y=2x-10
x=2y-10
x+10=2y
x+10/2=y
final answer: y=(x+10)/2
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{2}x+5}[/tex]
Step-by-step explanation:
[tex]f(x)=2x-10\to y=2x-10\\\\\text{we exchange each other x and y}\\\\x=2y-10\\\\\text{solve for y}\\\\2y-10=x\qquad\text{add 10 to both sides}\\\\2y=x+10\qquad\text{divide both sides by 2}\\\\y=\dfrac{1}{2}x+5[/tex]
Which value for x makes the following equation TRUE?
-2x - 4 = - 6
Answer:
1
Step-by-step explanation:
-2(1) = -2
then -2 - 4 = -6
-6 = -6
Answer:
1
Step-by-step explanation:
Move all terms that don't contain x to the right side & solve.
Please help me out with this
Answer:
x = 17
Step-by-step explanation:
For the parallelogram to be a rhombus then then the diagonal must bisect the given angle, thus
3x - 11 = x + 23 ( subtract x from both sides )
2x - 11 = 23 ( add 1 to both sides )
2x = 34 ( divide both sides by 2 )
x = 17
What should be the next number in the following series? 1 2 8 48 384 _ ?_
The answer should be 3840
PLS HELP!!!!
Drag a statement or reason to each box to complete this proof.
If x−24=2, then x=10.
Statement Reason
1. x−24=2 Given
2. 4(x−24)=4∙2 ?
3. ? Simplifying
4. x−2+2=8+2
5. ? ?
______________________________________________________________
simplifying multiplication property of equality
addition property of equality x=10 x-2=8
Answer:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation is [tex]\frac{x-2}{4}=2[/tex]
- The value of x is 10
- We want to a statement reason to each step to complete the proof
* Lets write each step with statement reason
1. [tex]\frac{x-2}{4}=2[/tex] ⇒ Given
2. [tex]4(\frac{x-2}{4})=4*2[/tex] ⇒ simplifying multiplication property of equality
3. x - 2 = 8 ⇒ Simplifying
4. x - 2 + 2 = 8 + 2
5. x = 10 ⇒ addition property of equality
- In step 2 we multiply both sides by 4 to cancel the denominator of
the left hand side (simplifying multiplication property of equality)
- Then we simplify the two sides to get (x - 2 = 8)
- Then we add two to both sides to cancel -2 in the left hand side
- Then after adding we find (x = 10) , (addition property of equality)
* The answer is:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
What does it mean when a scatter plot has a good or bad fit? And how can you tell if it has a good or bad fit?
Snake wnemwmammwmenkk ju jxi I I i I jus uo I j i I i I i I i I i i izj
A scatter plot has a good fit when data points cluster near the line of best fit and show a clear positive or negative correlation, suggesting a strong relationship between variables. A bad fit is characterized by scattered data points with no apparent pattern and large residuals between the points and the line, indicating a weak or no correlation.
When a scatter plot has a good fit, it means that the line of best fit accurately represents the trend in the data. This line minimizes the distances, or residuals, between itself and all the points on the graph. You can tell if a scatter plot has a good fit if the data points form a pattern that closely follows the line of best fit, indicating that the variables have a strong correlation. Conversely, a bad fit is evident when the data points are widely scattered and do not follow a distinct pattern, suggesting a weak or no correlation between the variables.
Signs of a Good Fit in Scatter Plots
Data points cluster near the line of best fit.Residuals (distances between data points and the line) are generally small.The pattern is either a clear positive or negative correlation.Signs of a Bad Fit in Scatter Plots
Data points are spread out with no discernible trend.Residuals are large, indicating significant variance from the line.No apparent correlation, positive or negative, is observable.Whether the X and Y variables in a scatter plot are good candidates for linear regression depends on the aforementioned signs. If there is a clear positive or negative correlation and data points approximate a linear trend, they are good candidates for linear regression.
Ashley is thinking of two numbers. The first number is four more than twice the second number. The sum of the two numbers is 16. Which system of equations can be used to determine the first number, x, and the second number, y?
x + y = 16
x = y^2 x 4
i hope this helps :)
good luck
I have no idea how to do this. I can’t cooperate with the imaginary number, please help me
Answer:
Step-by-step explanation:
This is a third degree polynomial because we are given three roots to multiply together to get it. Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root. Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.
Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):
If x = -4, then the factor is (x + 4)
If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)
If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)
Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):
(x - 2 - i)(x - 2 + i) = [tex]x^2-2x+ix-2x+4-2i-ix+2i-i^2[/tex]
Combining like terms and canceling out the things that cancel out leaves us with:
[tex]x^2-4x+4-i^2[/tex]
Remembr that [tex]i^2=-1[/tex], so we can rewrite that as
[tex]x^2-4x+4-(-1)[/tex] and
[tex]x^2-4x+4+1=x^2-4x+5[/tex]
That's the product of the 2 imaginary factors. Now we need to FOIL in the real factor:
[tex](x+4)(x^2-4x+5)[/tex]
That product is
[tex]x^3-4x^2+5x+4x^2-16x+20[/tex]
which simplifies down to
[tex]x^3-11x+20[/tex]
And there you go!
Match the rectangles formed by the sets of points to their corresponding areas. A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16) 50 square units E(30, 20), F(39, 29), G(49, 19), H(40, 10) 300 square units I(-6, 2), J(2, 2), K(2, -8), L(-6, -8) 100 square units M(5, 5), N(11, 5), O(11, -5), P(5, -5) 80 square units Q(10, 0), R(15, 5), S(25, -5), T(20, -10) U(0, 5), V(15, 20), W(25, 10), X(10, -5) arrowBoth arrowBoth arrowBoth arrowBoth
Answer:
The area of ABCD is 50 units²
The area IJKL is 80 units²
The area of QRST is 100 units²
The area of UVWX is 300 units²
Step-by-step explanation:
* Lets revise the area of the rectangle
- The area of any rectangle = its length × its width
- To solve the problem find the lengths of two adjacent sides and
consider that one of them is the length and the other is the width
- Use the rule of the distance between two points (x1 , y1) and (x2 , y2)
the distance = √[(x2 - x1)² + (y2 - y1)²]
# In rectangle ABCD
∵ A = (-9 , 8) , B = (-5 , 5) , C = (1 , 13)
∴ AB = √[(-5 - -9)² + (5 - 8)²] = √[(4)² + (-3)²] = √[16 + 9] = √25 = 5 units
∴ BC = √[(1 - -5)² + (13 - 5)²] = √[(6)² + (8)²] = √[36 + 64] = √100 = 10 units
∴ The area of ABCD = 5 × 10 = 50 units²
# In rectangle EFGH
∵ E = (30 , 20) , F = (39 , 29) , G (49 , 19)
∴ EF = √[(39 - 30)² + (29 - 20)²] = √[9² + 9²] = √[81 + 81] = √162 unit
∴ FG = √[(49 - 39)² + (19 - 29)²] = √10² + (-10)²] = √[100 + 100] = √200 units
∴ The area of EFGH = √162 × √200 = 180 units²
# In rectangle IJKL
∵ I = (-6 , 2) , J = (2 , 2) , K = (2 , -8)
∴ IJ = √[(2 - -6)² + (2 - 2)²] = √[8² + 0²] = √8² = 8 units
∴ JK = √[(2 - 2)² + (-8 - 2)²] = √[0² + (-10)²] = √10² = 10 units
∴ The area IJKL = 8 × 10 = 80 units²
# In rectangle MNOP
∵ M = (5 , 5) , N = (11 , 5) , O = (11 , -5)
∴ MN = √[(11 - 5)² + (5 - 5)²] = √[6² + 0²] = √6² = 6 units
∴ NO = √[(11 - 11)² + (-5 - 5)²] = √[0² + (-10)²] = √10² = 10 units
∴ The area of MNOP = 6 × 10 = 60 units²
# In rectangle QRST
∵ Q = (10 , 0) , R = (15 , 5) , S = (25 , -5)
∴ QR = √[(15 - 10)² + (5 - 0)²] = √[5² + 5²] = √[25 + 25] = √50 units
∴ RS = √[(25 - 15)² + (-5 - 5)²] = √[10² + (-10)²] = √[100 + 100] = √200 units
∴ The area of QRST = √50 × √200 = 100 units²
# In rectangle UVWX
∵ U = (0 , 5) , V = (15 , 20) , W = (25 , 10)
∴ UV = √[(15 - 0)² + (20 - 5)²] = √[15² + 15²] = √[225 + 225] = √450 units
∴ VW = √[(25 - 15)² + (10 - 20)²] = √[10² + (-10)²] = √100 + 100 = √200 units
∴ The area of UVWX = √450 × √200 = 300 units²
please help me with this geometry question
image attached
For this problem, you need to know how to use sin, cos, and tan or 'SOH-CAH-TOA' sin- opposite/hypotenuse cos-adjacent/hypotenuse toa- opposite/adjacent
in this case, you can use tan or toa
the equation should be set up like this:
4/x=1/0.848
solve, and you will get 3.39...
(you need to use the sin,cos,tan degree chart to find 0.848)
If the mean of a normal distribution is 18, what is the median of the distribution?
A) 22
B) 26
C) 14
D) 18
D. Normal distributions are symmetric, so the mean is the same as the median.
Answer:
18
Step-by-step explanation:
The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected. The probability that a randomly chosen person gets an incorrect result is .
[tex]\textrm{97 percent accurate for individual with the virus}[/tex]
[tex]\text{3 percent inaccurate}[/tex]
[tex]\textrm{99 percent accurate for an individual}[/tex]
[tex]\textrm{1 percent inaccurate probability}[/tex]
[tex]\textrm{Probability of infected:}[/tex]
[tex].0055[/tex]
[tex]\textrm{Probability of not being infected}[/tex]
[tex]1 - .0055 = .9945[/tex]
[tex]\textrm{Combine it all together}[/tex]
[tex]0.0055 * 0.03 + 0.9945 * 0.01 = 0.01011[/tex]
[tex]\textrm{The probability that a randomly chosen person gets an incorrect result is 0.01011}[/tex]
[tex]\textbf{Answer}[/tex]
[tex]\textrm{0.01011}[/tex]
The probability of an incorrect result for the test to detect respiratory syncytial virus is calculated by considering the test's sensitivity and specificity, along with the prevalence of the virus in the population.
Explanation:In order to calculate the probability that a randomly chosen person gets an incorrect result, we first need to understand how test accuracy works. Sensitivity refers to how often the test correctly identifies the presence of a disease when it is indeed there, while specificity refers to how often it correctly identifies the absence of a disease when it isn't there. In this case, the sensitivity is 97%, meaning it correctly identifies the virus in 97% of individuals who have the virus; the specificity is 99%, meaning it correctly identifies no virus in 99% of individuals who do not have the virus.
For the given population, 0.55% are infected. Hence, the probability of an incorrect result for a person with a virus is 3% (100% - 97%), and for a person without the virus is 1% (100% - 99%). Therefore, the total probability of getting an incorrect result is (0.55%/100 * 3%) + [(1 - 0.55%/100) * 1%].
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if f(x)=x-2 which of the following is the inverse of f(x) brainly
Answer:
The inverse of f(x) is [tex]f ^ {- 1}(x) = x + 2[/tex]
Step-by-step explanation:
To find the inverse of the function [tex]f (x) = x-2[/tex], perform the following steps:
1) do [tex]y = f (x)[/tex]
[tex]y = x-2[/tex]
2) Solve the equation for the variable x.
[tex]y + 2 = x -2 +2[/tex]
[tex]y + 2 = x[/tex]
3) exchange the variable x with the variable y
[tex]y + 2 = x[/tex] ----> [tex]x + 2 = y[/tex]
4) Change the variable y by [tex]f ^{- 1}(x)[/tex]
Finally the inverse function is:
[tex]f ^ {- 1} (x) = x + 2[/tex]
Answer:
f-1(x)=x+2
Step-by-step explanation:
What is the degree of the polynomial p(x) = [tex]17x^{4}-12x^3+51x^2-137x+2[/tex]
The degree of a polynomial is the highest exponent.
The highest exponent in this equation is 17x^4
The degree is 4.
Which point does NOT lie on the graph of y = 2x 3?
(1, 8)
(-1, -2)
(0, 0)
(2, 16)
[tex]\bf (\stackrel{x}{1},\stackrel{y}{8})\qquad y=2x^3\implies 8=2(1)^3\implies 8\ne 2~~\bigotimes \\\\\\ (\stackrel{x}{-1},\stackrel{y}{-2})\qquad y=2x^3\implies -2=2(-1)^3\implies -2=-2~~\checkmark \\\\\\ (\stackrel{x}{0},\stackrel{y}{0})\qquad y=2x^3\implies 0=2(0)^3\implies 0=0~~\checkmark \\\\\\ (\stackrel{x}{2},\stackrel{y}{16})\qquad y=2x^3\implies 16=2(2)^3\implies 16=16~~\checkmark[/tex]
For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced.
Step-by-step explanation:
x = a cos t, y = b sin t
cos t = x / a, sin t = y / b
cos² t + sin² t = 1
(x / a)² + (y / b)² = 1
If a = b, the conic section is a circle.
If a and b are different, the conic section is an ellipse.
The clothes is having a 60% off sale for shorts. Ben paid $14 for the shorts. What is the original price
Answer:
$35
Step-by-step explanation:
since it is 60% off, $14 is 40% of original price.
1% of original price (original price is 100%)
= $14 ÷ 40
= $0.35
original price
= $0.35 × 100
= $35
What is the value of x? Enter your answer in the box
x = 180° - 67° - 52°
x = 61°
So, the value of x is 61°
Lisa lives in Atlanta. She is going to a baseball game with her two sisters and her parents. They have $100 to spend. After they buy their tickets, how much money will they have left to buy refreshments?
Answer:
27.90
Step-by-step explanation:
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The amount of money that is left with Lisa after buying tickets is $27.90.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The total number of members in the family is 5 (Parents+2sisters+Lisa). Also, the cost of a single ticket in Atlanta is $14.42, therefore, the cost of five tickets will be,
The cost of 5 tickets = $14.42 × 5 = $72.10
The amount Lisa has to spend is $100, therefore, the money left with Lisa after buying the tickets is,
Amount left = $100 - $72.10 = $27.90
Hence, the amount of money that is left with Lisa after buying tickets is $27.90.
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Find the number of positive three-digit integers whose digits are among 9, 8, 7, 5, 3, and 1.
18
216
729
Answer:
216
Step-by-step explanation:
Each of the three digit positions can have any of 6 values, so there are ...
6^3 = 216
possible numbers that can be formed.
Please help me out please
Answer:
110.9 sq ft
Step-by-step explanation:
split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh
A=(1/2)(8)(13.86)= 110.9
Answer:
A = 64√2 ft² = approx. 90.5 ft²
Step-by-step explanation:
Because this is an equilateral triangle, the interior angles are also equal and are 60° each. We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle. We see from the diagram that the base is 16 ft.
Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get
sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that
h 1
----- = -----
16 √2 16
and so √2*h = 16, and h = -------
√2
1 16 16
Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------
2 1 √2
128 128√2
or A = ------- = ------------ = 64√2 ft² = approx. 90.5 ft²
√2 2
Brainliest + Points! Can someone please HELP ME
A spring has spring constant 0.3 m/newton. What force is necessary to stretch the spring by 1.5 meters?
Use Hooke's Law, F = kx. Show all your steps.
In the equation F=kx, F is the force, k is the spring constant, and x is the displacement. Plug in and solve:
F=0.3(1.5)
F=0.45N
Hope this helps!!
Please help me out please
Answer:
h=20
Step-by-step explanation:
h=3 (V/lw)
h= 3 (960/12*12)
Help with this question, please!! I don't understand!
Answer:
(0, 1)
Step-by-step explanation:
all of the points are the same number away: 2√5
Answer:
(0, 1)
Step-by-step explanation:
A, B, and C are points on a circle. You are being asked to find the center of the circle. You can do that any of several ways.
I find it useful to plot the points on a graph. Doing so reveals that AB is perpendicular to BC, so ABC is a right triangle, and the center you want is the midpoint of the hypotenuse (AC).
(A+C)/2 = ((2, -3) +(-2, 5))/2 = (2-2, -3+5)/2 = (0, 1) . . . . . coordinates of center
___
From a construction point of view, the center of the circle is the point of intersection of the perpendicular bisectors of the chords. In the attached, we have used a geometry program to draw the perpendicular bisectors of AB and BC. They meet at (0, 1).
___
From an algebra point of view, the points on the circle with center (h, k) and radius r satisfy the equation ...
(x -h)^2 +(y -k)^2 = r^2
Filling in the point values, you get three equations in the three unknowns (h, k, r):
(2-h)^2 +(-3-k)^2 = r^2(4-h)^2 +(3-k)^2 = r^2(-2-h)^2 +(5-k)^2 = r^2Finding the difference between any two pairs of these will result in two linear equations in h and k, so are easily solved.
First - second: (4 -4h +h^2) +(9 +6k +k^2) -(16 -8h +h^2) -(9 -6k +k^2) = r^2 -r^2
-12 +4h +12k = 0 . . . simplify
h +3k = 3 . . . . . . . . . put in standard form
Second -third: (16 -8h +h^2) +(9 -6k +k^2) -(4 +4h +h^2) -(25 -10k +k^2) = r^2 -r^2
-4 -12h +4k = 0 . . . . simplify
3h -k = -1 . . . . . . . . . put in standard form
Now, we can add 3 times the second of these equations to the first to find h:
(h +3k) +3(3h -k) = (3) +3(-1)
10h = 0
h = 0
Then either of the equations can be used to find k = 1.
The center is (h, k) = (0, 1).
Tom opened a lemonade stand to earn money to buy a new bike for $200. He sells a cup of lemonade for $1.00. On the first day he sold 8 cups of lemonade, on the second day he sold 16 cups and on the third day he sol 32 cups. If Tom keeps selling cups of lemonade this way on what day will he have a total of $200.
1 - 8
2 - 16
3 - 32
x - +200
Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.
4 - (32 x 2 = ) 64
8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.
5 - (64 x 2 = ) 128
120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.
Please help me out with this
Check the picture below.
9. A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?
Show your work
Answer:
4.22 meters per second.
Step-by-step explanation:
First multiply the revs per second by pi:
= 11pi = 34.558.
Now multiply this by the diameter which is 2*6.1 = 12.2 cm = 0.122 m.
Linear velocity = 0.122 * 34.558
= 4.22 m/s.
Linear velocity of the gear in meters per second is 4.22 m/s.
What is linear velocity?Linear velocity is the measure of “the rate of change of displacement with respect to time when the object moves along a straight path.” It is a vector quantity.
Given
Gear of radius = 6.1 cm
Gear of diameter = [tex]2 \times 6.1 = 12.2 cm[/tex] = 0.122 m
Revolutions per second = [tex]11\pi[/tex] = 34.558
Linear velocity of the gear = diameter × Revolutions per second
Linear velocity = 0.122 × 34.558
= 4.22 m/s
Linear velocity of the gear in meters per second is 4.22 m/s.
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Will mark as brainliest!!
Lorenz wants to build a bigger flower box for his home. The current box has dimensions of 18“ x 12“ x 36“. What happens to the volume of the box if you double each dimension
Answer:
The answer is 62208
Step-by-step explanation:
The reason is because 18*2=36 12*2=24 and 36*2=72
36*24*72=62208
Can I get brainliest
20 pts awarded and brainliest marked, plz help ASAP!!!!!!
Mark all the statements that are true.
- The equation of this line is x=3.
- And I think it's also, This graph is a function of whose range is set at {3}.
Answer:
D. The equation of this line is x=3
E. This graph is not a function because the value x=3 is assigned to mre than one y-value.
Step-by-step explanation:
The range is all real numbers.
The domain of this graph is x=3, but it is not a function
The graph is a vertical line whose equation is x=3 because the graph passes through (3,y).
This graph cannot represent a function because it will not pass the vertical line test.
In other words, the x-value of 3 is assigned to more than one y-value.
Therefore the correct answers are:
Option D and E
Please answer this correctly
Answer:
The missing number is 8
Step-by-step explanation:
Hope this helps (3
it will be 297,088 as the answer
1.) A multiple choice test has 7 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer 3 or more questions correctly?
0.311
0.0156
0.244
0.756
2.) In a survey of 300 college graduates, 63% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 4 or fewer of them entered a profession closely related to their college major?
0.149
0.0512
0.793
0.207
Final answer:
The probability that Judy guesses at least 3 questions correctly in a multiple-choice test is calculated using the binomial probability formula. For the survey question, the hypergeometric distribution is used to find the probability of 4 or fewer out of 9 people entering a profession related to their major. Exact probabilities require mathematical computation.
Explanation:
Probability of Answering Multiple-Choice and Survey Questions Correctly
For question 1, we must calculate the probability that Judy guesses at least 3 questions correctly on a 7-question multiple-choice test, where each question has 4 possible answers. Since only one answer is correct per question, her probability of guessing a question correctly is 1/4. To find the total probability of answering 3 or more questions correctly, we use the binomial probability formula which considers the probability of success (1/4) and the number of trials (7 questions). We sum the probabilities of getting exactly 3, 4, 5, 6, or all 7 questions correct.
For question 2, regarding the survey of 300 college graduates, we use the hypergeometric distribution since the samples are taken without replacement. We need to determine the probability that 4 or fewer of the randomly selected 9 survey subjects entered a profession closely related to their college major. We know that 63% of the entire group, which is 189 individuals, entered a relevant profession. We sum the probabilities of 0, 1, 2, 3, and 4 people from our sample of 9 falling into the group who are working in their field.
The correct probabilities from the provided choices are not directly calculable without doing the necessary computations using the respective formulas for each scenario, which are beyond the scope of this response as we do not have the calculations or the respective formulas provided within the context of this interaction.