The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.
Explanation:1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.
2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.
3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).
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Carpet sells for $3 per square foot and will cost you $810 to recarpet your rectangular room. if your room is 18 feet long, how many feet wide is it?
PLEASE HELP ME ON THIS
The ordered pairs below represent a function
(-2,-17.5),(5,8.75),(0,-10),(-1,-13.75),(3,1.25)
What is the rate of change of the function?Round to the nearest hundreth if necessary. PLEASE HELP ASAP WILL AWARD BRAINLIEST!!!
Answer:
The answer is 3.75.
Step-by-step explanation:
I did this before
Find a rational number that is between 9.5 and 9.7
Answer:
9.6
Step-by-step explanation:
It is a rational number as it has terminating decimal expansion
Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $ 32.
Carolina's charges can be represented by the linear equation y = 8 + 6x, where x represents hours worked and y represents the total fee charged for the service.
Explanation:The subject this question pertains to is Mathematics, specifically linear equations. Carolina's job can be modelled by a linear equation, where the independent variable is the number of hours worked and the dependent variable is the total fee charged.
In this case, Carolina charges an initial flat fee plus $6 per hour worked. Her total charge for a 4-hour job is $32, which means her initial fee can be deduced by subtracting four times her per-hour fee from the total fee, that is $32 - 4*$6 = $32 - $24 = $8. Therefore, the linear equation that models Carolina's job is y = 8 + 6x, where x is the number of hours worked and y is the total fee charged.
This is similar to the linear equation that represents Svetlana's tutoring job in Example 12.4, where each tutoring session earns her a one-time fee of $25 plus $15 per hour of tutoring, modeled by the equation y = 25 + 15x.
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Ron is five years older than twice his cousin Pat’s age. The sum of their ages is less than 35. What is the greatest age that Pat could be? 7,8, or 10? Please more then one response so I know its right,
Javier bought a 20 oz smoothie that contains 450 total calories how many calories does a smoothie contain per ounce
Analyze the graph of the quadratic function that contains the points (0,-2), (1,0) and (3,10). Create the equation of the function given the three points.
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
A) f(0) = 7
B) f(0) = −7
C) f(−7) = 0
D) f(7) = 0
When (x + 7) is a factor, f(-7) = 0. Thus, option C is correct: f(-7) = 0.
When the polynomial f(x) has (x + 7) as a factor, it implies that when x is replaced by -7, f(x) becomes zero.
This follows from the factor theorem which states that if (x - c) is a factor of a polynomial f(x), then f(c) = 0.
Therefore, to satisfy this condition, f(-7) = 0.
Consequently, option C, stating that f(-7) = 0, must be true when (x + 7) is a factor of f(x).
Thus, the correct answer is C) f(-7) = 0.
Mark has 36 drawings of horses and 4 drawings of spaceships. write and solve an equation to find how many times as many drawings of horses he has as spaceships.
In the diagram, m<2 = 123 degrees. Find m<3.
orginal price is 82$ the sales price is 65.60 what is the discount
What exponential function is the best fit for the data in the table?
x f(x)
2 −3
3 0
4 12
f(x) = 4(4)x − 1 + 4
f(x) = 4(4)x − 1 − 4
f(x) = one fourth(4)x − 1 + 4
f(x) = one fourth(4)x − 1 − 4
Among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard deviation is 2.9. What is the margin of error, assuming a 90% confidence level? Round your answer to the nearest tenth. 0.01
Answer:
The margin of error assuming a 90% confidence level is 0.3
Step-by-step explanation:
Size of the sample: n=320
Mean: m=24
Standard deviation: s=2.9
Confidence interval: 90%
100(1-α)=90
Solving for α: Dividing by 100 both sides of the equation above:
100(1-α)/100=90/100
1-α=0.9
Subtracting 1 both sides of the equation:
1-α-1=0.9-1
-α=-0.1
Multiplying the equation by -1:
(-1)(-α=-0.1)
α=0.1
n= [z(1-α/2) s / E]^2
where E is the margin of error
z(1-α/2)=z(1-0.1/2)=z(1-0.05)=z(0.95)=1.64 (Table standard normal distribution)
z(1-α/2)=1.64
Replacing the known values in the equation above:
320= [(1.64) (2.9) / E]^2
320= (4.756/ E)^2
Solving for E: Square root both sides of the equation:
sqrt(320)=sqrt[ (4.756/ E)^2]
17.88854382=4.756/E
Cross multiplication:
17.88854382 E = 4.756
Dividing both sides of the equation by 17.88854382:
17.88854382 E / 17.88854382 = 4.756 / 17.88854382
E=0.265868486
Rounding tho the nearest tenth:
E=0.3
A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each
sidhttps://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS7/7.043.pnge?
Answer:
I can't believe this guy above me has a verified answer and it is wrong.... anyway the true answer to this is 2. I checked it myself when I put 1 as the answer and got this question wrong, and it showed me the correct answer is 2 so don't believe the verified answer.
Step-by-step explanation:
Review Question #7:
The answer to this question is 2ft, not 1ft.
This is because:
So the width of the second rectangle can be represented by 10+2x, and the length of the second rectangle can be represented by 5+2x. Lets make 2x equal y to make things easier though. Because the product of both 10+2x and 5+2x is 84 square feet, we must multiply the two equations together first.
(10+y)(5+y)=84
This then equals:
50+10y+5y+y^2=84
Then add the like terms:
y^2+15y+50=84
Then set the equation to zero by subtracting 84 from both sides:
y^2+15y-34=0
From that, you can use the box method, or any method to get:
(y+17)=0 and (y-2)=0
Which would then simplify to:
y=-17 and y=2
However, we substituted y for 2x, so plug 2x into y:
2x=-17 and 2x=2
Then simplify from here:
x=-17/2 and x=1
The answer cannot be negative, so that means the answer is x=1, however, even though this is true, the answer is that 2ft was added to EACH SIDE, because the question was asking for what amount was added to each side.
If tan x=a/4 and cos x=4/b what is the value of sin x?
The value of sin x is sqrt(b^2 - 16)/16.
Explanation:
To find the value of sin x, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Given that tan x = a/4 and cos x = 4/b, we can use the Pythagorean identity (1 + tan^2(x) = sec^2(x)) to find the value of sin x:
1 + (a/4)^2 = (4/b)^2
Simplifying the equation, we get: 1 + a^2/16 = 16/b^2Multiplying both sides by 16, we get: 16 + a^2 = 256/b^2Substituting the value of cos x, we get: 16 + a^2 = 256/(16/b^2)Further simplifying, we get: 16 + a^2 = 16b^2/16Cross multiplying, we get: 16 + a^2 = b^2Substituting the value of tan x, we get: 16 + (4a)^2 = b^2Simplifying the equation, we get: 16 + 16a^2 = b^2Subtracting 16 from both sides, we get: 16a^2 = b^2 - 16Taking the square root of both sides, we get: 4a = sqrt(b^2 - 16)Dividing both sides by 4, we get: a = sqrt(b^2 - 16)/4Substituting the value of a in the equation sin x = a/4, we get: sin x = sqrt(b^2 - 16)/16
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use substitution to solve 3x-2y=11 and x+2y=9
If the sin 60° = square root of three over two, then which statement is true? (6 points)
cos 30° = square root of three over two, because the cosine and sine are complements
cos 30° = 0, because the cosine and sine are complements
cos 120° = square root of three over two, because the cosine and sine are supplements
cos 120° = 0, because the cosine and sine are supplements
Answer: The answer is (a) cos 30° = square root of three over two, because the cosine and sine are complements
Step-by-step explanation: Given that -
[tex]\sin 60^\circ=\dfrac{\sqrt 3}{2}.[/tex]
we are to select the correct statement from the given four options.
We know that sine and cosine functions are supplement of each other. So, we have
[tex]\sin 60^\circ=\cos(90^\circ-60^\circ)=\cos 30^\circ=\dfrac{\sqrt 3}{2}.[/tex]
Thus, the correct option is (a) cos 30° = square root of three over two, because the cosine and sine are complements.
Translate the following and then create real-world problems using these
expressions.
“6 less than a number”
“2 times the quotient of a number and two”
“4 times the difference of a number and 8”
Which graph represents the function on the interval [−3, 3] ?
How do you solve binomials
To solve binomials, one can use the binomial theorem, which involves the use of binomial coefficients calculated via factorials. For large numbers, Stirling's formula can help manage calculations by using approximations of factorials through logarithms.
Understanding Binomials and the Binomial Theorem
To solve binomials and expand binomial expressions, we often use the binomial theorem. This theorem expresses the expansion of the power of a binomial as a sum of terms in the form of coefficients multiplied by powers of the two parts of the binomial. A binomial coefficient, represented by (n), counts the number of ways to choose r objects from n without regard to order and is computed using factorials.
When dealing with large binomial coefficients, calculators may return overflow errors. To handle this, one might use Stirling's formula, an approximation for logarithms of factorials. This approach makes it more feasible to work with large numbers.
Using the example of expanding (1 + x)³, we get 1 + 3x + 3x² + x³, where the coefficients 1, 3, 3, and 1 represent the binomial coefficients for each term. This pattern applies generally when using the binomial theorem for expansion.
PLZ HELP ASAP WILL GIVE BRAINLIEST ANSWER!!!!!
What do you predict the current will be in the absence of sunlight?
Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
@ganeshie8,
Use the quadratic formula to find both solutions to the quadratic equation given below 2x^2-3x+1=0
Answer:
[tex]x_1=1\\x_2=\frac{1}{2} =0.5[/tex]
Step-by-step explanation:
Given a equation of the form:
[tex]ax^2+bx+c=0[/tex]
The roots of this equation can be found using the quadratic formula which is given by:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case we have this equation:
[tex]2x^2-3x+1=0[/tex]
So:
[tex]a=2\\b=-3\\c=1[/tex]
Using the the quadratic equation :
[tex]x= \frac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(1) } }{2(2)} = \frac{3\pm\sqrt{9-8 } }{4}=\frac{3\pm 1}{4}[/tex]
Therefore the two roots would be:
[tex]x_1=\frac{3+ 1}{4}=\frac{4}{4}= 1\\x_2=\frac{3- 1}{4}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
In circle C, what is the value of X?
X=112 degrees
X=90 degrees
X=68 degrees
X=22 degrees
Answer:
x=22 degrees
Step-by-step explanation:
We are given a circle C
Centre is at C
A line passes through the centre makes angle x and 68 on either side
A triangle is formed with angles x, 68 and another angle at the circumference.
Since the line passing through the centre is diameter of the circle, we have
the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)
In the triangle sum of three angles
=90+x+68 =180
x =22 degrees
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years? (1 point)
$1,671.74
$17,028.75
$1,710.61
$8,140.92
what is the y- coordinate of the y- intercept of the line that passes through the points (-4,-4) and (4,8)
1. Solve the equation. -4x = 0
X = -4
X = 4
X = 0
X = 1
2. decide whether the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17 ?
Yes or no
3. simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x2 + 8x
4. Name the property shown. 12x( y ) = 12(xy)
Find an nth degree polynomial function with real coefficients satisfying the given conditions. calculator
To find an nth-degree polynomial function with real coefficients given certain conditions, we can write the polynomial as a product of its linear factors using the given roots.
Explanation:To find an nth-degree polynomial function with real coefficients, we need to use the given conditions. Let's say the conditions include the roots of the polynomial. If we have n distinct real roots, the polynomial will have n factors. So, if the roots are a, b, c, ..., we can write the polynomial as P(x) = (x - a)(x - b)(x - c)...
Example:To find a quadratic polynomial with roots 2 and -3, we can write the polynomial as P(x) = (x - 2)(x - (-3)) = (x - 2)(x + 3) = x² + x - 6.
Similarly, for higher-degree polynomials, we use the same approach. We write the polynomial as a product of its linear factors using the given roots.
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In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.
(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.
Answer:
(a) The relation is RT × ST = TU²
(b) TU = 6
Step-by-step explanation:
(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).
Then RT × ST = TU²
(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²
Solving that equation, we have TU = √36 = 6
Thus TU = 6