Rob can lift less than 135 pounds at the weight room. There is already 48 pounds of weights on the bar. Write an inequality that shows the additional weight that Rob can add, w, without being over his maximum.

Graph: See attached image

Slope: [tex]-\frac{1}{3}[/tex]

Y- intercept: (0,5)

X-intercept: (15,0)

Domain: (-∞,∞)

Range: (-∞,∞)

I hope this helped! Good luck with your mathematics class!

Step-by-step explanation:

Here is your explanation:

((x4) - 3x2) - 18 = 0 Factoring  x4-3x2-18 

The first term is,  x4  its coefficient is  1 .

The middle term is,  -3x2  its coefficient is  -3 .

The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -18 = -18 

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -3 .

     -18   +   1   =   -17     -9   +   2   =   -7     -6   +   3   =   -3   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  3 

                     x4 - 6x2 + 3x2 - 18

Step-4 : Add up the first 2 terms, pulling out like factors :

                    x2 • (x2-6)

              Add up the last 2 terms, pulling out common factors :

                    3 • (x2-6)

Step-5 : Add up the four terms of step 4 :

                    (x2+3)  •  (x2-6)

             Which is the desired factorization

Find roots (zeroes) of :       F(x) = x2+3

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  3.

 The factor(s) are:

of the Leading Coefficient :  1

 of the Trailing Constant :  1 ,3

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      4.00        -3     1      -3.00      12.00        1     1      1.00      4.00        3     1      3.00      12.00   

Factoring:  x2-6 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

         A2 - AB + BA - B2 =

         A2 - AB + AB - B2 =

         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 6 is not a square !!(x2 + 3) • (x2 - 6) = 0 product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.Solve  :    x2+3 = 0 

 Subtract  3  from both sides of the equation : 

                      x2 = -3

 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                      x  =  ± √ -3  

 In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1 

Accordingly,  √ -3  =

                    √ -1• 3   =

                    √ -1 •√  3   =

                    i •  √ 3

The equation has no real solutions. It has 2 imaginary, or complex solutions.

                      x=  0.0000 + 1.7321 i 

                      x=  0.0000 - 1.7321 i 

Solve  :    x2-6 = 0 

 Add  6  to both sides of the equation : 

                      x2 = 6

 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                      x  =  ± √ 6  

 The equation has two real solutions  

 These solutions are  x = ± √6 = ± 2.4495  

 Solving  x4-3x2-18  = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Solve   x4-3x2-18 = 0

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using  w , such that  w = x2  transforms the equation into :

 w2-3w-18 = 0

Solving this new equation using the quadratic formula we get two real solutions :

   6.0000  or  -3.0000

Now that we know the value(s) of  w , we can calculate  x  since  x  is  √ w  

Doing just this we discover that the solutions of

   x4-3x2-18 = 0

  are either : 

  x =√ 6.000 = 2.44949  or :

  x =√ 6.000 = -2.44949  or :

  x =√-3.000 = 0.0 + 1.73205 i  or :

  x =√-3.000 = 0.0 - 1.73205 i

so we found four answers:

 x = ± √6 = ± 2.4495

  x=  0.0000 - 1.7321 i 

  x=  0.0000 + 1.7321 i 

sorry for taking time to answer

hope its helps

The correct option is A because [tex]x=\pm\sqrt{6}i[/tex] or [tex]x=\pm\sqrt{3}[/tex].

Given:

The given equation is:

[tex]x^4+3x^2-18=0[/tex]

To find:

The real and imaginary solutions of the given equation.

Explanation:

We have,

[tex]x^4+3x^2-18=0[/tex]

Substitute [tex]x^2=t[/tex] in the given equation.

[tex]t^2+3t-18=0[/tex]

Splite the middle term.

[tex]t^2+6t-3t-18=0[/tex]

[tex]t(t+6)-3(t+6)=0[/tex]

[tex](t+6)(t-3)=0[/tex]

Using zero product property, we get

[tex]t+6=0[/tex] or [tex]t-3=0[/tex]

[tex]t=-6[/tex] or [tex]t=3[/tex]

Substituting [tex]t=x^2[/tex], we get

[tex]x^2=-6[/tex] or [tex]x^2=3[/tex]

[tex]x=\pm\sqrt{-6}[/tex] or [tex]x=\pm\sqrt{3}[/tex]

[tex]x=\pm\sqrt{6}i[/tex] or [tex]x=\pm\sqrt{3}[/tex]

Therefore, the correct option is A.

Learn more:

https://brainly.com/question/20689398

Answer:

sorry little busy to calculate

Step-by-step explanation:

+5x+2y+z=15

3x +4y_z=19,,,choose which term u wanna eliminate first so u will be able to get your answer there

Answer:

A

Step-by-step explanation:

I am pretty sure the graph is skewed to the left, because the trailing tail is on the left. Sorry for the bad explanation lol

Answer:

i really am his alt

Step-by-step explanation:

Answer: (0, -2) & (1, 1)

Step-by-step explanation:

Answer:

y = 3/4 + 3/2

Step-by-step explanation:

Slope = 3/4

Solve for y-int.

0 = 3/4(-2) + b

-3/2 + b = 0

b = 3/2

y = 3/4x +3/2

Answer:

A horizontal line has a gradient = 0 and only has a y-intercept.

In the standard form this would mean that  

m =0,  and c =5  So, y  = 5

Step-by-step explanation:

i think it's correct so far

Answer:

yes it is correct so far

Answer:

A

Step-by-step explanation:

Answer:

D. -11/3b > 2/3

Step-by-step explanation:

We automatically can rule out B and C because it says is more than 2/3. The greater-than sign is >. B uses the less-than sign <, and C uses the greater-than or equal to sign ≥.

This leaves us with A. and D. The equation states One-third of a number b multiplied by -11. A. only has -11/b, but D. has -11/3 b. Because of this we can rule out A. so the answer is D.

I hope that this helps! :)

Answer:

Step-by-step explanation:

You put this in the wrong place, but I'll answer it anyway.

Let's see what we can get out of it.

1. It allowed western expansion.

2. It gave the United States a southern route to enhance trade.

3. It brought America closer to the slave trade which the southern states needed at the time. I don't like posting this answer, but it is a historical fact.

4. It made things a little difficult for the Spanish who had the ports in Louisiana.

5. It made the land route to the west coast a little easier to do. Not much but some.

6. Considering the cost of the land and how it was later developed, the price paid was a steal.

Answer:

x=2

Step-by-step explanation:

2/12 is equal to 12/72

Answer:

its 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

A is the answer

Answer:

Option A. f(x) = 4(3)x

is the answer.

Step-by-step explanation:

Answer:

x= 99

Step-by-step explanation:

first we open brackets

6x+36=7x-63

transpose

6x-7x= -63-36

-x=-99

the signs cancel each other so

x= 99

Answer:

110°

Step-by-step explanation:

y = 25

Angle 5 equals Angle 4 because of the Alternate Angles Postulate.

Angle 4 equals 110°

The measure of angle ∠4 is 110 degrees.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.

Given that the measure Angle 3= (2y+20) degrees, and the measure of Angle  5= (210-4y) degree

Then ∠3 + ∠5 = 180,  By Co-interior angles are supplementary

2y + 20 + 210 - 4y = 180

2y - 4y + 20 + 210 = 180  

-2y + 230 = 180

Now Subtract 230 from both sides;

-2y = 180 - 230

-2y = -50  

Then Divide both sides by (-2);

 y = -50/-2

y = 25

Now, ∠5 = 210 - 4y

      = 210 - 100

∠5 = 110

∠4 = ∠5    { by Alternate interior angles are equal}

∠ 4 = 110°

Learn more about supplementary angles here:

https://brainly.com/question/2882938

#SPJ2

Answer:

Mike 270

Molly 405

Step-by-step explanation:

Let Mike be x

Let Molly be x + 135

2/3 = x/(x + 135)                        Cross Multiply

2*(x + 135) = 3x                         Remove the brackets

2x + 270 = 3x                            Subtract 2x from both sides

2x-2x + 270 = 3x - 2x

270 = x

Mike gets 270

Molly gets 270 + 135

Molly gets 405

Answer:

( 1, -3)

Step-by-step explanation:

[tex]y=a(x-h)^2+k[/tex]

The vertex is at (h,k). For "h", swap the negative to positive and positive to negative.

So the vertex is (-1,3)

Answer:

223

Step-by-step explanation:

hope it helps!!!!......

Answer:

223

Step-by-step explanation:

892 ÷ 4 = 223

Can i get brainliest? plz!

the answer is 50:::::::_::::::::

Answer:

(-9/10, 23/10)

Step-by-step explanation:

Answer:

the 2nd, 5th and 7th are the correct ones.

Answer:

How is your day going lol

Step-by-step explanation:

was this supposed to be a question lol>

Answer:

(1, 7) (2, 10) (3, 5) (4, 7) (5, 9) hope that helps

Answer:

12 dimes

Step-by-step explanation:

1 dollar= 4 quarters

1 dime=10 cents

3.45-1.20=2.25

2 dollars= 8 quarters

2.25-2.20=.25

1 quarter=.25

SOOOO your answer is 12 dimes

Answer:

The last one

Step-by-step explanation: