The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
y
- 1
6
0
12
1
24
2
48
Answer:
f(x) = 12*(2)^x
Step-by-step explanation:
A generic exponential equation is written as:
f(x) = A*(r)^x
And we also know that this equation passes through:
(-1, 6)
(0, 12)
(1, 24)
(2, 48)
For the second point, (0, 12) we know that when f(0) = 12
Then:
f(0) = 12 = A*(r)^0
And for every real number different than zero, a^0 = 1
Then:
f(0) = A*1 = A = 12
Then the equation is:
f(x) = 12*(r)^x
Now we can use one of the other points, like (1, 24)
Then f(1) = 24
We can solve:
f(1) = 24 = 12*(r)^1 = 12*r
24/12 = r
2 = r
Then the equation is f(x) = 12*(2)^x
Now we need to check if this function also passes through the points (-1, 6) and (2, 24):
f(-1) = 12*(2)^-1 = 12/2 = 6
f(2) = 12*(2)^2 = 12*4 = 48
Nice.
So we can see that the function is f(x) = 12*(2)^x
alexander is counting his money from his piggy bank. he stacks four quarters per pile. there are 21 piles of quarters.
how many quarters does he have?
Answer:
He has 84 quaters
Step-by-step explanation:
all you really have to do is multiply 4 times the number of stacks and you get 84
On Monday morning, a school cafeteria had 97.88 gallons of milk. At lunch, the students drank 8
gallons of the milk. How much milk does the cafeteria have left?
gallons
Answer:
89.88 gallons of milk
Step-by-step explanation:
97.88-8=89.88
questions 13 & 14 FAST PLS ITS A TEST! WILL GIVE BRAINLIEST!
Please help me thank you!
The function ƒ(x) = 2x − 2 indicates:
a shift to the right of 1 unit.
a shift to the left of 2 units.
a shift to the right of 2 units.
None of these choices are correct.
Answer:
None of the choices are correct
Step-by-step explanation:
This is because it should be going down if it was subtracting but no answer says that so
A system of liner equation has been graphed in the diagram. Determine a responsible solution for the system of equation.
anybody know how to do this?????
Answer:
[tex]x = 30[/tex]
Step-by-step explanation:
In order A to be parallel to B, our alternate interior angles must be equal.
This means that
[tex]5x = 3x + 60[/tex]
[tex]2x = 60[/tex]
[tex]x = 30[/tex]
Can someone please help me with this question please help me.
James scored a total of 16 points during a basketball game. During the game, he made only free throws, worth 1 point each, and 3-point baskets. He made a total of 10 free-throws and 3-point baskets. Determine exactly how many free throws and how man 3-point basket James made during the game.
Answer:
x = 7 , y = 3 , or 7 free throws, and 3 3-pointers.
Step-by-step explanation:
James scored a total of 16 points during a basketball. Only free throws and 3-point baskets are used. Free throws = 1 point (x), 3-pointers = 3 points (y).
Set the equations:
16 = x + 3y
10 = x + y
First, isolate the variable x in the second equation. Divide y from both sides of the equation:
10 (-y) = x + y (-y)
x = 10 - y
Next, plug in 10 - y for x in the first equation:
16 = x + 3y
16 = (10 - y) + 3y
Simplify. Combine like terms:
16 = 10 - y + 3y
16 = 10 + (-y + 3y)
16 = 10 + 2y
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 10 from both sides of the equation:
16 (-10) = 10 (-10) + 2y
2y = 16 - 10
2y = 6
Next, divide 2 from both sides:
(2y)/2 = (6)/2
y = 6/2 = 3
Plug in 3 for y in one of the equations:
16 = x + 3y
16 = x + 3(3)
16 = x + 9
Isolate the variable, subtract 9 from both sides of the equation:
16 (-9) = x + 9 (-9)
x = 16 - 9
x = 7
x = 7 , y = 3 , or 7 free throws, and 3 3-pointers.
Plug in to check:
16 = x + 3y
10 = x + y
16 = (7) + 3(3)
16 = 7 + 9
16 = 16 (True)
10 = (7) + (3)
10 = 10 (True).
~
Answer:
x = 7 , y = 3 or 7 free throws, and 3 3-pointers.
Step-by-step explanation:
A 17 foot long lodder is leaning against a house the base of the ladder is 9 feet from the house how high up the house does the ladder reach
The quadratic function is given in both its standard and factored form below
x²+2x-15=(x+5)(x-3) there is nothing to factoriz
What is the slope of the line below?
The image is a graph of an x-axis and a y-axis. A line is drawn which passes through the points (2,3) and (-2,-7).
A. 5
B. 0.2 or 15
C. 2.5 or 52
D. 0.4 or 25
Answer:
The awnser is C. but please know I may be wrong
Step-by-step explanation:
Please help me and I’ll give you five stars and a Thanks
Find the slope of the line with x intercept 9 and y intercept of -2
Answer:
2/9
Step-by-step explanation:
Find the slope of the line with x intercept 9 and y intercept of -2
Given that the equation of the line is y = mx+b
x intercept occurs when y = 0
The coordinate of x intercept is (9,0)
y intercept occurs at x = 0
The coordinate of y intercept is (0, -2)
Slope m = y2-y1/x2-x1
m = -2-0/0-9
m = -2/-9
m = 2/9
Hence the required slope is 2/9
Helpp! Pls. I am desperate i will mark brainliest
find the probability that the pitcher will throw exactly 4 pitches
Answer:
[tex]\frac{3}{20}[/tex] = 0.15
Step-by-step explanation:
15 + 20 + 40 + 15 + 10 = 100
[tex]\frac{15}{100} = \frac{3}{20}[/tex] = 0.15
IL GIVE BRAINLY IF YOU CAN HELP ME ON THESE 2
Answer:
THE answers to both questions are A
Step-by-step explanation:
Answer:
a for both
Step-by-step explanation:
just move point c on the graph where it tells u to. a translation only affects location
I need 11 and 12 thanks!
Answer:
11. c > 5
12. option 1
Step-by-step explanation:
Help mee on this part I’m stuck on this problem and I’m confused
Answer:
point D = (2, -4)
Step-by-step explanation:
It's asking the dot's location.
Round your answer to the tenths place if necessary
Help me please! :(
Answer:
∠ B = 80.5°
Step-by-step explanation:
Since AB = AC then the triangle is isosceles with base angles congruent, so
∠ B = ∠ C , then
∠ B = [tex]\frac{180-19}{2}[/tex] = [tex]\frac{161}{2}[/tex] = 80.5°
Select all equations that have infinitely many solutions.
A. 2x + 5 = 4 + 2x + 1
B. 5x – 5 = 11x + 2 - 1
C. 3x + 2 - 2x = x + 2
Answer:
A
C
Step-by-step explanation:
Hope this helps.
Good luck.
Subtract 4 from 9 then subtract 5 from the result written expression for the sequence of operations described below
Answer:
( 9 - 4 ) - 5
Step-by-step explanation:
According to the scenario, expressions can be written as follows,
Subtract is denoted by (-) sign.
So, First sequence of operation,
= For subtract 4 from 9 can be written as ( 9 - 4)
= Second sequence of operation,
Now, subtract 5 from result can be written as ( 9 - 4) - 5
Hence, the final written expression will be ( 9 - 4) - 5.
True or False: A sector of a circle with a measure of 36" and radius of 12 cm has an arc length of about 15 cm. O True O False
Answer:
The answer of this question is False
21) Which expression is equivalent to 6(7x − 4)? A) 13x − 10 B) 13x − 24 C) 42x − 10 D) 42x − 24
Answer:
Answer is D) 42x − 24
Step-by-step explanation:
Opening the expression given in question
6(7x − 4)
6 will be multiplied by both items present inside parenthesis.
it can be written as
={(6 * 7x) - (6*4)}
=42x-24
Hope that clears the question.
The number 64 is a perfect_____.
A. square
B. cube
C. square and cube
Answer:
square and cube
square- 8
cube- 4
Answer:
C) square and cube
Step-by-step explanation:
Square: 4×4×4×4=64
Cube: 8×8=64
Can I please have Brainliest?
The Tober family built a square deck with an area of 75 m'. The length of one
side is between which two whole numbers
Answer:
Between 8 and 9
Step-by-step explanation:
The square root of 75 is about 8.6
Therefore the answer is between the number 8 and 9.
3/10 = N/10
Find the missing value to write an equivalent fraction.
Multiply the numerator and denominator by
.
The missing numerator is
.
Answer:
3 = N
Step-by-step explanation:
Multiply the numerator and denominator by 10:
10(3/10) = 10(N/10) becomes 3 = N
I had trouble plotting the midpoint lol but can someone plz help me :c
midpoint is (-1 and -1.5)
Answer:
Step-by-step explanation:
midpoint rule is x2+x1 / 2 , y2+y1 / 2
where point one is P1 = (x1,y1) = (4,3)
and point two is P2 = (x2,y2) = -6,-6
for x then, -6+4 / 2 = -2 / 2 = - 1
for y then, -6+3 / 2 = -3 / 2 = - [tex]\frac{3}{2}[/tex]
mid point is ( -1 , - [tex]\frac{3}{2}[/tex] )
the polynomial y = x^{5} + x^{3} - x^{2} - 1 factors into (x^{2} + 1) (x^{3} - 1). what is the multiplicity of the root (x^{3} - 1)?
Answer:
The multiplicity of the root is 1
Step-by-step explanation:
Firstly, we need to understand what multiplicity is
By multiplicity, we simply refer to the number of times we have the certain root repeating itself
From the factorization, each of the given roots were only repeated once
That indicates that the given multiplicity is 1
Please help! The question is:
In a marketing survey involving 1,000 randomly chosen people, it is found that 630 use brand P, 420 use brand Q, and 210 use both brands. How many people in the survey use brand P and not brand Q?
By Set theory, 420 many people in the survey use brand P and not brand Q.
What is Set theory?
The mathematical concept of sets, which are well-defined collections of things that are referred to as their members or elements, is known as set theory. As only sets are the subject of pure set theory, the only sets that are taken into account are those whose members are also sets.
The major reason why set theory is significant is because it offers the axioms upon which the rest of mathematics is constructed. We study sets and their characteristics in the area of mathematical logic known as set theory. A collection of items or a group of items is referred to as a set. These items are frequently referred to as elements or members of a set.
P use = 630 people
Q use = 420 people
both P&Q use ie P∩Q = 210 People
use brand P but not brand Q = P/ P∩Q
= 630 - 210
= 420
Learn more about Set theory
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Camille put $1,250 in a new account at her bank. - The bank pays 2.25% interest compounded annually on this account. - Camille makes no additional deposits or withdrawals. Which amount is the closest to the balance of the account at the end of 5 years?
Answer:
FV= $1,397.1
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,250
Interest rate (i)= 2.25% compounded annually
Number of periods (n)= 5 years
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
FV= 1,250*(1.0225^5)
FV= $1,397.1