As per the concept of simple interest the term principal refers the original amount invested.
Simple interest:
Basically, the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given,
Here we need to find the correct definition of the term principal.
As per the definition of the concept simple interest, then term principal refers the amount to be invested on the particular assets.
And at the nd of the particular, period the principal amount is either increase or decrease based on the interest applied on it.
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Consider the equation:
0=x^2+4x+10=x
2
+4x+10, equals, x, squared, plus, 4, x, plus, 1
1) Rewrite the equation by completing the square.
Your equation should look like (x+c)^2=d(x+c)
2
=dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c)
2
=dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d.
2) What are the solutions to the equation?
1. The rewritten form of the equation is (x + 2)² = -6
2. The solutions to the equation are 0.45 and -4.45
Given,
The equation;
0=x^2+4x+10
1. We have to rewrite the equation;
x² + 4x + 10 = 0
x² + 4x = -10
Add the square of the half of coefficient of x to both sides
4/2 = 2
x² + 4x + 2² = -10 + 2²
x² + 4x + 4 = -6
(x + 2)² = -6
Therefore,
The rewritten form of the equation is (x + 2)² = -6
2. Calculate the value of x
(x + 2)² = -6
Square root both sides
√(x + 2)² = ±√6
x + 2 = ±2.45
x= ±2.45 - 2
x = 2.45 - 2 and -2.45 - 2
x = 0.45 and -4.45
Hence the solutions to the equation are 0.45 and -4.45
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Answer:
0=x²+4x+1
3=(x+2)²
x=−2± [tex]\sqrt{3}[/tex]
Step-by-step explanation:
What is the best account to get a higher interest-rate but you cannot access the money for a fixed period of time? Why is this the best choice? Choose from CD, checking account, savings account,or money market account
A savings account with a set term and interest rate is known as a certificate of deposit (CD). While CDs often provide greater rates than traditional savings accounts, you can't get to your money right away until the term is over.
What account has the best interest rate?Interest rates on bank savings accounts.A savings account with a set term and interest rate is known as a certificate of deposit (CD). While CDs often provide greater rates than traditional savings accounts, you can't get to your money right away until the term is over.For a set amount of time, such as six months, a year, or five years, a certificate of deposit (CD) is a savings account that earns interest from the issuing bank. Your initial investment plus any accumulated interest is returned when you cash in or redeem your CD.To learn more about Certificate of Deposit (CD) refer to:
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Order each list of numbers from least to greatest. -0.6, 0, 0.5, 0.7,-0.2
Answer:
-0.6, -0.2, 0, 0.5, 0.7
Step-by-step explanation:
To find out this answer, we know first that negatives are the least. And -0.6 is farther away from 0 than -0.2, so we can have -0.6, -0.2 as our last numbers.
Then, 0.5 and 0.7 are greater than 0, so, then we have -0.6, -0.2, 0.
Then, 0.7 is greater than 0.5, so we can arrange the final numbers:
-0.6, -0.2, 0, 0.5, 0.7
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer: -0.6,-0.2, 0, 0.5, 0.7
Step-by-step explanation: Use a number line
WILL GIVE BRAINLIEST!! PLEASE
A car travels 12 km North and then turns left to travel 5 km West before coming to a stop. What is the car’s displacement?
The answer will be 13 km that is displacement of the car.
What is displacement?
When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.
A car travels 12 km north and turns left to travel 5km.
So the final position of car from the initial position is :
So the placement of the car is √(12²+5²) = √169 =13km
Hence the Displacement of the car is 13 km
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Find the volume and surface area of a right circular cylinder with a diameter of 200 cm and a height of 100 cm
The volume of the right circular cylinder is 3141592.65 centimeter cube and the surface area is 125663.70 centimeter square
The diameter of the right circular cylinder = 200 cm
The radius = 200/2
= 100 cm
The height of the right circular cylinder = 100 cm
The volume of the right circular cylinder = π × [tex]r^2[/tex] × h
Where r is the radius
h is the height
Substitute the values in the equation
The volume = π × [tex]100^2[/tex] × 100
= 3141592.65 centimeter cube
The Surface area = 2πrh + 2π[tex]r^2[/tex]
Substitute the values in the equation
= 2×π×100×100 + 2×π×[tex]100^2[/tex]
= 62831.85 + 62831.85
= 125663.70 centimeter square
Hence, the volume of the right circular cylinder is 3141592.65 centimeter cube and the surface area is 125663.70 centimeter square
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Factor the following expression using the common factor -3
-9z - 21y - 2.4
The expression -9z - 21y - 2.4 when -3 is factored out is -3(3z + 7y + 0.8)
How to determine the factored expression?From the question, we have the following expression that can be used in our computation:
-9z - 21y - 2.4
The common factor is given as
-3
So, we divide -9z - 21y - 2.4 by 3
The results of these divisions are
-9z/3 = -3z
- 21y/3 = -7y
- 2.4 /3 = -0.8
So, we have the following results
-9z - 21y - 2.4 = -3(3z + 7y + 0.8)
Hence, the factored expression is -3(3z + 7y + 0.8)
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Need help with question
The required derivatives of the given hyperbolic functions are
d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.
The differentiation formulas for the hyperbolic functions are below as
d/dx(sinhx) = coshx
d/dx(coshx) = sinhx
d/dx(tanhx) = sech²x
d/dx(cothx) = −csch²x
d/dx(sechx) = −sechxtanhx
d/dx(cschx) = −cschxcothx
As per the given question,
⇒ d/dx(sinh3x)
Using formula d/dx(sinhx) = coshx,
⇒ cosh3x × (d/dx(3x))
⇒ cosh3x (3)
⇒ 3cosh3x
⇒ d/dx(tanh6x) = 6sech²6x
⇒ d/dx(coth5x) = −5csch²5x
⇒ d/dx(sech3x) = −3sech3xtanh3x
⇒ d/dx(csch7x) = −7csch7xcoth7x
Thus, the required derivatives of the given hyperbolic functions are
d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.
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What's the point slope for Y = 1/2 X + 3/2
Answer:
1/2
Step-by-step explanation:
The equation given is put in slope intercept form
y = mx + b
where m = slope and b = y intercept
In the equation y = 1/2x + 3/2,
"1/2" takes the spot of "m" meaning that the slope of the equation is 1/2
a pool contains 14,000 gallons of water if the pool leaks at a rate of 0.5 gallons per minute, write a linear equation to model this scenario.
with no water replacement, how much water would be left after 1.5 hours.
please show steps and help me fast :(
Answer:
See below
Step-by-step explanation:
Amount of water in pool = 14 000 - .5 x where x is in minutes
1.5 hr = 90 minutes
amount of water in pool = 14 000 - .5(90) = 13 955 gal
14.
Solve for x.
8/6 = 12/x
Answer:
∴ [tex]x = 9[/tex]
Step-by-step explanation:
[tex]\frac{8}{6} = \frac{12}{x}[/tex]
[tex](\frac{8}{6})(6x) = (\frac{12}{x})(6x)[/tex]
[tex]8x = 72[/tex]
∴ [tex]x = 9[/tex]
The value of x for the given question 8/6 = 12/x is 9.
In the given problem, we know that we need to perform fraction multiplication and algebra to find the value of x.
Here, on the left hand side, we have ⇒ 8/6 (i)
On the right hand side, we have ⇒ 12/x (ii)
To find the value of x, we perform cross multiplication between both sides (LHS and RHS). After performing this function, we get
⇒ 8x = 72
Solving this problem even further, we get
⇒ x = 9
Therefore, the value of x is 9 for the given problem.
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The heaviest freshwater fish caught in region A weighs 279 lb, and the
heaviest freshwater fish caught in region B weighs 619 lb. What
fractional parts of an English ton are each of these fish?
The both fractional parts of an English ton are each of these fish.
What is fractions?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.The English ton, also known as the long ton, is equivalent to 2,240 pounds. Therefore, the fractional parts, of each of the two fish, of the English ton are:
Fish caught in region A weights = 279 lb
Therefore, fish caught in region A
A = 279 ÷ 2240
Fish caught in region B weights = 619 lb
Therefore, fish caught in region B
B = 619 ÷ 2240
Both fractions are irreducible.
So, both fractional parts of an English ton are each of these fish.
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what is the inverse of r(t)=5^t
Answer:
t(r) = log(r)/log(5) = log₅(r)
Step-by-step explanation:
You want the inverse of r(t)=5^t.
Solve for tAn exponential function is solved using logarithms.
[tex]r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}[/tex]
The change of base formula can be used to simplify this a bit.
[tex]\boxed{t(r)=\log_5(r)}[/tex]
__
Additional comment
The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.
The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).
You are welcome to make use of whatever inverse function notation will satisfy your grader.
PLEASE HELP ASAP!!!! FULL ANSWERS!!!! NO SCAMS OR TOMFOOLERY!!!!
A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h ( t ) = − 16 t 2 + 80 t + 384 .
What is the rocket's maximum height? ______________ feet
How long does it take for the rocket to reach its maximum height? ___________ seconds
After it is fired, the rocket reaches the ground at t= ___________ seconds
The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.
Define parabola.A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given,
A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h ( t ) = − 16 t 2 + 80 t + 384
Following is our relationship between height and time:
h ( t ) = − 16 t 2 + 80 t + 384
The vertex of the equation above is as follows because it is a parabola equation.
In this case, a = -16, b = 96, and c = 2560.
The highest point at:
= -96/(2×(-16)
= 96/32
= 3 sec.
Maximum height at three seconds later:
h = -16 ×3² + 96 × 3 + 2560
h = 2704 feet
The rocket reaches the ground at y = 0, adding the following value to the parabolic equation:
0 = 16t² + 96t + 2560
Once we've solved it, we'll get:
t = 16 or
t = -10
Time cannot be negative, so we will choose t = 16 seconds.
The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.
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Please answer need to turn it in
Answer:
Step-by-step explanation:
c
Answer:
It's A
Step-by-step explanation:
I=Prt
I=$660(3.5%)5
I=23.1(5)
I=$115.50
6. In the coordinate plane, line D has slope 1 and y-intercept (0, 0). Line T is the result of dilating line D by a factor of 2 with center (3, 4). What are the slope and y-intercept of line T?
The slope of the line T will be 1 and the y-intercept will be (0,4) in the given coordinate plane.
What is slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. In the case of the equation y = 3x - 7, the slope is 3 and the y-intercept is (0, 7). And b is the value of b in the point that is the y-intercept (0, b). By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Here,
The slope of line D=1
y-intercept=(0,0)
factor=2
coordinate=(3,4)
The slope will not change that will be 1.
y-intercept=0+4
=4
y-intercept=(0,4)
In the given coordinate plane, the y-intercept of line T will be (0,4) and its slope will be 1.
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In a survey of 2329 adults, 712 say they believe in UFOs.
Construct a 95% confidence interval for the population proportion of adults who believe in UFOs.
A 95% confidence interval for the population proportion is
(Round to three decimal places as needed.)
A 95% confidence interval for the population proportion is ( 0.297, 0.335 ).
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level.
Given that,
Point estimate = sample proportion = p' = x / n = 738 / 2336 = 0.316
1 - p' = 1 - 0.316 = 0.684
Z(α/2) = Z(0.025) = 1.96
A 95% confidence interval for population proportion p is ,
p' ± E
= 0.316 ± 0.019
= ( 0.297, 0.335 )
With 95% confidence, it can be said that the population proportion of adults who believe in UFO's is between the endpoints of the given confidence interval
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A car leaves Rockford, Illinois, at the rate of 70 mph, bound for Madison, Wisconsin. At the same time, a truck leaves Madison at the rate of 50 mph, bound for Rockford. If the cities are 72 miles apart, how long will it take for the car and the truck to meet?
Answer:
36 minutes
Step-by-step explanation:
The total distance covered by the two vehicles per hour: 70 + 50 = 120 miles.
Time is distance over velocity.
[tex]t=\frac{72}{120}[/tex] hours
Which simplifies to
[tex]\frac{3}{5}[/tex] hours.
Convert hours to minutes.
There is 60 minutes in 1 hour.
[tex]\frac{1}{60}=\frac{\frac{3}{5} }{x}[/tex]
[tex]x=36[/tex]
A plane has a cruising speed of 300 miles per hour when there is no wind. At this speed, the plane flew 600 miles with the wind in the same amount of time it flew 400 miles against the wind. Find the speed of the wind.
Solving a system of equations we will see that the speed of the wind is 60mi/h.
How to find the speed of the wind?When the plane flies with the wind, the two speeds adds up, while if the plane flies against the wind, the speeds need to be subtracted.
We know that the speed of the plane is 300 mi/h.
If the speed of the wind is W, then we can write the two equations:
(300 mi/h + W)*t = 600mi
(300mi/h - W)*t = 400mi
So we have a little system of equations, if we take the quotient between them we get:
[(300 mi/h + W)*t]/[(300mi/h - W)*t ] = 600mi/400mi
(300 mi/h + W)/(300mi/h - W) = 6/4
Now we can solve this for W.
(300 mi/h + W) = (6/4)*(300 mi/h - W)
W + (6/4)*W = (6/4)*300mi/h - 300 mi/h
W*(10/4) = 150 mi/h
W = (4/10)*150 mi/h
W = 60 mi/h
That is the speed of the wind.
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Use the arc length formula to find the length of the graph of the function y = x ^ (3/2) + 4 from x = 2 to x = 9 (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answer:
[tex]\frac{1}{27}((13)^{\frac{3}{2}}-(6)^ {\frac{3}{2}})[/tex]
Step-by-step explanation:
IXL Help Fast Please !
Answer:
y=-2/5x+4/5
Step-by-step explanation:
it’s parallel so it will have the same slope
2=-2/5(-3)+4
2=6/5+4
2=1 1/5+4
2=5 1/5
5 1/5-2=3 1/5
We know this is 3 1/5 to big so we subtract it from y intercept
4-3 1/5
4/5 is the new y intercept
2=-2/5(-3)+4/5
2=6/5+4/5
2=10/5
2=2
So now the equation is true
Hopes this helps
PLEASE HELP ME ON THIS QUESTION!!! IT DUE TODAY SO PlEASE HELP MEEE
Answer:
Step-by-step explanation: xxxdadyxxx12 snap
y
What 3x+6=21 will mark brainliest
Answer: x = 5
Step-by-step explanation:
3x + 6 = 21
3x = 21 - 6
3x = 15
x = 15/3
x = 5
Answer: X =5
Step-by-step explanation: Subtract both sides by 6 to isolate 3x:
3x+6-6=21-6
3x=15
Divide both side by 3 to come up with x:
X=5.
A shortcut method but it does not follow the correct rules of math but if you're in a hurry it works:
3x+6=21
transfer +6 converting the sign to a -6
3x-=21-6
Subtract 3x=15
Divide by the number with x (3)
x=5
An amount of $ 48,000$ is borrowed lord 9 years at $6 \% 6 interest, compounded annually. If the loan is paid in full at the end of that period, thaw Mach must be paid back?
Use the calculator provided and round your answer to the rarest dollar.
By using the formula for compound interest, it can be calculated that
He must pay back $81095 after 9 years
What is Compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially, rather than linearly, then the interest earned is called compound interest
If p is the principal, r is the rate and t is the time, then the amount is calculated by the formula
[tex]A = p(1 + \frac{r}{100})^n[/tex]
The difference between the amount and the principal gives the compound interest.
Principal = $48000
Rate = 6%
Time = 9 years
Amount = [tex]48000(1+ \frac{6}{100})^9\\[/tex]
= $81095
He must pay back $81095 after 9 years
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Five subtracted from seven times a number is 86
Answer:
7x-5=86
Step-by-step explanation:
After selling tickets to dance for $3.25 each, the student council brought in $1020.50 from ticket sales. How many students attended the dance?
3317
3140
314
31.4
Answer
314
Step-by-step explanation:
hope this helps ya
how much more will $28,000 earn in interest than $16,000 if both invested in savings accounts with APYs of 5.8% for a year
The $28,000 investment will earn $696 more than the $16,000 investment if both make a 5.8% (APY) annual percentage yield for a year.
What is the APY?APY means annual percental yield.
Annual Percentage Yield describes the real interest rate earned on an investment in a year.
The Annual Percentage Yield refers to the interest an investment, saving, and loan attracts for the time value of money and inflationary effects.
The Annual Percentage Yield is applied to the investment amount for a year to calculate the interest earned.
Plan A Plan B
Investments $28,000 $16,000
Interest earned $1,624 $928 ($16,000 x 5.8%)
The difference in interest earned = $696 ($1,624 - $928)
Thus, when an investor puts $28,000 in a savings account at 5.8%, they earn $696 more than investing $16,000 at the same APY.
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If f(x) = 2*+5, fill out the following table of values:
-1
0
x
What type of function is this?
1
2
3
Answer:
2
Step-by-step explanation:
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A house has increased in value by 15% since it was purchased. If the current value is 299,000, what was the value when it was purchased?
The value of the house when it was purchased is 260,000 units
How to find the value the house was purchased?The house has increased in value by 15 percent since it was purchased. The current value is 299,000.
The value of the house when it was purchased can be calculated as follows:
let the amount purchased = x
Hence,
15% of x + x = 299000
0.15x + x = 299000
1.15x = 299000
divide both sides by 1.15
Hence,
x = 299000 / 1.15
x = 260000
Therefore, the value of the purchase is 260,000 units
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√2-√x+6= -√x
Please show how to answer
Answer:
So you see what happened there
the sides are not equal so there is no answer
the answer that is the closest is 8 = 0
Step-by-step explanation:
Add x to both sides
2 - x + 6 + x = -x + x
simplify
2 + 6 = 0
simplify 2 + 6: 8
8 = 0
What is $68.61 divided by 6?
Answer: 68.61/6 = 11.435
