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2 years ago

How do you factor: 5x^3+30x^2+45x (please show steps)

Mathematics

2 answers:

zheka24 [161]2 years ago

7 0

Answer:

5x³ + 30x² + 45x = 5x (x+3)²

Step-by-step explanation:

Given: 5x³ + 30x² + 45x

Take 5x as a common

5x³ + 30x² + 45x

= 5x ( x² + 6x + 9) ⇒ Factor ( x² + 6x + 9)

= 5x (x+3) (x+3)

= 5x (x+3)²

Natasha2012 [34]2 years ago

3 0

Answer:

Idk

Step-by-step explanation:idk

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1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her j

ArbitrLikvidat [17]

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

$m=(17-16)/(2-0)=\frac{1}{2}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=\frac{1}{2}$

$b=16$ -----> the point (0,16) is the y-intercept

substitute

$y=\frac{1}{2}x+16$

convert to function notation

f(x)=y

$f(x)=\frac{1}{2}x+16$

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

$m=(-2-0)/(5-5)=\frac{-2}{0}$

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

$m=(1-2)/(3+1)=-\frac{1}{4}$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{4}$

$point\ (3, 1)$

substitute

$y-1=-\frac{1}{4}(x-5)$

Convert to standard form

Multiply by 4 both sides to remove the fraction

$4y-4=-(x-5)$

$4y-4=-x+5$

$x-4y=-4-5$

$x-4y=-9$

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)

The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

5 0

2 years ago

Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)

Ksju [112]

Well, here's one way to do it at least...

For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). 

Let P=(4,0) be the projection of B onto the x-axis. 
Let Q=(-3,0) be the projection of C onto the x-axis. 

Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). 

Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). 

Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. 

||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) 
||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) 

Using the Law of Cosines... 
||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) 
||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) 
||a||^2 = 86 - 36 
||a||^2 = 50 
||a|| = sqrt(50) 

Now apply the Law of Sines to find the other two angles. 

||b|| / sin(B) = ||a|| / sin(A) 
sqrt(41) / sin(B) = sqrt(50) / .9080 
(.9080)sqrt(41) / sqrt(50) = sin(B) 
.8222 = sin(B) 
asin(.8222) = B 
55.305 = B 

Two down, one to go... 

||c|| / sin(C) = ||a|| / sin(A) 
sqrt(45) / sin(C) = sqrt(50) / .9080 
(.9080)sqrt(45) / sqrt(50) = sin(C) 
.8614 = sin(C) 
asin(.8614) = C 
59.470 = C 

So your three angles are: 

A = 65.225 
B = 55.305 
C = 59.470

8 0

1 year ago

The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 10 unit

kozerog [31]

Answer:

Step-by-step explanation:

that the triangular prism has more volume

3 0

2 years ago

Kelvin's monthly allowance is $42 and Mike's monthly allowance is $63. How many times Mike's monthly allowance is Kelvin's month

earnstyle [38]

It is 1.5 times because $63 divided by $42 is $1.5.
I hope this is what you meant.

3 0

2 years ago

The partial factorization of x2 – 3x – 10 is modeled with algebra tiles. Which unit tiles are needed to complete the factorizati

kkurt [141]

Answer:

(x - 5)(x + 2)

Step-by-step explanation:

x² - 3x - 10 =

= x² + 2x - 5x - 10

= x(x + 2) - 5(x + 2)

= (x - 5)(x + 2)

6 0

2 years ago