The amount of the money borrowed is 864.941
So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x where r is the growth rate (interest rate)
So the equation can be written as
m=(1.04)^t
Where m represents the amount of money over time, P represents the principal amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount
[tex]I=P(1.04)^t-P[/tex] where I represent the interest paid.
plug the values into the equation
[tex]108=P(1.04)^3-P\\P=864.941[/tex]
Therefore the amount of the money borrowed is 864.941.
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Which of these numbers are larger 1.201 or 1.2 recurring
Answer:
1.2
Step-by-step explanation:
because recurring means endless repeating.
Factorize
ху
+ 3x +3y
+ 18
Answer:
(x+6)(y+3)
Step-by-step explanation:
xy + 3x + 6y + 18x(y + 3) + 6(y+3)(x+6)(y+3)Solve for x: 4(x + 2) = 3(x-2)
Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 ab b2)
Answer:
Step-by-step explanation:
Expanding the right-hand side,
[tex](a-b)(a^{2}+ab+b^{2})=a^{3}+a^{2}b+ab^{2}-a^{2}b-ab^{2}-b^{3}=a^{3}-b^{3}[/tex]
Thus, the identity is true.
asapppppp please i need help i need to pass
Answer:
Option 2 which is r^6
Step-by-step explanation:
You need to apply the exponent rules.
Since the r's are the same, you can subtract the exponents.
r^9 - r^3 = r^6
Notice that the bases ("r") stayed the same.
Answer: Choice [B] -r^6 ✅
Step-by-step explanation:
Hii!
Do you need to know the answer to your question? No problem!
We can use the Exponents' Property of division to work out the answer to this particular problem. (:
This property says that if you divide two numbers with the same base, you subtract their exponents.
Do we have the same base here? Yea', sure! The same variable can't stand for two different numbers in the same expression.
Let's work out the answer!
[tex]\LARGE\boldsymbol{r^9/r^3=r^{9-3}=r^6}[/tex]
Voila! There's our answer, cheers!
--
Hope that this helped! Best wishes.
--
this is really confusing please help
Step-by-step explanation:
you don't know the meaning of
[tex]y = {h}^{ - 1} (x)[/tex]
it means it is the inverse function to h(x).
the regular function assigns an y value to every x value.
the inverse function now turns this around and finds for a given y value the original x value.
so, the inverse function is easier understood, if we would write it
[tex]x = {h}^{ - 1} (y)[/tex]
but just for formal reasons, we don't define functions this way but do it like above (x is the input, y the output value).
just, the understanding of an inverse function is a I just described it.
that means for the points, simply x and y values trade places.
the point (1, 9) turns into (9, 1) (it means 1 was the original x value when the original function delivered 9 a result).
and the point (3, 2) turns into (2, 3).
so, move the 2 green dots to these coordinates.
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate of 3.5 km per hour, for how long will Anne walk
Anne will walk a distance of 7 km, and she takes 2 hours to walk that distance.
For how long will Anne walk?
The total distance is 18.5 km.
She travels 10km by train and 1.5km by bus, for a total of 11.5km.
The distance that she walks is given by:
18.5km - 11.5km = 7km
So she walks for a distance of 7 km, at a speed of 3.5km per hour.
Remember the relation:
distance = time*speed
That can be rewritten to:
time = distance/speed.
Then the time that she walks is given by:
T = (7 km)/(3.5 km/hour) = 2 hours
She walks for 2 hours.
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Find the value of X in the given
right triangle.
10
x= [?]°
Enter your answer as a decimal rounded to the
nearest tenth.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answer:
2nd and third option
Step-by-step explanation:
The second option just combines the 6.5p and the 0.01p on the right side to obtain 6.49p. The third option just multiplies both sides by 100.
Help me O people!
Please!
Answer:
the answer is L
Step-by-step explanation:
that's just how u round
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answer:
f(x) = -2x+1
Step-by-step explanation:
See attached image
The equation of line will be;
⇒ f (x) = - 1/2x + x
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 3) and (4, -1).
Now,
Since, The equation of line passes through the points (- 4, 3) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (3)) / (4 + 4)
m = - 4 / 8
m = - 1/2
Thus, The equation of line with slope - 1/2 is,
⇒ y - (3) = - 1/2 (x + 4)
⇒ y - 3 = - 1/2x - 2
⇒ y = - 1/2x + x
Therefore, The equation of line will be;
⇒ f (x) = - 1/2x + x
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the radis of the cylinder is (2/7) units and height of the cylinder is (8/11 units find the volume of the cylinder use =22/7
The volume of the cylinder is 64/3773 cubic units
Volume of a cylinderThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
where
r is the radius
h is the height
Given the following parameters
r = 2/7units
h =8/11 units
Substitute
V = 22/7 * 2/7 * 2/7* 8/11
V = (2/7)³ * 8/11
V = 8/343 * 8/11
V = 64/3773 cubic units
Hence the volume of the cylinder is 4/3773 cubic units
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On the day of his 18th birthday, David decided to start saving money regularly.
a) Starting on that day, he could save £ 60 on the same date every month.
How much would he have saved by the day before his 60th birthday?
b) David explored another option.
Starting on his 18th birthday, he could save £ 100 on the same date every year.
If he saved in this way, how old would he be by the time he saved £ 2000?
a) The person will save $15,120 by the day before his 60th birthday. b) David would have had £2000 when he is 37 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
a) Let x be a number of months.
Now, we will find a number of years between 60 and 18 years.
There will be 42 years from 18th birthday to 60th birthday.
Now, we will convert 42 years into months.
42 × 12 = 504
In order to find the total amount saved in 504 months, we will substitute in expression:
30x = 30(504) = 15120
Hence, the person will save $15,120 by the day before his 60th birthday.
b) David starts saving £100 annually from his 18th birthday
We would save £2000 after
(2000/100) years = 20 years
Since his 18th birthday is the first of the 20 years and so he will save £950 for the next 19 years, which is
18 + 19 = 37 years old
Hence, David would have had £2000 when he is 37 years old.
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A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza. Chee purchased a membership to this pizza shop. How much would Chee have to pay the pizza shop if she bought 12 slices of pizza this month? What would be the monthly cost for x slices of pizza?
Monthly cost with 12 slices:
Monthly cost with x slices
need answer quickly
The Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza.
Cost for 12 slices = 12×1.25 = $15
Total cost = 20 + 15 = $35 (for this month if she bought 12 slices of pizza)
The monthly cost for x slices of pizza:
= 1.25x + 20
x is the number of slices
Thus, the Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)
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This is confusion please help
Answer:
c = 5√5
Step-by-step explanation:
When we have a right triangle, there is a property about its measurements that is always true, and its called the "Pythagorean Theorem"
First, let's understand the basic terms we use to describe the sides of a triangle:
we can call one leg "a", the other leg "b" and the slanted side "c"
("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)
the pythagorean theorem:
a² + b² = c²
here, our "a" is 5, our "b" is 10 {and we don't know what c is}
let's try plugging these values into our formula:
a² + b² = c²
5² + 10² = c²
25 + 100 = c²
125 = c²
now, we know what c² is--but we want to know c,
so we must take the square root of both sides
√125 = √c²
√125 = c
now, while √125 is our answer, we can simplify further!
this is because 125 can be made up of 5 · 25
so, [tex]\sqrt{125} = \sqrt{5*25}[/tex]
and
[tex]\sqrt{5*25}=\sqrt{5}*\sqrt{25}[/tex]
we can take out the square root of 25 (5):
[tex]=\sqrt{5}*5[/tex]
we write this as such: [tex]5\sqrt{5}[/tex]
so, in simplest radical form, c = 5√5
(√125)
hope this helps!! have a lovely day :)
a sunflower has increased in height from 72.4cm to 86.2 cm. what is the percentage increase?
Answer:
initial hieght = 72.4 cm
final hieght = 86.2 cm
change in hieght = 9.8 cm
percentage increase = (9.8 ÷ 72.4 ) * 100 = 13.59 %
On a coordinate plane, triangle 1 is reflected across the x-axis to form triangle 4, is reflected across a diagonal to form triangle 3, is reflected across the y-axis to form triangle 2.
Use the figure to complete the statements.
Triangle 1 is the image of triangle 2 reflected over the
.
Triangle 2 is the image of triangle 3 reflected over the
.
Reflecting triangle 4 over the y-axis results in triangle
.
The complete statements are; Triangle 1 is the image of triangle 2 reflected over the y-axis. Triangle 2 is the image of triangle 3 reflected over the x-axis. Reflecting triangle 4 over the y-axis results in triangle 3.
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in the opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Triangle 1 is across from triangle 2. If we make the triangles bisect, they will touch the y-axis.
Triangle 2 is above triangle 3. If we make the triangles bisect, they will touch the x-axis.
we can translate it (a congruent shape that is on a different axis and is the same distance from that axis) and rotate it to 90 degrees.
The complete statements are;
Triangle 1 is the image of triangle 2 reflected over the y-axis.
Triangle 2 is the image of triangle 3 reflected over the x-axis.
Reflecting triangle 4 over the y-axis results in triangle 3.
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Graph the rational function
f(x) = 2x+3
———
X-4
Answer:
Step-by-step explanation:
what is is i^30?
A. -i
B. -1
c. 1
D.i
[tex]i^{30}=(i^2)^{15}=(-1)^{15}=-1[/tex]
Instructions: Simplify the algebraic expression.
−12(32x−10y)
Answer:
-384x - 120y
Step-by-step explanation:
General Concepts and Formulas:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Steps:
1) Distribute
[tex]-12(32x-10y)[/tex]
We must distribute the expression above by multiplying -12 by the coefficients and then adding the variables.
So first, multiple -12 by 32 and add the variable 'x' when getting the product:
-12(-384x - 10y)
Now that we have one part, let's solve the other part.
We now must multiple -12 by -10, which gets us 120, now we must plug in:
(-384x - 120y)
(Remove parenthesis)
⇒ -384x - 120y
Si un celular Cuesta 4500 y tiene un descuento de 76%cuamto vq a pagar por el teléfono
De acuerdo con las definiciones de precio a pagar, porcentaje de descuento y porcentaje remanente, el precio a pagar por el celular es $ 1080.
¿Cuánto cuesta un celular con descuento?
En esta situación una persona recibe un descuento por la compra de su celular, el precio a pagar es el producto de multiplicar el coste sin descuento y el porcentaje remanente en forma fraccionaria. El porcentaje remanente se calcula al restar el descuento del cien por ciento. A continuación, procedemos al cálculo requerido:
x = 4500 × (1 - 76/100)
x = 1080
De acuerdo con las definiciones de precio a pagar, porcentaje de descuento y porcentaje remanente, el precio a pagar por el celular es $ 1080.
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Please help!
What is the first step in solving the function below?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow C.\:factor \:\: out \:\: 2x [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{3} - 18 {x}^{2} + 40x[/tex]
[tex]\qquad \tt \rightarrow \: 2x(x {}^{2} ) - 2x(9x) + 2x(20)[/tex]
[tex]\qquad \tt \rightarrow \: 2x( {x}^{2} - 9x + 20)[/tex]
Henceforth, The most efficient first step in factorising the given trinomial is to factor out 2x
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The vertical line test can be used to determine the given relation/graph is a
Which of the following is equal to 5 1/3?
OA. 1/5
OB. 5 3
O C. √5.3
OD. √5
The correct answer is option B which is ( 5 / 3)
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
The value will be calculated as:-
[tex]5\times \dfrac{1}{3}[/tex] = [tex]\dfrac{5}{3}[/tex]
1.67 = 1.67
Therefore the correct answer is option B which is ( 5 / 3)
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Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15
Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
which of the following sets are discrete?!? check all that apply.
which of the following sets are discrete?
Answer: C. {2,4,6,8}
Step-by-step explanation:
because constituting a separate entity : individually distinct several discrete sections. 2a : consisting of distinct or unconnected elements : noncontinuous. b : taking on or having a finite or countably infinite number of values discrete probabilities a discrete random variable.
Expand . ( 3x –2 ) 2 please help me with this.
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
The number 1.41421356 is a rational or irrational number
Answer:
The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as 2 (1.41421356..., the square root of 2, an irrational algebraic number).
The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1
On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3
On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
The graph of the function has an axis of symmetry at x = 3 will be D. f(x) = x² - 6x - 1. On a coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
What is axis of symmetry?It should be noted that the axis of symettry is the line that divides an object into two equal halves.
Here, the graph of the function has an axis of symmetry at x = 3 is option D. On the coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
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Answer: D. f(x) = x² - 6x - 1
Right on Edge 2023 :)
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by
train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate
of 3.5 km per hour, for how long will Anne walk?
Answer:
Anne will walk for 2 hours.
Step-by-step explanation:
Distance formula = velocity × time
Total distance is 18.5 km
Anne travels by train = 10 km
and by bus = 1.5 km
let the distance covered by anne by walking be x
10 + 1.5 + x = 18.5
x = 18.5 - 10 - 1.5
x = 7km
Rate of walking is 3.5 km per hour
the time she will take while walking = 7 ÷ 3.5 = 2 hours.
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