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kotykmax [81]
3 years ago
12

Solve the following system of equations graphically. Click on the graph until the correct solution of the system appears.

Mathematics
1 answer:
krok68 [10]3 years ago
6 0
Solution is (1,1) where two lines intersect 

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The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the
omeli [17]
Given:

The volume of the rectangular prism is 

b^{3}+8 b^{2} +19b+12,

the height is h=(b+3)

1. The volume of a rectangular prism is (base area)*height

also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be (mb^{2}+nb+k)

 
2

b^{3}+8 b^{2} +19b+12=(mb^{2}+nb+k)*(b+3)


notice that  b^{3} is the product of the largest 2 terms: mb^{2} and b, so m must be 1

also, notice that 12 is the product of the constants, k and 3

so k*3=12, this means k=4

3
we write the above equality again:

b^{3}+8 b^{2} +19b+12=(b^{2}+nb+4)*(b+3)


(b^{2}+nb+4)(b+3)= b^{3}+3 b^{2} +nb^{2}+3nb+4b+12

== b^{3}+(n+3)b^{2}+(3n+4)b+12


4
now compare the coefficient with the left side:

8 b^{2}=(n+3)b^{2}

8=n+3

n=5


substituting n=5: 

the base area is b^{2}+5b+4

Answer: b^{2}+5b+4


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3 years ago
How to now your timetables by your hands
Ivenika [448]
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Hold your hands out in front of you with your palms facing up. Each of your ten fingers represent a number. Moving from your left thumb to your right thumb, count out the numbers from one to ten. 2 Point the finger you want to multiply by nine down towards your body. For example, if you want to solve (9x3) you will want to hold down your middle finger on your left hand. The middle finger represents the number three because, if you count your fingers from one to ten beginning with your left thumb, your middle finger is the third finger. 3 Solve the problem by counting fingers to the left and right. First count the fingers to the left of your bent finger - in this case there should be two. Next count the fingers to the right of your bent finger - in this case there should be seven. The first digit of the answer is 2 and the second digit is 7. The answer is 27![1]
7 0
3 years ago
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If you choose one student at random, what is the probability (±0.0001) that the student's score is between 20 and 30?
nordsb [41]
Z-score for 30 = (30 - 25) / 5.8 = 0.8621
z-score for 20 = (20 - 25) / 5.8 = -0.8621
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Note find probabilities from z-tables
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Probability ( 20 < X < 30 ) = 0.8051 - 0.1949 = 0.6102
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3 years ago
Plz help me with this
Mkey [24]

Answer: B) A = 750(1.04)ⁿ

<u>Step-by-step explanation:</u>

The formula for compounded annually is: A = P(1 + r)ⁿ   where

  • A (amount accrued) = <em>unknown</em>
  • P (amount invested) = $750
  • r (interest rate) = 4% -->(0.04)
  • t (time in years) = <em>unknown</em>

A = 750(1 + 0.04)ⁿ

  = 750(1.04)ⁿ

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3 years ago
The binomial expansion 1.728x^3+ 3,456x² + 2,304x + 512 can be expressed as (ax + b)^3. What is the value of b?
viva [34]

Answer:

C: 8

Step-by-step explanation:

8^3=512

if it was -8^3 it would equal -512

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2 years ago
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