Answer:
Family: exponential functions
Step-by-step explanation:
The given function is:
[tex]y = 3*2^x - 6[/tex]
It is in the form of exponential function:
[tex]y = a*b^x + c[/tex]
where "a", "b", and "c" are constants.
The parent function of an exponential function is:
[tex]y = b^x[/tex]
where "b" is the base of the exponential function. In this case, the parent function would be:
The given function is a member of the family of exponential functions with base 2 and with a vertical shift of -6 units and a vertical stretch by a factor of 3.
Answer:
Exponential function family with base 2.
[tex]\textsf{Parent function:} \quad y=2^x[/tex]
Step-by-step explanation:
The given equation is in the form of an exponential function with a vertical stretch and vertical shift.
The standard form of this type of exponential function is:
[tex]y=ab^x+c[/tex]
where:
a is the vertical stretch factor.b is the base (growth/decay factor) in decimal form.c is the vertical shift.y = c is the equation of the horizontal asymptote.If |a| > 1 then it is a vertical stretch, and if 0 < |a| < 1 it is a vertical "compression".
The parent function of this type of exponential function is y = bˣ, where b is the base.
Given function:
[tex]y=3 \cdot 2^x-6[/tex]
Therefore, the parent function of the given function is:
[tex]\boxed{f(x)=2^x}[/tex]
The given function is a vertical stretch by a factor of 3, followed by a vertical shift downwards by 6 units, from the parent exponential function with base 2.
Hence, the family of functions that this equation belongs to is the exponential function family with base 2, and the parent function is [tex]y = 2^x[/tex].
Non mutually exclusive events !
The missing probability is P(A or B) = 131/200
How to calculate the probabilityIt should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)
Simplifying the expression, we get:
P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200
The probability is 131 / 200.
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Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). HELP ASAP! This is due in 15 minutes!!
Answer:
Step-by-step explanation:
The standard form equation for an ellipse with center at the origin is:
x^2/a^2 + y^2/b^2 = 1
where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.
In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.
We also know that the distance from the center to the focus is 'c', and that:
c^2 = a^2 - b^2
Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:
c^2 = a^2 - b^2
1^2 = 3^2 - b^2
b^2 = 3^2 - 1^2
b^2 = 8
b = sqrt(8) = 2sqrt(2)
Substituting these values into the standard form equation, we get:
x^2/3^2 + y^2/(2sqrt(2))^2 = 1
Simplifying:
x^2/9 + y^2/8 = 1
So, the equation in standard form for the given ellipse is:
9x^2 + 8y^2 = 72
A list 7 members at the gym 10, 64, 52, 46,54,67,54. find the median
The calculated value of the median of the A-list 7 members at the gym is 54
Finding the median of the A-list 7 members at the gymFrom the question, we have the following parameters that can be used in our computation:
10, 64, 52, 46,54,67,54.
When the numbers are sorted in ascending order, we have
Sorted list = 10, 46, 52, 54, 54, 64, 67
The median is the middle number of the sorted list
So, we have
Middle number = 54
Thsis means that
Memdian = 54
Hence. the median of the A-list 7 members at the gym is 54
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$800000 into a 25:17 ratio. How much do each get
Answer: Therefore, the first person gets $476,190.48 and the second person gets $323,809.52.
Step-by-step explanation: To divide $800,000 into a 25:17 ratio, we first need to add the ratio terms (25 + 17 = 42) to determine the total number of parts. Then, we divide the total amount by the total number of parts to determine the value of each part. Finally, we multiply the value of each part by the respective ratio term to determine the amount that each person gets.
The calculation steps are as follows:
Determine the total number of parts: 25 + 17 = 42
Determine the value of each part:
Value of each part = Total amount / Total number of parts
= $800,000 / 42
= $19,047.62 (rounded to two decimal places)
Determine the amount that each person gets by multiplying the value of each part by the respective ratio term:
First person gets: 25 parts * $19,047.62 per part = $476,190.48
Second person gets: 17 parts * $19,047.62 per part = $323,809.52
M7|L5
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Enter ✔
Answer:
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
For the function f(x)=|x-3 | select all the true statements. A. The function is increasing on the interval [3, 5) B. The function is increasing of the Interval (0, 3) C. The vertex is (0, 3) D. The vertex is (3, 0). E. The y-intercept is (0, 3). F. The y-intercept is (3, 0).
Answer:
D and E----------------------
See attached graph to help with answer choices.
Given function:
f(x) = | x - 3 |Answer choices:
A. The function is increasing on the interval [3, 5) - False, correct interval is [3, + ∞)B. The function is increasing on the Interval (0, 3) - False, as shown aboveC. The vertex is (0, 3) - False, the vertex is (3, 0)D. The vertex is (3, 0) - TRUEE. The y-intercept is (0, 3) - TRUEF. The y-intercept is (3, 0) - False, the correct one is given aboveCan someone help with this and give the right answer I am on a time limit
The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers: [tex]k = y/x^a \times z/x^b,[/tex] where a and b are the powers of x in the expressions for y and z, respectively. when [tex]x = -3[/tex] and [tex]y = 4[/tex] , z is equal to -81/16.
What is the constant of variation?In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:
[tex]y = 54 = (8^a) \times k = > a = 3[/tex]
[tex]z = 144 = (8^b) \times k = > b = 2[/tex]
Substituting these values into the formula for k, we get:
[tex]k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64[/tex]
Therefore, the constant of variation is 27/64.
Using the same formula as above, we can solve for z when x = -3 and y = 4:
[tex]k = y/x^a \times z/x^b[/tex]
We need to determine the powers of x in the expressions for y and z:
[tex]y = 4 = (-3)^a * k = > a = -1[/tex]
[tex]z = ? = (-3)^b * k = >[/tex] we don't know b or z yet
Substituting these values into the formula for k, we get:
[tex]k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2[/tex]
Simplifying this expression, we get:
[tex]k = -12z/9 = -4z/3[/tex]
Now we can solve for z:
[tex]-4z/3 = 27/64[/tex]
Multiplying both sides by 3/(-4), we get:
[tex]z = -81/16[/tex]
Therefore, when [tex]x = -3[/tex] and [tex]y = 4, z[/tex] is equal to [tex]-81/16.[/tex]
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15 POINTS! HELP PLEASE ASAP!!
Answer:
C
Step-by-step explanation:
The equation is:
y = [tex]\frac{1}{4}[/tex]x - 8
If you plug in the x and y value from the table, you find they are solutions to the equation.
(36,1)
y = [tex]\frac{1}{4}[/tex]x - 8 Substitute in 36 for x and 1 for y
1 = [tex]\frac{1}{4}[/tex](36) - 8
1 = 9 - 8
1 = 1
You can do the same thing for all of the other points on the table.
Helping in the name of Jesus.
PLEASE HELP I have 30 minutes! What is the end behavior of this equation and how did you get it?
The limit of the function will be:
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
How to explain the functionThe limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.
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In the quadratic formula, the number for a is filled in with the coefficient of x
In the quadratic formula, the number for "a" is filled in with the coefficient of x².
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For instance, given the quadratic equation 2x² - 3x - 1 = 0, we have:
a = 2
b = -3
c = -1
[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 + 8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]
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Use mathematical induction to prove 2^n>=2n is true for all positive integers.
By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
The given inequality is 2ⁿ≥2n.
Let n = 1
2^1 ≥ 2^1
2 ≥ 2 which is true
Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.
We need to prove that 2^(k+1) ≥ 2^(k+1)
2^(k+1) ≥ 2*2^k (by the inductive hypothesis)
2^(k+1) ≥ 2*2^(k+1)
2^(k+1) ≥ 2^(k+1) which is true
Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
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What is the value of "x", when 1/3x = 9 1/3?
Answer:
x=28
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
have a good day :)
Answer
x=3 1/9
Step-by-step explanation:
For the right triangle below, find the measure of the angle.
Figure is not to scale.
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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Sarah uses a square and two semicircular7 inches regions to design a heart shaped poster find the area of the heart then find the approximate area by using 3.14radius
The poster has an area equal to 192.423 square inches.
How to determine the area of a heart shaped poster
In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:
A = D² + (π / 4) · D²
Where:
A - Area of the heart shaped poster, in square inches.D - Side length of the square, in inches.If we know that π = 3.14 and D = 7 in, then the area of the poster is:
A = 7² + (π / 4) · 7²
A = (5π / 4) · 7²
A = 192.423 in²
The area of the poster is equal to 192.423 square inches.
Remark
The image is missing and the statement is not well explained. A correct statement is shown below:
Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.
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Bree is replacing the wire on her farm paddock fences. She has measured a couple of the sides and drawn a sketch of the paddock shape. (pic below)
a. Find the two missing sides and calculate the perimeter of the paddocks
Perimeter?
b. The cost of fencing wire is $5 per meter. How much will the wire cost
Cost?
a. The perimeter of the paddock is 120 meters
b. The cost of the wire will be $600
a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.
The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:
20m - 10m = 10m.
The missing side on the right is equal in length to the known side of 40m.
Now we can calculate the perimeter by adding up all the side lengths:
Perimeter = 10m + 40m + 20m + 10m + 40m
= 120m.
b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.
Wire Cost = Perimeter × Cost per meter
= 120m × $5/m
= $600.
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Someone help i really need help with this
The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.
How to find the equation ?The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.
There are 4 tickets purchased so the equation would be:
4 x Cost of tickets - Parking cost = Total spent
4 x - 25 = 175
The cost of each admission ticket is:
4 x - 25 = 175
x = 150 / 4
x = $ 37.50
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A number rounded to the nearest thousand is 47,000 which number could be the number that was rounded
Answer:
Anything greater than or equal to 46,500, and less than or equal to 47,499 could be the answer.
For example, a number, let's say 46,589 falls within that range and may have been the number that was rounded.
If mZRST = 70, mZQST = 2x, and mZQSR = 3x - 10, what is the mZQSR
16
48
32
38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
Explain about the adjacent angles:If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.
We may infer from our criteria and the aforementioned instances that any pair of neighbouring angles has a shared vertex and a common side. They really aren't adjacent if one of these elements is absent. By searching for these two characteristics, we can categorise pairs of angles as neighbouring or not adjacent.There are numerous unique connections between angles in pairs. You can recognise other angle connections, such as supplementary and complementary angles, by recognising nearby angles.Given data:
m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10From the figure:
m∠RST = m∠QST + m∠QSR
Put the values
70 = 2x + 3x - 10
5x = 80
x = 16
Thus,
m∠QSR = 3x - 10 = 3(16) - 10
m∠QSR = 38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
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Complete question:
If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.
The figure is attached:
16
48
32
38
Can someone please help me with this? I'll mark anyone who answers for helping
Which expression is equivalent to 2^3 . 5^-2 ?
Correct answer gets brainliest!!!!
Answer:is b
A line segment has both of its end-points fixed and so it has a definite length.
Step-by-step explanation:
pl z give me brianlieyst and have a good day
:)
You’re planning to buy a car and you want to have $25,000 to purchase a car in cash in 5 years. If you’re able to receive 10% interest rate for investing the money, how much money should you invest today in order to have $25,000 in 5 years?
You have to invest $15,506.08
How to solve for the investmentPV = FV / (1 + r)^n
where:
PV = present value (amount of money you need to invest today)
FV = future value (amount of money you want to have in 5 years, which is $25,000)
r = interest rate (10% or 0.1)
n = number of periods (5 years)
Plugging in the values into the formula:
PV = $25,000 / (1 + 0.1)^5
PV = $25,000 / 1.61051
PV = $15,506.08
Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.
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If a, b, c are in H.P.; prove that b+ca+ca+b ac' ab bc are also in A.P.
If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.
How to prove Harmonic Progression and Arithmetic Progression?Given a, b, c are in H.P.:
1/a + 1/b = 2/c
Multiplying both sides by abc:
bc + ac = 2ab
Adding c to both sides:
bc + ac + c = 2ab + c
Rearranging the terms:
c + ab = ac + bc
Adding the terms b + ca and ca + b to both sides:
b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b
Simplifying:
b + ca + ca + b + ac' + ab + bc = 2ac + 2b
Dividing both sides by 2:
(b + ca + ca + b + ac' + ab + bc)/2 = ac + b
Hence, b+ca+ca+b ac' ab bc are in A.P.
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Malik opens a savings account with an initial deposit of $2500. The account earns 2.1% annual interest compounded quarterly? Round to the nearest cent.
Answer:
Step-by-step explanation:
Is 93 + 7 positive or negative?
Answer:
93 + 7 = 100
Step-by-step explanation:
I would assume positive because 100 is above the x-axis not below it.
Expand the expression below. Express each answers in terms of log or log y to log8x^2
Expressing the expansion of the logarithm in terms of log y, we can write: log(8x^2) = log(8) + 2*log(y), where y = x
What is the value of the expansion of the logarithm?Using the logarithmic identity that states log(a^b) = b*log(a), we can expand log(8x^2) as:
log(8x^2) = log(8) + log(x^2)
Note that a logarithmic identity is a mathematical relationship or equation that involves logarithms.
We can further simplify log(x^2) as:
log(x^2) = 2*log(x)
Therefore, we can write:
log(8x^2) = log(8) + 2*log(x)
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How many games did the team play last season?
The number of games that the team did play in the last season is 23.
What is the frequency?The frequency is the number of times an event happens. Therefore, frequency is the number of repetitions of a digit or an event.
The given frequency table represents the frequency of different runs scored by the team in the entire season.
The frequency is written in tally form, which means that each of the vertical lines represents the count of 1, while a group of fours lines such that the four lines are vertical while the fifth line cuts the other four represents a count of 5 as shown in the second column of the second row.
Therefore, the frequency table can be made as:
Number of runs Frequency
0 8
1 5
2 3
3 6
4 1
Total: 23
Hence, the team played 23 games.
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A triangle with area 184 square inches has a height that is two less than six times the width. Find the height and the width of the triangle.
The height of the triangle is √(115) - 1 inches and the width is (1 + √(115)) / 6 inches.
Let's begin by assigning variables to the height and width of the triangle. We'll use h for height and w for width.
From the problem statement, we know that the area of the triangle is 184 square inches:
Area = (1/2) * base * height
where the base is equal to the width. We can rearrange this formula to solve for the height:
height = 2 * Area / base
Since the area is given as 184 square inches and the base is equal to the width, we can write:
h = 2 * 184 / w
We also know that the height is two less than six times the width. Writing this as an equation, we have:
h = 6w - 2
Now we can substitute the expression for h from the second equation into the first equation:
2 * 184 / w = 6w - 2
Multiplying both sides by w gives:
2 * 184 = w * (6w - 2)
Expanding the right side gives:
2 * 184 = 6w² - 2w
Simplifying further gives:
6w² - 2w - 368 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
where a = 6, b = -2, and c = -368. Plugging in these values gives:
w = (2 ± √(2² - 4 * 6 * (-368))) / 2(6)
Simplifying further gives:
w = (1 ± √(115)) / 6
Taking the positive value gives:
w = (1 + √(115)) / 6
Plugging this value back into either equation for h gives:
h = 6w - 2 = 6((1 + √(115)) / 6) - 2 = 1 + √(115) - 2 = √(115) - 1
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FIND THE AREA PLEASE
Answer:
the area of the shape is 48m
Step-by-step explanation:
10*4=40
2*4=8
40+8=48
brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.
