Answer: [tex]f(x)=4^x[/tex]
Step-by-step explanation:
The general exponential function is given by :-
[tex]f(x)=Ab^x[/tex], where A is initial amount , b is multiplicative growth rate and x is time period.
Also, the multiplicative growth rate is the common ratio of the consecutive terms.
From the given table , [tex]b=\dfrac{256}{64}=4[/tex]
Substitute, x = 3 , f(x)=64 and b=4 , we get
[tex]64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1[/tex]
Hence, the exponential function represents the data in the table is
[tex]f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x[/tex]
ray and hunter sell newspapers after school. ray earns $11 more than hunter. if ray earns $25,how much money does hunter earn?
Answer:
$14
Step-by-step explanation:
This should be simple, if ray earns $11 more, than hunter earns $25-$11, or $14
To find out how much Hunter earns, we subtract the $11 that Ray earns extra from Ray's total earning of $25, resulting in Hunter earning $14.
The student has asked a question regarding how much Hunter earns if Ray earns $25 which is $11 more than Hunter. To solve this, we subtract $11 from Ray's earnings to find Hunter's earnings:
Ray's earnings = $25Hunter's earnings = Ray's earnings - $11Hunter's earnings = $25 - $11Hunter's earnings = $14Therefore, Hunter earns $14.
15 points and show steps
Solve for x. Write the smaller solution first, and the larger solution second. -2x^2-9=-107
Answer:
x = -7 and x = 7Step-by-step explanation:
[tex]-2x^2-9=-107\qquad\text{add 9 to both sides}\\\\-2x^2-9+9=-107+9\\\\-2x^2=-98\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}=\dfrac{-98}{-2}\\\\x^2=49\to x=\pm\sqrt{49}\\\\x=-7\ \vee\ x=7[/tex]
What is the standard form equation of the line shown below? (1 point) Graph of a line going through negative 2, 3 and 1, negative 3
y + 3 = −2(x − 1)
y = −2x − 1
2x + y = −1
−2x − y = 1
Answer:
y= -2x-1
Step-by-step explanation:
In solving, find the gradient from coordinates given , then use the gradient with one of the pairs to find the equation in form of y=mx+c
finding the gradient
points(-2,3) and (1,-3)
m=change in y/change in x
change in y=-3-3=-6
change in x=1--2=3
m=-6/3 =-2
taking the coordinates (1,-3) and (x,y), the equation will be
y=mx+c, where m=-2
(y--3)/(x-1) =-2
(y+3)/(x-1)= -2
(y+3) = -2(x-1)
y+3=-2x+2
y=-2x+2-3
y= -2x-1
A rectangular note card has an area of 28 square inches. Its perimeter is 22 inches. What are the dimensions of the note card?
Answer: 4 inches x 7 inches
Step-by-step explanation: Knowing that the formula for the area is length times width, 4 x 7 = 28 square inches. The perimeter of the rectangle with 2 sides that are 4 inches and 2 sides that are 7 inches is 22 inches. (2 x 4) + (2x7) = 8 + 14 = 22 inches.
The dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.
Let l be the length of the rectangular note card and w be its width.
Since the area of the rectangular note card is 28 square inches, we have that
lw = 28 (1)(the area of a rectangle).
Also, the perimeter of the rectangular note card is 22 inches. We have that
2(l + w) = 22 (2) (perimeter of a rectangle)
So, l + w = 11 (3)
From (3), l = 11 - w.
Substituting l into (1), we have
(11 - w)w = 28
11w - w² = 28
re-arranging, we have
w² - 11w + 28 = 0
Factorizing, we have
w² - 7w - 4w + 28 = 0
w(w - 7)- 4(w - 7) = 0
(w - 7)(w - 4) = 0
w - 7 = 0 or w - 4 = 0
w = 7 or w = 4
Since l = 11 - w,
substituting w = 7 into l, we have
l = 11 - 7 = 4 inches
substituting w = 4 into l, we have
l = 11 - 4 = 7 inches.
So, we have l = 4 and w = 7 or l = 7 and w = 4
So, the dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.
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Can you guys please help me out
A. ability to access cash value
hope this helps!!
A bag contains 6 red and 10 black
marbles. If you pick a marble from the
bag, what is the probability that the
marble will be black?
plz help
Answer:10/16 (can simplify I think)
Step-by-step explanation: First you do 10+6 to find out the total of all the marbles which is 16. There are 10 blacks so you do 10/16 AS you wanna find out the probability of getting the black.
Answer:
62.5%
Step-by-step explanation:
First you add up all the marbles and then divide 100 into the sum of all of the marbles and then you times it by the black marbles to find the percent
100/(6+10)*10=%
If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
1) 14³
2) 3¹⁴
3) 14 ⋅ 3
4) 14 ⋅ 14 ⋅ 14
➷ This will make sense once you see the formula:
volume = length x width x height
As it is a cube, all lengths are the same
Substitute the values in:
volume = 14 x 14 x 14
Exponents are when you multiply a value by itself
For example, 2 x 2 can be written as [tex]2^{2}[/tex]
In this case, the answer would be option 1. [tex]14^{3}[/tex]
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
14 x 14 x 14
Step-by-step explanation:
Use the distributive property to evaluate each expression 7(9 - 4) = ???
Answer:
7*9-7*4
63-28
35
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
multiply each number in the parenthesis by the 7 outside
7(9 - 4)
= (7 × 9) + (7 × - 4) = 63 + ( - 28) = 63 - 28 = 35
a store manager sends an email survey to customers who have registered at the store's websites. Why is this survey biased?
The survey is biase because it is only surveying shoppers that have registered on the website,.
Gia went to the movies with her 7-year old daughter and her 70-year-old mother. Movie tickets are half-priced for children under 12 years old, and there is a 25% discount for senior citizens. If Gia's $8.00 ticket was the regular retail price, what percent of the full retail price did Gia pay for the three tickets?
A.60% B.66.6% C.70% D.75%
Answer:
D. 75%
Step-by-step explanation:
Percent of full retail price = 8+(1/2)(8)+(3/4)(8)/24
This simplifies to 0.75, which is equivalent to 75 percent.
$24 is full retail price so by dividing the amount Gia paid by it, you can find the percent of the full retail price.
Gia paid 75% of the full retail price for the three movie tickets.
Explanation:To calculate the percent of the full retail price that Gia paid for the three tickets, we need to determine the total amount Gia paid and the full retail price for the three tickets.
Gia's $8.00 ticket is the regular retail price, so she paid the full price for her ticket. Her daughter's ticket is half-priced, which is $8.00 divided by 2, equaling $4.00. Her mother's ticket has a 25% discount, so she paid 75% of the full price, which is $8.00 multiplied by 0.75, equaling $6.00.
The total amount Gia paid is $8.00 + $4.00 + $6.00 = $18.00. The full retail price for the three tickets is $8.00 + $8.00 + $8.00 = $24.00. Therefore, Gia paid $18.00/$24.00 = 0.75, which is 75%, of the full retail price.
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please help me anyone
Answer:
57 in²
Step-by-step explanation:
S=1/2*8*3=12
4s+9=4*12+9=57
Which statement describes what these four powers have in common?
Answer:
"All the powers have a value of 1 because the exponent is 0"
Step-by-step explanation:
To answer this, we need to recall the property that "ANYTHING to the power 0 is ALWAYS equal to 1" (except 0^0).
Here, we see that the base of all of the 4 choices are integers (and NOT ZERO) and all of them are raised to 0th power. So all of them are EQUAL TO 1.
Hence, the correct answer is "All the powers have a value of 1 because the exponent is 0"
Answer:
All the powers have a value of 1 because the exponent is 0
Step-by-step explanation:
Can you help me with 5. 6. 7. 8. Please!!!!
Answer:
8,if it broke some tiny thing from that it will fail but if it not broke it will be heavy then the broke one. the one that do not broke is the heavy one.
Step-by-step explanation:
all real numbers between -4 and 6
The real numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.
Explanation:The question asks for all real numbers between -4 and 6. In this case, the numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.
Learn more about Real Numbers here:https://brainly.com/question/2742555
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The points (4,1) and (x,-6) lie on the same line. If the slope of the line is 1, what is the value of x?
*show work + explain*
urgent!!!
Answer:
x = -3
Step-by-step explanation:
Substitute the values m = 1 and from the points into the slope formula. Then solve for x.
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\1 = \frac{1--6}{4-x}\\\\1 = \frac{7}{4-x}\\\\4-x = 7\\\\-3 = x[/tex]
A stone fell from the top of a cliff into the ocean.
In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s, before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?
Answer:
Time the stone fall in the air = 7 seconds
Time it fall in the water = 5 seconds
Step-by-step explanation:
Given in the question,
speed of stone in the air = 16 m/s
speed of stone in the water = 3m/s
The total distance from the top of the cliff to the seabed = 127 m
the total time it took to hit the seabed = 12 s
Suppose time took to hit the water = x
so the time took from top of water to seabed = 12 - x
Formula to use
distance = speed x timeTotal distance = first distance + second distance127 = 16x + 3(12-x)
127 = 16x + 36 - 3x
127 - 36 = 16x - 3x
91 = 13x
x = 91/13
x = 7 seconds
12 - x = 12 - 7 = 5 seconds
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have?
4p + 7 = 3 + 4 + 4p
subtract 4p on both sides
7=7
since the equation equals it is infinite many solutions or...
all real numbers
Answer:
Infinite solutions!!
Step-by-step explanation:
4p + 7 = 3 + 4 + 4p
7 = 3 + 4
7 = 7
What are the perpendicular sides???
Answer:
For triangle VZX, VZ and ZX are perpendicular to each other.
This is because, perpendicular sides intersect to make a right angle.
Hope this helps,
♥A.W.E.S.W.A.N.♥
which is an equation of the given line in standard form (-3, -1 ) (1/2, 2)
Answer:
6x - 7y = -11
Step-by-step explanation:
To write the equation of a line when given two points, calculate the slope and substitute it into the point slope form of a line. From this form of the equation, you can simplify and convert to the standard form.
First, find the slope using the formula.
[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--1}{\frac{1}{2} --3} =\frac{3}{\frac{7}{2}} = \frac{6}{7}/tex]
Substitute m = 6/7 and the point (-3,-1) into the point slope form [tex](y-y_1) = m(x-x_1)[/tex].
[tex]y--1=\frac{6}{7}(x--3)\\y + 1 = \frac{6}{7}(x+3)\\7y + 7 = 6(x + 3)\\7y + 7 = 6x + 18\\-6x + 7y + 7 = 18\\-6x + 7y = 11\\6x - 7y = -11[/tex]
To convert to standard form, multiply the equation by 7. This means each term is multiplied by 7 to clear the denominator. Then multiply using the distributive property. You will now need to move terms across the equal sign. Begin by subtracting 6x from both sides. Then subtract 7 from both side. Lastly, multiply the equation by -1 since the leading coefficient in standard form cannot be negative.
What is the rate of change of this function?
Answer:
50 miles per day
Step-by-step explanation:
Answer:
Step-by-step explanation:
35 per day
Which best describes the graphs of the line that passes through (0,2) and (6,4) and the line that passes through (2,1) and (5,7)?
Answer:
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Both are increasing.
Step-by-step explanation:
Compare the lines by finding the slope between each pair of points.
Using the slope formula, substitute the points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Find the value of the variable leave answer in simplest radical form
X is 7 and y is 7 square root of 3.
Answer:
x = 7 and y = 7√3
Step-by-step explanation:
Let's review, and then apply, the definition of "cosine."
cos Ф = adjacent side / hypotenuse.
Here, x is the adjacent side, Ф is the angle and is 60°, and 14 represents the length of the hypotenuse. cos Ф = adjacent side / hypotenuse becomes:
adjacent side = hypotenuse * cos Ф.
Here, Ф = 60° and cos Ф = cos 60° = 1/2. Therefore,
in this case, x = 14(1/2), or 7.
Applying the definition of sine:
sin Ф = opp / hyp. In this case, sin Ф = sin 60° = y/14, so that
y = 14 sin 60°, or y = 14(√3 / 2) = 7√3.
In summary, x = 7 and y = 7√3.
determine if each example is positive or negative earn $25 which one is it is your feet below sea level or 4 degrees below zero
Answer:
I would say
earned $25 is positive
0 feet below see level is negative
4 degrees below zero is negative
Step-by-step explanation:
An estimated three out of every 25 men are left-handed what percent of the men are left-handed?
Answer:
12%
Step-by-step explanation:
3/25 x 100 = 12
Answer:12%
Step-by-step explanation:
3/25 * 100 ☺
What is a simpler form of the expression?
(2n^2 + 5n +3)(4n - 5)
Answer:
8n³ + 10n² - 13n - 15
Step-by-step explanation:
Distribute the factors by multiplying each term in the first factor by each term in the second factor, that is
4n(2n² + 5n + 3) - 5(2n² + 5n + 3) ← distribute both parenthesis
= 8n³ + 20n² + 12n - 10n² - 25n - 15 ← collect like terms
= 8n³ + 10n² - 13n - 15
Answer:
[tex]\large\boxed{(2n^2+5n+3)(4n-5)=8n^3+10n^2-13n-15}[/tex]
Step-by-step explanation:
[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2n^2+5n+3)(4n-5)\\\\=(2n^2)(4n)+(2n^2)(-5)+(5n)(4n)+(5n)(-5)+(3)(4n)+(3)(-5)\\\\=8n^3-10n^2+20n^2-25n+12n-15\\\\\text{combine like terms}\\\\=8n^3+(-10n^2+20n^2)+(-25n+12n)-15\\\\=8n^3+10n^2-13n-15[/tex]
G(x)= 3/4x+6
What is the value of g(12)?
Answer:
G(12) = 15
Step-by-step explanation:
When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.
So you get 3/4(12) + 6.
Then simplify to get g(12) = 15
In the diagram, AB CD. If m<3=115, what is m<6=?
55°
65°
75°
115°
Answer:
65°
Step-by-step explanation:
<3 + <6 = 180 because they are same side interior angles
115 + <6 = 180
Subtract 115 from each side
115-115 +<6 = 180 -115
<6 = 65
When John bought his new computer, he purchased an online computer help. Service.
The help service has a yearly fee of $25.50 and a $10.50 charge for each help session a person uses. If John can only spend $170 for the computer help his year, what is the maximum number of help seccion he can use this year?
Final answer:
John can afford a maximum of 13 help sessions with his $170 budget for the year, after accounting for the $25.50 annual fee and the $10.50 per session charge.
Explanation:
To find the maximum number of help sessions John can use within his budget, we need to set up a simple algebraic equation. The total cost for the online help service consists of an annual fee plus the charge per help session. The equation to represent this situation will be:
Total Cost = Annual Fee + (Charge per Session × Number of Sessions)
We know the Annual Fee is $25.50, the Charge per Session is $10.50, and John's budget, or the Total Cost, is $170.
Let's denote the Number of Sessions as 'x'. The equation therefore becomes:
$170 = $25.50 + ($10.50 × x)
Subtracting the annual fee from both sides gives us:
$170 - $25.50 = $10.50 × x
$144.50 = $10.50 × x
Dividing both sides by $10.50 gives us the number of sessions John can afford:
x = $144.50 / $10.50
x = 13.7619...
Since John can't have a fraction of a session, we round down to the nearest whole number. John can afford a maximum of 13 help sessions within his budget of $170 for the year.
If the perimeter of the regular octagon is 48in what’s is the area ? ( round it to the nearest tenths)
Answer:
The area of the octagon is [tex]173.8\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular octagon is equal to the area of eight isosceles triangle
The base of each isosceles triangle is equal to the length side of the regular octagon
The vertex angle of each isosceles triangle is equal to
[tex]360\°/8=45\°[/tex]
The area of each isosceles triangle is equal to
[tex]A=\frac{1}{2}bh[/tex]
where
b is the length side of the regular octagon
h is the height of each isosceles triangle
Find the length side of the regular octagon b
The perimeter of a octagon is equal to
[tex]P=8b[/tex]
[tex]P=48\ in[/tex]
so
[tex]48=8b[/tex]
[tex]b=6\ in[/tex]
Find the height of each isosceles triangle h
[tex]tan(45\°/2)=(b/2)/h[/tex]
[tex]h=(b/2)/tan(45\°/2)[/tex]
substitute the values
[tex]h=(6/2)/tan(22.5\°)=7.24\ in[/tex]
Find the area of the octagon
[tex]A=8[\frac{1}{2}bh][/tex]
[tex]A=8[\frac{1}{2}(6)(7.24)]=173.8\ in^{2}[/tex]
Write an equation to describe the relationship in this table.
Answer:
y = x+5
Step-by-step explanation:
you cant times it by anything but 1 so x then how much does it go up by 5 so y= x+5
Answer:
1 , 5
Step-by-step explanation: