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Tanya [424]
3 years ago
12

Please help me i need the answer right now. The lesson is Rational Root Theorem.

Mathematics
1 answer:
Debora [2.8K]3 years ago
6 0

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

  • x+4.(3x+1)(x)
  • The volume is 720.
  • Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is

(3x + 1)(x + 4)

(3 {x}^{2}  + 13x + 4)x = 720

Multiply it by x.

3 {x}^{3}  + 13 {x}^{2}  + 4x = 720

3{x}^{3}  + 13 {x}^{2}  + 4 x - 720

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

x = 5

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

1 - 2 - 5 + 6 = 0

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

{x}^{2}  - x - 6

We can then factor this into

(x - 3)(x + 2)

So our roots or factors is

(x - 1)(x - 3)(x + 2)

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igor_vitrenko [27]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
What is a numerical expression? Give an example.
seropon [69]

Answer:

Step-by-step explanation:

The term numerical expression is made up of two words, numerical meaning numbers, and expression meaning phrase. ... A numerical expression in mathematics can be a combination of numbers, integers combined using mathematical operators such as addition, subtraction, multiplication, or division.

6 0
3 years ago
Pls help for this question! no wrong answers pls
ankoles [38]

Answer:

41.29 cm²

Step-by-step explanation:

From the question,

Area of the shaded portion = Area of the circle - area of the square.

A' = πr²-L²...… Equation 1

Where A' = Area of the shade portion, r = radius of the circle, L = length of the square, π = pie

Given: r = 4 cm, L = 3 cm

Constant: π = 22/7.

Substitute these values into equation 1

A' = [(22/7)×4²]-3²

A' = 50.29-9

A' = 41.29 cm²

Hence the area of the shaded portion is 41.29 cm²

8 0
3 years ago
7. Which of the following can be determined from the graph below?
tatyana61 [14]

Answer:

The ordered pair (6,25) is a solution to both

y=-\frac{5}{2}x+40  and  y=\frac{5}{3}x+15

Step-by-step explanation:

Part 7)

<em>step 1</em>

Find the equation of the line with positive slope

take the points (0,15) and (9,30)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{30-15}{9-0}

m=\frac{15}{9}

simplify

m=\frac{5}{3}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{5}{3}

b=15

substitute

y=\frac{5}{3}x+15

<em>step 2</em>

Find the equation of the line with negative slope

take the points (0,40) and (8,20)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{20-40}{8-0}

m=-\frac{20}{8}

simplify

m=-\frac{5}{2}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-\frac{5}{2}

b=40

substitute

y=-\frac{5}{2}x+40

step 3

Find the solution of the system

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is (6,25) ----> see the graph

therefore

The ordered pair (6,25) is a solution to both y=-\frac{5}{2}x+40  and  

y=\frac{5}{3}x+15

7 0
3 years ago
Which expression shows a way to find 20% of 950? Please I need help thanks.
wolverine [178]

Answer:

the answer of the expression is 190

Step-by-step explanation:

Given expression as :

20 % of 950

Or, \frac{20}{100} times 950

Or, \frac{20}{100} × 950

Or, 20 × \frac{950}{100}

or, 20 × 9.5

∴ 190

7 0
3 years ago
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