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Vitek1552 [10]
2 years ago
13

Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Wr

ite an inequality that would be used to solve for the least amount of money he needs to deposit to avoid a fee. 727.29 + 248.50 − x ≥ 500 727.29 + 248.50 − x ≤ 500 727.29 − 248.50 + x ≥ 500 727.29 − 248.50 − x ≤ 500
Mathematics
1 answer:
deff fn [24]2 years ago
5 0

Answer:

727.29 − 248.50 + x ≥ 500 727.29 − 248.50 − x ≤ 500. Hope this helps!

Step-by-step explanation:

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If (5, 4) and (7,2) are the endpoints of a diameter of a circle, what is the equation of the circle?
STatiana [176]

Answer:

  (x -6)^2 +(y -3)^2 = 2

Step-by-step explanation:

The midpoint (C) is the center of the circle:

  C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)

A circle with center (h, k) that goes through point (a, b) can be written as ...

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

Using the values for this problem, we get ...

  (x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2

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8 0
3 years ago
Read 2 more answers
Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview
svetlana [45]

Answer:  The required solution is

y=(-2+t)e^{-5t}.

Step-by-step explanation:   We are given to solve the following differential equation :

y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let us consider that

y=e^{mt} be an auxiliary solution of equation (i).

Then, we have

y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.

Substituting these values in equation (i), we get

m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.

So, the general solution of the given equation is

y(t)=(A+Bt)e^{-5t}.

Differentiating with respect to t, we get

y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.

According to the given conditions, we have

y(0)=-2\\\\\Rightarrow A=-2

and

y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.

Thus, the required solution is

y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.

6 0
3 years ago
A pendulum is 18 feet long. Its central angle is 44º. The pendulum makes one back and forth swing every 12 seconds. Each minute,
expeople1 [14]
Radius: r=18 feet
Cental Angle: A=44°
Each cycle (one back and forth) lasts 12 seconds
In each cycle the pendulum swings:
L=(A/360°) 2 pi r
L=(44°/360°)(2)(3.141592654)(18 feet)
L=(0.122222222)(113.0973355 feet)
L=13.82300764 feet
Rounded to 3 decimal places:
L=13.823 feet

Each minute (60 seconds) the pendulum makes:
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Then, each minute, the pendulum swings:
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Answer: Each minute, the pendulum swings 69.115 feet. 
8 0
3 years ago
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Step-by-step explanation:

step 1. x intercepts are where y = 0

step 2. y = 0 when factors are equal to zero

step 3. the x intercepts are 0, sqr(3), -sqrt(3), -1/5

step 4. answer: 4.

6 0
2 years ago
What is the absolute deviation and range of the data set 134 139 145 152 174
malfutka [58]
The answer or range would be 40
6 0
2 years ago
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