Since the domain is restricted to one side of the axis of symmetry of the full graph of f(x), an inverse does exist.
Letting [tex]f(x)=y[/tex],
[tex]x=y^2 +y-6\\\\x=\left(y+\frac{1}{2} \right)^2 -\frac{25}{4}\\\\x+\frac{25}{4}=\left(y+\frac{1}{2} \right)^2[/tex]
Since the domain is restricted to the right hand side of the axis of symmetry, and since the range of the inverse is the same as the domain of the original function, we take the positive square root.
[tex]\sqrt{x+\frac{25}{4}}=y+\frac{1}{2}\\\\y=f^{-1}(x)=\sqrt{x+\frac{25}{4}}-\frac{1}{2}[/tex]
The domain of the inverse is the range of the original function, which is [tex]\left[-\frac{25}{4}, \infty \right)[/tex].
The range of the inverse is the domain of the original function, which is [tex]\left[-\frac{1}{2}, \infty)[/tex],
48% of people in a certain country like to cook and 54% of people in the country like to shop, while 26% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or both? The probability that a randomly selected person in the country enjoys cooking or shopping or both is ________
The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
48% of people in a certain country like to cook.
And, 54% of people in the country like to shop, while 26% enjoy both activities.
Now,
Probability to like the cook P (C) = 48%
Probability to like the shop P (S) = 54%
Probability to like the both activity P (C∩S) = 26%
So, Probability to like the both activity P (C ∪ S) is calculated as;
P (C ∪ S) = P (C) + P (S) - P (C ∩ S)
P (C ∪ S) = 48% + 54% - 26%
P (C ∪ S) = 102% - 26%
P (C ∪ S) = 76%
P (C ∪ S) = 0.76
Thus, The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
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Using the line AB, name two line segments.ACBA,BoAB, CAC, CBCB,B
Point C is between points A and B, this point divides the line AB into two segments:
One segment goes from point A to point C and can be named line segment AC
The second segment goes from point C to point B and can be named line segment CB
The correct option is the third one AC,CB
A restaurant serves sandwiches using slices of bread in the shape of a right triangle. If the legs of the
triangle are each 6 inches, how long is the hypotenuse in inches? Round your answer to the nearest inch.
6 inches
8 inches
10 inches
12 inches
Answer: 8 inches
Step-by-step explanation:
1) Set up the equation
If you know both sides of the triangle are 6 inches you can set a Pythagorean equation. C is the hypotenuse
[tex]6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} = \sqrt{c^2} \\8.485 = c[/tex]
2) Rounding
After you found 8.485, the tenth place is less the 5, so it will round down to 8 inches.
The answer is 8 inches
use the provided equation below to complete the table and graph
Answer:
Explanation:
To complete the table, we need to replace each value of x and calculate the value of y.
So, if x = - 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}x-2 \\ y=\frac{3}{8}(-16)-2 \\ y=-6-2 \\ y=-8 \end{gathered}[/tex]If x = -8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(-8)-2 \\ y=-3-2 \\ y=-5 \end{gathered}[/tex]If x = 0, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(0)-2 \\ y=0-2 \\ y=-2 \end{gathered}[/tex]If x = 8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(8)-2 \\ y=3-2 \\ y=1 \end{gathered}[/tex]If x = 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(16)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]So, the complete table is:
x y
-16 -8
-8 -5
0 -2
8 1
16 4
Finally, we can graph the table, so:
A linear function r models the growth of your right index fingernail. The length of the fingernail increases 0.7 millimeter every week. Graph r when r(0)=12.
A nail's length in x weeks of m=0.7 slope with a growth rate of mm per week b starting length follows.
The slope-intercept form of a straight-line equation is indicated by y = mx + b. X and y denote the line's distance from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is.
Given, r(0) = 12
According to the question, fingernail increases by 0.7 millimeters every week. So, m = 0.7 which is the slope of the equation of a straight line.
r(0) = 12 is the b of the y = mx + b.
Now, the final equation is:
r(x) = 0.7x + 12
As a result, the slope of r(x) length of a nail in x number of weeks of m=0.7, with growth rate in mm per week b starting length.
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The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores areshown below. Find the mean score. Round your answer to the nearest tenth.563 524 357 347 637358 351 528 470 482pls be fast
Answer:
[tex]461.7\Rightarrow\text{ Option \lparen D\rparen}[/tex]Explanation: We have to find the mean of the total scores shown, the formula for the mean is as follows:
[tex]A=\frac{a_1+a_2+a_3+a_4+...+a_N}{N}\rightarrow(1)[/tex]Using the formula (1) the mean of the score is calculated as follows:
[tex]\begin{gathered} A=\frac{563+524+357+347+637+358+351+528+470+482}{10} \\ \\ A=\frac{4617}{10}=441.7 \\ \\ A=461.7\rightarrow\text{ \lparen D\rparen} \end{gathered}[/tex]Therefore the answer is Option(D).
what is the equation for the line passing through the points: (3,-10.5) and (1,-7.5)
The equation of the line passing through the points: (3,-10.5) and (1,-7.5) is [tex]3x+2y+12=0.[/tex]
How to find equation of a line by two-point form?Every point on a line fulfills the equation of that line, which means that every point on the line represents every other point on the line.
The equation of a line passing through two-points [tex](x_{1} ,y_{1} )[/tex] and [tex](y_{1} ,y_{2} )[/tex] is given by the formula,
[tex]y-y_1= \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, the equation of the line passing through the points (3,-10.5) and (1,-7.5) will be-
⇒[tex]y-(-10.5)=\frac{-7.5-(-10.5)}{1-3} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{-7.5+10.5}{-2} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{3}{-2} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{-3x}{2} +\frac{9}{2}[/tex]
⇒[tex](y+10.5)*2=-3x+9[/tex]
⇒[tex]2y+21=-3x+9[/tex]
⇒[tex]2y+3x+21-9=0[/tex]
⇒[tex]3x+2y+12=0[/tex]
Hence, the equation of the line passing through the points (3,-10.5) and (1,-7.5) is [tex]3x+2y+12 =0[/tex].
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What is the least common multiple of 4 and 8?
Enter your answer in the box.
Step-by-step explanation:
answer is 8
detail is in the picture
Hey can someone please help me? I’m confused. I’ll give brainliest
Answer:
1.50t + 3 < 9
Step-by-step explanation:
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
total cost of taking and Gatorade is less than $9
Answer:
1.50t + 3 < 9
Step-by-step explanation
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
the total cost of taking and Gatorade is less than $9
A manufacturer throws out gaskets with weights that have an absolute deviation of more than 0.06 pound from the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Which gaskets should be thrown out? Use an absolute value inequality to justify your answer.
If the weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. The gaskets that should be thrown out is 0.53 and the inequality is: 0.54 ≤ w ≤ 0.66.
Means and inequalityUsing this formula to determine the mean
Mean = ∑x/n
Mean = 0.58 + 0.63 + 0.65 + 0.53 + 0.61 /5
Mean = 3/6
Mean = 0.6
Since the mean is 0.6 the gasket that are less than 0.53 and more than 0.66 (0.6±0.06) should be thrown out which in turn means that 0.53 should be thrown out.
Inequality :
0.54 ≤ w ≤ 0.66
Therefore 0.53 should be thrown out.
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Mowgli usually walk from home to the beach, and returns on an elephant It takes him 40 minutes altogether. One day he traveled on the elephant from homebto the beach and back, which took 32 minutes. How much time would he need to travel the same distance on foot?
The time it would take Mowgli from the home to the beach and from the beach to the home on foot is 48 minutes.
What is the time it would take to travel on foot?Based on the assumption that the average speed that Mowgli travels from the home to the beach and from the beach to the home is constant, the time it takes from the home to the beach and from the beach to the home should be equal.
Time from the home to the beach = 32 /2 = 16 minutes
The time it took Mowgli to walk from the home to the beach = 40 - 16 = 24 minutes
Time it would take Mowgli to travel from the home to the beach and from the beach to the home = 24 x 2 =48 minutes
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Plot the point then make a staircase using the given slope connect the points to form a line answer the questions below
What type of reasoning is used to find the next amount of train cars? Explain your answer.
The type of reasoning used to find the next amount of train cars is an arithmetic sequence, it can be assumed that the next amount of train cars that in the sequence is 6.
What is an arithmetic sequence?The difference between successive words in an arithmetic series is known as the common difference y. The existence of the nth term of an arithmetic sequence is given by the following rule:
x1 = x1 + (n-1)y;
Where x1 is the first term.
In the context of this problem, from the image, the number of train cars can be modeled by the following sequence exists (0, 2, 4, ...).
Which exists an arithmetic sequence with:
The first term of 0.A common ratio of 2.Therefore the next term of the sequence is given by:
4 + 2 = 6.
This is because 4 is the last term and 2 is the common ratio.
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can you please cancer C what is the explicit function and the relationships for the term please I dont understand
EXPLANATION
Given the sequence:
C. 3, 12, 27, 48, 75
First, we need to calculate the difference between terms:
12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27
Arithmetic relationship: 9, 15 , 21, 27
To obtain the sequence we use the following formula:
[tex]a_n=a_1+(n-1)d[/tex]Now, we need to calculate the appropriate difference between terms:
15-9 = 6 21-25 = 6 27 - 21 = 6
So the constant difference is 6 and the nth term will be:
nth = 6n + 3
*a1=3
So, the relationship will be:
n Value Relationship
1 12 3 + (6*1 +3)
2 27 12 + (6*2 + 3)
3 48 27 + (6*3 + 3)
4 75 48 + (6*4 + 3)
5 108 75 + (6*5 + 3)
n n-1 + (6n+3) n-1 + (6n+3)
Explicit function: y = (n-1) + (6n+3)
b) Describe the function over each part of its domain. State whether it is constant,
increasing, or decreasing, and state the slope over each part.
Description of the function over each part of its domain is:
Slope = 0 and the domain is constant at (0,12000).Domain (12000, 38000) is declining with a negative slope.What is a function?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x.So, we examine the displayed graph.
The y values are constant from x = 0 to x = 12,000.
There is no increase or decrease in y's value; it is constant.Consequently, the graph's cost is constant from x=0 to x=12000.So slope = 0.
Then,
Slope = 0 and the domain is constant at (0,12000).
The y values are decreasing from x = 12,000 to x = 38,000.The slope is negative for y values that are decreasing.The slope is therefore negative.Domain (12000, 38000) is declining with a negative slope.
Therefore, description of the function over each part of its domain is:
Slope = 0 and the domain is constant at (0,12000).Domain (12000, 38000) is declining with a negative slope.Know more about functions here:
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Look at this graph: 101 9 8 7 6 5 4 3 2. 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
The slope can be calculated as the quotient between the difference in the y-coordinates of two points, and the difference in the x-coordinates of the same two points.
We pick any 2 known points, like (0,2) and (5,4).
We calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{5-0}=\frac{2}{5}=0.4[/tex]Answer:
The slope is m=2/5=0.4
Find the area of the figure
Answer:
126.5 cm²
Step-by-step explanation:
Hello!
This shape can be split into a rectangle and a triangle.
The rectangle's dimensions are 8 and 11, and the base and height of the triangle are 11 and 7 respectively.
Area of Rectangle:A = b * hA = 8 * 11A = 88Area of Triangle:A = b*h/2A = 11 * 7/2A = 77/2A = 38.5The combined area is 88 + 38.5 which is 126.5 cm².
Find the value of x. Write an equation andsolve, showing ALL the work.
Given:
The objective is to find hte value of x.
The value of x can be calculated by basic proportionality theorem.
[tex]\frac{12}{14}=\frac{9}{x}[/tex]Thus, the required equation is obtained.
The value of x is,
[tex]\begin{gathered} x=9\cdot\frac{14}{12} \\ x=\frac{9\cdot14}{12} \\ x=\frac{126}{12} \\ x=10.5 \end{gathered}[/tex]Hence, the value of x is 10.5
Calculate the correlation coefficient for the given data below:
x y
2 21
3 22
48
5 11
6 15
7 14
Round your final result to two decimal places.
The correlation coefficient of the data provided is -0.52.
What is the correlation coefficient?Correlation is a measure that is used in statistics to determine the linear relationship that exists between two variables. Correlation can be positive, negative or zero.
Positive correlation is when two variables move in the same direction. Negative correlation is when two variables move in opposite directions. Zero correlation is when there is no relationship between the variables.
Correlation can be determined using a financial calculator. When the financial calculator is used, the correlation coefficient is -0.52
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hey please help. this has to do with exponential functions. i have to do 225 problems before midnight. it’ll mean a lot!!!
Answer:
Explanation:
To complete the missing values, we have to evaluate the function at the x-values given.
For example, to find the number below x = -1, we will put in x = -1 into y = (1/6)^x.
Putting in x = - 1 in y = (1/6)^x gives
[tex]y=(\frac{1}{6})^{-1}[/tex]which simplifies to give
[tex]y=\frac{1}{1/6}[/tex][tex]\rightarrow y=6[/tex]Similarly, for the missing value below x = -2, we put in x = - 2 into y = (1/6)^x to get
[tex]y=(\frac{1}{6})^{-2}[/tex]which simplifies to give
[tex]y=\frac{1}{(1/6)^2}[/tex][tex]\begin{gathered} \rightarrow y=6^2 \\ \rightarrow y=36 \end{gathered}[/tex]Similarly, for the missing value below x = 2, we put in x = 2 in y = (1/6)^x to get
[tex]y=(\frac{1}{6})^2[/tex]which simplifies to give
[tex]y=\frac{1}{36}[/tex]Hence, the missing value to be put in is 36.
To summerise, the missing values are
x | -2
help meeeeeee pleaseee !!!!
The function that represents the cost function is c(x) = 75 + 0.25x
What is the Cost FunctionTo find the cost function c(x), we have to write a linear equation or linear function to represent this.
Initial charge = 75charge per copy = 0.25x = number of copiesThe cost function can be expressed as a function of the number of copies made which can be represented as
[tex]c(x) = 75 + 0.25x[/tex]
The cost of printing x number of pages is c(x) = 75 + 0.25x
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3/4 times x equals 3.45 solve for x
4.6
1) Since 3/4x = 3.45, then we can solve it for x
3/4x = 3.45 Multiply both sides by 4 to eliminate the fraction
3x =13.80 Divide both sides by 3
x= 4.6
2) So x is equal to 4.6, and that is the answer
Pls helppppppppppp
It’s not c
Answer: it would be D because m∠NSO+m∠OSL+m∠LSM+m∠MSN=360°
and m∠LSM+m∠SML+m∠MLS≠360° doesnt equal 360 degrees so that one is wrong ∠LSM≅∠NSM is a false statement same with m∠LSO+m∠MSO=180° its false so it would be (D)
hope i helped
Step-by-step explanation:
The number of Americans over age 100 can be approximated by P(t) = 0.07e^0.54t, where is P(t) measured in millions and t is measured in decades. Also, t=0 corresponds to 2000.
a. How many Americans over age 100 were there in 2000?
b. How fast was the number of Americans over age 100 changing in 2000? Use the correct units.
There are 7 % of Americans over age 100 who were there in 2000 and the number of Americans growing by 54% over age 100 changed in 2000.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The number of Americans over age 100 can be approximated by
[tex]P(t) = 0.07e^{0.54t}[/tex]
where is P(t) measured in millions and t is measured in decades.
Also, t = 0 corresponds to 2000.
⇒ [tex]P(t) = 0.07e^{0.54t}[/tex]
Substitute the t = 0 in the above function, and we get
⇒ [tex]P(t) = 0.07e^{0.54\times0}[/tex]
⇒ P(t) = 0.07 e°
⇒ P(t) = 0.07
Convert decimals into fractions, and we get
⇒ P(t) = 7 / 100
This represents 7 out of 100 which is 7 % of Americans over age 100 who were there in 2000.
Thus, the number of Americans growing by 54% over age 100 changed in 2000.
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Create an image of rectangle ABCD that is
translated 6 units to the right and 3 units up
by plotting the corresponding vertices.
Plot the vertex that corresponds to A.
The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .
In the question ,
a rectangle is given
the vertex of the rectangle ABCD is given as
A(-10,-6) , B(-10,-2) , C(-6,-2) , D(-6,-6) .
On applying the translation 6 units to right and 3 units up ,
the rule is (x,y)→(x+6,y+3)
by applying the rule for the translation
we get image as
A'(-4,-3) ,B'(-4,+1) , C'(0,1) , D'(0,-3)
The image is plotted below .
Therefore , The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .
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The diameter of the earth at its equator is about 8000 miles. The diameter of Saturn at its equator is about 74,000 miles. Saturn's diameter is about how many times as large as the Earth's diameter?
A. 9.25×10^3
B. 9.25 × 10^2
C. 9.25×10^1
D. 9.25 x10^0
Answer:
C
Step-by-step explanation:
[tex]\frac{74000}{8000}=9.25 \times 10^1[/tex]
What will it cost to buy fencing to go around a rectangular garden with a length of 25 ft. and a width of 30 ft.? The fencing costs $3.17 per linear foot.
It will cost $348.7 to buy fencing to go around the rectangular garden.
The length of the rectangular garden is 25 feet.The width of the rectangular garden is 30 feet.The cost of fencing per linear foot is $3.17.We need to buy fencing to go around the whole rectangular garden.This means we need the total length of the boundary.The boundary is the same as calculating the perimeter of the rectangular garden.The perimeter of the rectangular garden is two times the sum of its length and its breadth.The perimeter is 2*(25+30) = 110 feet.The total cost of fencing the whole rectangular garden is the product of the cost of fencing per foot and its perimeter.The total cost of fencing the rectangular garden is 3.17*110 = $348.7.To learn more about perimeter, visit :
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hey there Ms or Mr could you help me out with this please?
If a quadrilateral is a parallelogram, then its opposite sides are congruent therefore:
[tex]\begin{gathered} GH\cong JI \\ and \\ GJ\cong HI \end{gathered}[/tex]Using the distance formula:
[tex]\begin{gathered} GH=\sqrt[]{(5-1)^2+(3-1)^2} \\ GH=\sqrt[]{16+4} \\ GH=\sqrt[]{20} \\ JI=\sqrt[]{(0-4)^2+(3-5)^2} \\ JI=\sqrt[]{16+4} \\ JI=\sqrt[]{20} \\ GH\cong JI \end{gathered}[/tex][tex]\begin{gathered} GJ=\sqrt[]{(0-1)^2+(3-1)^2} \\ GJ=\sqrt[]{1+4} \\ GJ=\sqrt[]{5} \\ HI=\sqrt[]{(4-5)^2+(5-3)^2} \\ HI=\sqrt[]{1+4} \\ HI=\sqrt[]{5} \\ GJ\cong HI \end{gathered}[/tex]Step 2:
The diagonals are given by:
[tex]\begin{gathered} JH=\sqrt[]{(0-5)^2+(3-3)}^2 \\ JH=\sqrt[]{25} \\ JH=5 \\ GI=\sqrt[]{(4-1)^2+(5-1)^2} \\ GI=\sqrt[]{9+16} \\ GI=\sqrt[]{25} \\ GI=5 \\ JH=GI \\ 5=5 \\ so\colon \\ JH\cong GI \end{gathered}[/tex]Assume that Lines L and M are parallel. Find a pair of acute, corresponding angles.
Select all that apply.
A. q and w
B. r and y
C. x and s
D. q and y
E. s and y
F. r and x
G. t and w
H. t and z
Answer:
Choice E and F
Step-by-step explanation:
acute = less than 90
Write a numerical expression then match words with the expression
Numerical expression: 30 - 10 - 7
In words: Elizabeth had $30, if she spent $10 to buy some pizza and $7 on a soda, how much money does she have left?