Answer:
14
Step-by-step explanation:
10000 = 5000[tex](1.05)^{t}[/tex]
2 = [tex](1.05)^{t}[/tex]
ln(2) = t ln(1.05)
t = ln(2)/ln(1.05)
[tex]\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots[/tex]
For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.
How to find the compound interest?If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,
then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
For $5000 invested at 5% p.a. compound interest with yearly
rests to double in value, we need to find the time.
So,
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
[tex]10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21[/tex]
Hence, The time will be 14 years. So, option D is correct.
Learn more about compound interest here:
https://brainly.com/question/1329401
#SPJ2
What is the volume of the cylinder?
5767 cm3
2887 cm3
967 cm3
1921 cm3
PLEASE HELP ME I WILL MARK BRAINLIEST!
compute the range of the figures into the table
3x+1/x^(2)-1=2/x-2+x/x-1
Answer:
x = 0 and 3 other real roots. See below.
Step-by-step explanation:
This is what you wrote:
[tex] 3x + \dfrac{1}{x^2} - 1 = \dfrac{2}{x} - 2 + \dfrac{x}{x} - 1 [/tex]
I don't think that is what you meant to write.
I think you meant to write this:
[tex] 3x + \dfrac{1}{x^2 - 1} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
I'm going to answer the second equation because that is what I think you meant.
[tex] 3x + \dfrac{1}{(x - 1)(x + 1)} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
[tex] 3x(x - 1)(x + 1)(x - 2) + (x - 2) = 2(x - 1)(x + 1) + x(x + 1)(x - 2) [/tex]
[tex] (3x^2 - 6x)(x^2 - 1) + x - 2 = 2x^2 - 2 + x(x^2 - x - 2) [/tex]
[tex] 3x^4 - 3x^2 - 6x^3 + 6x + x - 2 = 2x^2 - 2 + x^3 - x^2 - 2x [/tex]
[tex] 3x^4 - 7x^3 - 4x^2 + 9x = 0 [/tex]
[tex] x(3x^3 - 7x^2 - 4x + 9) = 0 [/tex]
[tex] f(x) = 3x^3 - 7x^2 - 4x + 9 [/tex]
[tex] f(-3) = -123 [/tex]
[tex] f(-2) = -35 [/tex]
[tex] f(-1) = 3 [/tex]
[tex] f(0) = 9 [/tex]
[tex] f(1) = 1 [/tex]
[tex] f(2) = -3 [/tex]
[tex] f(3) = 15 [/tex]
One root is x = 0.
There is a root between x = -2 and x = -1.
There is a root between x = 1 and x = 2.
There is a root between x = 2 and x = 3.
Plot the graph of f(x) = 3x^3 - 7x^2 - 4x + 9 and try to read the other three roots.
ok please help i don't understand part of the question, I will try and give brainly
Answer:
j' = (1,-2) k'=(3,-1) L' = (3,-3)
Step-by-step explanation:
I think that you just multiply all the x,y values for the three points by 1/5?
5 1
-10 -2
j' = (1,-2)
~~~~~~~~~~~~~~~~~~
15 3
-5 -1
k'=(3,-1)
~~~~~~~~~~~~~~~
15 3
-15 -3
l' = (3,-3)
The polygons in each pair are similar. find the missing side length
If both are similar ratio of sides will be same
[tex]\\ \sf\longmapsto \frac{x}{25} = \frac{7}{5} \\ \\ \sf\longmapsto 5x = 7 \times 25 \\ \\ \sf\longmapsto 5x = 175 \\ \\ \sf\longmapsto x = \frac{175}{5} \\ \\ \sf\longmapsto x = 35[/tex]
help me guys! 50 points!
Answer:
The volume of the irregular figure would be 144 [tex]cm^3[/tex].
Step-by-step explanation:
If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be 12 * 3 * 3 = 12 * 9 = 108 [tex]cm^3[/tex], and the volume of the smaller rectangular prism would be 4 * 3 * 3 = 12 * 3 = 36 [tex]cm^3[/tex]. So the volume of the entire irregular figure would be 108 + 36 = 144 [tex]cm^3[/tex].
Answer:
144 cm^3
Step-by-step explanation:
Large rectangle:
12 × 3 × 3 = 36 × 3 = 108
Small rectangle:
7 - 3 = 4
4 × 3 × 3 = 12 × 3 = 36
Both:
36 + 108 = 144
Hope this helped.
Which figures are polygons?
Answer: A,C,D
Step-by-step explanation:
Answer:
pretty sure it's a, c, and d
Step-by-step explanation:
polygons have straight sides, not curved. it's a 2d figure, and it is enclosed. b doesn't fit the criteria of that because of the fact that the shape is a bit curved, as the other options do fit that criteria.
Consider the following function.
Place the steps for finding f -1(x) in the correct order.
↓
↓
↓
↓
Answer:
if f(x) = ax + b then f-1(x) = (x - b)/a
Step-by-step explanation:
Now
f(x)=ax + b
then y = ax + b
interchanging x and y , we get
or, x = ay + b
or, x - b = ay
or, (x - b)/a = y
therefore,f-1(x) = (x - b)/a
150°
2x + 100°
X =
degrees
Answer:
x = 25°
Step-by-step explanation:
The 2 angles are vertical angles and are congruent , then
2x + 100 = 150 ( subtract 100 from both sides )
2x = 50 ( divide both sides by 2 )
x = 25°
Answer: x = 25°
Step-by-step explanation:
⇒2x + 100 = 150
⇒2x = 150-100
⇒x = 50/2
⇒x = 25
Reason (VOA) vertically opposite angles are equal.
please click thanks and mark brainliest if you like :)
if y - 1/y =8 then find the value of y^2-1/y^3
Step-by-step explanation:
[tex] {y}^{2} - \frac{1}{ {y}^{3} } [/tex]
factorise out y² ;
[tex] = {y}^{2} (1 - \frac{1}{y} ) \\ \\ = 8 {y}^{2} [/tex]
please help don’t understand question!
Answer:
[tex]{ \sf{ - 2 {a}^{5} + 4 {a}^{4} + 5 {a}^{3} + \frac{2}{3}a }}[/tex]
Answer:
D
Step-by-step explanation:
A polynomial is in standard equation when the degree of the polynomial are in descending order.
PLEASE HELP!!! Super important!!!
Answer:
5n
Step-by-step explanation:
output=5x
where x is = input
there fore if input is n, output is 5n
⁴⁄₇ × ²⁄₃
Click the picture so that you can see the whole question
Answer:
8/21
Step-by-step explanation:
just multiply the numerator and denominator
help please coordinates for math
Answer: Slope = c / a + b
Concept:
Here, we need to know the idea of a slope.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Slope = Rise / Run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)
Solve:
STEP ONE: Identify the points
A (0, 0)
C (a + b, c)
STEP TWO: Apply the formula
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (c - 0) / (a + b - 0)
Slope = c / a + b
Hope this helps!! :)
Please let me know if you have any questions
Help. Step By Step Explanation. Ron and two of his friends ate one fourth each of an eight slice pizza. Find remaining slice of the pizza
Answer:
2 remaining slices
Step-by-step explanation:
It sounds complicated so firstly, let's break it down.
Ron and two of his friends
There are three people involved in this question.
ate one fourth each
These three people ate one fourth of the pizza each
of an eight slice pizza.
From a pizza with eight slices
Find remaining slice of the pizza
The main question : remaining slice of the pizza
So since there were three people and they ate one fourth of the pizza
( One fourth's [tex]\frac{1}{4}[/tex] by the way )
We need to find out how much have they ate.
Simply multiply 3 with [tex]\frac{1}{4}[/tex] .
3 × [tex]\frac{1}{4}[/tex] = [tex]\frac{12}{4}[/tex] × [tex]\frac{1}{4}[/tex]
= [tex]\frac{3}{4}[/tex]
And there you go! Ron and his friends ate [tex]\frac{3}{4}[/tex] of the pizza.
But that's not the end.
The main question : Remaining slice of the pizza
It's an eight slice pizza, so a slice would be : [tex]\frac{1}{8}[/tex]
A full eight slice pizza would be one.
So, to find the remaining slice of pizza, simply subtract [tex]\frac{3}{4}[/tex] from 1.
1 - [tex]\frac{3}{4}[/tex] = [tex]\frac{4}{4}[/tex] - [tex]\frac{3}{4}[/tex]
= [tex]\frac{1}{4}[/tex]
Now there's a remainding of [tex]\frac{1}{4}[/tex] of the pizza.
But the question asked for remaining slices.
So, simply convert the denominator into 8!
( Just in case you don't know what's a denominator )
[tex]\frac{numerator}{denominator}[/tex]
So, simply multiply the denominator by 2 to turn 4 into 8!
And also, whenever the denominator is multiplied/ divided by any number, so do the numerator.
[tex]\frac{1 times 2}{4 times 2}[/tex] = [tex]\frac{2}{8}[/tex]
Your answer's the numerator, 2!
So your final answer should be 2 remaining slices out of the eight sliced pizza.
HOPE THIS ANSWER HELPED :)factorize
a)a²x+2ax-3x+5a²+10a-15
b)(a+b)(a-b)-a+b
c)x³-x²+x+x²y-xy+y
Answer:
(a)x(a^2+2a-3)+5(a^2+2a-3)
Asha found that a vertical line intersects the graph of x = StartAbsoluteValue y EndAbsoluteValue at two points. What can Asha conclude about x = StartAbsoluteValue y EndAbsoluteValue?
It is a function of x but not a relation.
It is a relation but not a function of x.
It is both a function of x and a relation.
It is neither a function of x nor a relation.
Answer:
what can i help u with
Step-by-step explanation:
The graph of x = |y| is as shown in the figure.
When we draw a vertical line, it intersects the graph at two points.
This means for the same value of x , we have two values of y.
Or in other words, for the same pre image, we have two images.
Hence it is not a function.
But for every value of x, we do have a value of y, hence it is a relation.
x = |y| is a relation but it is not a function
Answer:
:B
Step-by-step explanation:
hope that can help
Which rule is a recursive rule for the sequence
1, – 6, 36, – 216,
...?
Ο o An
-
6. An-1
ο o an
.
6
An-1
o an
6. An-1
1
ο o an
-
.
6
an-1
1
2
3
12. Classify the following number. (Select all that apply)
*
5/3
Natural
Whole
Integer
Rational
Irrational
Answer:
rational is the answer....
what is the graph of the following function??
PLEASE HELP!!
Answer:
umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...
Step-by-step explanation:
Determinar la altura de una antena que, A cierta hora del día,Arroja una sombra de 2.85 m, En ese preciso momento Marta que Mide 1.65 m Proyecta una sombra de 1.16 m
Answer:
La altura de la antena es 4.054 metros.
Step-by-step explanation:
La altura del objeto es perpendicular a la longitud de la sombra, tanto el triángulo rectángulo de la antena como el triángulo rectángulo de Marta son semejantes. La altura de la antena se determina mediante la siguiente relación:
[tex]\frac{h}{l} = \frac{H}{L}[/tex] (1)
Where:
[tex]h[/tex] - Altura de Marta, en metros.
[tex]l[/tex] - Longitud de la sombra de Marta, en metros.
[tex]L[/tex] - Longitud de la sombra de la antena, en metros.
[tex]H[/tex] - Altura de la antena, en metros.
Si sabemos que [tex]h = 1.65\,m[/tex], [tex]l = 1.16\,m[/tex] y [tex]L = 2.85\,m[/tex], entonces la altura de la antena es:
[tex]H = h\cdot \left(\frac{L}{l} \right)[/tex]
[tex]H = 1.65\,m \times \left(\frac{2.85\,m}{1.16\,m} \right)[/tex]
[tex]H = 4.054\,m[/tex]
La altura de la antena es 4.054 metros.
IssaC is now x years old. Erika is 7 years older than Issac. In terms of how old was Erika 4 years ago ?
Answer:
Isaac = x
Step-by-step explanation:
Erika is 3y older than Isaac
Isaac is x years old
Answer: x+3
Work Shown:
x = Issac's age right now
x+7 = Erika's age right now
(x+7)-4 = x+3 = Erika's age four years ago
Hay 31 estudiantes en una clase. Ocho (8) estudiantes miden más de 6 pies de altura. Diecisiete (17) estudiantes miden 5-6 "a 6'-0" de altura. Seis (6) estudiantes miden menos de 5-2". ¿Cuál es la razón entre el número de estudiantes de menos de 5'-2" y el número de estudiantes de más de 6 'de altura?
Answer:
4/3
Step-by-step explanation:
Find the area of the shaded region. Use 3.14 for at as necessary. PLEASE HELP ASAP!!
A. 53.5cm^2
B. 132 cm^2
C. 26.8 cm^2
D. 17.1 cm^2
9514 1404 393
Answer:
A. 53.5cm^2
Step-by-step explanation:
The area of the circle is ...
A = πr²
A = 3.14(5 cm)² = 78.5 cm²
The area of the triangle is ...
A = 1/2bh
A = 1/2(10 cm)(5 cm) = 25 cm²
The shaded area is the difference between the circle area and the triangle area:
shaded = 78.5 cm² -25 cm² = 53.5 cm²
_____
Additional comment
As with many multiple-choice questions, you can simply pick the answer that is not outlandish. The circle will fit into a square that is 10 cm on a side, so its total area is less than 100 cm² (eliminates choice B).
The shaded area is definitely more than 1/4 of that 100 cm² square, so choices C and D are eliminated, too. The only choice that is not unreasonable is choice A.
Answer:
A.) 53.5 cm2
Step-by-step explanation:
I got it correct on founders edtell
If you save a hundred dollars every two weeks for five years how much money would you have?
Answer:
$13,000
Step-by-step explanation:
52 weeks in a year means 26 two week periods (fortnights, if you feel it is important in social studies). This means 2600 dollars per year. Multiplty by 5 to get $13,000. Hope this helps!
What were the dimensions of the original photo? 4 inches by 4 inches 6 inches by 6 inches 10 inches by 10 inches 12 inches by 12 inches
Answer:
6 inches by 6 inches
Step-by-step explanation:
Area of the square = 256 inches ²
Given equation:
(x + 10)² = 256
Where,
x = side measure of the original square
(x + 10)² = 256
(x + 10)(x + 10) = 256
x² + 10x + 10x + 100 = 256
x² + 20x + 100 = 256
x² + 20x + 100 - 256 = 0
x² + 20x - 156 = 0
Solve the quadratic equation by factorization
Find two numbers whose product is -156 and sum is 20
The numbers are -26 and 6
x² + 26x - 6x - 156 = 0
x(x + 26) - 6(x + 26) = 0
(x + 26) (x - 6) = 0
x + 26 = 0 or x - 6 = 0
x = -26 or x = 6
Side length of a square can not be negative
Therefore,
x = 6 inches
6 inches by 6 inches
Verizon charges a $40 sign up fee and $60 a month for their new hotspot. T-Mobile charges a $100 sign up fee and then $40 per month for their new hotspot. After how many months of service will the two company's fees be the same?
It will take 3 months for both company's fees be the same
Let
y = total charges
x = number of months
Verizon:
y = 40 + 60x
T-Mobile:
y = 100 + 40x
Number of months it will take both companies to charge the same fee
Equate the total charges of both companies
40 + 60x = 100 + 40x
40 - 100 = 40x - 60x
-60 = - 20x
x = -60 / -20
x = 3 months
https://brainly.com/question/24374422
Complete the solution of the equation. Find the
value of y when x equals 17.
-X + y = -27
Enter the correct answer.
000
DONE
Clear all
#00
11?
Answer:
y = -10
Step-by-step explanation:
When x = 17, the equation be -17 + y = -27 when you plug in 17 for x
Then, add 17 to both sides to get y = -10
Answer: " y = -10 . "
___________________
Step-by-step explanation:
___________________
The question:
Find the value of "y" when "x" equals 17.
Given the equation:
- x + y = -27 ;
___________________
We plug in the given value: "17" ; for "x" ; and solve for "y" :
- 17 + y = -27 ;
_____________________
↔ y + (-17) = -27 ;
Rewrite as:
y − 17 = -27 ; {since: "adding a negative value" is the same
as "subtracting a positive value."}.
_____________________
Now, we add "17" to each side of the equation;
to isolate "y" on one side of the equation; and to solve for "y" :
y − 17 + 17 = -27 + 17 ;
to get:
y = - 10 .
_____________________
Hope this is helpful to you.
Best wishes to you in your academic pursuits—
and within the "Brainly" community!
_____________________
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have.(hint: one is the other simplified)
Answer:
0.05N - 0.1N + 1.7 (in dollars
1.7 - 0.05N (in dollars)
Step-by-step explanation:
Given :
Total number of coins = 17
Number of nickels = N
Number of dimes = 17 - N
1 nickel = 5 cent = $0.05
1 dime = 10 cent = $0.1
The amount of money :
(Value of nickel * number of nickels) + (value of dime * number of dime)
(0.05 * N) + (0.1 * (17-N))
0.05N + 1.7 - 0.1N
0.05N - 0.1N + 1.7
-0.05N + 1.7 = 1.7 - 0.05N
The area of the regular hexagon is 169.74 ft2. A regular hexagon has an apothem with length 7 feet and an area of 169.74 feet squared. What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft
Answer: [tex]48.5\ ft[/tex]
Step-by-step explanation:
Given
Area of the regular hexagon is [tex]169.74\ ft^2[/tex]
Length of the apothem is [tex]l=7\ ft[/tex]
Suppose the side of the hexagon is a
Hexagon can be divided into six equal triangles with same area
Area of a single triangle is
[tex]\Rightarrow A_1=\dfrac{1}{2}\times 7\times a\\\\\Rightarrow A_1=3.5a\ ft^2[/tex]
Area of hexagon will be equal to area of 6 equal area triangles
[tex]\Rightarrow 6A_1=169.74\\\Rightarrow 6\times 3.5a=169.74\\\Rightarrow a=8.08\ ft[/tex]
Perimeter of the hexagon is
[tex]\Rightarrow P=6a\\\Rightarrow P=6\times 8.08\\\Rightarrow P=48.49\approx 48.5\ ft[/tex]
Thus, the perimeter of the hexagon is [tex]48.5\ ft[/tex]
Answer:
C
Step-by-step explanation:
edge 2021
