The value of given expression for x=0 is 1, x=-2 is 0.44 and x=2 is 2.25.
Given the expression is (3/2)ˣ.
Firstly, we will simplify the given expression (3/2)ˣ for x=0.
Substitute the value x=0 in given expression, we get
(3/2)ˣ =(3/2)⁰
As we know that something raise to power zero is 1.
So, we get
(3/2)ˣ =1
Now, we will simplify the given expression (3/2)ˣ for x=-2.
Substitute the value x=2 in given expression, we get
(3/2)ˣ =(3/2)²
Now, we will square the expression to simplify it, we get
(3/2)ˣ =9/4
(3/2)ˣ =2.25
Furthermore, we will simplify the given expression for x=-2.
Substitute the value x=-2 in given expression, we get
(3/2)ˣ =(3/2)⁻²
Now, we will square the given expression, we get
(3/2)ˣ =(9/4)⁻¹
Further, we will divide it above expression by 1 to remove negative sign, w eget
(3/2)ˣ =1/(9/4)
(3/2)ˣ =4/9
(3/2)ˣ =0.44
Hence, the value of expression (3/2)ˣ for x=0, 2 and -2 is 1, 2.25 and 0.44.
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Question Progress Homework Progres 23/2 Solve the quadratic equation 3x + x-5 = 0 Give your answers to 2 decimal places.
The value of x is 1.14 or x = -1.47
We find the value of x in the quadratic equation 3x^2 +x-5=0
Using the formula: (-b ± √ (b²- 4 a c)) / (2a)
Where the value of a = 3, b = 1 and c = -5
Substituting the above values (a = 3, b = 1 and c = -5)
in the formula:
(-1 ± √ (1²- 4 3 (-5))) / (2*3)
= (-1 ± √ (1+60)) / (6)
= (-1 ± √ (61)) / (6)
= (-1 ± 7.81) / (6)
= (-1 + 7.81) / (6) or (-1 -7.81) / (6)
= (6.81) / (6) or (-8.81) / (6)
=1.135 or -1.468
Hence the value of x= 1.14 or -1.47
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The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer weights
For the given word problem on the recommended weight of a soccer ball, we have:
An absolute value equation to find the minimum and maximum acceptable soccer weights is |x - 430| ≤ ±20. The minimum and maximum acceptable soccer weights are equal to 410 grams and 450 grams respectively.What is an absolute value equation?An absolute value equation can be defined as a type of equation that consist of an algebraic equation, which is placed within absolute value symbols.
In order to write and solve this absolute value equation, we would assign a variable (x) to the actual weight and then evaluate the resulting algebraic equation as follows:
Let x represent the actual weight.
Next, we would write an absolute value equation as follows:
|x - 430| ≤ ±20
-20 ≤ x - 430 ≤ 20
By applying the addition property of inequalities, we have:
x ≤ 430 - 20
Minimum acceptable soccer weights, x = 430 - 20 = 410 grams.
x ≤ 430 + 20
Maximum acceptable soccer weights, x = 430 + 20 = 450 grams.
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Does the table represent a function? Why or why not?
X23345
45677
у
A. Yes, because every x-value corresponds to exactly one y-value.
OB. No, because one x-value corresponds to two different y-values.
C. Yes, because there are two x-values that are the same.
OD. No, because there are two y-values that are the same.
Based on table shown above, we have that: B. No, because one x-value corresponds to two different y-values.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Based on table shown above, we can reasonably infer and logically deduce that this table does not represent a function because one x-value corresponds to two different y-values.
In conclusion, this table is not a function because no function can have the same x-values (3) for different y-values (5 and 6).
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20. Complete the multiples of 4.
4
24
52
Answer:
4, 8, 12, 16, 20, 24, 28,32, 36, 40, 44, 48, 52
Someone help me with this please, I literally can’t figure it out
There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.
What value of b is needed for a quadratic equation such that the minimum value is equal to - 1?
In this problem we know a quadratic equation of the form g(x) = x² + b · x, of which we must determine the value of b such that the y-value of the minimum is - 1. Graphically speaking, quadratic equations are represented by parabolae, which have either a minimum or a maximum know as vertex.
First, we must determine the vertex form of the equation of the parabola:
y = x² + b · x
y = x² + 2 · (b / 2) · x
y + b² / 4 = x² + 2 · (b / 2) · x + b² / 4
y + b² / 4 = (x + b / 2)²
The coordinates of the vertex are (h, k) = (- b / 2, - b² / 4). Then, the y-coordinate of the vertex is:
- b² / 4 = - 1
b² / 4 = 1
b² = 4
b = ± 2
There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.
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A red plastic strip binds the three identical cylinders. The cross-sectional area enclosed by the strip is 115 cm². What is the radius of each cylinder? What is the length of the plastic strip?
The radius of each cylinder is approximately 3.49 cm and the length of the plastic strip is approximately 65.84 cm.
Cylinder is a basic 3 dimensional solid with a curved surface. A cylinder can be identified as a prism with circular base.
The cross-section of a cylinder gives a circle whose area can be represented by πr² where r is the radius of the base of the cylinder.
Here the plastic wire encloses the area of cross-section of three cylinders.
Therefore area of cross-section of one cylinder=115÷3=(115/3) cm ²
Since area of cross-section of a cylinder=πr²
Therefore πr²=(115/3)
or, r=3.4931...
or, r≈3.49 cm
Hence the radius of each cylinder is approximately 3.49 cm
Now the plastic strip covers 3 cylinders .
Circumference of each cross-section of cylinder is given by =2πr
Total length of 3 cylinders = 2πr×3 = 6πr cm
Therefore total length= 64.843...cm ≈ 65.84 cm
Therefore the length of the plastic strip is approximately 65.84 cm
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In 2019, the distribution of golfer Lexi Thompson’s driving distance had a mean of 276 yards. Assuming that her distribution of driving distance is approximately normal with an 80th percentile of 290 yards, calculate its standard deviation.
Standard Deviation = ___ yards. (Round to 2 decimal places.)
If mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.
Given that mean is 276 yards, percentile is 80, sample mean is 290 yards.
We are required to find the value of standard deviation.
A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values.
Z=(X-μ)/σ--------1
Z score for 80th percentile is 0.842.
X is given as 290 and μ as 276.
We have to just put the values of mean and Z score in formula 1 to find the standard deviation.
0.842=(290-276)/σ
σ=14/0.842
σ=16.63
Hence if mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.
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Ayudaaa por favor
Tenemos un barril del que vaciamos la mitad y luego 3⁄4 de lo que
queda. ¿Qué fracción del barril ha quedado con agua? Si el barril tiene
una capacidad de 80 litros, ¿qué cantidad de líquido queda?
Answer:
1/8th
10 litres
Step-by-step explanation:
Read each question. Then write the letter of the correct. answer on your page. The population of a town is modeled by the equation P=16,581 e⁰.⁰²t where P represents the population t years after 2000 . According to the model, what will the population of the town be in 2020 ?
(A) 16,916
(B) 17,258
(C) 20,252
(D) 24,736
The correct option is (D) 24,736.
The population growth of the town be in 2020 is 24,736.
What is termed as exponential population growth?Charles Darwin was heavily influenced by English clergyman Thomas Malthus in developing his theory of natural selection.
In 1798, Malthus published a book in which he stated that population numbers with unlimited natural resources expand quickly, but then population growth slows as resources deplete. This accelerating sequence of population growth is known as exponential growth.The stated condition is; P = 16,581 e(⁰.⁰²t)
Where, t = total number of years after 2000.
P = population t years after 2000
The total number of years between 2020 and 2000
t = 2020 - 2000
t = 20 years.
Substituting the value of the number of years 't' in the given exponential expression,
=> P = 16,581 e(⁰.⁰²×20)
=> P = 16,581 e∧(0.4)
=> P = 16,581×1.49
=> P = 24,735.94
=> P = 24,736
Therefore, the population growth of the town be in 2020 is found to be 24,736.
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allowed
This is a new version of the question. Make sure you start new workings.
Gavin and Amna converted some pounds (£) into euros (€) at
two different shops.
< Back to task
Gavin converted £30 into €36.60 at shop A.
Amna converted £73 into €86.14 at shop B.
Caleb converted some pounds at one of these shops and
received €71.98.
What is the smallest amount that he could have converted?
The smallest amount that Caleb could have converted will be £ 59.
We are given that:
At shop A, Gavin converted £ 30 into € 36.60
At shop B, Amna converted £ 73 into € 86.14
Also, Caleb converted some pounds and got € 71.98.
Rate of conversion at shop A is:
£ 30 = € 36.60
£ 1 = € 36.60 / 30
£ 1 = € 1.22
rate of conversion at shop B is:
£ 73 = € 86.14
£ 1 = € 86.14 / 73
£ 1 = € 1.18
Now, we can see that the rate of conversion is more at shop A.
So, the smallest amount that Caleb might have converted will be:
Pounds = € 71.98 / € 1.22
Pounds = £ 59
Therefore, the smallest amount that Caleb could have converted will be £ 59.
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A theme park collected $900 in entry fees for 150 visitors on Friday. The amount collected varies directly with the number of visitors on a particular day.
Write an equation that gives the amount collected in fees,f for a given number of visitors,v
The equation which gives relation between entry fee collected and number of visitors in theme park: f = 6v.
What is defined as the direct proportional?A direct proportion is an arithmetical comparison of two numbers whose ratio is equal to a fixed value."When the relation between different quantities is so that if we increase one, the second will also increase, so if we decrease one, the other will also decrease, therefore the two quantities are considered to be in a direct proportion," according to the definition.The given condition is;
The total collect cost for entry in theme park = $900.
The total number of visitors = 150.
Let 'f' be the collected fee.
Let 'v' be the number of visitors.
Then, the amount collected varies directly with the number of visitors on a particular day.
f ∝ v
Removing proportional will bring the constant k;
f = kv .......eq1
v = 150 and f = 900
Put the values;
900 = 150 k
k = 6 ; put in eq 1.
f = 6v
Thus, the relation between fee and number of visitors is given by equation; f = 6v.
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Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%. How much state and local tax should be withheld from her weekly pay?
The state and local tax that will be paid by Mei will be $17 and $12.50 respectively.
How to calculate the tax?From the information, Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%.
The state tax that will be paid will be:
= Rate × Income
= 6.4% × $265.85
= 0.064 × $265.85.
= $17
The local tax that will be paid will be:
= Rate × Income
= 4.7% × $265.85
= 0.047 × $265.85.
= $12.50
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A hole the size of a photograph is cut from a red piece of paper to use in a picture frame. 5 4 3 2 photograph -5-4-3-2-1₁- 2/9 -2. -3- red paper -5 1 2 3 5 X What is the area of the piece of red paper after the hole for the photograph has been cut? O 17 square units 25 square units 39 square units 47 square units
Answer:57
Step-by-step explanation:
Which situation shows the expressions ordered from LEAST to GREATEST?
OA.
B.
-6-(-8)
2.5-8
-1.9-4.3
-6-(-8)
-1.9-4.3
-1.9-4.3
2.5 8
2.5 8
2.5-8
-6-(-8)
-6-(-8)
-1.9-4.3
Answer: I hope this helps.
Step-by-step explanation:
find the missing terms
_,-9,_,3,9
Answer:
-15,-9,-3,3,9
Step-by-step explanation:
Question 2(Multiple Choice Worth 4 points)
(01.01 LC)
Simplify the following expression:
3x-8y + 2x² + 3y - 8x
02x²-5x - 5y
02x²-11x-5y
02x²-5x-11y
02x²-11x-11y
Answer:
A
Step-by-step explanation:
3x-8y+2x^2+3y-8x
2x^2-5x-5y
Rewrite: [tex]\frac{42}{5}[/tex]% as a decimal.
d=rt (Distance formula distance=rate•time)
t
if d=150 when r=60, find t
Answer:
25
Step-by-step explanation:
if the formula for distance is distance = rate times time then you have to divide the rate 60 by the distance 150 to get 25 .
Evaluate (3n)! for n=2.
Find the area of a rectangle with a base of 2 and a height of 6.
Answer:
12
Step-by-step explanation:
2 x 6 = 12
to find area you multiply length x width or in this case base x height
An equation of a line through (3, 10) which is parallel to the line y = 5x + 4 has slope:
And y-intercept at:
Parallel lines have the same slope, so the slope is 5.
The equation in point-slope form is y-10=5(x-3). Substituting x=0, we get y - 10 = -15, and thus the y intercept is (0, -5).
If you divide an inequality with a less than sign by -3, what inequality sign would it
change to?
The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster, you must be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. How many downloaded songs, d, must be purchased for the monthly price of Napster to be the same as iTunes?
Answer:
I think the answer is 11 in my opinion
For each function, identify the transformation from the parent function y=b x . y=-2 . 3 x
Transformation of y= b*x into y = 2.3 *x will take place by vertical dilation by a scale factor of 2.3.
A parent function is the simplest form of a particular family of functions. A family of operations is a group of tasks with the same highest degree and therefore the same graph shape.
Function transformations "move" "resize" or "mirror" the graph of the parent function.
Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means it is a reflection here, 'a' stands for vertical stretch, 'b' stands for horizontal stretch, 'c' stands for horizontal movement, 'd' stands for vertical movement
We have given two functions y=b x and y = 2.3x which means that first, y changes into 2.3 x i.e., vertical dilation by a scale factor of 2.3.
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Find the domain and the range of each function.
y=log₂(x-3)
The domain of the function is (3,∞) , {x|x>3}
and the range of the function is (−∞,∞), {y|y ∈ R}
given the function is y = log₂(x ₋ 3)
Set the argument in log₂(x ₋ 3) greater than 0 to find where the expression is defined.
x ₋ 3 > 0
Add 3 to both sides of the inequality.
x > 3
The domain is all values of x that make the expression defined.
Interval Notation:
(3,∞)
Set-Builder Notation:
{x|x>3}
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
(−∞,∞)
Set-Builder Notation:
{y|y∈R}
Determine the domain and range.
Domain: (3,∞) , {x|x>3}
Range : (−∞,∞), {y|y ∈ R}
Hence we get the required domain and range of the given function.
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Find the values of a and b such that x2-4x+9 = (x+a)^2+b
The values of a and b are - 2 and 5, respectively.
How to find the values of the coefficients related to a quadratic polynomial
In this problem we must expand the quadratic polynomial and find the values of two coefficients by direct comparison, the complete procedure is now introduced:
x² - 4 · x + 9 = (x + a)² + b
x² - 4 · x + 9 = x² + 2 · a · x + a² + b
Then, by direct comparison, we find the following system of equations:
2 · a = - 4 (1)
a² + b = 9 (2)
By (1):
a = - 2
(1) in (2):
b = 9 - a²
b = 9 - (- 2)²
b = 5
The values of a and b are - 2 and 5, respectively.
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A web designer charges customers an initial consultation fee plus an hourly rate. The table shows the linear relationship between x, the number of hours and y, the total cost of hiring the designer. a. Find the rate of change b. What does the rate of change represent in the context of the situation?
The rate of change means that the designer hourly charge is $55 per hour
Linear equation
A linear equation is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost of hiring the designer after x hours.
From the table, using the point (0, 125) and (15, 950):
m = y₂-y₁/x₂-x₁= 950- 125/15-0 = 55The rate of change means that the designer hourly charge is $55 per hour
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i dont know how if tried quite a few times and cant get it
Answer:
2/3 and 3/2
Step-by-step explanation:
→ Divide the smaller triangle by the larger one for the first one
8 ÷ 12 = 8/12 = 2/3
→ Divide the larger triangle by the smaller one for the second one
12 ÷ 8 = 12/8 = 3/2
What is the slope of the line that passes through the points (2,8) and (-3,14)?
The slope of the line that passes through the coordinates is -6/5.
What is defined as the slope of the line?The slope of a line is a measurement of its steepness and direction. Whatever two distinct points on a line can be used to calculate the slope of that line. The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line. The net y coordinate change is Δy, whereas the net x coordinate change is Δx.The slope of the line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
Where, the coordinates are given.
(x₁ ,y₁) = (2, 8)
(x₂, y₂) = (-3, 14)
Put the value in the slope;
m = (14 - 8)/(-3 - 2)
m = 6/-5
m = -6/5
Therefore, the slope of line passing from the points is -6/5
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Write each expression in simplest form. (x¹/₃ / y²/₃)⁹
[tex]x^{3} / y^{6}[/tex] is the simplest form
The expression is
[tex](x^{1/3 }/ y^{2/3} ) ^{9}[/tex]
We have to multiply the root of 9 with the root of the numerator and denominator.
So we will get
[tex](x^{1/3} )^{9} /( y^{2/3})^{9}[/tex]
[tex]x^{1/3*9} / y^{2/3 *9}[/tex]
We will get
[tex]x^{9/3} /y^{18/3}[/tex]
=[tex]x^{3} / y^{6}[/tex]
So now we get the equation in the simplest form in the form of x and y
i.e [tex]x^{3} / y^{6}[/tex]
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