Given:
An exponential function [tex]f(x)=ab^x[/tex] passes through the points (0, 12000) and (2, 3000).
To find:
The values of a and b.
Solution:
We have,
[tex]f(x)=ab^x[/tex] ...(i)
It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get
[tex]12000=ab^0[/tex]
[tex]12000=a(1)[/tex]
[tex]12000=a[/tex]
Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get
[tex]3000=12000b^2[/tex]
[tex]\dfrac{3000}{12000}=b^2[/tex]
[tex]\dfrac{1}{4}=b^2[/tex]
Taking square root on both sides.
[tex]\pm \dfrac{1}{2}=b[/tex]
For an exponential function b cannot be negative. So, [tex]b=\dfrac{1}{2}[/tex].
Therefore, the value of a is 12000 and the value of b is [tex]\dfrac{1}{2}[/tex].
I know what the answer is but the teacher wants me to explain helpppppp
answer: 8
Steps / explaination
You are in the buy and sell business. find out the wholesale price of an item (e.g. t-shirt, soap,toy) suppose you buy 24 pieces of that item at wholesale price. atleast at what price should you tell each item to have a 25% profit? how much will be your total profit in pesos from these items?
With explanation please!!
The wholesale price isn't given, suppose the wholesale price is $5
Answer:
$6.25 ; 1441.8 pesos
Step-by-step explanation:
Number of items purchased = 24
Wholesale price of item = x
To obtain a 25% profit, the sales price would be :
Wholesale price = wholesale price + 25% of wholesale price
(x = x + 0.25x) per unit
For 24 items :
24x + 0.25 * 24x
Unit wholesale price = 5
24(5) + 0.25*24(5)
= $150
Hence, sale price per unit will be :
$150 / 24
= $6.25
Total profit in pesos :
1 dollar = 48.06 pesos
Total profit = $150 - 24(5) = $150 - $120 = $30
$30 = (30 * 48.06) = 1441.8 pesos
In which family of functions can students calculate an average rate of
change? *
non-linear functions
Average Rate of Change is used primarily with non-linear functions, since all linear functions have a constant rate of change.
What is the minimum value of the function g (2) = x2 - 6x – 12?
-21
3+ V21
3
3-21
Answer:
g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12?
Step-by-step explanation:
Answer:
minimum value is -21; ordered pair of min value is (3, -21)
Step-by-step explanation:
graph the function and find the lowest point on the curve
GIVING BRAINLIEST PLEASE HELP
Answer:
The answer is B
Step-by-step explanation:
Answer:
ans is B sorry if it's direct
9% ___ 0.4 will give brainliest
pls help :)
Answer:
9% is less than 0.4. 0.4 is really 4/10 which is 40% 40 is greater than 9 therefore 9% is less than 0.4! So your answer is 9%<0.4! I hope this helped!
Step-by-step explanation:
Darron bought a new PS5. He made a down payment of $300, and he will pay $50 each month until the phone is paid off. Which equation represents the relationship between x, the number of monthly payments Darron has made, and y, the total amount he has paid?
A. y= 50x + 300
B. y= -50x + 300
C. x= 50y + 300
D. y= 50x – 300
Answer:
C
Step-by-step explanation:
 tell me how to answer this please I WILL MARK BRAINLIEST
Answer:
It equals 3
Step-by-step explanation:
To solve this it is basically like a normal problem you would just take out the X in it and divide 7 by 21 which leaves you with 3.
Simplify the expression:
7(1 + 8v)
7 ( 1 + 8 )
simplify
1. rearrange terms
7(1 + 8v)
7(8v + 1)
2. Distribute
7(8v + 1)
56v + 7
Solution
56v + 7Help Fast. The question is in an image because there is a graph to see.
Answer:
the answer is (3, 2)
Step-by-step explanation:
the formula to find the centroid of a triangle is
{( x1+x2+x3)/3 , ( y1+y2+y3)/3}
if there are 93 calories in 3/4 cups how many calories are in 1 cup
Answer:
124
Step-by-step explanation:
Cross Multiply
(93x4)/3
I need help with this ASAP and can you explain so i can understand?!
Answer:
Adult tickets sold = 225
Student Tickets sold = 375
Step-by-step explanation:
Let:
Adult tickets sold = x
Student Tickets sold = y
Total tickets sold = 600
So, we can write: x+y = 600
Total money collected = 3037.50
Cost of 1 Adult ticket = $6.00
Cost of one Student ticket = $4.50
So, we can write: 6x+4.5y=3037.50
Now, we get a system of equations, that if solved we can find values of x and y
Let:
[tex]x+y = 600--eq(1)\\6x+4.5y=3037.50--eq(2)[/tex]
We can solve using substitution method.
Finding value of x from eq(1) and putting it in eq(2)
[tex]We\:have\\x+y=600\\x=600-y[/tex]
Put in eq(2)
[tex]6x+4.5y=3037.50\\6(600-y)+4.5y=3037.50\\3600-6y+4.5y=3037.50\\-1.5y=3037.50-3600\\-1.5y=-562.5\\y=\frac{-562.5}{-1.5}\\y=375[/tex]
So, we get value of y = 375
Now put value of y in eq(1) to find value of x
[tex]x+y=600\\Put\:y=375\\x+375=600\\x=600-375\\x=225[/tex]
So, we get value of x = 225
The Tickets sold will be:
Adult tickets sold = x = 225
Student Tickets sold = y = 375
can anyone answer 2(3x+5)+7x and show work ?
Answer: -12 I believe I’m sorry if I’m wrong I’m not smart
Step-by-step explanation:
Simplifying
2(3x + -5) = 7x + 2
Reorder the terms:
2(-5 + 3x) = 7x + 2
(-5 * 2 + 3x * 2) = 7x + 2
(-10 + 6x) = 7x + 2
Reorder the terms:
-10 + 6x = 2 + 7x
Solving
-10 + 6x = 2 + 7x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7x' to each side of the equation.
-10 + 6x + -7x = 2 + 7x + -7x
Combine like terms: 6x + -7x = -1x
-10 + -1x = 2 + 7x + -7x
Combine like terms: 7x + -7x = 0
-10 + -1x = 2 + 0
-10 + -1x = 2
Add '10' to each side of the equation.
-10 + 10 + -1x = 2 + 10
Combine like terms: -10 + 10 = 0
0 + -1x = 2 + 10
-1x = 2 + 10
Combine like terms: 2 + 10 = 12
-1x = 12
Divide each side by '-1'.
x = -12
Simplifying
x = -12
Answer:
13x + 10
Step-by-step explanation:
First distribute, (2)(3x) + (2)(5) + 7x
This gives you 6x + 10 + 7x
Then combine then like terms 6x + 10 + 7x
To get (6x + 7x) + (10)
And a final answer of 13x + 10 :)
I don’t understand this
Answer:
your just finding area so
1.5×2.5=
1.5×1.5/2=
1.5×2.5=
I will put the answers in the comments I need to use a calculator
Answer:
Step-by-step explanation:
Think of it as two rectangles and one triangle.
The first rectangle is 1.5 * 2.5 = 3.75 square feet.
There is two of these rectangles, so you can do 3.75 *2 = 7.5 square feet.
Finally, the triangle is 1.5 by 1.5, so the area is 1.5 * 1.5 / 2 = 1.125.
To find the total area, add the two together: 7.5 + 1.125 = 8.625 square feet
Is x2 + 10x + 20 a perfect square trinomial?
Yes or no
Answer:
=
(
x
−
5
)
2
Step-by-step explanation:
=(x-5) exponent 2
Yes
No, x² + 10x + 20 is not a perfect square trinomial.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
A quadratic polynomial,
x² + 10x + 20.
A perfect square trinomial is an expression that may be constructed from the binomial equation's square.
That means, the roots are repeated.
Solving the equation, we get,
x = (-5 ± √5)
The roots are not repeated.
Therefore, it is not a perfect square trinomial.
To learn more about the quadratic function;
https://brainly.com/question/11485644
#SPJ2
X^2+3x+4=(x+a)^2+b what is A and B equal please help me
Answer:
a = 1.5, b = 1.75
Step-by-step explanation:
Expand the right side using FOIL, then compare the coefficients of like terms with the expression on the left side.
(x + a)² + b
= x² + 2ax + a² + b , then compare to
x² + 3x + 4
Comparing the coefficients of the x- terms
2a = 3 ( divide both sides by 2 )
a = 1.5
Comparing the constant terms
a² + b = 4
1.5² + b = 4
2.25 + b = 4 ( subtract 2.25 from both sides )
b = 1.75
7x^2a+7xa^2
Find the greatest common factor
Answer:
GCF is 7xa
Step-by-step explanation:
Answer:
hCf is 7ax
plz refer to the picture
plz mark as brainliest
pls help I literally don’t get this
Which graph represents the system of inequalities?
3x+5y<10
x−y≤1
Answer:
I believe it's the one on the bottom left
Step-by-step explanation:
I'm still taking my test so I'll come back later to tell you if it's correct.
Answer:
It's the one on the bottom left
Step-by-step explanation:
Help with his plz ASAP!!
Answer:
what do you need help on?
$2000 is invested at a rate of 4.2% compounded annually. Identify the compound interest function to model the situation. Then find the balance after 7 years. A = 2000(1.042)^t; $2667.50 A = 2000(1.42)^4t; $2557.50 A = 2000(1.042)^t; $2337.50 A = 2000(14.2)^4t; $2447.50
Answer:
A = 2000(1.042)^t; $2667.50
Step-by-step explanation:
The formula or model for Compound Interest is given as:
A = P(1 + r/n)^nt
Where:
A = Amount or Balance after t years
P = Principal or initial amount invested = $2000
r = Interest rate = 4.2% = 0.042
t = Time in years = 7 years
n = Compounding frequency = Annually = per year = 1
Hence, the compound interest function to model for the situation (Question) with time t above is:
A = 2000(1 + 0.042) ^1 ×t
A = 2000(1.042)^t
Therefore solving for the balance
A = 2000(1.042)^7
A = 2,667.50
A = $2667.50
Therefore, option a =
A = 2000(1.042)^t; $2667.50
is the correct option.
Proving parallel lines
Answer:
Are you making a new post?
Step-by-step explanation:
In the hospital, 80 people were admitted Friday, 25% of these admissions were women in labor to have babies. How many women were in labor? O A 25 OB. 20 O C. 35 O D. 30
Answer:
Step-by-step explanation:
25% it means 1/4 of the total
1/4 of 80 is 20 (80/4=20)
answer B
How can the slope of the line be interpreted? Every 98 words requires 312 minutes to read. Every 312 words requires 98 minutes to read. In each additional minute, approximately 98 more words are read. In each additional minute, approximately 312 more words are read.
Answer:
In each additional minute, approximately 312 more words are read.
Step-by-step explanation:
Given tbe sentences :
The slope is the rate of change per unit: in the context of the question, the number of word reads increases. By 312.
Hence, the slope according to the slope of the graph interpretation is that, the number of words read per minute increases by 312 as the value of minute increases by one minutes.
look at this please it would really help
What is the solution of the system of equations shown in the graph below?
Answer:
Answer is (-1,-2) As where 2 lines bisect, that point be the answer. And in given scenario, both the lines bisected at (-1,-2)
Step-by-step explanation:
UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement. G X 240 DI F 48 Next * Previous
Answer:
The answer is;
54.4
Step-by-step explanation:
The given parameter are;
Triangle ΔFGH = Right triangle
The length of segment [tex]\overline {FH}[/tex] = 48
The measure of ∠HFG = 28°
The measurement required = The measure of segment [tex]\overline {FG}[/tex] = x
The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle
Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°
∠FGH = 62°
By sine rule, we have;
[tex]\overline {FH}[/tex]/(sin ∠FGH) = [tex]\overline {FG}[/tex]/(sin(∠FHG)
By substituting the known values, we have;
48/(sin 62°) = x/(sin(90°)
sin(90°) = 1, therefore, we have;
x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)
x = 54.4
expand and simplify (x-3)(2x+1)(3x-2)
Answer:
6x³ - 19x² + x + 6
General Formulas and Concepts:
Algebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)Step-by-step explanation:
Step 1: Define
(x - 3)(2x + 1)(3x - 2)
Step 2: Expand
Expand [FOIL]: (2x² + x - 6x - 3)(3x - 2)Combine like terms: (2x² - 5x - 3)(3x - 2)Expand: 6x³ - 15x² - 9x - 4x² + 10x + 6Combine like terms: 6x³ - 19x² + x + 6which the of triangles is similar to PQR
Answer:
D
Step-by-step explanation
18/15=1.2
21/1.2=17.5
They Match!
Help please due now!!
Answer:
60
Step-by-step explanation:
Answer:
Step-by-step explanation:
a = 2 ; b = 4
4a + 2b² - 2(a -3b) = 4*2 + 2(4)² - 2 (2 - 3*4)
= 4*2 + 2*16 - 2(2 -12)
= 4*2 + 2*16 - 2* (-10)
= 8 + 32 + 20
= 60