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3 years ago

Write a simplified expression for the perimeter of the figure at right.

Mathematics

1 answer:

Mila [183]3 years ago

7 0

Answer:

3xup2

Step-by-step explanation:

xup2+3x=3xup2

my answer needs to be atleast 20 words long

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3 years ago

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2 years ago

What is the completely factored form of x^4+8x^2-9

denis-greek [22]

Remark

You'll see it a whole lot easier if you make a substitution so that it looks like something you have already seen

Solution

let y = x^2

x^4 = x^2 * x^2

x^4 = y * y

x^4 = y^2

Now the expression becomes

y^2 + 8 y - 9 = z

(y + 9)(y - 1) = z

Now put the x^2 back in.

(x^2 + 9) ( x^2 - 1) = z

x^2 - 1 becomes x + 1 and x - 1. At this level x^2 + 9 can't be factored.

Answer

(x^2 + 9) (x + 1)(x - 1)

3 0

4 years ago

Read 2 more answers

TIME REMAINING

Diano4ka-milaya [45]

Answer:

h=2

Step-by-step explanation:

f is translated right 2 units (so h=2) and up 2 units (so k=2)

3 0

3 years ago

Read 2 more answers

4) The path of a satellite orbiting the earth causes it to pass directly over two

Naily [24]

Answers:

Satellite is approximately <u>2446.43 km</u> from station A.
Satellite is approximately <u>2441.61 km</u> above the ground.

=========================================================

Explanation:

I'm assuming tracking stations A and B are at the same elevation and are on flat ground. In reality, this is likely not the case; however, for the sake of simplicity, we'll assume this is the case.

The diagram is shown below. Points A and B describe the two stations, while point C is the satellite's location. Point D is on the ground directly below the satellite. We have these lengths

AB = 60 km
AD = x
CD = h

Focusing on triangle ACD, we can apply the tangent rule to isolate h.

tan(angle) = opposite/adjacent

tan(A) = CD/AD

tan(86.4) = h/x

x*tan(86.4) = h

h = x*tan(86.4)

We'll use this later in the substitution below.

--------------------

Now move onto triangle BCD. For the reference angle B = 85, we can use the tangent rule to say

tan(angle) = opposite/adjacent

tan(B) = CD/DB

tan(B) = CD/(DA+AB)

tan(85) = h/(x+60)

tan(85)*(x+60) = h

tan(85)*(x+60) = x*tan(86.4) ............. apply substitution; isolate x

x*tan(85)+60*tan(85) = x*tan(86.4)

60*tan(85) = x*tan(86.4)-x*tan(85)

60*tan(85) = x*(tan(86.4)-tan(85))

x*(tan(86.4)-tan(85)) = 60*tan(85)

x = 60*tan(85)/(tan(86.4)-tan(85))

x = 153.612786190499

--------------------

We'll use this approximate x value to find h

h = x*tan(86.4)

h = 153.612786190499*tan(86.4)

h = 2441.60531869599

h = 2441.61 km is how high the satellite is above the ground.

Return to triangle ACD. We'll use the cosine rule to determine the length of the hypotenuse AC

cos(angle) = adjacent/hypotenuse

cos(A) = AD/AC

cos(86.4) = x/AC

cos(86.4) = 153.612786190499/AC

AC*cos(86.4) = 153.612786190499

AC = 153.612786190499/cos(86.4)

AC = 2446.43279498247

AC = 2446.43 km is the distance from the satellite to station A.

6 0

3 years ago