What is the inverse of the equation y=x²-4, x≤ 0
The inverse of the equation y = x² - 4, x≤ 0 is [tex]y = \sqrt{x + 4[/tex]
How to determine the inverse of the equation?The equation is given as:
y = x² - 4, x≤ 0
Swap the x and y values
x = y² - 4
Add 4 to both sides
y² = x + 4
Take the square root of both sides
[tex]y = \sqrt{x + 4[/tex]
Hence, the inverse of the equation y = x² - 4, x≤ 0 is [tex]y = \sqrt{x + 4[/tex]
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In the following exercises, multiply the binomials. Use any method.
256. (r + s)(3r + 2s)
Answer:
Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4z-y)(z-6).We have to multiply the given expression.Multiply the (4 z-y) by -6, multiply the (4 z-y) by z then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]
________________
[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
______________________
[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]
A rectangle field is ten times as long as it is wide. If the perimeter of the field is 1650 feet, what are the dimensions of the field
Answer:
Below in bold.
Step-by-step explanation:
If the width is x feet then the length is 10x feet, so:
2(x + 10x) = 1650
22x = 1650
x = 75 feet.
So the width is 75 feet and the length is 750 feet,
The math question is on the image
find the nth term of the sequence
Notice how Pattern 2 is Pattern 1 with 4 balls added in the bottom row.
Pattern 3 is Pattern 2 with 5 more balls.
Pattern 4 is Pattern 3 with 6 more balls.
Generalizing the trend, we expect Pattern [tex]n[/tex] to be identical to Pattern [tex]n-1[/tex] with [tex]n+2[/tex] more balls.
If [tex]b_n[/tex] is the number of balls in the [tex]n[/tex]-th pattern, then we have the recursive relation
[tex]\begin{cases} b_1 = 6 \\ b_n = b_{n-1} + n + 2 & \text{for } n>1 \end{cases}[/tex]
We can solve this recurrence by substitution. Using the definition of [tex]b_n[/tex], we have
[tex]b_{n-1} = b_{n-2} + (n-1) + 2 \\\\ \implies b_n = (b_{n-2} + (n-1) + 2) + n + 2 \\\\ \implies b_n = b_{n-2} + 2\times2 + \bigg(n + (n-1)\bigg)[/tex]
[tex]b_{n-2} = b_{n-3} + (n-2) + 2 \\\\ \implies b_n = (b_{n-3} + (n-2) + 2) + 2\times 2 + \bigg(n + (n-1)\bigg) \\\\ \implies b_n = b_{n-3} + 3\times2 + \bigg(n + (n-1) + (n-2)\bigg)[/tex]
and so on, down to
[tex]b_n = b_1 + (n-1)\times2 + \bigg(n + (n-1) + (n-2) + \cdots + 2\bigg)[/tex]
Recall that
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
Then we find
[tex]\displaystyle b_n = 6 + 2(n-1) + \sum_{i=2}^n i[/tex]
[tex]\displaystyle b_n = 2n + 4 + \left(\sum_{i=1}^n i - 1\right)[/tex]
[tex]\displaystyle b_n = 2n + 3 + \frac{n(n+1)}2[/tex]
[tex]\displaystyle \boxed{b_n = \frac{n^2+5n+6}2}[/tex]
Answer:
28balls
Step-by-step explanation:
according to me:
from pattern 1 to 2 four balls were added
from 2 to 3 five balls were added
from 3 to 4 6 balls were added
so you can see that there is a certain sequence that is coming up
that is 4,5,6 so just added 7.
so 21 plus other 7 balls will give us 28 balls
How many ink cartridges can you buy with 105 dollars if one cartridge costs 15 dollars ?
Answer:
7
Step-by-step explanation:
105/15=7
7 ink cartridges you can buy with 105 dollars.
What is a linear equation in math?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.One cartridge costs = 15 dollars
No of cartridge we buy in 105 dollars = 105 /15
= 7
Therefore, 7 ink cartridges buy can with 105 dollars.
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A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.
The y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a
Intercept of a lineGiven the coordinate points on a line as (p , a) and ( p , − a )
Determine the slope
Slope = -a-a/p-p
Slope = infinity
If the value p is zero, hence the coordinate points will become (0, a) and (0, -a)
Since the y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a
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Can someone solve this?
Answer:
[tex]\frac{5}{6}[/tex], [tex]\frac{5}{6}[/tex], and "Yes"
Step-by-step explanation:
We will do as the instructions say.
-> See attached.
math. is 1.096 x 10 ^4 the right answer?
Work Shown:
[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]
Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.
In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relate to the pythagorean theorem?
Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.
What is Pythagoras Theorem?
The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.
The formula for Pythagoras Theorem is given by,
[tex]h^{2}=a^{2} +b^{2}[/tex]
Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.
Each Subtraction in view of Pythagoras Theorem
It is is given that,
[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
or [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]
Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.
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What is the first step to solve the following system of equations using substitution? 3x+y=15 5x-3y=11Divide the second equation by 3. Multiply the first equation by 3. Solve the first equation for y. Add the two equations together.
Answer:
(4, 3)
Step-by-step explanation:
#1. Isolate x:
3x + y = 15
y = 15 - 3x
Substitute and solve for x:
5x - 3y = 11
5x - 3(15 - 3x) = 11
5x - 45 + 9x = 11
5x + 9x = 11 + 45
14x = 56
x = 4
Substitute and solve for y:
y = 15 - 3x
y = 15 - 3(4)
y = 15 - 12
y = 3
Answer:
C. Solve the first equation for y
===================
Given system3x + y = 155x - 3y = 11If we are looking for substitution, then should solve one of the equations for one of the variables. This will allow us to substitute same into other equation and solve for the other variable.
Let's see what would be easy solution.
Equation 1Solving for x is not straight away (we isolate x and divide all terms by its coefficient) as it has coefficient of 3.
Solving for y is easy, we just need to isolate it:
3x + y = 15 ⇒ y = - 3x + 15Equation 2Both of the variables have coefficients that are not factors of the constant term, so the easiest option is to solve the first equation for y.
This gives us the answer choice C.
In which triangle is the value of x equal to tan−1(startfraction 3.1 over 5.2 endfraction)?
The given value of x will be found in a right-angled triangle with a base of length 5.2 units and perpendicular of length 3.1 units.
What is a right-angled triangle?
A triangle is said to be a right-angled triangle if one of its inner angles is 90 degrees, or if any one of its angles makes a right angle.
What is the value of x?
(Consider the given figure for reference)
[tex]tan x=\frac{perpendicular}{base}[/tex]
As seen from the figure,
perpendicular = 3.1 units
base = 5.2 units
∴ [tex]tan x =\frac{3.1}{5.2}[/tex]
⇒ [tex]x=tan^{-1} \frac{3.1}{5.2}[/tex]
This is the required value of x.
Therefore, it can concluded that the value of x in a right-angled triangle with a base of length 5.2 units and perpendicular of length 3.1 units is equal to [tex]tan^{-1}\frac{3.1}{5.2}[/tex]
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Answer: d
Step-by-step explanation:
edge 2023
Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:
[tex]a\sqrt{x+b} +c=d[/tex]
The radical equation that has an extraneous solution is 5✓x + 10 - 15 = 30
How to calculate the equation?Based on the information given, the radical equation that has an extraneous solution is 5✓x + 10 - 15 = 30.
This will be:
5✓x + 10 - 15 = 30
Collect like terms
5✓x = 30 - 10 + 15
5✓x = 35
✓x = 35/5
✓x = 7
x = 7² = 49
The equation that does not have an extraneous solution will be ✓x + 1 + 7 = 4. Here, ✓x = -4 and has no solution.
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You have a box filled with cash. Cash value is uniformly and randomly distributed from 0 to 1000. You are trying to win the box in an auction: you win the box if you bid at least the value of the cash in the box; you win nothing if you bid less (but you lose nothing). If you win the box, you can resell it for 150% of its value. How much should you bid to maximize the expected value of your profit (resale of box minus bid)
We would bid $0 as the expected value of this game is always negative.
I’ll assume that cash means there will not be fractions of a dollar in the box. Let X be the payout of the box and Y be the amount that we pay for the box after bidding. Then we have
P(X)=1.5X−Y, X≤Y
as ur profit function. Since E[P(X)]=1.5E[X]−Y, we first need to find the expected value of X and Y. Each integer between 0 and 1000 is equally likely to be in the box
(P(X=x)={1}/{1001}
Since we only realize the payout of the box if X≤Y we only need to sum up to Y:
E[X]= x=0∑Y1/1001 = Y(Y+1)/2002
To find the expected value of Y, note that we will pay Y dollars for the box if X≤Y and 0 otherwise. Given a Y, the probability that X≤Y is {Y+1}/{1001}
since each potential value of X shy of Y has probability {1}/{1001}
Then{E}[Y] = {Y(Y+1)}/{1001}
It follows that
[tex]\begin{aligned} \mathbb{E}[P(X)] &= 1.5\mathbb{E}[X] - E[Y] = \frac{1.5Y(Y+1)}{2002} - \frac{Y(Y+1)}{1001} \\ &= \frac{-3Y(Y+1)}{4004} \end{aligned}[/tex]
E[P(X)]=1.5E[X]−E[Y]= 1.5Y(Y+1)/2002 − Y(Y+1)/1001 = −3Y(Y+1)/4004
which is always negative so we should not bid any amount for the box. Our optimal bid then is $0, with expected payoff $0. Note that my original assumption was the impetus for using a summation; should I have assumed that any value was possible in the box, then we would have to approach X as though it were a continuous variable.
So, We would bid $0 as the expected value of this game is always negative.
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A landscaping company placed three orders with a nursery. The first order was for 13 bushes, 4 trees, and 7 bundles of flowers, and totaled $579. The second order was for 6 bushes, 2 trees, and 3 bundles of flowers, and totaled $272. The third order was for 9 bushes, 5 trees, and 8 bundles or flowers, and totaled $548. The bills do not list the price per item. What was the cost per bush, tree and bundle of flowers?
Answer:
each bush is $23 and each tree is $47
Step-by-step explanation:
с
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Tan A
Check
50
30
A
40
B
Using relations in a right triangle, it is found that:
tan(A) = 3/4 = 0.75.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 40.The opposite side to A has length 30.Hence the tangent of A is:
tan(A) = 30/40 = 3/4 = 0.75.
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Use a graphing calculator to find the value of the correlation coefficient r to determine if there is a strong correlation among the data.
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
The value for r = - 0.8535 , there is strong correlation between the variables.
What is a correlation coefficient ?Correlation coefficient describes the relationship between the two variables in the data .
The data given is
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
Assuming Linear Regression ,
The data is plotted on the graphing calculator
The value for r = - 0.8535
as the value is in the range of - .85 to -1 , therefore there is strong correlation between the variables.
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The height of a cone is twice the radius of its base.
2x
X
What expression represents the volume of the cone, in
cubic units?
O 2x³
O 47x³
Answer: O253
Step-by-step explanation:
The correct expression which represents the volume of the cone is,
V = 2x³π/3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The height of a cone is twice the radius of its base.
Let radius of cone = x
Then, The height of cone = 2x
Hence, The volume of cone is,
V = 1/3πr²h
V = 1/3 × π × x² × 2x
V = 2x³π/3
Thus, The correct expression which represents the volume of the cone is,
V = 2x³π/3
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The area of a circle is 47.39cm2. find the length of the radius rounded to 2 dp.
The length of the radius rounded to 2 decimal points is 3.88cm.
In geometry, the area enclosed by a circle of radius r is pie π[tex]r^2[/tex].
How to round decimals?
Rounding decimals consists of rounding a decimal number to a certain number of decimal places, to save time and help us express really long numbers in shorter terms. There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.
The area of circle is [tex]47.39cm^2[/tex].
Putting it in the formula we get
[tex]47.39cm^2[/tex] = π[tex]r^2[/tex]
[tex]r^2[/tex] = 47.39 / π
r^2 = 15.0847
r = 3.88 cm
Hence the length of the radius rounded to 2 decimal points is 3.88cm.
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Point P is the center of dilation. Triangle S T U is dilated to create triangle S prime T prime U prime. The length of P T is 2. The length of T T prime is 10.
Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Select two options.
The triangle pre-image is closer to the point of dilation than the image.
The triangle image is closer to the point of dilation than the pre-image.
The value of the scale factor, One-sixth, is between 0 and 1.
The value of the scale factor, 6, is greater than 1.
The vertices of the pre-image are collinear with the vertices of the imag
The statements that justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor include:
A. The triangle pre-image is closer to the point of dilation than the image.
D. The value of the scale factor, 6, is greater than1.
What is dilation?It should be noted that dilation refers to the transformation of an object.
In this case, the triangle pre-image is closer to the point of dilation than the image and the value of the scale factor, 6, is greater than1.
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f(x)=x2 Translate left 2 units Translate down 2 units
Clara writes the equation (x – 13)(x 8) = 196 to solve for the missing side length of a rectangle represented by the factor x 8. what is the missing side length represented by x 8 units of the rectangle?
Answer:
28 units
Step-by-step explanation:
First, we are going to solve the equation to find the value ^^
Let's solve the equation step by step
Step 1. Use the distributive property to destroy the parenthesis
Step 2. Subtract 196 to both sides of the equation
Step 3. Factor the expression
Step 4. Set each factor equal to zero and solve
Since we are dealing with lengths here, and lengths cannot be negative, the only valid solution is 28.
Now, we know from our problem that the missing side of the rectangle is given by the expression , so to find the actual length, we just need to replace with 8 in the given expression and simplify!
We can conclude that the missing side length represented by x + 8 units of the rectangle is 28 units.
The following measurements (in picocuries per liter) were recorded by a set of carbon dioxide detectors installed in a manufacturing facility:
828.1,812.1,805.9,810,831.3 1. Using these measurements, construct a 95% confidence interval for the mean level of carbon dioxide present in the facility. Assume the population is approximately normal.
2. Find the critical value that should be used in constructing the confidence interval.
The confidence interval for the mean level of carbon dioxide present in the facility is (806.05,828.91) and the critical value is 2.77 which is used to find out the confidence interval.
Given measurement of carbon dioxide :828.1,812.1,805.9,810,831.3
We have to construct a confidence interval for 95% for the mean level of carbon dioxide present in the facility.
n=5
sample mean=817.48 (calculated in figure)
sample standard deviation=[tex]\sqrt{(x_ -x_{bar} )^{2} /n-1 }[/tex]
=[tex]\sqrt{522.768/4}[/tex]
=11.43
We have to apply t test as n<30
t critical at 95% with degree of freedom=4 (5-1)
=2.77
Confidence interval=X bar ±standard error
Standard error= t*s/[tex]\sqrt{n}[/tex]
=2.77*11.43/[tex]\sqrt{5}[/tex]
=14.13
Lower boundary=817.48-11.43
=806.05
Upper boundary=817.48+11.43
=828.91
Hence the confidence interval is (806.05,828.91).
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On a coordinate plane, a line is drawn from point R to point Q. Point R is at (4, negative 1), and point Q is at (negative 5, 3).
What are the coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q? Round to the nearest tenth, if necessary.
(, )
The coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q is; (-3.5, 2.3)
How to find line segment partition?We are to find the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q.
We are to find the coordinates of point P.
The ratio in which the point 'P' dives the line segment RQ will be;
m:n = 5:1
The coordinates of the end-points of line segment RQ are
R(4, -1) and Q(-5, 3).
If a point H divides a line segment with end points (p, q) and (s, t) in the ratio m : n, then the coordinates of the point H are;
H = [(ms + np)/(m + n)], [(mt + nq)/(m + n)]
H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]
H = (-21/6, 14/6)
H = (-3.5, 2.3)
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Answer:
-3.5, 2.3
Step-by-step explanation:
That's what the other person said
What is the slope of line a? 48 POINTS
Answer:
-3
Step-by-step explanation:
[tex]Slope = \frac{Change in Y}{Change in X}[/tex]
Take two points
(1, -5) and (-1, 1)
Plug in their y and x coordinates
[tex]\frac{-5 - 1}{1-(-1)} =\frac{-6}{2} = -3[/tex]
Answer:
1st answer is correct.
Step-by-step explanation:
First, let us take two coordinates of the line.
( 0 , -2 ) ⇒ ( x₁ , y₁ )
( -1 , 1 ) ⇒ ( x₂ , y₂ )
We have to use the below formula to find the slope of the line.
Slope = m
[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]
Let us find it now.
[tex]m = \frac{-2-1}{0-(-1)}\\m = \frac{-3}{1}\\m=-3[/tex]
Hurrry help number is chosen at random form 1 to 50 find the probiotic of selecting prime numbers
Answer: [tex]\frac{3}{10}[/tex] or 30%
Step-by-step explanation:
We will divide the wanted outcomes by the possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of prime number}}{\text{number of numbers 1 through 50}} =\frac{15}{50}=\frac{3}{10}\;\; \text{or 30\%}[/tex]
The prime numbers from one through fifty are; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
-> This is 15 numbers
Simplify the expression completely.
The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be solved as follows:-
E = [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]
E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]
E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]
E = 7x³y⁶√3.
Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
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Can someone help me out on these geometry questions? Its urgent, gotta have answers fast
5) Transitive property of equality
6) Addition property of equality
7) Subtraction property of equality
8) Division property of equality
9) Multiplication property of equality
10) Transitive property of congruence
11) Substitution property of equality
12) Addition property of equality [add XY to both sides then use segment addition postulate]
13) Subtraction property of equality [subtract XY from both sides then use segment subtraction postulate]
14) Angle addition postulate
15) Addition property of equality [add angle 2 to both sides then use angle addition postulate]
16) Transitive property of equality
What phrases can be
used to describe the line
representing the relationship between the number of
balloons remaining and the number of hats created?
Select three options.
D positive slope
O negative slope
O constant slope
D increasing function
D decreasing function
A researcher conducted an experiment to investigate the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work settings. In this study, the dependent variable is
In a research of investigating the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work setting , working is a depending variable and crowding is an independent variable.
Given aim of the research is to investigate the effects of working in crowded conditions and uncrowded conditions.
We know that depending variable is a variable whose value is dependent on the other variable. Independent variable is a variable whose value does not dependent on the other variables.
In the given question working may be affected negatively in crowded environment means there will be less work in crowded environment and more work in uncrowded environment.
Hence the depending variable in research is working.
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what is metamorphosis
Answer:
The transformation of an organism throughout life :)
Step-by-step explanation:
This can be seen through the life of frogs, butterflies, moths, and more!
Have an amazing day!!
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