1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a? 2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)? 3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g? 4. If f(x) is a polynomial, is f(x^2) also a polynomial 5. Consider the polynomial function g(x) = x^4-3x^2+9 a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial

Answer:

Step-by-step explanation:

6x - y = 3

4x + 3y = 1

Solve the equation for y

y = -3 + 6x

4x + 3y = 1

Substitute the given value of y into the equation

4x + 3y = 1

plug the value

[tex]4x + 3( - 3 + 6x) = 1[/tex]

Distribute 3 through the parentheses

[tex]4x - 9 + 18x = 1[/tex]

Collect like terms

[tex]22x - 9 = 1[/tex]

Move constant to R.H.S and change its sign

[tex]22x = 1 + 9[/tex]

Calculate the sum

[tex]22x = 10[/tex]

Divide both sides of the equation by 22

[tex] \frac{22x}{22} = \frac{10}{22} [/tex]

Calculate

[tex]x = \frac{5}{11} [/tex]

Now, substitute the given value of x into the equation

y = -3 + 6x

[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]

Solve the equation for y

[tex]y = - \frac{3}{11} [/tex]

The possible solution of the system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equations

[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]

[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]

Simplify the equalities

[tex] 3 = 3[/tex]

[tex]1 = 1[/tex]

Since all of the equalities are true , the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

Answer: not enough data shown to proceed with this question

Step-by-step explanation:

Answer:

x=3.9 or 39/10 and   y=3.13333 or 47/15

Step-by-step explanation:

Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:

       6x-3y=14 and 3-2x+6y=14

Simplify the equations

       6x-3y=14 and -2x+6y=11

Now, line the equations up and pick a variable (either x or y) to eliminate

        6x-3y=14

        -2x+6y=11

In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y

Multiply (6x-3y=14) by 2 to get:

      12x-6y=28

Line the equations up and add or subtract the terms accordingly

      12x-6y=28

      -2x+6y=11

This becomes:

     10x+0y=39

Isolate for x

   x= 39/10 or x= 3.9

Now substitute the x value into either of the original equations

    6x-3y=14

    6(3.9)- 3y=14

Isolate for y

   23.4-14=3y

   3y= 9.4

  y= 3.1333 (repeating)  or y= 47/15

Answer: x = 39/10, y = 94/30

Step-by-step explanation:

6x - 3y = 3 - 2x + 6y,

Now solving this becomes

6x + 2x -3y - 6y = 3

8x - 9y = 3 ------------------- 1

3 - 2x + 6y. = 14

-2x + 6y = 14 - 3

-2x. + 6y = 11

Now multiply both side by -1

2x. - 6y = -11 ----------------- 2

Solve equations 1 & 2 together

8x - 9y. = 3

2x - 6y = -11

Using elimination method

Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8

16x - 18y = 6

-16x - 48y = -88 ------------------------- n, now subtract

30y = 94

Therefore. y = 94/30.

Now substitute for y in equation 2

2x - 6y = -11

2x - 6(94/30) = -11

2x - 94/5 = -11

Now multiply through by 5

10x - 94 = -55

10x = -55 + 94

10x = 39

x = 39/10

Answer:

The probability of the event BC

= the probability of B * C = 48.6667% * 70%

= 34.0667%

Step-by-step explanation:

Probability of A, students with children = 44/150 = 29.3333%

Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%

Probability of C, students working at least 10 hours per week = 105/150 = 70%

Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week

= 48.6667% * 70%

= 34.0667%

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

Answer:

With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.

Step-by-step explanation:

Hello!

Given the variables:

X₁: height of a teenage boy.

n₁= 46

[tex]\frac{}{X}[/tex]₁= 195cm

S₁²= 58cm²

X₂= height of a teenage girl

n₂= 66

[tex]\frac{}{X}[/tex]₂= 165cm

S₂²= 75cm²

If the boys are taller than the girls then you'd expect μ₁ > μ₂ or expressed as a difference between the two population means: μ₁ - μ₂ > 0

To estimate the difference between both populations you have to calculate the following interval:

([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) + [tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]

[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{110; 0.925}= 1.450[/tex]

Point estimate: ([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) = (195-165)= 30

Margin of error:[tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]= 1.450*0.54= 0.783

30 ± 0.783

[29.217; 30.783]

With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.

I hope this helps!

Answer:

Step-by-step explanation:

Hello,

We can write three equations thanks to Pythagoras

   [tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]

So it comes

[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]

Hope this helps

Answer:

x = [tex]\sqrt{21}[/tex]

Step-by-step explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values

[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex]

Answer:

your third answer

Step-by-step explanation:

its easy just plug in each domain into your function and the result will be the range

Answer:

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)

Answer:

Event B is mutually exclusive

Step-by-step explanation:

The mutually exclusive events are one which cannot happen together. The observation is made regarding male biology age. It is not possible that all male biology are 20 years old. There can male biology who are less than or greater than 20 years of age. The can not be all together 20 years old. The event is then considered as mutually exclusive.

Answer: see below

Step-by-step explanation:

[tex]f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}[/tex]

[tex]f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0[/tex]

[tex]gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}[/tex]

Answer:

the graph of g(x) is horizontally stretched by a factor of 3

Step-by-step explanation:

Answer:

Convenience sampling.

Step-by-step explanation:

To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.

Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.

In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.

Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.

Answer:

24.5 mpg

Step-by-step explanation:

(23,695 - 23,252) / 14 = 24.5mpg

Answer:

The car averaged a total of 24.5 miles per gallon between the two fillings

Step-by-step explanation:

Firstly, we calculate the difference between the mileages.

This will give us the total distance traveled.

That would be 23,695 - 23,352 = 343 miles

The tank capacity obviously is 14 gallons

So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon

Answer:

Area = 7 square units

Perimeter = 14 units

Step-by-step explanation:

The figure shown above consists of 7 squares, each having a side length of 1 unit.

==>Area of shape = area of 1 square × 7

Area of shape = s² × 7.

Where, s = side length = 1 unit

Area of shape = 1² × 7

= 1 × 7

Area = 7 square units

==>Perimeter of shape:

The perimeter of the shape is the sum of all the external sides of the 7 squares that form along the boundary of the shape. Check the attachment to see each side length that makes up the length of the entire boundary.

Perimeter of shape = 1 + 1 + 1 + ½ + ½ + 1 + 1 + ½ + 1½ + 1 + 4 + 1 = 14 units.

Answer:

(D)R: x+2=7

Step-by-step explanation:

Given the statement P:x=5

An equivalent statement will be a statement whose result is exactly x=5.

From the given options:

R: x+2=7

R: x=7-2

R: x=5

Therefore, R is an equivalent statement.

The correct option is D.

Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):

[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]

Simplify the leading term as

[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]

Quotient rule:

[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]

Chain rule:

[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]

[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]

Put everything together and simplify:

[tex]\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}[/tex]

[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}[/tex]

[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}[/tex]

[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}[/tex]

[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]

[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]

[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

axis of symmetry x=3

vertex (3, 52)

Step-by-step explanation:

y = -5x² + 30x + 7

x = -b/2a = -30/2(-5) = -30/-10 = 3

y = -5(3)² + 30(3) + 7

y = -45 + 90 + 7

y = 52

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer: 32

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

x=12-4

x=8

Answer:

8

Step-by-step explanation:

x+4=12, so 12-4=x (if you use an the inverse operation of addition, subtraction.)

12-4=x, so all you have to do is subtract and, there you have it, 8. It makes sense, 8+4=12. :)

Answer:

Hey there!

0.5(8.4)(h)=69.3

4.2h=69.3

h=16.5

Hope this helps :)

Answer:

[tex] \boxed{\sf Height \ of \ the \ triangle = 16.5 \ mm} [/tex]

Given:

Area of the triangle = 69.3 mm²

Base of the triangle = 8.4 mm

To Find:

Height of the triangle

Step-by-step explanation:

[tex]\sf \implies Area \ of \ the \ triangle = \frac{1}{2} \times Base \times Height \\ \\ \sf \implies 69.3 = \frac{1}{2} \times 8.4 \times Height \\ \\ \sf \implies 69.3 = \frac{1}{ \cancel{2}} \times \cancel{2} \times 4.2 \times Height \\ \\ \sf \implies 69.3 = 4.2 \times Height \\ \\ \sf \implies 4.2 \times Height = 69.3 \\ \\ \sf \implies Height \times \frac{ \cancel{4.2}}{ \cancel{4.2}} = \frac{69.3}{4.2} \\ \\ \sf \implies Height = \frac{16.5 \times \cancel{4.2}}{ \cancel{4.2}} \\ \\ \sf \implies Height = 16.5 \: mm[/tex]

Answer:

2√2−3

Step-by-step explanation:

Simplify each term.

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

Hope this can help

Answer:

[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]

Step-by-step explanation:

divide each term by 2y^3

Multiply through by the least common denominator.

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer:  m = -5

Step-by-step explanation:

[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]

Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:

(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)

Multiply binomials, add like terms, and solve for m:

(m² + 6m + 9) - (3m + 3) = m² - 9

    m² + 6m + 9 - 3m - 3 = m² - 9

                  m² + 3m + 6 = m² - 9

                           3m + 6 =  -9

                                  3m = -15

                                    m = -5  

Answer:

variable A and Variable B are more negatively related than variable C and variable D.

Step-by-step explanation:

Variables A and B have a covariance = 45

Variables C and D have a covariance = 627

Comparing the relationship between variable A AND B with the relationship between variable C and D

variable A and Variable B are more negatively related than variable C and variable D. this is because the covariance between variable A and Variable B are less positive

Answer:

x^2 + 2x - 20 = 0

x^2 + 2x - 20 + 20 = 0 + 20  ( add 20 to both sides)

x^2 + 2x = 20

x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)

( x + 1 )^2 = 21

x = [tex]\sqrt{21}-1[/tex]

x = [tex]-\sqrt{21}-1[/tex]

Answer:

A)  x = –1 ± square root 21

is the answer:)