To find the inverse of the function y = x² + 4x + 4, we first replace y with x and x with y:
x = y² + 4y + 4
Next, we rearrange the equation to isolate y on one side of the equation:
x - 4 = y² + 4y
y² + 4y = x - 4
Now, we complete the square by adding (4/2)² = 4 to both sides of the equation:
y² + 4y + 4 = x
We can rewrite the left side of the equation as (y + 2)²:
(y + 2)² = x
Finally, we take the square root of both sides of the equation and solve for y:
y + 2 = ±√x
y = ±√x - 2
Since the original function is not one-to-one, we need to restrict the domain to obtain the inverse function. Specifically, we restrict the domain of the original function to x ≥ -2, since for values of x less than -2 there are two corresponding y-values. Therefore, the inverse function of y = x² + 4x + 4 for this restricted domain is:
y = ±√x - 2, x ≥ -2
what is 33=32x-31 i need help with this problem
Answer:
x=2
Step-by-step explanation:
33=32x-31
64=32x
2=x
Answer: [tex]x = 2[/tex]
Reflect coordinate ( -12, 16) over the x-axis.
Answer:
(- 12, - 16 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
(- 12, 16 ) → (- 12, - 16 )
Give 1 example of a binomial of degree 35, and a monomial of degree 100.
Answer:
For the binomial with a degree of 35 it would be 2x35+4
For the monomial with a degree of 100 would be 5y100
Step-by-step explanation:
PLS PLS PLS help me I'm reposting this question bc no one helped me
Determine whether line segment AB is a diameter of the circle.
O Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
O Yes, The endpoints of line segment AB lie on the circle, so line segment AB is a diameter by the definition of a diameter.
O No, because line segment AB does not bisect line segment CD, line segment AB cannot be a diameter
O No, line segment AB is not perpendicular to line segment CD, so the Perpendicular Chord Bisector Theorem cannot be used to conclude that line segment AB is a diameter
Answer:
Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
Answer:
1st option
Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.
What question can be answered by finding 10 divided by 2 11/20
The question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".
What is mixed number?A mixed number is a representation of both a whole integer and a legal fraction. In most cases, it denotes an integer that falls between any two whole numbers. Look at the illustration; it shows a fraction that is larger than 1 but less than 2 (see the given image). Therefore, it is a composite number.
The expression "10 divided by 2 11/20" can be simplified as a mixed number or fraction as follows:
10 divided by 2 11/20 = 10 ÷ (2 + 11/20)
= 10 ÷ (40/20 + 11/20)
= 10 ÷ (51/20)
= 10 × (20/51)
= 400/51
= 7 43/51 (in mixed number form)
Therefore, the question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".
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If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'
If a point's preimage is P(x, y), then its image after a dilation with a scale factor of k and centered at the origin (0, 0) is P'(kx, ky).
What is Pre picture of a point?The set of all points in a function's domain that correspond to a given point in the range is known as the preimage of a point in mathematics.
Formally, let f be a function that goes from a set A to a set B, and let y be a point in B. The preimage of y is the set of all points x in A where f(x) = y, or the set of all points in the domain that the function maps to the given point in the range.
If the preimage of the point P has facilitates (x, y), and the expansion focused at the beginning with a scale component of k is applied, then the directions of the picture point P' can be tracked down utilizing the accompanying recipe:
The x- and y-coordinates of P' are determined by multiplying the corresponding coordinates of the preimage point P by the scale factor k; consequently, the coordinates of the image point P' following the dilation with the origin centered on k would be (kx, ky).
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Complete question: If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'.
What are the coordinates of point P'?
Which set of side lengths form a right triangle?
Responses
7 cm, 8 cm, 10 cm
7 cm, 8 cm, 10 cm
3 ft, 6 ft, 5 ft
3 ft, 6 ft, 5 ft
10 in., 41 in., 40 in.
10 in., 41 in., 40 in.
15 m, 20 m, 25 m
Answer:
Here is the correct answer:
15 m, 20 m, 25 m
PLease help me with this I can't understand it it is easy
What is the surface area of the triangular prism?
Use the net to help you. Surface area of triangular prism = triangle base + triangle base + rectangle face + rectangle face + rectangle face
Blue Rectangle
Orange Rectangle
Red Rectangle
One Green Triangle
Total Surface area
_______________
The total surface area of the triangular prism is 200 square inches.
What is a triangular prism?A triangular prism is a three-dimensional geometric shape that consists of two parallel triangular bases connected by three rectangular faces.
To find the surface area of the triangular prism using the net provided, we need to find the area of each face and then add them together.
Using formulas,
Area of rectangle= [tex]length\times width[/tex] square unit.
Area of triangle = [tex]\frac{1}{2}\times Base \times Height[/tex] square unit.
The blue rectangle has a length of 5 inches and a width of 4 inches, so its area is
=> 5 x 4 = 20 square inches.
The orange rectangle has a length of 12 inches and a width of 4 inches, so its area is
=> 12 x 4 = 48 square inches.
The red rectangle has a length of 13 inches and a width of 4 inches, so its area is
=> 13 x 4 = 52 square inches.
The green triangles have a base of 12 inches and a height of 5 inches, so each triangle's area is
=> [tex]\frac{1}{2}\times12\times5[/tex]= 30 square inches.
To find the total surface area, we add the area of each face:
=> 20 + 20 + 48 + 52 + 30 + 30 = 200 square inches.
Therefore, the surface area of the triangular prism is 200 square inches.
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A bushwalker walks 14 km east and then 9 km south. Find the bearing of his finishing position from his starting point.
Answer:
Step-by-step explanation:
To find the bearing of the bushwalker's finishing position from his starting point, we can use trigonometry and the concept of bearings.
First, we can draw a diagram to visualize the bushwalker's journey:
(9 km south)
|
|
(Starting point)
O-----|-------------------> (14 km east)
|
|
(Finishing point)
Next, we can use the tangent function to find the angle between the bushwalker's starting point and finishing point:
tan θ = opposite / adjacent
In this case, the opposite side is 14 km (the distance traveled east), and the adjacent side is 9 km (the distance traveled south):
tan θ = 14 / 9
We can use a calculator or reference table to find that the angle θ is approximately 56.31 degrees.
However, this is not the bearing we are looking for. In the context of bearings, the bearing of a point is the angle measured clockwise from north to the line connecting the starting point and the point in question.
To find the bearing of the bushwalker's finishing point, we need to adjust the angle θ to take into account the fact that bearings are measured from north.
First, we can find the direction of the line connecting the starting point and finishing point. This line travels 14 km east and 9 km south, so it has a slope of -9/14. We can find the angle this line makes with the horizontal axis by taking the arctangent of the slope:
tan α = -9/14
α = -30.96 degrees
Note that we use a negative sign because the line slopes downwards (southward) from left to right.
Finally, we can add this angle to the angle θ we found earlier:
Bearing = 360 - (θ + 90 + α)
= 360 - (56.31 + 90 + (-30.96))
= 287.7 degrees
Therefore, the bushwalker's finishing position has a bearing of approximately 287.7 degrees from his starting point.
[tex] \bf{Answer }[/tex]
We can use trigonometry to find the bearing of the finishing position from the starting point.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = a² + b²
where c is the length of the hypotenuse, a is the distance traveled east (14 km), and b is the distance traveled south (9 km).
Substituting the given values, we get:
c² = (14 km)² + (9 km)²
c² = 196 km² + 81 km²
c² = 277 km²
c ≈ 16.67 km (rounded to two decimal places)
Now, we can use trigonometry to find the angle between the hypotenuse and the east direction.
tan(θ) = opposite/adjacent
where θ is the angle between the hypotenuse and the east direction, opposite is the distance traveled south (9 km), and adjacent is the distance traveled east (14 km).
Substituting the given values, we get:
tan(θ) = 9 km / 14 km
θ ≈ 32.47° (rounded to two decimal places)
Therefore, the bearing of the finishing position from the starting point is approximately 32.47° south of east. Alternatively, we can describe the bearing as 157.53° east of south (180° - 32.47°), or simply as southeast.
The distance from here to the beach at Little Boar’s Head is 10 miles. If you walked there at 4 mph and returned jogging at 8 mph, how much time would the round trip take? What would your overall average speed be?
(Trig word problems)
From a hot-air balloon, Enola measures a 22° angle of depression to a landmark that’s 310 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Step-by-step explanation:
See image
helppp please, do all the tasks from a to b.
Thank u very much
the task is in the photo
a) 1) x=0 or x=-2 , 2) x=0 or x=2 3) x=0 or x=-2 4) x=0 or x=-2
b) 1) x=0 or x=-5/3 2)x=0 or x=5/3 3) x=0 or x=5/3 4) x=0 or x=-5/3 .this equations can be solved by factorization and simplification.
what is factorization?
Factorization is the process of expressing a given number or algebraic expression as a product of two or more factors. The factors are the numbers or expressions that when multiplied together result in the original number or expression.
In the given question,
a) x²+2x=0:
x(x+2)=0
x=0 or x=-2
x²-2x=0:
x(x-2)=0
x=0 or x=2
x²+2x=0:
x(x+2)=0
x=0 or x=-2
-x²-2x=0:
-x(x+2)=0
x=0 or x=-2
b)
3x²+5x=0:
x(3x+5)=0
x=0 or x=-5/3
3x²-5x=0:
x(3x-5)=0
x=0 or x=5/3
-3x²+5x=0:
x(-3x+5)=0
x=0 or x=5/3
-3x²-5x=0:
x(-3x-5)=0
x=0 or x=-5/3
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Given the function ƒ(x) = x^2 - 4x - 5
1. Identify the zeros using factorization.
2. Draw a graph of the function. Its vertex is at (2, -9).
Step-by-step explanation & Answer
f(x) = x² - 4x -5, factored is simply f(x) = (x - 5)(x + 1).
If you zero out f(x), namely 0=(x-5)(x+1), that simply gives you the zeros of 5 and -1.
Now, from ----- -1------0---------------------------------5,
Notice from -1 to 5, there are 6 units, and half of 6 is 3, so, the half-way is 3 units away from either zero.
We can get to the half-way point by -1 + 3, or 2, x = 2, that's where the vertex is at, but you already knew that, and of course the y-coordinate is at f(2) = (2)² - 4(2) - 5, which is -9, so the vertex is indeed at (2, -9).
Well, surely you can, simply use the zeros location, -1 and 5, and draw a bowl between them, with the bottom of the bowl at 2, -9.
a
=
900
rounded to the nearest 10
b
=
90.7
rounded to 1 DP
Find the minimum of
axb
The minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. It is expressed as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The given values are:
A = 900 rounded to the nearest 10 = 900
B = 90.7 rounded to 1 decimal place = 90.7
We need to find the minimum value of AxB.
Multiplying A and B directly, we get:
AxB = 900 x 90.7 = 81,630
To find the minimum value of AxB, we can use the concept of AM-GM inequality which states that for two positive real numbers a and b, their arithmetic mean (AM) is greater than or equal to their geometric mean (GM):
AM ≥ GM
or
(a+b)/2 ≥ √(ab)
Applying this to our values of A and B, we get:
(A+B)/2 ≥ √(AxB)
Substituting the given values of A and B, we get:
(900 + 90.7)/2 ≥ √(AxB)
Simplifying this, we get:
495.35 ≥ √(AxB)
Squaring both sides, we get:
245,376.72 ≥ AxB
Therefore, the minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).
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Complete question:
A = 900 rounded to the nearest 10
b = 90.7 rounded to 1 DP
Find the minimum of a x b
Please help!!!!!!!!!!!
Answer: F= 4
Step-by-step explanation:
rise over run!
-4 (from the run in the slope) plus 8 (your x axis) is 4
Factor completely 3x − 12.
a. 3(x − 4)
b. 3(x + 4)
c. 3x(−12)
d. Prime
Answer:
Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?
ask every tenth student she sees ac a concert
ask every fifth student entering her school in the morning
ask every third student she encounters at the mall
ask every student at a local movie theater
Step-by-step explanation:
The circle graph shows how a family budgets its annual income. If the total annual income is $125,000, what amount is budgeted for Clothing?
Answer:
Step-by-step explanation:
125,000 x 16% = $20,000
(23%) 28,750 + (8%) 10,000 + (9%) 11,250 + (12%) 15,000 + (16%) 20,000 + (19%) 23,750 + (13%) 16,250 = $125,000
The members of a consulting firm rent cars from three rental agencies. It is estimated that 0.36 percent of cars come from agency 1, 0.06 percent of cars come from agency 2, and 0.58 percent of cars come from agency 3. It is also estimated that 0.05 percent of cars from agency 1 need a tune-up, 0.02 percent of cars from agency 2 need a tune-up, and 0.02 percent of cars from agency 3 need a tune-up. Answer the following questions, rounding your answers to two decimal places where appropriate.
(a) What is the probability that a rental car delivered to the firm will need a tune-up?
(b) If a rental car delivered to the firm needs a tune-up, what is the probability that it came from agency 2?
The probability that a rental car delivered to the firm will need a tune-up is 0.03% or 0.000306 and the probability that it came from agency 2 is 39.15% or 0.3915.
(a) Let P(A1), P(A2), and P(A3) be the probabilities that a rental car comes from agency 1, agency 2, and agency 3, respectively, and let P(T) be the probability that a rental car needs a tune-up. Then, using the law of total probability, we have:
P(T) = P(T|A1)P(A1) + P(T|A2)P(A2) + P(T|A3)P(A3)
P(T) = 0.05(0.0036) + 0.02(0.0006) + 0.02(0.0058)
P(T) = 0.00018 + 0.000012 + 0.000116
P(T) = 0.000306
Therefore, the probability that a rental car delivered to the firm will need a tune-up is 0.03% (or 0.000306 as a decimal).
(b) Using Bayes' theorem, we can calculate the conditional probability that a rental car came from agency 2 given that it needs a tune-up:
P(A2|T) = P(T|A2)P(A2) / P(T)
P(A2|T) = 0.02(0.0006) / 0.000306
P(A2|T) = 0.3915
Therefore, if a rental car delivered to the firm needs a tune-up, the probability that it came from agency 2 is 39.15% (or 0.3915 as a decimal).
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which of the following are characteristics of frequency tables? multiple select question. they can be used for quantitative data. they can be used for qualitative data. an observation can fit into more than one class. no observation can fit into more than one class.
This two are characteristics of frequency tables
1. They can be used for quantitative data.
2. They can be used for qualitative data.
Frequency tables have the following characteristics:
1. They can be used for quantitative data:
Frequency tables display the number of occurrences of each value in a dataset, which is particularly useful when dealing with numerical or quantitative data.
2. They can be used for qualitative data:
Frequency tables can also be used for non-numerical or qualitative data, such as categories or groups, by counting the number of occurrences for each category.
4. No observation can fit into more than one class:
In a frequency table, each observation or data point is assigned to only one class or category, ensuring that there is no overlap between classes.
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Find the volume of the sphere.
Use 3.14 for T. Round your
answer to the nearest tenth.
Enter your answer in cm³ (type in
the number only without units).
7.2 cm
Answer:
I think it will help u (:
Step-by-step explanation:
Assuming the given measurement is the diameter of the sphere, we can find the radius as follows:Radius (r) = Diameter / 2 = 7.2 / 2 = 3.6 cmThe formula for the volume of a sphere is:V = (4/3) * π * r³Substituting the values, we get:V = (4/3) * 3.14 * (3.6)³
V = 4.19 * 46.656
V = 195.4 cm³Rounding this to the nearest tenth, we get:V ≈ 195.4 cm³Therefore, the volume of the sphere is approximately 195.4 cm³.
a survey of 100 randomly selected customers found the mean age was 31.84 years. assume the population standard deviation for age was 9.84 years.2.find the margin of error if we want a 90% confidence interval for the true population mean age?a.1.62b.30.22c.5.83d.4.57e.9.84
The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.
We can use the formula for the margin of error:
Margin of error = z × (σ / √(n))
where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.
For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:
Margin of error = 1.645 × (9.84 / √(100)) = 1.62
Therefore, the margin of error is 1.62 years, which is option (a).
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What is the scale factor used?
Step-by-step explanation:
You will need to find two lengths of corresponding sides
LH = sqrt 5
L'H' = sqrt(20) which is four times larger than sqrt5
scale factor 4
1 it’s 102 the other ones??
Step-by-step explanation:
Vertical angles are equal soooo 1 and 3 are equal = 102 degrees
then 1 plus 2 forma straight line = 180 degrees
so 2 = 78 degrees
then vertical angles again, 2 and 4 are equal = 78 degrees
how do you interpret an odds ratio of 0.75? group of answer choices if exposed the outcome is .75 the odds of the outcome in the unexposed (there is a protective effect) there is no difference between groups because the odds ratio is close to 0 if not exposed the outcome is less likely since the odds ratio if less than 1 if exposed the outcome is .75 times greater than for the unexposed.
The correct interpretation of an odds ratio of 0.75 would be (a) If not exposed the outcome is less likely since the odds ratio is less than 1.
An odds ratio of less than 1 indicates a decreased odds of the outcome in the exposed group compared to the unexposed group. Specifically, an odds ratio of 0.75 suggests that the odds of the outcome occurring in the exposed group is 25% lower than the odds of the outcome occurring in the unexposed group.
Option b is incorrect as an odds ratio of 0.75 is not necessarily close to 0, and option c is incorrect because an odds ratio of 0.75 means that the odds of the outcome in the exposed group is lower than the unexposed group, not 75 times greater. Option d is also incorrect as a protective effect would be observed if the odds ratio were less than 1.
Therefore, the correct option is (a) If not exposed the outcome is less likely since the odds ratio is less than 1.
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The given question is incomplete, the complete question is:
How do you interpret an odds ratio of 0.75? a) If not exposed the outcome is less likely since the odds ratio if less than 1 b) There is no difference between groups because the odds ratio is close to 0 c) If exposed the outcome is 75 times greater than for the unexposed. d) if exposed the outcome is 75 the odds of the outcome in the unexposed (there is a protective effect)
Aika is building a square garden. She places a garden post at (3.5 3.5). What is the location of the corner that reflects (3.5, 3.5) across the y-axis
Answer:
(-3.5, 3.5)
Step-by-step explanation:
When reflected across the y-axis, the sign of the x will change to the opposite.
Our points (3.5, 3.5)
What is the location of the corner that reflects (3.5, 3.5) across the y-axis?
(-3.5, 3.5)
if nevada has 4 elected members in congress (4 in the house of representatives and 2 senators), how many electoral votes does the state of nevada have in the electoral college?
The number of electoral votes does the state of nevada have in the electoral college is 6 electoral votes.
Nevada will be having a total of 6 electoral votes in the electoral college. The number of electoral votes for each state is equal to the total number of its members in Congress, which will be including its representatives in the House of Representatives and its two senators.
Therefore, since Nevada has 4 members in the House of Representatives and 2 senators, the state has a total of 6 members in Congress, and hence it can be concluded that a total of 6 electoral votes will be there in the Electoral College.
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a couple has two children. one is a son. what is the probability that the other child is a daughter?
Answer:
1/2 it’s like flipping a coin it can either come up heads or tails.
Step-by-step explanation:
The probability that the other child is a daughter is 1/2 or 50%.
The gender of each child is independent, and there are two equally likely outcomes for each child (male or female). Therefore, the probability of having a son is 1/2 and the probability of having a daughter is also 1/2. Since one child is already known to be a son, that does not affect the probability of the other child being a daughter. Thus, the probability of having a daughter as the other child is also 1/2 or 50%.
Therefore, the answer to the question is that the probability that the other child is a daughter is 1/2 or 50%
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GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
Answer:
the area of the trapezoid is (3/2)x^2 + 2x square units.
Step-by-step explanation:
Let's use "x" to represent the height of the trapezoid. According to the problem, one base measures 5 feet more than the height, so we can use "x + 5" to represent the length of that base. The other base is one foot less than twice the height, so we can use "2x - 1" to represent the length of that base.
The area of a trapezoid is given by the formula:
Area = (1/2)(sum of the bases)(height)
Substituting the expressions for the bases and the height, we get:
Area = (1/2)(x + 5 + 2x - 1)(x)
Simplifying the expression inside the parentheses, we get:
Area = (1/2)(3x + 4)(x)
Expanding the expression, we get:
Area = (3/2)x^2 + 2x
the area of the trapezoid is (3/2)x^2 + 2x square units.
What coordinates would it be? How would I do it?
Answer:
In the images
Hope this helps!
Step-by-step explanation:
Clockwise is the direction the arrow is pointing, counter-clockwise is the other direction.
Please Help!
Which line of music shows a reflection?
the answer would be b.