tex]°

60 times 0.14 = 8.4

You would give $8.40 as a tip of 14% from a bill of $60

Final answer:

To calculate a 14% tip on a $60 bill, you multiply 0.14 by $60, resulting in a tip of $8.40.

Explanation:

To find out how much a 14% tip is on a $60 bill, we need to convert the percentage into a decimal by dividing by 100.

This gives us 0.14 as the decimal form of 14%.

We then multiply this decimal by the total bill amount to calculate the tip: 0.14 × $60 = $8.40

Therefore, the tip would be $8.40.

we know that

distributive property of multiplication over addition:

[tex]a \times (b+c)=a \times b + a \times c[/tex]

now, we will verify each options

option-A:

4 × (7 + 6) = (4 × 7) + 6

We can see that right side does not match with property

so, this is FALSE

option-B:

4 × (7 + 6) = (4 × 7) + (4 × 6)

We can see that both sides match with property

so, this is TRUE

option-C:

4 × (7 + 6) = (4 + 7) × (4 + 6)

We can see that right side does not match with property

so, this is FALSE

Answer:

hey the correct answer is C.

Have a great day!

Area of Parallelogram ABCD is equivalent to the area of rectangle AXBY.

Area of rectangle AXBY= Length AX * Length AB= 3 ft * 4√2 ft = 12√2 sq.ft.

Thus Area of Parallelogram is 12√2 sq.ft.

Hello...

Students - 30

Boys - 13

Girls - ?

30 - 13 = 17

There are 17 girls!

Percentage:

17 / 30 = 0.56666666667...

= 56.6...

Answer:

56% are girls

44% are boys

56.66% is the percentage of the class are girls.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

Total students= 30

Number of boys= 13

Number of girls = 30- 13 = 17

So, percentage of the class are girls

= 17 /30 x 100

= 0.56666x 100

= 56.66%

Hence, 56.66% is the percentage of the class are girls.

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Answer:

9x^2 − 42xy + 49y^2

Step-by-step explanation:

The product of [tex](3x + 7y)^2[/tex] is: D)[tex]9x^2 + 42xy + 49y^2[/tex]

The product of (3x + 7y)^2 can be found using the formula for squaring a binomial:

(3x + 7y)^2 = (3x + 7y)(3x + 7y)

To calculate this product, you can use the distributive property (FOIL method):

(3x + 7y)(3x + 7y) = (3x * 3x) + (3x * 7y) + (7y * 3x) + (7y * 7y)

Now, simplify each term:

(9x^2) + (21xy) + (21xy) + (49y^2)

Combine like terms:

9x^2 + 42xy + 49y^2

So, the product of [tex](3x + 7y)^2[/tex] is:

D)[tex]9x^2 + 42xy + 49y^2[/tex]

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A) If a figure has ten vertices, then it is a star. This is the correct conditional statement.

Conditional statement can be simplified as : if a, then b. Here 'a' is one condition and 'b' is second condition. So, based on this, option A is correct.

Answer:

The correct option is D.

Step-by-step explanation:

The given statement is "Stars have ten vertices".

If a complete statement has two sub statements p and q, then the conditional statement is "If p, then q", where p is a hypothesis and q is a conclusion.

In the given statement,

p = A figure is a star.

q = It has ten vertices

So, the conditional statement of the given statement is

If a figure is a star, then it has ten vertices.

Therefore the correct option is D.

Answer:

0

4z^5

Step-by-step explanation:

We are asked to

Simplify m - {n - [p + (m + n - p)]}.

For that we remove first internal bracket and then next in the same order.

= m - {n - [p + m + n - p]}. (by removing the inner bracket)

Now we simplify the term inside by cancelling p

=  m - {n - [ m + n ]}.  Next is multiply by - the term m+n.

= m-[n-m-n].  Now n cancels out.

=m-(m) = 0

Finally we get 0 as answer.

0

2m

-2m + 2p

2.Select the correct difference.

-3z^ 5 - (-7z^ 5)

= 3z^5+7z^5

= 4z^5

Answer:

Quotient = x^4 + x^3 + x^2 + x + 1

Remainder = 0

Step-by-step explanation:

(x^5 +1) is divided by (x - 1) as shown below:

(x^5 +1) / (x - 1)

where x^5 is divided by (x - 1) when multiplied by x^4 (quotient) to give x^4 - 1.

Now x^4 - 1 is divided by is divided by (x - 1) when multiplied by x^3 (quotient) to give x^3 - 1.

Then again x^3 - 1 is divided by (x - 1) when multiplied with x^2 (quotient) to give x^2 -1.

x^2 - 1 is divided by (x - 1) when multiplied by x to give (x - 1).

Lastly, (x - 1) is divided by (x - 1) when multiplied by 1 to cancel the terms with remainder 0.

answer will be equal to 3250 divided by 250 which is 13

Answer:

The ratio of dogs to animals  [tex]\frac{9}{16}[/tex].

Step-by-step explanation:

If the shelter captures 9 dogs they also catch 7 cats.

So,

the total number of Animals = Total number of Dogs + Total number of Cats

                                                = [tex]9+7[/tex]

                                                 =[tex]16[/tex]

Therefore,

The ratio of dogs to animals    = Number of Dogs / Total number of animals

                                                   = [tex]\frac{9}{16}[/tex]

7/16

7 is dog 9 is cat

7+9=16

Directrix:

If the vertex of the parabola is at (0, 0) and the focus is (0, -4) which is 4 units down then the directrix will be the line 4 units UP.

Answer: y = 4

Equation of parabola:

[tex]y = \frac{1}{4p}x^{2}[/tex]  ; where p is the distance from the vertex to the focus.

As stated above, the focus is 4 units down, so p = -4

[tex]y = \frac{1}{4(-4)}x^{2}[/tex]

[tex]y = \frac{1}{-16}x^{2}[/tex]

Answer: [tex]y = -\frac{1}{16}x^{2}[/tex]

Given condition is: Sam took out an 80/20 mortgage on a $205,000 home.

Here, 80/20 refers to 80% mortgage amount means it will be paid as mortgage and 20% loan amount.

So, to find the amount financed under the first mortgage, we will find 80% of 205000.

[tex]\frac{80}{100}\times205000[/tex]

= $164000

Hence, option A is the correct answer.

c : evaluate using order of operations ( pemdas )

Option: C is the correct answer.

 C-   Evaluate using order of operations

We know that while solving a algebraic expression we must follow the rule:

                       PEMDAS

whose full form is:

  Parenthesis , Exponents,Multiplication division addition and subtraction.

This means that parenthesis is to be solved first then the preference is given to the exponent, then division and multiplication are treated at the same level and the last preferred operation is addition and subtraction.

     Hence, the correct answer is:

          Option: C

The zero of a function is the x-value where the function crosses the x-axis. With a graph, it is easier often to just look at where the function crosses the x-axis instead of calculating it mathematically.

Answer:

7

Step-by-step explanation:

Given that there are 5 number cards.

They are 2,5,7,8,9

Total of all numbers in the cards = 2+5+7+8+9= 31

One card is removed say with number x.

Now sum new would be =31-x   ..  i

Average of remaining 4 cards = 6

So sum of remaining 4 cards = 6(4) = 24 ... ii

i and ii represent the sum of remaining 4 cards. Hence they should be equal

31-x =24

Subtract 31 from both sides to get

-x=-7

Or x =7

Given that there are 5 number cards.

They are 2,5,7,8,9

Total of all numbers in the cards = 2+5+7+8+9= 31

One card is removed say with number x.

Now sum new would be =31-x

Average of remaining 4 cards = 6

So sum of remaining 4 cards = 6(4) = 24

represent the sum of remaining 4 cards. Hence they should be equal

31-x =24

Subtract 31 from both sides to get

card 7

Suppose you have two lines, and consider the system of their equations:

[tex] \begin{cases} y = mx+q\\y=m'x+q'\end{cases} [/tex]

Suppose that a certain point [tex] (x,y) [/tex] belongs to the first line. This means that his x and y coordinates follow the rule [tex] y=mx+q [/tex]. Similarly, if another point [tex] (x',y') [/tex] belongs to the second line, his x and y coordinates follow the rule [tex] y'=m'x'+q' [/tex].

A system is solved by the points that satisfy both equations simultaneously. But satisfying an equation means to belong to the graph that the equation represents.

So, the solution to the system is the point that belongs to both lines, i.e. that satisfies both equations.

Answer:

The metric system is based on the number 10.

Step-by-step explanation:

We have been given an incomplete statement. We are asked to fill in the blank for given statement.

The metric system is based on the number ___.

We know that metric system is an alternative system of measurement used in most countries including the United States. This system includes prefixes like kilo-, hecto-, deka-, deci-, centi-, and milli.

The metric system is based on number 10 as all these units are based on power of 10.

Therefore, option C is the correct choice.

The metric system is based on the number 10.

Here, we have,

The metric system is a decimal-based system of measurement that is widely used around the world. It is designed to be a coherent and consistent system, with units of measurement that are related to each other by powers of 10.

In the metric system, there is a base unit for each quantity being measured, such as meters for length, grams for mass, and liters for volume. The prefixes are then used to indicate multiples or fractions of the base unit. These prefixes are based on powers of 10, which allows for easy conversions between different units within the system.

For example, when we go from a larger unit to a smaller unit within the same measurement category, we move the decimal point to the right by powers of 10. Likewise, when we go from a smaller unit to a larger unit, we move the decimal point to the left by powers of 10.

This decimal-based nature of the metric system makes it highly convenient for scientific and everyday use, as it simplifies calculations and conversions.

The metric system is based on number 10 as all these units are based on power of 10.

Therefore, option C is the correct choice.

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Answer:

A. Because it pass the vertical line test.

Step-by-step explanation:

Let us first understand the Vertical Line test. In this test , we draw few random vertical lines on graph and check whether any one or more than one line intersect the graph, no matter once or more. If there exists a line which intersects the graph , we say graph passes the vertical line test.

Hence this graph passes vertical line test because there are many vertical lines which intersect it.

Answer:

A.Yes, because it passes the vertical line test

Step-by-step explanation:

Answer:

it is a neg slope

Step-by-step explanation:

(1)

(f+g)(x) = 6x^2+2x-7+4x-3=6x^2+6x-10

(f-g)(x)=6x^2+2x-7-4x+3 = 6x^2-2x-4

(2)

(f+g)(x)=2x-3x+1-2x=-3x+1

(f-g)(x)=2x-3x-1+2x=x-1