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kumpel [21]
3 years ago
8

The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+-2i What is the other root? Use a graphing calculator and a

system of equations.
A. -3
B. -1
C. 3
D. 10
Please hurry!

Mathematics
1 answer:
kirill115 [55]3 years ago
7 0

Answer:

B. -1

Step-by-step explanation:

x^3-4x^2+2x+10=x^2-5x-3

We know it has 3 roots since it is a 3rd degree polynomial.

Two of the roots are (3+2i) and (3-2i)

Subtract x^2-5x-3 from both sides

x^3-4x^2+2x+10-(x^2-5x-3)=x^2-5x-3 -(x^2-5x-3)

Distribute the minus sign

x^3-4x^2+2x+10-x^2+5x+3=x^2-5x-3 -x^2+5x+3

x^3 -5x^2+7x +13 =0

Graphing this equation , we see that it crosses the x axis at x=-1

That covers the three roots, 1 real and two complex

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The ancient Greeks could bisect an angle using only a compass and straightedge.A. TrueB. False
Gala2k [10]

Answer: True.

The ancient Greeks could bisect an angle using only a compass and straightedge.

Step-by-step explanation:

The ancient Greek mathematician <em>Euclid</em> who is known as inventor of geometry.

The Greeks could not do arithmetic. They had only whole numbers. They do not have zero and negative numbers.

Thus, Euclid and the another Greeks had the problem of finding the position of an angle bisector.

This lead to the constructions using compass and straightedge. Therefore, the straightedge has no markings. It is definitely not a graduated-rule.

As a substitute for using arithmetic, Euclid and the Greeks learnt to solve the problems graphically by drawing shapes .

5 0
3 years ago
Read 2 more answers
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
Step2247 [10]
Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)




Answer
5 0
3 years ago
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Please help. The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes?
Mrac [35]
They can make 9000 crayons in 15 minutes
7 0
3 years ago
1) Find the measure of ∠θ. Round to one decimal place.
I am Lyosha [343]

Answer/Step-by-step explanation:

Reference angle = θ

Opposite side = 11.9

Adjacent side = 10

Applying the trigonometric ratio, TOA, we have:

Tan θ = opp/adj

Tan θ = 11.9/10

θ = tan^{-1}(11.9/10)

θ = 49.9584509° ≈ 50.0° (to one d.p)

Apply pythagorean theorem to find AB:

Thus:

AB = √(11.9² + 10²)

AB = √241.61

AB ≈ 15.5 (to 1 d.p)

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3 years ago
Solve the system of linear equations by substitution.<br><br> 5x+2y=9<br><br> x+y=-3
Hatshy [7]
Step 1: subtract x from -3. New equation should be y=-3-x.
Step 2: plug that equation into top equation. Should be 5x + 2(-3-x) = 9.
Step 3: use distribitive properties on 2(-3-x). New equation is 5x - 6 - 2x = 9.
Step 4: combine like terms. New equation 3x - 6 = 9.
Step 5: work it out. Divide 3x and 9 by 3. New equation is x - 6 = 3. Add 6 to -6 and 9. Final eqaution is x = 9.
Step 6: swap 9 for x in second equation. New equation is 9 + y = -3
Step 7: subtract 9 from 9 and -3. New equation is y = -12
: = = -
8 0
3 years ago
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