The inverse function of g(x) = 2x² - 8 for each case is given as follows:
x ≥ 0: y = √(0.5x + 4).x < 0: y = -√(0.5x + 4).Inverse functionTo find the inverse function, we exchange the variables x and y in the original function, and then isolate the variable y.
The original function in this problem is given as follows:
g(x) = 2x² - 8.
The function is not one-to-one, hence the inverse is different for x ≥ 0 and for x < 0.
Exchanging the variables, we have that:
x = 2y² - 8.
Isolating the variable y, we have that:
2y² = x + 8
y² = 0.5x + 4 (the entire equation was divided by 2 to isolate y)
y = ± sqrt(0.5x + 4).
For non-negative values, the inverse function is:
y = sqrt(0.5x + 4) = √(0.5x + 4).
For negative values, the inverse function is:
y = -sqrt(0.5x + 4) = -√(0.5x + 4).
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Answer: 0,2,3,-3
Step-by-step explanation:
The ratio of Jaynee's money to Owen's money is 3:11. If Jaynee has $33,
how much money do Jaynee and Owen have ALL TOGETHER?
Answer:
42 dollars
Step-by-step explanation:
Jaynee's money is 11 out of (11+3) = 14 or 11/14ths of the total
11/14 x = 33
x = total amount = 33 * 14/11= 42 dollars
Given AC = AB + AB
Prove AB = BC
HELP PLEASE
The segment AB = AC is proved for the given line AC.
What is defined as the mid point?A midpoint is a point in the center of a line connecting two points. The two points of reference are the line's endpoints, and the midpoint is located between the two. The midpoint splits the line connecting these 2 points in half. Furthermore, a line drawn to bisect the line connecting these two points passes through midpoint.For the given question;
AC = AB + AB
This can be written as;
AC = 2AB
or AB = (1/2)AC
It means, B is the mid point of AC
So, B will also divide the complete line segment AC into two equal halves.
AB = AC
Thus, the segment AB = AC is proved for the given line AC.
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you were in the garden, there are 34 people in the yard. you kill 30. how many people are in the garden?
In linear equation, You are the only person in the garden at the time the 34 people.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.You are the only person in the garden at the time the 34 people are on their homicidal spree.
Alternatively, if the backyard and garden are in the same place, then there are no longer any individuals in the garden because you would officially count as one of the 34 people who are all killed.
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the length of pregnancy isn't always the same. in pigs, the length of pregnancies varies according to a normal distribution with mean 114 days and standard deviation 5 days. what percent of pig pregnancies are longer than 109 days?
95.61 percent of pig pregnancies are longer than 109 days with 0.8413 probability.
A standard normal distribution or z-table can be used to approximate the probability of multiple ranges of values for a random normal variable X with a particular mean and standard deviation. This method entails changing X to a typical normal variable Z.
The normal, random variable X equals the length of pregnancy.
The mean and standard deviation are then calculated.
u, Mean = 114 days
σ, Standard deviation = 5 days
Then, as follows, transform X to its standard normal variable:
Z = (X - u) ÷ σ
Z = (X - 114) ÷ 5
To determine the likelihood of a pregnancy lasting more than 109 days,
P(X ≤ 109) = P(Z ≤ 114 - 109 ÷ 5)
P(X ≤ 109) = P(Z ≤ 1)
P(Z ≤ 1) = 0.8413 when using a typical normal distribution or z-table.
The percentage of pig pregnancies that last more than 109 days,
P = (109 ÷ 114) × 100
P = 95.61%
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7.
A bookrack is 61 1/4 inches wide. I want to place a set of
encyclopedias
on the rack., each measuring 1 3/4 inches wide. How many
will fit on the rack?
35 encyclopedias can be fit on the bookrack.
What is an encyclopedia?
An encyclopedia (American English) or encyclopaedia (British English) is a reference source or compendium that provides summaries of general or specific information to a certain topic or discipline. Encyclopedias are organized into articles or entries that are either alphabetically sorted by article name or by subject categories, or are hyperlinked and searchable by random access. The entries in encyclopedias are longer and more thorough than those in most dictionaries. In general, encyclopedia articles focus on factual information about the subject specified in the title, as opposed to dictionary entries, which focus on linguistic information about words, such as their derivation, meaning, pronunciation, use, and grammatical forms.
Width of bookrack = 61 1/4 inches
Width of an encyclopedia = 1 3/4 inches
no. of encyclopedias to be fit = (61 1/4)/(1 3/4)
= (245/4)/(7/4)
= 245/7
= 35
Hence, 35 encyclopedias can be fit on the bookrack.
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Please someone help me please i need help with this question answer asap
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
the perpendicular bisector of AB passes through the midpoint of AB at right angles.
find the midpoint using the midpoint formula
with A (- 2, 0 ) and B (0, 6 )
midpoint = ( [tex]\frac{-2+0}{2}[/tex] , [tex]\frac{0+6}{2}[/tex] ) = ( [tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )
find the gradient m of AB using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (0, 6 )
m = [tex]\frac{6-0}{0-(-2)}[/tex] = [tex]\frac{6}{0+2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
given a line with gradient m then the gradient of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]
the equation of a line in gradient- slope form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 1, 3 ) into the partial equation
3 = [tex]\frac{1}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{1}{3}[/tex] = [tex]\frac{8}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of perpendicular bisector
What are the constraints to this problem?
A Virginia Beach farmer has 480 acres of land on which to grow either corn or soybeans.
He figures he has 800 hours of labor available during the crucial summer season. The farmer
can expect a profit of $40 per acre on corn and $30 per acre on soybeans. He knows that
corn requires 2 hours per acre to raise, and soybeans require 1 hour per acre to raise. How
many acres of each should he plant to maximize profit? What is his maximum profit?
He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit and the maximum profit is [tex]\$18,200[/tex].
A Virginia Beach farmer has [tex]480[/tex] acres of land on which to grow either corn or soybeans.
He has labor available during the crucial summer [tex]=800[/tex] hours
The farmer can expect a profit of [tex]\$40[/tex] per acre on corn.
The farmer can expect a profit of [tex]\$30[/tex] per acre on soybeans.
The corn requires hours to raise [tex]=2[/tex] hours per acre.
The soybeans requires hours to raise [tex]=1[/tex] hours per acre.
We have to find how many acres of each should he plant to maximize profit and his maximum profit.
To solve the question we let he plant [tex]x[/tex] acres of corn and [tex]y[/tex] acres of soybeans.
Total land is available for grow either corn or soybeans is [tex]480[/tex] acre.
So the equation should be
[tex]x+y\leq 480\dots\dots Equation (1)[/tex]
He requires [tex]2[/tex] hours to raise corn per acre and [tex]1[/tex] hours to raise soybeans per acre and he has 800 hours of labor available during the crucial summer season.
So the equation should be
[tex]2x+y\leq 800\dots\dots Equation (2)[/tex]
He expect a profit of [tex]\$40[/tex] per acre on corn and [tex]\$30[/tex] per acre on soybeans.
So profit equation should be
[tex]P=40x+30y[/tex]
Now the subject of constraints
[tex]x+y\leq 480[/tex]
[tex]2x+y\leq 800[/tex]
[tex]x,y\geq 0[/tex]
Now solving the equation [tex]1[/tex] and [tex]2[/tex] to find the value of [tex]x[/tex] and [tex]y[/tex].
Multiplying the equation [tex]1[/tex] by [tex]2[/tex].
After multiplying with [tex]2[/tex] the equation [tex]1[/tex]
[tex]2x+2y\leq 960\dots\dotsEquation (3)[/tex]
Now subtracting Equation [tex](3)[/tex] and Equation [tex](2)[/tex].
[tex]2x+2y-(2x+y)\leq 960-800[/tex]
[tex]2x+2y-2x-y\leq 960-800[/tex]
[tex]y\leq 160[/tex]
Now putting the value of [tex]y[/tex] in Equation [tex](1)[/tex]
[tex]x+160\leq 480[/tex]
Subtract [tex]160[/tex] on both side
[tex]x+160-160\leq 480-160[/tex]
[tex]x\leq 320[/tex]
He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit.
The maximum profit
[tex]P=40x+30y\\P=40\times320+30\times180\\P=12,800+5400\\P=18,200[/tex]
The maximum profit is [tex]\$18,200[/tex].
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Write the equation in standard form, (2x+1)(3x-2)=0
Answer:
6x^2-x-2
Step-by-step explanation:
which one?Please help its extra credit!
Answer:
12 weeks
Step-by-step explanation:
if 280=420
then 8=×
cross multiply
280×=420×8
280×=3360
divide both sides with the co efficient of x
280×/280=3360/280
leaving the answer to be 12
name the sets of number to which - 2/5 belongs
The sets of number to which - 2/5 belongs is a rational number.
What is a rational number?If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. A rational number is any number that can be expressed as a ratio (or fraction) of two integers.
P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.
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b. If the volume of a cube is 4096 cm³ find diagonal of the cube
A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges.
The diagonal of a cube is √3 side.
If the volume of a cube is 4096 cm³ the diagonal of a cube is 16√3 cm.
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges.
The volume of a cube is given as:
Volume = side³
The diagonal of a cube = √3 side.
We have,
The volume of a cube = 4069 cm³
The volume of a cube = side³
4096 = side³
side = ∛4096
side = 16 cm
Now,
The diagonal of a cube:
= √3 side
= √3 x 16
= 16√3 cm
Thus,
The diagonal of a cube is 16√3 cm.
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how do i do two step equations with variables and decimals
I need the dercreasing intervel and my grade is at risk so pls be correct
Answer: You are correct
The decreasing interval is (-3, infinity)
This is the same as writing [tex](-3, \infty)[/tex]
===============================================
Explanation:
If a < b and f(a) > f(b), then the function is decreasing.
Visually this means that if the graph is going downhill when moving to the right, the function is decreasing.
The graph shown goes downhill throughout its entire domain of (-3, infinity)
Please help ASAP, will mark as brainliest!
Answer:
61 degrees
Step-by-step explanation:
Bro its that easy
If TU = 6 units, what must be true?SU + UT = RT
RT+ TU = RS
RS + SU = RU
TU + US = RS
The following must be true:
SU + UT = RT
What is meant by length of side?By dividing the base's length by its height, one may calculate any quadrilateral's surface area. We can conclude that all of the sides are the same length because the shape is square. Using the square root of the area to determine the length of one side, we can then work backwards from this information. A square has four sides, thus to determine the length of one side, divide the perimeter by 4. Assumed Area: Since s2 is the formula for a square's area and that number corresponds to one of its sides, you must get the square root of the area. A side is the line segment that connects two vertices of a shape or two-dimensional figure according to the definition of geometry.
Length of SU
= RS - RT - TU
= 24 - 12 - 6
= 24 - 1
= 6
Thus, the length of the US is 6 units.
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Consider this equation of a circle. x^2-2x+y^2+6y-4=0
The answer is bellow!!!
Answer:
A
Step-by-step explanation:
x² - 2x + y² + 6y - 4 = 0 ( add 4 to both sides )
x² - 2x + y² + 6y = 4
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
= x² + 2(- 1)x + 1 + y² + 2(3)y + 9 = 4 + 1 + 9
(x - 1)² + (y + 3)² = 14 ← in standard form
Desde un daro y una altura de 30 metros sobre el nivel del agua , se divisan dos barcos pesqueros . El ángulo de depresión al más sercano es de 8°; mientras al más lejano es de 5°, encuentra la distancia entre ambos barcos
Por medio de expresiones trigonométricas y el diagrama geométrico se concluye los dos barcos tienen una distancia aproximada de 129.441 metros.
¿Cómo determinar la distancia entre los dos barcos?En este problema se debe determinar la distancia entre dos barcos. La situación es representanda por dos triángulos rectángulos con un cateto vertical común, correspondiente a la altura del faro. La distancia entre los barcos se determina mediante la siguiente expresión trigonomética:
d = 30 / tan 5° - 30 / tan 8°
d ≈ 129.441 m
La distancia entre los dos barcos es aproximadamente 129.441 metros.
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The wholesale price for a necklace is $10.the mark up percent is 200%.what is the mark up
The mark up is $30.
What is markup?As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
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y = x + 3
y = x² - 2x + 3
Answer:
y=3 / y=6
x=0 / x=3
Step-by-step explanation:
Follow the steps given in the picture attached above.
While birdwatching, Natalie saw 8 robins. If 40% of the birds she saw were robins, how many birds did Natalie see in all?
40% of 8 is 3.2
hope this helped
carmen pulled transactions from the month of march to see if there is an association between coffee and breakfast sandwich purchases. after running through confidence and expected confidence calculations, she calculated the lift ratio at 1.52. what association does a calculated lift ratio of 1.52 reflect?
A lift ratio of 1.52 implies that identifying a person who purchases coffee and a breakfast sandwich is 52% better than guessing that a random person will purchase a breakfast sandwich.
What is the lift ratio about?Stronger relationships are indicated by higher lift values.We divide the confidence ratio by the support of the consequent to arrive at the lift ratio.
Lift ratios greater than one are typically thought to imply a significant link between the components. Lift ratios below 1 indicate that a purchase of the items is unlikely. Lift is simply the ratio of target response divided by the average response.
Carmen analyzed data from the month of March to see if there was a link between coffee and breakfast sandwich purchases. She calculated the lift ratio to be 1.52 after running confidence and expected confidence calculations.
In this case, she wants to know the association between coffee and breakfast sandwich purchases. There's 52% better off than a random individual.
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I’LL MARK BRAINLIEST!! Graph - 5x + 10y = 20
Answer:
Step-by-step explanation:
See screenshot
:]
lol I'm improve my rank so brainliest would help a lot :]
Which is true add a short explanation why it is true thank you if u help
Answer:[tex]\sqrt{36} > 5 \\[/tex]
Step-by-step explanation:
because [tex]\sqrt{36} =6[/tex]
Therefore 6 > 5
Question 5 of 10Which inequality represents all values of x for which theproduct below is defined?x-5.X+2A. X2-2B. X55O C. X25O D. X20SUBMIT
Answer:
[tex]x\ge-2[/tex]Explanation: The product has two square-roots being multipled together, the inside of each of the root must be greater than or equal to zero, this in Mathematics can be written as follows:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \end{gathered}[/tex]Therefore, applying the condition leads us to the following conclusion:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \therefore\rightarrow \\ x-5\ge0\rightarrow x\ge5 \\ x+2\ge0\rightarrow x\ge-2 \end{gathered}[/tex]
Therefore it follows that x must be:
[tex]x\ge-2[/tex]
Simplify by combining like terms
4y+3x+6+2y+3
Answer:
6y + 3x + 9
Step-by-step explanation:
→ Combine all equivalent terms
4y + 2y + 3x + 6 + 3
→ Simplify
6y + 3x + 9
Answer:
3x + 6y + 9
Step-by-step explanation:
Combine like terms.
4y + 2y = 6y
6 + 3 = 9
3x does not have a like term.
6y + 3x + 9
Order the variables in alphabetical order. (In this case, x goes before y.)
Simplify.
3x + 6y + 9
A box is to be made by cutting a square measuring 4 centimeters on a side from a square piece of cardboard. If the volume of the box is to be 100 cubic centimeters, find the length of a side of the original square. Round the answer to the nearest tenth of a centimeter.
Given the volume of the box is 100 cm^3
And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.
so, the height of the box = 4 cm
so, the volume = height * area of the base
100 = 4 * area of the base
Area of the base = 100/4 = 25 cm^2
so, the side length of the base of the box =
[tex]\sqrt[]{25}=5[/tex]so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm
A musicians hair was originally 3 inches long. She asked her hair dresser to cut 5/6 of it off. How many inches did she have cut off?
Answer: 2.5 inches
Step-by-step explanation: 3*5/6= 2.5
Solve 19 - 3x = 2x + 4
x=…
Answer:
3
Step-by-step explanation:
We need to isolate x in order to solve it:
First, subtract 4 from both sides
15 - 3x = 2x
Add 3x to both sides
15 = 5x
Divide each side by 5 to get x
x = 3
Solve for x, y, and z
Using angle sum property we found that ∠ x = 113°, ∠y = 67° and ∠z = 49°
What is angle sum property of a triangle?The angle sum property of triangle states that the sum of all the interior angles of a triangle is 180°.
If ΔABC is a triangle then,
m ∠A + m ∠B + m ∠C = 180°
Given from the figure in the question that 28°, 39° and x° are interior angles of a triangle, then using angle sum property:
28° + 39° + x° = 180°
⇒ 67° + x° = 180°
⇒ x° = 180° - 67° = 113°
∠x and ∠y are on the same line same point therefore their sum will be 180°
⇒ x° + y° = 180°
⇒ 113° + y° = 180°
⇒ y° = 180° - 113° = 67°
Also an exterior angle of a triangle is equal to sum of interior opposite angles.
∴ y ° = 28° + 39° = 67°
Now, 64° , y° and z° are interior angles of same triangle from the figure in the question.
∴ Using angle sum property,
64° + y° + z° = 180°
⇒ y ° + z° = 180° - 64° = 116°
⇒ y° + z° = 116°
⇒ z° = 116° - y° = 116° - 67° = 49°
Therefore ∠x, ∠y , ∠z are 113° , 67° and 49° respectively
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the diameters of ball bearings are distributed normally. the mean diameter is 139 millimeters and the variance is 36. find the probability that the diameter of a selected bearing is greater than 152 millimeters. round your answer to four decimal places.
The probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.
What is termed as the z-score?The Z-score indicates how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value affiliated with this z-score. This p-value represents the probability that the measure's value is less than X, or the percentile of X.For the given question;
The data for the ball bearing is given as-
mean diameter μ = 139 millimetersvariance σ = 36 millimeterssample mean x = 152 millimetersZ-score = (x - μ)/σ
Put the values;
z = (152 - 139)/36
z = 0.36
P(x > 125) = P(z > 0.36), see p values from z table for 0.36.
P(x > 125) = 0.6405
P(x > 125) = 64.05%
Thus, the probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.
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