Using an exponential function, it is found that the loan balance b after n years is given by:
[tex]b(n) = 1000(1.12)^n[/tex]
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that:
She took a $1,000 loan, hence A(0) = 1000.The interest rate is of r = 0.12.Hence the balance b after n years is given by:
[tex]b(n) = 1000(1.12)^n[/tex]
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What is the solution to 2x²+8x=x²-16?
Ox=-4
Ox=-2
Ox=2
Ox=4
Answer:X is equal to -4 twice
Step-by-step explanation:
The solution to the equation 2x² + 8x = x² - 16 is x = -4.
Option A is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:
2x² + 8x - x² + 16 = 0
Simplifying further, we get:
x² + 8x + 16 = 0
This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.
We can solve this equation by factoring it:
(x + 4)(x + 4) = 0
This gives us two solutions:
x + 4 = 0 or x + 4 = 0
x = -4 or x = -4
Therefore,
The solution to the equation 2x² + 8x = x² - 16 is x = -4.
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A ring-shaped region is shown below.
Its inner diameter is 16 ft. The width of the ring is 2 ft.
it
16 ft
Find the area of the shaded region.
Use 3.14 for . Do not round your answer.
X5?
Answer:
Area = 213.52 sq.ft
Step-by-step explanation:
[tex]A_{s} =\pi (18)^{2} -\pi (16)^{2} =324\pi -256\pi =68\pi[/tex]
[tex]\pi =3.14[/tex]
[tex]A_{s} =68(3.14)=213.52sq.ft[/tex]
Hope this helps
Answer:
113.04 ft²
Step-by-step explanation:
The area of the ring can be found by multiplying its center-line length by its width.
__
The diameter of the circle that is the center-line of the ring is ...
16 ft + 2 ft = 18 ft . . . . center-line diameter
The length of the center-line is then ...
C = πd
C = 3.14(18 ft) = 56.52 ft
And the area of the ring is ...
A = LW = (56.52 ft)(2 ft) = 113.04 ft²
The shaded area is 113.04 square feet.
Match y = 3x – 1 with its graph
express one hour in seconds,in standard form
Answer:
Hi! There are 3600 seconds in one hour.
Step-by-step explanation:
60 min. = one hour
60 seconds = one minute
:)
HELP
type of equation:
equation:
f(5)=
Answer:
Types of Equations and Examples
Types of Equations and Examples
There are various types of equations, such as,
Linear equation
Equation with one variable
Equation with two variables
Equation with three variables
Polynomial equation
Monomial Equations
Binomial Equation
Trinomial Equation
Quadratic equation
Trigonometric equation
Radical equation
Exponential equation
Rational equation
types of equations
types of equations
1. Linear Equation:
A linear equation is an algebraic equation. In linear equation, each term is either a constant or the product of a constant and a single variable. If there are two variables, the graph of linear equation is a straight line.
General form of the linear equation with two variables is given below:-
y = mx + c, m ≠ 0.
Equation with one Variable: An equation who have only one variable, e.g.
12x – 10 = 0
Step-by-step explanation:
A sequence is defined recursively by the formula f(n 1) = –2f(n). the first term of the sequence is –1.5. what is the next term in the sequence? –3.5 –3 0.5 3
Given that the first term of the sequence is –1.5, the next term of the sequence would be 3
How to determine the next term?The recursive function is given as:
f(n + 1) = -2f(n)
Substitute 1 for n
f(1 + 1) = -2f(1)
Evaluate
f(2) = -2f(1)
Given that the first term is -1.5, the equation becomes
f(2) = -2 * -1.5
Evaluate
f(2) = 3
Hence, the next term of the sequence is 3
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Answer:
(D) 3
Step-by-step explanation:
1. it has at least 10 values. 2. it has at least 3 values that are different. 3. it has a mean and median of 12.
Answer: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Step-by-step explanation:
First, we can ensure that 12 is the median by putting it in the middle and putting the same amount of numbers to its left and right side. To make the values have a mean of 12, the easy why to do it is to subtrate one as you move to the left and add one as you move to the right, that way they will cancel each other out and keep the mean at 12. The answer has a total of 11 values, has more than 3 values that are different, and has a mean and median of 12.
7+8+9+10+11+12+13+14+15+16+17=132
132/11=12
There are 5 values to each side of 12, making 12 the median.
f(x)
=
2x + 7 - x2
4
f(2)
=
Be sure to simplify your answer.
Enter
Answer:
[tex]f(2)=\frac{7}{4}[/tex]
Step-by-step explanation:
Step 1: Input 2 for x and solve
[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]
[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]
[tex]f(2)=\frac{4+7-4}{4}[/tex]
[tex]f(2)=\frac{7}{4}[/tex]
Answer: [tex]f(2)=\frac{7}{4}[/tex]
If a perfume store currently sells perfume for $30 a bottle and averages 2000 bottles sold per month, what sales might they anticipate if they raise the price to $40 a bottle
The sales they might anticipate if they raise the price to $40 a bottle is $1,500.
Anticipated salesUsing this formula
Anticipated sales=(Current selling price÷Increase in price)×Number of bottle sold
Let plug in the formula
Anticipated sales=($30÷$40)×2,000
Anticipated sales=$0.75×2,000
Anticipated sales=$1,500
Therefore the sales they might anticipate if they raise the price to $40 a bottle is $1,500.
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Please help BRAINLIEST FOR RIGHT ANSWER
Answer:
x = 17
Step-by-step explanation:
4x + 7 = 75 (as the 2 angles are interior alternate angles)
4x = 75 - 7 = 68
x = 68/4 = 17
Answer:
x = 17
Step-by-step explanation:
4x + 7 = 75 (as the 2 angles are interior alternate angles)
4x = 75 - 7 = 68
x = 68/4 = 17
I need help with math!!! please help
Answer:
x = 10
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
6x-6 + 7x+1 +55 = 180
Combine like terms
13x+50=180
Subtract 50 from each side
13x+50-50=180-50
13x = 130
Divide by 13
13x/13 =130/13
x = 10
The answer is A!
From this, we will get the equation
(13x -5) + 55 = 180
+ 5 on both sides
13x + 55 = 185
-55 on both sides
13x = 130
Divide by 13 on both sides
x = 10
PLEASE HELP! URGENT! ASAP! WILL GIVE BRAINLEST!
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф = [tex]\frac{\sqrt{2} }{2}[/tex]
→ Inverse cosine [tex]\frac{\sqrt{2} }{2}[/tex]
cos⁻¹ ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = 0.25π
Answer:
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф =
→ Inverse cosine
cos⁻¹ ( ) = 0.25π
Step-by-step explanation:
The number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:
B(d)= 2425e to the power of 0.15 d
How many days will it take for the bacteria to reach 3,700?
The time taken by the bacterias to reach 3,700 will be 2.81 days.
What will be the time?
It is given in the question that:-The the number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:
[tex]B(d)=2425\ e^{0.15d[/tex]
[tex]3700= 2425\ e^{0.15d}\\\\\\e^{0.15d}=\dfrac{3700}{2425}\\\\\\0.15d=ln\dfrac{3700}{2425}\\\\\\[/tex]
d = 2.81 days
Hence the time taken by the bacteria to reach 3,700 will be 2.81 days.
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Having a hard time finding the Surface Area, help?
(Formula is SA=hp+2B)
Answer:
89.3 cm. sq.
Step-by-step explanation:
Just find the area of each face and then add those areas together.
hope this helps
have a good day
in veronica's neighborhood the ratio of cats to dogs is 3 to 4. if there are 28 dogs, how many cats are there
Answer:
21 cats!
Step-by-step explanation:
the ratio is 3:4
4 being dogs - 28/4 = 7 - 7 * 3 = 21
hope this helps!!! <3
Tara made a scale drawing of a boarding school. she used the scale 1 centimeter : 7 meters. a building at the school is 12 centimeters long in the drawing. how long is the actual building?
Answer:
84cm
Step-by-step explanation:
Given that;
1cm = 7m
12cm = x
Cross Multiply
x = 12×7
x = 84m
4w<32
Help about to fail my math class lol
Factor completely.
Show all work.
a) ²−7−18
b) 2²−26+24
c) 10²+37+7
d) ²−25
e) 42−4+1.
f) 144²−36
Answer: First find the GCF ( greatest Common Factor):-
GCF of 16, 24 and 48 is 8
GCF of the x terms is x^3
GCF of the y terms is y^4
So GCF is 8x^3y^4
Factoring:-
= 8x^3y^4 ( 2x^6y^4 - 16x^2y^2 + 3) answer
Step-by-step explanation:
Mamadou surveyed 500 of the students in the school about their favorite color students could choose between blue and red 390 students said their favorite color was red what percentage of the surveys students said their favorite color was blue
Answer:
22%
Step-by-step explanation:
so 500-390 = 110
110 students said their favorite color was blue.
110/500 = ?/100
110 times 100 = 11000
11000/500 = 22
give brainliest, please!
hope this helps :)
How many different combinations of six people can sit in four chairs?
assume one person sits in each chair.
Answer:
15Step-by-step explanation:
the number of combinations of 4 people we can form from 6 is :
[tex]C^{4}_{6}=\frac{6!}{4!\left( 6-4\right) !} = 15[/tex]
19. Find the x- and y-intercepts of the equation -x + 2y = 8. Write your answers as ordered pair.
The measures of the angles of a triangle are shown in the figure below solve for X
Answer:
29 degrees
Step-by-step explanation:
The interior angles of all triangles equals 180. We know already that we have 101 and 50 degrees. If we add that, we get 151. To find x, we have to simply subtract 151 from 180. If we do this, we get 29. x=29.
Hope this helps!
The surface area of a sphere is 1,017.36 square inches. What is the volume of the sphere? Use 3.14 for pi
Aaron set the bottom of a ladder on the ground 10 feet from the house and it reached just to the bottom of the window he was about to clean. The bottom of the window is 38 feet off the ground. What is the angle between the ladder and the ground?
Answer:
36
Step-by-step explanation:
A^2+B^2=C^2
10^2+B^2=38^2
We are solving for B squared
So 100+B^2=1444
-100
1344 and now take the square root of that number and you have your answer of 36
I hope this helps and have a good night!
need answer quick pls i’ll give brainlist to correct answer
Answer: Okay, I believe it is mean and 4inches
Step-by-step explanation:
If you add altogether, it is 40 and of course divide by 10 (the number of data) it’s 4
3.3 Factorise fully: 3.3.1 x²-x-6
Answer:
(x-3)(x+2)
Step-by-step explanation:
¹ you open brackets.
² you put the "x" in both brackets
³ you then check for factors, that will give you a "6" when you multiply them and give you the "x" when you add or subtract them.
Last month, Korey’s Comics had $4,350 in net sales with a gross profit of $3,320 and a net income of $1,850. Calculate Korey’s net profit margin. a. 42.5% b. 55.7% c. 76.3% d. 179.5%
b. 55.722
Step-by-step explanation:
1850/3320
I assume that you know what the question is asking to solve for.
The net profit margin for Korey's Comics is 42.5%.
Option A is the correct answer.
What is a profit?Profit is the difference between the selling price and the cost price.
We have,
Net profit margin is calculated by dividing net income by net sales and multiplying the result by 100 to get a percentage.
Net Profit Margin = (Net Income / Net Sales) x 100%
Substituting the given values.
Net Profit Margin = (1,850 / 4,350) x 100%
Net Profit Margin = 0.425 x 100%
Net Profit Margin = 42.5%
Therefore,
The net profit margin for Korey's Comics is 42.5%.
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is the only plane shape in which every point on the figure is the exact same distance from the center.
The only plane shape in which every point on the figure is the exact same distance from the center is; The Circle
How to Identify a Circle?
There are different types of plane shapes such as Square, rectangle, Circle, Trapezoid, Parallelogram, Rhombus, Kite, Triangle e.t.c.
Now, Except for the circle and Triangle, every other listed plane shape above is a quadrilateral because they have 4 sides. Now, no quadrilateral has all its' sides equal from the center. Likewise, no triangle has all its' sides equal from the center.
The only plane shape with all its' sides equal from the center is the circle because the radius is equal all through.
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y X X
y = 85 when x = 17
Using the information above, write an equation for y in terms of x.
y=
?
Answer:
y= x5
Step-by-step explanation:
y = 5 times the number of x.
what is this please hurry it's a limited time test i'm counting on you guys
Answer:
see below-
Step-by-step explanation:
1st one- congruent
boxes- m1 and m2 , m2 and m3
2nd line- supplementary
m1 and m3
