Substitution method-
r = -3s
r= 10 - 4s

Answers

Answer 1

Answer: $r=-3s\nr=10-4s\n\n-3s=10-4s\ \ \ \ |add\ 4s\n-3s+4s=10\ns=10\n\nr=-3\cdot10=-30$

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The average annual cost of living in Illinois, California, and Oregon are displayed inthe table below:36StateAverage Annual Cost ofLiving9Illinois$58,000California$70,0001Oregon$64,000Suppose you are earning a salary of $95,000 per year in California. Your employerasks you to transfer to the Oregon office. Based on the average annual cost of living,what is the lowest possible salary you will accept? Round your answer to the nearestwhole dollar. Explain your reasons.
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Match the sequence (term) with the correct type of sequence (definition).Match Term Definition
128, 32, 8, 2, ... A) Arithmetic, common difference is 5
1, 3, 9, 27, ... B) Arithmetic, common difference is -3
5, 10, 15, 20, ... C) Geometric, common ratio is 0.25
20, 17, 14, 11, ... D) Geometric, common ratio is 3

Answers

The correct answer among all the other choices is 20, 17, 14, 11, ... D) Geometric, common ratio is 3. This is the sequence (term) with the correct type of sequence (definition) among the examples given. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

Use Synthetic Division to Factor the following polynomials completely by given factors or roots and Find all the zeros; When you reach quadratic equation, performance regular factoring or Quadratic Formula. $x^(5) -9x^(3) -x^(2) +9;(x-3),(x-1)$ , as factors and -3 as a root

Answers

Answer:

The factors are (x - (1 - i√3)/2) , (x - (1 + i√3)/2) , (x - 3) , (x + 3) , (x - 1)

The zeroes are 1 , 3 , -3 , (1 - i√3)/2 , (1 + i√3)/2

Step-by-step explanation:

$(x^(5)+0-9x^(3) -x^(2)+0+9)$ ÷ (x - 3) =

$(x^(4)-9x^(3)-x^(2)+0+9)$ ÷ (x - 3) =

$x^(4)+3x^(3)+(-x^(2)+0+9)$ ÷ (x - 3) =

$x^(4)+3x^(3)-x+(-3x+9)$ ÷ (x - 3) =

$(x^(4)+3x^(3)-x-3)$

$(x^(4)+3x^(3)+0-x-3)$ ÷ (x - 1) =

x³ + (4x³ + 0 - x - 3) ÷ (x - 1) =

x³ + 4x² + (4x² - x - 3) ÷ (x - 1) =

x³ + 4x² + 4x + (3x - 3) ÷ (x - 1) =

x³ + 4x² + 4x + 3

∵ -3 is a root ⇒ (x + 3) is a factor

(x³ + 4x² + 4x + 3) ÷ (x + 3) =

x² + (x² + 4x + 3) ÷ (x + 3) =

x² + x + (x + 3) ÷ (x + 3) =

x² + x + 1 ⇒ use the formula to find the factors of this quadratic

∵ a = 1 , b = 1 and c = 1

∴ $x=\frac{-1+\sqrt{(1)^(2)-4(1)(1)} }{2(1)}=(-1+√(-3))/(2)=(-1+i√(3))/(2)$

∴ $x=(-1-i√(3) )/(2)$

∴ The factors are (x - (1 - i√3)/2) , (x - (1 + i√3)/2) , (x - 3) , (x + 3) , (x - 1)

The zeroes:

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = -3

x - 1 = 0 ⇒ x = 1

x - (1 - i√3)/2 = 0 ⇒ x = (1 - i√3)/2

x - (1 + i√3)/2 = 0 ⇒ x = (1 + i√3)/2

The zeroes are 1 , 3 , -3 , (1 - i√3)/2 , (1 + i√3)/2

When solving for x, the sine of 33º is used. What other angle and trigonometric function could be used to solve for x? a. cos 57º c. tan 57º b. tan 33º d. cos 33ºhurry

Answers

Answer:

The answer is A.Cos 57.

Step-by-step explanation:

Took the test..

A pool measuring 8 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1008 square meters, what is the width of the path?

Answers

Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.

Combined Area = (2x + 26)*(2x + 8) = 1008

2x*(2x + 8) + 26*(2x + 8 ) = 1008

4x² + 16x + 52x + 208 = 1008

4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.

Multiply first and last coefficients: 1*-200 = -200

We look for two numbers that multiply to give -200, and add to give +17

Those two numbers are 25 and -8.

Check: 25*-8 = -200 25 + -8 = 17

We replace the middle term of +17x in the quadratic expression with 25x -8x

x² +17x - 200 = 0

x² + 25x - 8x - 200 = 0

x(x + 25) - 8(x + 25) = 0

(x+25)(x -8) = 0

x + 25 = 0 or x - 8 = 0

x = 0 -25 x = 0 + 8

x = -25 x = 8

The width of the path can not be negative.

The only valid solution is x = 8.

The width of the path is 8 meters.

the spaceship you are riding to get to mars is going 1000 mph how long will it take to get to mars at that rate of speed if you are 15,000 miles away?

Answers

Answer:

15 hours

Step-by-step explanation:

Speed is defined as the distance moved per unit time hence s=d/t and making t the subject of the formula then t=d/s where t is time taken, d is distance covered and s is the speed.

Substituting 15000 miles for d and 1000 mph for s then

T=15000/1000=15 hours

Therefore, maintaining the same speed, it will take 15 hours to get to mars

B2 - 4ac > -1 means the root is real. true or false??