Answer: y = -1/3x - 1
Step-by-step explanation:
Slope of perpendicular line is opposite reciprocal --> -1/3Using point given (-6, 1), find b.1 = -6(-1/3) + b1 = 2 + b-1 = b
How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).
Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:
100 * (1+1.07)x = 400
Then we will take 400 and divide it by 100 getting:
1.07X = 4
Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X
Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.
2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula
where:
P (principal) is equal to hypothetical $100
E (e) is a mathematical constant, which is approximately 2.718
R (rate) is the interest rate, in our case it is 5.5%
T (time) is the time required for money to grow
A (amount) is the final amount desired, which is 4 times larger of $100, thus $400
We have the following:
400 = 100 * e0.055t
400/100 = e0.055t
4 = e0.055t
Then we will apply natural log to both sides of the equations and get the following:
ln(4) = ln(e0.055t)
Since e is the base of ln(x) the equation simplifies to:
ln(4) = 0.055t
Using the calculator to find ln(4) we are getting:
1.38629 = 0.055t
Lastly find t
t = 1.38629/0.055
t = 25.20535202
Plug the answers back to the original equation to verify the answers.
1st part of the question answer: t = 20.4895
2nd part of the question answer: t = 25.20535202
Benjamin is going to drive from his house to City A without stopping. An equation that determines Benjamin's distance from City A tt hours after leaving his house is D=260-65t.D=260−65t. What is the slope of the equation and what is its interpretation in the context of the problem?
Given:
The Benjamin's distance from City A, t hours after leaving his house is
[tex]D=260-65t[/tex]
To find:
The slope of the equation and what is its interpretation in the context of the problem?
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m (coefficient of variable x) is slope and b is y-intercept.
We have, the equation
[tex]D=260-65t[/tex]
It is a linear equation and the coefficient of variable t is -65. So, the slope of the equation -65.
It means, the Benjamin's distance from City A is decreases at the rate of 65 units per hour or we can say the speed of Benjamin is 65 units per hour.
Therefore, slope of the equation -65. It means, Benjamin's distance from City A is decreases at the rate of 65 units per hour.
Answer:
The slope of the function is -65 which reveals the average speed that Benjamin travels, in miles per hour.
Step-by-step explanation:
The slope shows how much the distance to City A decreases each hour, implying that Benjamin is driving an average speed of 65 miles per hour.
Have a good day :)
A rectangle has a perimeter of 22cm with a length of 10m. What is the width of one side?
Step-by-step explanation:
We know that
1m = 100cm
according to question
perimeter of rectangle = 2 (l+b)
22cm = 2 (100+b)cm
2×(100+b)cm = 22cm
100+b cm = 22/2cm
100+b cm = 11 cm
b = 100 -11 cm
hence, breadth = 89 cm .thanks for ask question.
HURRY PLZ!!!!!!BY 10:30
One inch is around 2 11/20 centimeters.What fraction of an inch is 1 centimeter?
A) 13/20
B) 17/20
C) 20/51
D) 20/11
Plz get this right!! for some reason it is worth 25 points on this test!! And it is a MIDTERM
Answer: C
Step-by-step explanation: Trust me on this ok?
What percent of 18 is 24?
Answer:
133.33%
Step-by-step explanation:
you can find this by doing 24/18x100, which is equal to 133.33
Answer:
133%
Step-by-step explanation:
We're going to divide [tex]\frac{24}{18}[/tex].
That equals about 1.33 repeating.
Next, we're multiplying that decimal by 100.
That gets us 133.
Please Solve!!!!
And show steps
log(x+4)+ log(x)= log(x+4)
Answer: log(x+4) + log(x)=log(x+4)
Group like terms
log(x+4)-log(x+4)=-log(x)
Log((x+4)/(x+4))=-log(x)
log(1)= -log(x)
log(1)=0
=> 0=log(x)
x=10^0
x=1
Step-by-step explanation:
Before one can solve log questions, he/she must know the laws.
Put x= 1 in to the main equation to test your answer
Log(5) +log(1)=log(5)
log (1) is 0
log(5)=log(5)
BRAINLIEST! URGENT! Please help, I'm not quite good with functions. If you know that answer, please provide an explanation. Thank you.
Answer:
D
Step-by-step explanation:
It must be D because first of all you need the 1.01 because its a 1 percent increase and because when you write out what it would be for lets say 3 years it would be (310*1.01)*1.01)*1.01 so if we drop the parentheses because this is all multiplication you would have 310*1.01^3 which would be 3=t
Answer:
the pollen grain deposited were initially estimated at 310 with a annual increase rate of 1%
thus, there is an increase by 1.01 every year
for the first year after the year the grains were deposited there will be an increase of 310 (1.01)
similarly the following year will have an increase of 310(1.01)
(1.01) or 310(1.01)2-this 2 is a square
also the third, fourth, fifth....year will have an increase of 310(1.01)3-this 3 is a square, 310(1.01)4-this four is a square, 310(1.01)5-also this five is a square
respectively and thus, t years, there will be an increase of 310(1.01)t
ans:D
Note I did not did this I received help
What is (29-7) x 7^2+6
Answer:
used bedmas
Step-by-step explanation:
=(22)x49+6
= 1070+6
=1076
HELP PLSS !!
Margot is studing the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression (line of best fit) to by y=47.3+0.73x
If an additional 1 inch of rain fell, how many MORE bushels of wheat would be yielded
0.78
60.64
48.08
47.3
Answer:
its c 48.08 im pretty sure
Step-by-step explanation:
Help me please! I'm stuck and I need the answer now! Thx so much!
Answer:
34Step-by-step explanation:
Given
z = -3 + 5iConjugate of z is:
z' = -3 - 5iProduct zz' is:
zz' = (-3 + 5i)(-3 - 5i) = (-3)² - (5i)² = 9 - 25(-1) = 9 + 25 = 34If ,
[tex]\bold{z=-3+5i }[/tex]
so,conjugate of z
[tex]\overline{ z }[/tex]=[tex]\bold{-3-5i }[/tex]
Because, in argand plane [tex]\overline{ z }[/tex] is the reflection of z in x-axis.
so,
According to the question,
z[tex]\overline{z}[/tex]=(-3+5i)(-3-5i)
[tex]\bold{(-3)^2-(5i)^2 }[/tex]
[tex]\bold{9-25(-1) }[/tex]
[tex]\bold{ 9+25 }[/tex]
[tex]\bold{ 34 }[/tex]
What is the slope of the line that passes through the points (-7. 10) and (-5,5)?
If h = 12 units and r= 4 units, what is the volume of the cone shown above?
Use 3.14 for .
A.
12.56 cubic units
B.
50.24 cubic units
C.
200.96 cubic units
D. 602.88 cubic units
The area of a 12-cm-wide rectangle is 180cm. what is its length?
Answer:
15cm
Step-by-step explanation:
180/12=15
What is the 10th term of 300, 150, 75
Answer:
So the pattern is dividing in half
So 300, 150, 75
We have the first 3 terms
The 4th term: 37.5, 18.75,
So we get the 10th term: 0.58
What is the slope of the line?
Answer:
-8/3
Step-by-step explanation:
-8/3
you count up from when the line intercepts a secure point that would be 8
then 3 over
its negative because it points down on the right
In the figure, AC is perpendicular to DB.
Which of the following statements is TRUE?
Answer:
B. Angle 5 and Angle 6 are complementary
Step-by-step explanation:
Definition of complementary- either of two angles who sum is 90°
As, Line AC and Line DB are perpendicular, Angle DO(the middle point)C is equal to 90°.
Angle DOC = 90°
Angle DOC = Angle 6 + Angle 5
Therefore, Angle 6 + Angle 5 are equal to 90°, so they are complementary.
Good luck!
Guys I really need help on this please
Answer:
The answer is 26.2.
Step-by-step explanation:
To get the answer we take the miles done in the race, in this case 18.34 and he is 70% done the race. To find out how much total miles are in the race, we convert 70% into a decimal which is 0.70. then we have 18.34 and 0.70 to multiply. 18.34 x 0.70=26.2 Which is your answer.
Hope this helps!
I NEED HELP PLEASE !!!
Answer:
The first choice
Step-by-step explanation:
Perpendicular lines intersect to form right angles, like the x- and y-axis on a coordinate plane.
Answer:
option 1 or A
Step-by-step explanation:
it is the definition of perpendicular lines
Pls help and SHOW WORKINGS..
*URGENT* I NEED HELP WITH THIS QUICK
Answer:
A. Choice 2
B. Choice 1
C. Choice 2
D. Choice 1
Step-by-step explanation:
So basically if it's being multiplied by something each time, then it's choice 2 and if it's being add by something each time, then it's choice 1.
A. You can see in the diagram that each time you multiply the y-value by 2, so it's choice 2
B. In the equation you can tell that every time you will be adding 16, so choice 1
C. Since it's being multiplied by 0.75 each time, it's choice 2
D. Every time y grows by 12, so it's choice 1.
Determine the value of x.
Answer:
the answer is your first choice
pls help asap will give brainliest
Answer:
270.5
Step-by-step explanation:
*sigh* here we go again ok
separate it into a rectangle and semicircle
12*16=192
circle is pi(r)^2/2 so
5^2=25
25*3.14=78.5
78.5+192=270.5
A store is having a 25% off sale on all shirts. Select all of the possible ways to calculate the sale price for a shirt that normally costs $24.
A. 24 - (0.25 x 24)
B. (0.75) x 24
C. (0.25 x 24) x 3
D. (0.25 x 24)
E. (24 + 0.25)
Answer:
A,B, and C
Step-by-step explanation:
25%of 24 is 6, 24-6=18(new price)
A.24-(0.25×24)=24-6=18
B.(0.75)×24=18
C.(0.25×24)×3= 6×3=18
Help please! worth a lot of points! Screenshot included
Answer:
x=44444444444444444444444444444444
Step-by-step explanation:
Answer:
.2
Step-by-step explanation:
3. Q3) What is the smallest number of identical squares
that will fit in this rectangle?
Answer:
Minimum 3 squares.
Step-by-step explanation:
Let the number of identical squares that will fit in the rectangle = x
Sum of the area of the squares = Area of the given rectangle
x(Side length of the square)²= (length of the rectangle × width of the rectangle)
x(S)²= (40 × 90)
x(S)²= 3600 cm²
For the minimum numbers of the squares,
If x = 1,
S = √3600 = 60 cm
But the length of the rectangle is 40 cm, so can't be fitted in the rectangle.
If x = 2,
2S² = 3600
S² = 1800
S = √1800
S = 42.43 cm
Since, length of the rectangle is 40 cm, so the given square can't be fitted in the rectangle.
If x = 3,
3S² = 3600
S² = 1200
S = √1200
= 34.64 cm
Therefore, minimum 3 squares can be fitted in the given rectangle.
a packet contains 6 maths books each of length 25 CM 20 cm and height 2 cm what is the volume of the packet
Step-by-step explanation:
1book valume = 25cm×20cm×2cm=1000cm³
a packet valume = 6×1000cm³ = 6000cm³
Answer:
216000 cm3
Step-by-step explanation:
length of packet = 6 × 25 cm = 150 cm
breadth of packet = 6 ×20 cm = 120 cm
height of packet = 6 × 2 cm = 12 cm
Now,
volume of packet = l×b×h = 150 cm × 120 cm × 12 cm
= 216000 cm3
Solve using quadratic formula.
[tex]4 {s}^{2} + 8s + 4 = 0[/tex]
Which expression represents the volume of the pyramid? One-thirdn(n − 1) units3 One-thirdn(n − 1)2 units3 One-thirdn2(n − 1) units3 One-thirdn3(n − 1) units3
Answer:
The answer is "[tex]\bold{\frac{1}{3} \ n^2 (n - 1) \ units^3}[/tex]"
Step-by-step explanation:
Please find the complete question in the attachment file.
The volume of a pyramid: [tex]V=\frac{1}{3} (\text{base area}) \times (\text{height})[/tex]
In the question if:
[tex]Area= n^2 \ units^2 \\\\height= (n-1) \ units\\[/tex]
apply the value in the volume formula:
[tex]V=\frac{1}{3}\ n^2 \ units \times (n-1) \ units^2\\\\[/tex]
[tex]= \frac{1}{3}\ n^2 \times (n-1) \ units^3\\\\ = \frac{1}{3}\ n^2 (n-1) \ units^3\\\\[/tex]
Answer:
option C). 1/3^2(n − 1) units3
Step-by-step explanation:
just took test
A rational number, by definition, is any number that can be written as a
or two integers.
O quotient
O difference
sum
product
Answer:
Two Integers
Step-by-step explanation:
A party planner wants 220 balloons in each of the 3 rooms. If balloons come in packages of 50 balloons, how many packages must be bought to fill the 3 rooms?
Answer:
14 packages.
Step-by-step explanation:
The total number of balloons needed is 3 * 220 = 660 balloons
To find the number of packages
660 / 50 = 13 with a remainder of 10.
Normally, you would round down, but not with this question. You need to buy a whole package to get the 10 left over balloons.
The answer is 14 packages.