Answers
Answer:
The x coordinate of S is b.
Step-by-step explanation:
a)
The coordinates of Point Q are:
(2a+2b)/2, 2c/2
= [(a + b), c].
The slope of the line AB
= (0-2c)/(2b-2a)
= -c/(b-a)
So The slope of the line QS = (b - a) / c = (b - a)/c.
Its equation is
y - c = (b - a)/c ( x - (a+b))
y = (b - a)/c ( x - (a+b)) + c.
The coordinates of Point P are:
(2a+0)/2, 2(c+ 0)/2
= (a, c)
The slope of the line AO
= (2c)/2a
= c/a
So The slope of the line PS = -a/c
Its equation is
y - c = -a/c(x - a)
y = -a/c(x - a) + c
b)
So:
(b - a)/c ( x - (a+b)) + c
= -a/c(x - a) + c
(b - a)(x - a - b) + c^2 = -a(x - a) + c^2
(b - a)(x - a - b) = -a(x - a)
bx - ab - b^2 - ax + a^2 + ab = -ax + a^2
bx - ax + ax + a^2 - a^2 - ab + ab = b^2
bx = b^2
x = b = the x coordinate of S.
c). The point R has the same x coordinate as S So RS is perpendicular to OB.
Related Questions
A forest contains 24 elk, of which, 8 are captured, tagged, and released. a certain time later, 4 of the 24 elk are captured. what is the probability that 3 of these 4 have been tagged?
Answers
The probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053.
To solve this problemWe can use the concept of combinations.
The total number of ways to choose 4 elk out of 24 is given by the combination formula:
C(24, 4) = 24! / (4!(24-4)!) = 10,626
Now, we need to consider the number of ways to choose 3 tagged elk out of the 8 tagged elk and 1 untagged elk. The number of ways to do this is given by:
C(8, 3) * C(1, 1) = 8! / (3!(8-3)!) * 1! / (1!(1-1)!) = 56
Therefore, the probability that 3 out of the 4 captured elk have been tagged is:
P = (Number of ways to choose 3 tagged elk out of 8 tagged elk and 1 untagged elk) / (Total number of ways to choose 4 elk out of 24)
P = 56 / 10,626
Calculating this division gives us the probability:
P ≈ 0.0053
So, the probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053 .
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Lucy's dog lost 6 pounds. How much weight does her dog need to gain in order to have a net change of 0 pounds?
Answers
Answer:
Lucy's dog needs to gain 6 pounds.
Step-by-step explanation:
Lucy's dog lost 6 pounds so the dog will have to gain 6 pounds.
The Dog need to gain 6 pounds for net change of zero pounds.
We have Lucy's whose dog lost 6 pounds.
We have to find out how much weight does her dog need to gain in order to have a net change of 0 pounds.
If you have 'x' toffees and you lost 'y' toffees, then how many toffees you have to buy to recover the lost toffees?Number of toffees left after loosing 'y' toffees = x - y
The number of toffees to buy = x - (x - y) = x - x + y = y
A/Q -
Let the Dog's initial weight be - W
After loosing 6 pounds, the weight will be - W - 6
For a net change of zero pounds, he needs to add = W - (W - 6) = W - W + 6 = 6 Pounds.
Hence, he need to gain 6 pounds for net change of zero pounds.
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Please answer , with work . Thank you !
Answers
Sergio and three friends went golfing two other friends rented clubs for six dollars each the total cost of the rented clubs in the green fees was $76 what was the cause of the green fees for each person
Answers
The cost of Green fees for each person is $16.
As per the question statement, Sergio went golfing with 3 other friends and two of them rented clubs for $6 each, the total cost of the rented clubs and the green fees being $76.
We are required to calculate the cost of Green fees for each person.
Let us assume that the cost of Green fees for each person is "x".
We will now form a linear equation of single variable "x" based on the conditions mentioned in the question statement, and solving for x, we will obtain our desired answer.
\([4x+(2*6)]=76\\or,4x+12=76\\or, 4x=76-12\\or, 4x=64\\or, x=\frac{64}{4}=16\)
That is, the cost of Green fees for each person is $16.
Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line, as the name "Linear" itself suggests. Here, each term is of exponent 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept.To learn more about Linear Equations, click on the link below.
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What is the average rate of change for this function for the interval from x = 2 to x = 4?.
Answers
The average rate of change over the interval from x = 2 to x = 4 is 2.
The average rate of change for a function over an interval is the slope of the secant line that connects the two points on the graph. The average rate of change can be found by using the formula:
Average Rate of Change = (y2 - y1) / (x2 - x1)
For the given function, the average rate of change over the interval from x = 2 to x = 4 can be found by substituting the appropriate values into the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
Substituting the function values, we get:
Average Rate of Change = (6 - 2) / (4 - 2)
Simplifying, we get:
Average Rate of Change = 4 / 2
Therefore, the average rate of change over the interval from x = 2 to x = 4 is 2.
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In a simple regression model, unexplained variation in the response variable is calculatedby summing the squares of errors.
Answers
In a simple regression model, the unexplained variation in the response variable is determined by summing the squares of errors. This method, known as residual sum of squares (RSS), quantifies the discrepancy between the observed values and the predicted values by the regression model.
In a simple regression model, the goal is to find a line that best fits the relationship between a single predictor variable (X) and a response variable (Y). However, due to various factors and sources of variability, the observed values of the response variable may not perfectly align with the predicted values based on the regression line.
The errors, or residuals, are the differences between the observed values and the predicted values. To quantify the unexplained variation, the errors are squared to eliminate negative values and emphasize larger deviations. These squared errors are then summed up, resulting in the residual sum of squares (RSS).
By calculating the RSS, one can assess the amount of unexplained variation or "error" in the regression model. A smaller RSS indicates that the model provides a better fit to the data, as it suggests less unexplained variation. On the other hand, a larger RSS implies a less accurate fit, with more unexplained variation in the model.
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a local bbq restaurants offers 2 side dishes with a lunch plate. there are 7 side dishes. how many choices of side dishes does a customer have? note: there is no requirement that the customer chooses different side dishes (i.e. he or she can choose say baked beans twice as their side dish).
Answers
The number of choice out of 7 that consumer have are 42.
What is permutation?The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.
According to given data:Number of choices of side dishes does a customer have,
total dishes(n)=7 , r = 2
ⁿP₂
⁷P₂
7×6 = 42
Thus required number of ways are 42.
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Find the inverse of the function. Is the inverse a function? f(x) = (x − 2)2
Answers
Answer:
\(f^{-1}(x)=\sqrt{x}+2\)
Step-by-step explanation:
Given function is,
f(x) = (x - 2)²
Step - 1
Rewrite the function in the form of a equation.
y = (x - 2)²
Step - 2
Interchange the variables 'x' and 'y',
x = (y - 2)²
Step - 3
Solve the equation for y,
x = (y - 2)²
y - 2 = √x
y = 2 + √x
Step - 4
Rewrite the equation in the form of a function,
\(f^{-1}(x)=\sqrt{x}+2\)
14.) Is 136 divisible by 5? yes O
Answers
Answer:
The answer is no
Step-by-step explanation:
Is because if we divide 136 by 5 is gonna give us 27.2 and we don’t want the decimal. So we can’t divide 136 by 5. Another method is you can you at the last digit in this case is 6, six is not in the table of 5 so always the answer is going to be in decimal. 136\(:\)5= 27.2
Which expression is equivalent to 17s-10+3(25+1)?
23s-9
23s-7
115-7
115-9
Answers
Answer:
17s + 68.
Step-by-step explanation:
17s - 10 + 3(25 + 1)
= 17s - 10 + 3 * 26
= 17s - 10 + 78
= 17s + 68.
Hope this helps!
Answer:
its b 23s - 7
Step-by-step explanation:
took the test
Find any integer between
-3.92 and 12,4
Answers
Answer:
There are 16 integers between -3.92 and 12.4
Step-by-step explanation:
If we want to find the integers between two numbers we just need to subtract the integer numbers of the interval.
The integer interval will be:
\([-3,12]\)
Now, we subtract them:
\(12-(-3)=12+3=15\)
Let's recall that 0 is an integer
Therefore, the answer will be 16.
I hope it helps you!
If ST=17 and RT=41, find RS. Use the number line below.
Answers
The length of segment RS is given as follows:
RS = 24.
What does the angle addition postulate state?The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.
The segment RT is the combination of segments RS and ST, hence:
RT = RS + ST.
Hence the length of segment RS is given as follows:
41 = RS + 17
RS = 24.
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Choose the equation for the graph.
A
a) y = 2x - 3| +1
b) y = -2x - 3| +1
c) y = 2|x - 3|- 1
d) y = -2|x + 3) - 1
e) y = 2x + 3| +1
Answers
Answer:
a) y=2x-3|+1
b)y= - 2×-3| - 1
How many liters of water are in a tank with a volume of 4,500 cm3
1 L = 1,000 cm
04.0L
0 4.5 L
0 45 L
0 0.45 L
Answers
Another statement is, "Volume is directly proportional to the number of moles."
The volume increases as the number of moles increases. It does not depend on the sizes or the masses of the molecules.
V
∝
n
, where
V
is the volume, and
n
is the number of moles.
V
n
=
k
, where
k
is a proportionality constant.
We can rewrite this as
V
1
n
1
=
V
2
n
2
Equal volumes of hydrogen, oxygen, or carbon dioxide contain the same number of molecules.
STP is 0 °C and 1 bar.
One mole of an ideal gas occupies 22.71 L at STP. Thus, its molar volume at STP is 22.71 L
Example Problem
A 6.00 L sample at 25.0 °C and 2.00 atm contains 0.500 mol of gas. If we add 0.250 mol of gas at the same pressure and temperature, what is the final total volume of the gas?
Solution
The formula for Avogadro's law is:
V
1
n
1
=
V
2
n
2
V
1
=
6.00 L
;
n
1
=
0.500 mol
V
2
=
?
;
m
m
l
n
2
=
0.500 mol + 0.250 mol = 0.750 mol
V
2
=
V
1
×
n
2
n
1
V
2
=
6.00 L
×
0.750
mol
0.500
mol
=
9.00 L
Find the 49th term.
-15, -10, -5, O, 5, ...
49th term = [?]
1st term + common difference(desired term - 1)
Enter
Answers
Answer:
49th term = 225
Step-by-step explanation:
The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.
An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.
The general formula, for the nth term of an arithmetic progression, is thus:
Tn = a + (n - 1)d, where a = first term, and d = common difference.
In the sequence: -15, -10, -5, 0, 5...,
a = -15, and d = -10--15 = 5
T49 = -15 + (49 - 1)5 = 225
∴ 49th term = 225
The perimeter of a rectangular window is 242 cm.
If the length of the window is 66 cm, what is its width?
Width of the window: 0
cm
Answers
Answer:
The width of the window is 176 cm
Step-by-step explanation:
The perimeter is the outside of a shape. If the perimeter is 242 cm and we know the length is 66 cm, we use what we have. We take 242 and subtract it by 66 and get 176 cm
Which relation in the below table(s) represents a function?
Answers
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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What is your dependent variable? (page 3 of investigation) question 2 options: temperature height ball bounces type of ball
Answers
The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment. It is the variable that you control to determine how the changes will impact the subject being investigated.
Height the ball bounces is your dependent variable, which varies based on the other variables.The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph.
The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph. The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment.
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Identify the antecedent and the consequent for each of the following conditional sentences. Assume that a, b, and f represent some fixed sequence, integer, or function, respectively.
(a) If squares have three sides, then triangles have four sides.
(b) If the moon is made of cheese, then 8 is an irrational number.
(c) b divides 3 only if b divides 9.
(d) The differentiability of f is sufficient for f to be continuous.
(e) A sequence a is bounded whenever a is convergent.
(f) A function f is bounded if f is integrable.
(g) 1 + 2 = 3 is necessary for 1 + 1 = 2.
(h) The fish bite only when the moon is full.
(i) A time of 3 minutes, 48 seconds or less is necessary to qualify for the Olympic team.
Answers
(a) Antecedent: Squares have three sides
Consequent: Triangles have four sides
(b) Antecedent: The moon is made of cheese
Consequent: 8 is an irrational number
(c) Antecedent: b divides 3
Consequent: b divides 9
(d) Antecedent: The differentiability of f
Consequent: f is continuous
(e) Antecedent: A sequence a is convergent
Consequent: a is bounded
(f) Antecedent: A function f is integrable
Consequent: f is bounded
(g) Antecedent: 1 + 2 = 3
Consequent: 1 + 1 = 2
(h) Antecedent: The moon is full
Consequent: The fish bite
(i) Antecedent: Time of 3 minutes, 48 seconds or less
Consequent: Qualification for the Olympic team
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find the limit l (if it exists). if it does not exist, explain why. (if an answer does not exist, enter dne.) lim x→49 x − 7x − 49
Answers
The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.
The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:
lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009
So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.
So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.
Therefore, lim x→49 x^2 - 7x - 49 = 343.
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add 16k to the quotient of 4m divided by 11
Answers
Answer:
\(\Large \boxed{\frac{4m}{11}+16k}\)
Step-by-step explanation:
The quotient is the result from division.
4m divided by 11 is:
\(\displaystyle \frac{4m}{11}\)
16k is added to the result.
\(\displaystyle \frac{4m}{11}+16k\)
Whats 21 square root of 98 divided by 7 square root of 21
Answers
The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407
A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.
Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.
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help if you can plzz
Answers
Answer:
you forgot the attachment
Step-by-step explanation:
Tres profesores compraron libros: uno de ellos pago $845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial. Otro pago $580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial. El último de ellos pago $605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial. ¿Cuál es el costo de cada libro según su tema?
Answers
Usando un sistema de ecuaciones, se encuentra que
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Para el sistema, hay que:
x es el costo de un libro de Algebra.y es el costo de un libro de Geometría Analítica.z es el costo de un libro de Calculo Diferencial.$845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial, o sea:
\(3x + 5y + 3z = 845\)
$580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial, o sea:
\(4x + 2y + z = 580\)
$605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial, o sea:
\(x + 3y + 3z = 605\)
Reemplazando la segunda equación en las otras duas:
\(z = 580 - 4x - 2y\)
\(3x + 5y + 3z = 845\)
\(3x + 5y + 3(580 - 4x - 2y) = 845\)
\(-9x - y = -895\)
\(9x + y = 895\)
\(y = 895 - 9x\)
\(x + 3y + 3z = 605\)
\(x + 3y + 3(580 - 4x - 2y) = 605\)
\(-11x - 3y = -1135\)
\(11x + 3y = 1135\)
\(y = 895 - 9x\), por eso:
\(11x + 3(895 - 9x) = 1135\)
\(-16x = -1550\)
\(x = \frac{1150}{16}\)
\(x = 96.875\)
\(y = 895 - 9x = 895 - 9(96.875) = 23.125\)
\(z = 580 - 4(96.875) - 2(23.125) = 146.25\)
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Un problema similar, que también envuelve un sistema de ecuaciones, es dado en https://brainly.com/question/24646137
PLEASE HELP ME FASTTT!!
Answers
i need help with this !!!!
Answers
Explanation: If you try A, B, and C, you’ll find they are all correct, however D seems to be false.
the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.80.8. based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
Answers
The correct statement is C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
How can the correct statement be determined?The coefficient of determination (R2), which ranges from 0 to 1, expresses how accurately a statistical model forecasts a result.
The correlation Coefficient R = 0.8, which demonstrates the strong correlation between children's age and height. With the correlation coefficient value, we can calculate the coefficient of determination (R2), which indicates the proportion of variation that the regression model can account for.
Coefficient of determination \((R^{2} ) = 0.8^{2}\)
= 0.64.
0.64 of the variation in children's height that can be attributed to age and 0.36 to other factors.
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missing Options :
A.) On average, the height of a child is 80% of the age of the child.
B.) The least-squares regression line of height versus age will have a slope of 0.8.
C.) The proportion of the variation in height that is explained by a regression on age is 0.64.
D.) The least-squares regression line will correctly predict height based on age 80% of the time.
E.) The least-squares regression line will correctly predict height based on age 64% of the time.
Ms. Oliver is making masks for her son's class. She uses 2/3 of a yard of material for each
mask. How many masks can she make if she has 18 yards of material?
Answers
Answer: 27 masks
Step-by-step explanation: 2/3 = 1 mask
1 yard = 3/2
18 yards=3/2 * 18 = 27 masks
Find the slope between points (1,1) and (0,6)
Answers
Answer:
6-1/0-1=5/-1
Step-by-step explanation:
change in y over change in x gives you gradient.therefore the gradient is negative 5
12
Calculate the area of the given segment. Round your answer to the nearest tenth, if necessary.
60
8 in.
Answers
Check the picture below.
\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)
