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bogdanovich [222]
3 years ago
13

Simplify. (x3 + 2x − 3)(x4 − 3x2 + x)

Mathematics
1 answer:
harina [27]3 years ago
8 0

Step-by-step explanation:

x¹²-3x6-x⁴+2x⁴-6x³+2x²-3x⁴+9x²-3x

x¹²-3x6-2x⁴-6x³+11x²-3x

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5/28
natulia [17]

Answer:

Part a) The rule of the sequence is A(n)=50(0.52^{n-1})

Part b) The height of the ball will be 13.52\ cm

Step-by-step explanation:

Part a) Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.

we know that

In a <u>Geometric Sequence</u> each term is found by multiplying the previous term by a constant called the common ratio (r)

In this problem we have a geometric sequence

Let

n-----> the number of path

a1 ----> is the initial height

r -----> the common ratio

we have

a1=0.5\ m=0.5*100=50\ cm

r=52\%=52/100=0.52

The rule for the sequence is equal to

A(n)=a1(r^{n-1})

substitute

A(n)=50(0.52^{n-1})

Part b) What height will the ball be at the top of the third path?

For n=3      

substitute in the equation

A(3)=50(0.52^{3-1})  

A(3)=50(0.52^{2})

A(3)=13.52\ cm

4 0
3 years ago
Define the height of a triangle use the words vertex and base.
yaroslaw [1]

Answer: The height of a triangle is the perpendicular segment that joins the base with its opposite vertex.

Step-by-step explanation:

The base can be any side of the triangle.

8 0
3 years ago
PLS HELP DUE SOON WILL MARK BRAINLIEST
Eva8 [605]

Answer:

you have 9 yes and 3 no. so 3/9=1/3=.333

6 0
3 years ago
PLEASE HELP, BEEN STUCK FOR AN HOUR
djverab [1.8K]

Answer:

Step-by-step explanation:

To sketch a quadratic function we need two things:

1)  Nature of the curve

2) Vertex

3) y-intercept

The completing square form of the quadratic equation is:

y=a(x-h)^2+k

where,

a represents the nature of the graph it can be maximum or minimum , meaning, if a > 0 then minimum(u shaped curve/happy face) and if a < 0 then maximum(n shaped curve/sad face).

h represents the x-coordinate of the vertex.

k represents the y-coordinate of the vertex.

Now if we compare g(x) with our completing square form we get the following:

g(x)=(x-4)^2+12\\y=a(x-h)^2+k\\

When we simply compare the following we get ,

a = 1 , which means a > 0 since 1 is greater than 0 the nature of the curve will be minimum(happy face/u shaped)

h = 4, which means the x-coordinate of the vertex is 4

k = 12, which means the y-coordinate of the vertex is 12

Now we have the nature of the curve, we have the vertex now all we need is the y-intercept.

For y-intercept:

For y-intercept meaning at which point will the graph cross the y-axis(0 , y)

For that we expand the formula and turn it into the standard quadratic equation form by using the formula (a - b)^2

y=(x-4)^2+12\\y=((x)^2-2(x)(4)+(4)^2)+12\\y=x^2-8x+16+12\\y=x^2-8x+28\\

now we compare with the standard quadratic form:

y=ax^2+bx+c

here c is the y-intercept and while comparing we can see that c = 28 ,

so the curve cuts the y-axis at (0 , 28)

So we have all the three things that we need to graph our function.

So we just plot the y-intercept , the vertex , and join the dots. Just a tip draw a dotted line on the x-coordinate of the vertex because the vertex point is also called as a turning point where the graph goes in the opposite direction just like a mirror reflection. I attached 2 images you can check them out. One is handmade(i know i suck at drawing but still xD) , one is sketched by online graphing calculator.

5 0
3 years ago
Formula One race cars can reach speeds of approximately 100 meters per second. What is this speed in meters per minute?
WARRIOR [948]
Set up multiplication/division of ratios to cancel out units you don't need for the final answer and introduce those that you do.

We have m/s and we want m/min so

(100m/s)(60s/min)=6000m/min

5 0
3 years ago
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