Answers
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula and equate to the given slope
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(a)
(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )
[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then
[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )
y + 4 = 6 ( subtract 4 from both sides )
y = 2
ordered pair is (0, 2 )
(b)
(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )
[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then
[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )
3(x + 2) = 21 ( divide both sides by 3 )
x + 2 = 7 ( subtract 2 from both sides )
x = 5
ordered pair is (5, 5 )
(c)
(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )
[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then
[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )
- 5(1 - x) = - 20 ( divide both sides by - 5 )
1 - x = 4 ( subtract 1 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
ordered pair is (- 3, 5 )
(e)
(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )
[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then
[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )
- 7(2 - y) = 14 ( divide both sides by - 7 )
2 - y = - 2 ( subtract 2 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
ordered pair is (- 6, 4 )
Related Questions
What is the domain and range of the function below?
Answers
And the range is also all real numbers (from negative infinity to infinity)
Juliana wrote -16+x=8 on the board
Answers
Answer: x = 24
Step-by-step explanation:
-16 + 24 = 8
What lines would you use to solve –3x – 2 = 2x + 8? Graph the line for the left side of the equation. Graph the line for the right side of the equation.
Answers
Answer:
See attached graph for lines
Left side line is y = -3x-2
Right side line is y = 2x + 8
Point of intersection is at (-2,4)
Step-by-step explanation:
The line graphs are attached
The solution for (x, y) is the point of intersection of the two lines
This is at point (2,4)
We can also solve this algebraically by solving first for x and then y
–3x – 2 = 2x + 8
The two line equations are
y = -3x - 2 and y = 2x+8
3x – 2 = 2x + 8
==> 3x -2x - 2 = 2x-2x + 8 (subtract 2x on both sides)
==> -5x -2 = 8
==> -5x -2 + 2 = 8 + 2 (add 2 on both sides to isolate the x term)
==> -5x = 10==> -5x/5 = 10/5 (divide by 5 both sides)
==> x = -2
Plug this value of x into the RHS giving
y = 2(-2) + 8 ==> y = -4 + 8 ==> y = 4
So (-2,4) is the point of intersection of the two lines and is consistent with the point of intersection on the graph
Will mark brainly-est. Please Help me with this Geometry question.
Answers
In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices
Answers
In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.
What is Analysis of variance ?
With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.What are some instances where ANOVA has been applied?
An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.Learn more about Analysis of variance
brainly.com/question/28274784
#SPJ4
Find a general solution. show the steps of derivation. check your answer by substitution.y'=e^(2x-1)y^2
Answers
The general solution of the given equation is y² = 8x²Inx + cx².
Linear first order differential equation:A first-order linear differential equation is one that has the formula:
[tex]\frac{d y}{d x}+p(x) y=q(x)[/tex]
where p(x) and q(x) are continuous functions of x.
We begin by determining the integrating factor for the first-order linear differential equation.
I.F. = [tex]e^{\int p(x) d x}[/tex]
The solution to the first order linear differential equation is:
[tex]y \cdot e^{\int p(x) d x}=\int q(x) \cdot e^{\int p(x) d x} d x+c .[/tex]
Where c is the constant of integration.The solution to the first order linear differential equation is:
[tex]\int \frac{1}{x} d x=\ln x+c[/tex]
Where c is the constant of integration.So, given: [tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
The above differential equation can be written as:
[tex]\begin{aligned}&\frac{d y}{d x}=4 \frac{x}{y}+\frac{y}{x} \\&\frac{d y}{d x}-\frac{y}{x}=\frac{4 x}{y} \\&y \frac{d y}{d x}-\frac{y^2}{x}=4 x\end{aligned}[/tex]
Substitute, [tex]y^2=t, 2 y \frac{d y}{d x}=\frac{d t}{d x}[/tex].
[tex]\begin{aligned}&\frac{1}{2} \frac{d t}{d x}-\frac{t}{x}=4 x \\&\frac{d t}{d x}-\frac{2 t}{x}=8 x\end{aligned}[/tex]
Because this is a first-order linear differential equation, we must first determine the integrating factor:
[tex]\text { I. F. }=e^{-2 \int \frac{1}{x} d x}=e^{-2 \ln x}\\\text { I.F. } F=\frac{1}{x^2}[/tex]
As a result, the following is the general solution to the given IVP:
[tex]$$t \cdot(I . F .)=\int(I . F .) \cdot 8 x d x+c$$$t \cdot\left(\frac{1}{x^2}\right)=\int\left(\frac{1}{x^2}\right) \cdot 8 x d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \int \frac{1}{x} d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \ln x+c$$t=8 x^2 \ln x+c x^2$[/tex]
By reversing the value of t:
[tex]y^2=8 x^2 \ln x+c x^2[/tex]
We now test the solution by substituting [tex]y^2=8 x^2 \ln x+c x^2[/tex] it in the original differential equation.
[tex]\begin{aligned}&\frac{d}{d x}\left(y^2\right)=\frac{d}{d x}\left(8 x^2 \ln x+c x^2\right) \\&2 y \frac{d y}{d x}=16 x \ln x+8 x+2 c x \\&\frac{d y}{d x}=\frac{16 x \ln x+8 x+2 c x}{2 y} \\&\frac{d y}{d x}=\frac{8 x \ln x+4 x+c x}{y}\end{aligned}[/tex]
We calculated the value of [tex]y^2[/tex] and [tex]\frac{d y}{d x}[/tex] from the original differential equation:
[tex]\begin{aligned}&\frac{8 x \ln x+4 x+c x}{y}=\frac{4 x^2+8 x^2 \ln x+c x^2}{x y} \\&8 x \ln x+4 x+c x=8 x \ln x+4 x+c x .\end{aligned}[/tex]
Therefore, the general solution of the given equation is y² = 8x²Inx + cx².
Know more about differential equations here:
https://brainly.com/question/1164377
#SPJ4
The complete question is given below:
For the following ODE, find a general solution, show the steps of derivation and check your answer by substitution.
[tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y
Answers
Lines can be perpendicular or parallel to one another.
The parallel line's equation is y = mx - am + c.The perpendicular line's equation is y = -(x/m) + a/m + c.What do we mean by linear equation?
A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.So,
A linear equation is written as: y = mx + b
Where, m = slope.
(A) Parallel equation:
The slope of a line parallel to y = mx + b is the same as the slope of y = mx + b, that is the slope is the equation in m.
The equation is then solved as follows:
y = m(x - x₁) + y₁Where:
(x₁,y₁) = (a,c)Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁ as follows:
y = m (x - a) + c
y = mx - am + c
So, the equation of a line is y = mx - am + c.
(B) Parallel equation:
The slope (m2) of a perpendicular line to y = mx + b is:
m₂ = -(1/m)The equation is then solved as follows:
y = m₂(x - x₁) + y₁Where:
(x₁,y₁) = (a,c)m₂ = -(1/m)Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁
y = -(1/m)(x - a) + cy = -(x/m) + a/m + cThe perpendicular line's equation is y = -(x/m) + a/m + c.
Therefore, lines can be perpendicular or parallel to one another.
The parallel line's equation is y = mx - am + c.The perpendicular line's equation is y = -(x/m) + a/m + c.Know more about the linear equation here:
https://brainly.com/question/2030026
#SPJ4
The correct question is given below:
Find the equations for the lines through the point (a,
c.that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. use y for the dependent variable and all letters in lower case.
what is the value of a?
A.-16
B.-3
C.3
D.16
Answers
Answer:
Which equation do I refer to?
Step-by-step explanation:
1/3 x =5 solved, please help me if anyone can! :)
Answers
If you meant ACTUALLY 1/3 x =5, both equations 1/3x = 5 and 1/3 x =5 are both equally x = 15
solve the literal equation for y
4x+1=9+4y show steps please i am confused
Answers
The solution to the literal equation is y = x - 2.
What is the solution to inequality?To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.
From the given information:
4x + 1 = 9 + 4y
To solve for y, we have to switch the sides:
9 + 4y = 4x + 1
Subtract 9 from both sides
9 - 9 + 4y = 4x + 1 - 9
4y = 4x - 8
Divide both sides by 4
[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]
y = x - 2
Learn more about inequality here:
https://brainly.com/question/24372553
#SPJ1
Does the figure below appear to have line symmetry if so how many lines of symmetry
Answers
11. The following describes the United States nuclear stockpile from
1944 to 1974. From 1944 to 1958, there was a gradual increase in the
number of warheads from 0 to about 5000. From 1958 to 1966, there
was a rapid increase in the number of warheads to a maximum of
about 32,000. From 1966 to 1970, there was a decrease in the number
of warheads to about 26,000. Finally, from 1970 to 1974, there was
a small increase to about 28,000 warheads. Sketch a graph of the
function.
10.
Answers
nxhudkdodisuhaiioavsbos
The sum of 2, 6, and a number amounts to 15. Find the number.
Answers
2 + 6 + n = 15
We can solve this using steps:
1. Simplify
8 + n = 15
2. Subtract 8 from both sides
(8 - 8) + n = 15 - 8
3. Simplify
n = 7
Let’s plug in 7 to see if it makes sense:
2 + 6 + 7 = 15
Because this equation is true, we have found our number.
Our unknown number is 7.
the lcm of (1/√2) + (1/√2)
Answers
Answer: LCM would be [tex]\sqrt{2}[/tex]
Step-by-step explanation:
First we need to find number of which we need to find lcm
here we dont have any two number but operator (+) is present
so
first we need to solve this operation
=1/[tex]\sqrt{2}[/tex] + 1/[tex]\sqrt{2}[/tex]
=[tex]\sqrt{2}[/tex]
so lcm of [tex]\sqrt{2}[/tex] would be [tex]\sqrt{2}[/tex].
Learn more about lcm here
https://brainly.com/question/28492379
#SPJ9
Laila needs 6 1/4 feet of chain to complete a project an outdoor project. She has two small pieces measuring 1 1/4 feet and 2 1/2 feet. How many feet of chain does laila need to purchase?
Answers
First you want to make the fractions have equal denominators. So you want to convert 1/2 to 2/4. Now you can add 1 1/4 to 2 2/4. After adding that subtract it from 6 1/4. Whatever your answer is will be how much more she needs.
We know circle A is a congruent to circle B because
Answers
Since the radii of Circle A and Circle B are the same length, we know they are congruent.
What is defined as the congruent circles?Congruency is a geometric term that refers to objects that share the same size and shape (dimension).
Two circles, as well as other geometrical shapes such as triangles, quadrilaterals, or polygons, can be congruent. The center and radius of a circle are the two properties that define it. Because congruency is independent of location and then a circle remains the same irrespective of rotation and reflection, the radius of a circle determines its congruence.Again, because a radius 'r' is a constant (its value does not change) and is only equal to some other constant, all circles that have the same radius (and any value dependent on radius) are congruent to each other.For the given two circles, A and B are said to be congruent if the radii of both the circles are equal.
Thus, for circles to be congruent, the radii must be equal.
To know more about the congruent circles, here
https://brainly.com/question/12044225
#SPJ9
An inductive proof that p(n) is true for all n always starts with the base case. what is the base case?
Answers
The base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
What is Mathematical Induction?Mathematical induction refers to a strategy for demonstrating a theorem's correctness by first demonstrating that, if it holds true in one particular situation, it will also hold true in all subsequent cases in the series.
Now,
The proof of mathematical induction is based upon showing the given expression true for one value, assuming that it will be true for some other value and finally proving that it will be true for all the values.The base case is the proof for which the expression is showed to be true in the beginning.In general cases, this initial value is 1 when the expression is defined for the values of variables belonging to Natural Numbers, i.e., the proof starts by showing that the given expression is true for the value of variable = 1.Hence, the base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
To learn more about Mathematical induction, refer to the link: https://brainly.com/question/24672369
#SPJ4
A random sample of 10 subjects have weights with a standard deviation of kg. What is the variance of their weights? be sure to include the appropriate units with the result.
Answers
The variance of their weights is 128.87270 kg².
It is required to find the variance of their weights.
What is standard deviation ?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Let n=sample size=10 subjects
Standard deviation=11.352211.3522 kg
Using this formula
Variance=(Standard deviation)²
By the formula we get,
Variance=(11.352211.3522 kg)²
Variance=128.87270 kg²
Therefore, the variance of their weights is 128.87270 kg².
Learn more about standard deviation here:
https://brainly.com/question/16555520
#SPJ4
3. the difference of two-thirds of a number x and
6 is at least -24. which inequality represents all
possible values for x?
Answers
The inequality which represents all the possible values for x is (2x/3) - 6 ≥ 24.
It is given in the question that the difference of two-thirds of a number x and 6 is at least -24.
We have to find the inequality which represents all the possible values for x.
In mathematics, Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Hence, according to the data given in the question, we can write,
(2x/3) - 6 ≥ 24
Here, we can also find the possible values of x.
(2x/3) - 6 ≥ 24
2x/3 ≥ 24 + 6
2x/3 ≥ 30
x ≥ 30*3/2
x ≥ 45
Hence, every number greater than or equal to 45 will be a possible value of x.
To learn more about inequality, here:-
https://brainly.com/question/20383699
#SPJ4
Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.
In triangle TRS, VZ = 6 inches. What is RZ?
Answers
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The centroid Z of the triangle TRS. Line sections TW, RV, and SU are created by drawing lines from every point to the center of the opposing side.
We know that the centroid divides the median of the triangle in a ratio of 2: 1.
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be
RZ / ZV = 2 / 1
RZ / 6 = 2
RZ = 6 x 2
RZ = 12 inches
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
Simplify this expression
12g+9g
Answers
Answer:
21g
Step-by-step explanation:
12 + 9 = 21 then add the variable.
After Simplify this expression 12 g + 9 g. We get, 21g.
To simplify this expression
12 g + 9 g,
Add ( 12 + 9) ,which is 21
So, 12 g + 9 g = 21 g.
Therefore, the final answer is 12 g + 9 g = 21 g.
Learn more about expression here;
https://brainly.com/question/28519328
#SPJ6
How to right 730,812 in word form
Answers
Step-by-step explanation:
seven-hundred thirty thousand eight-hundred twelve
Rubén put an empty cup underneath a leaking faucet after 1 1/2 hours Ruben had collected 1/4 cup of water. What is the rate in cups per hour at which the water is leaking from the faucet
Answers
The rate of water leaking from the faucet is 0.167 cups per hour.
What is defined as the flow rate?The volume of fluid which flows through with a given cross-sectional unit of time is defined as flow rate.The volume per time unit offered to the flow of gases or even other fluid substances that emerge from an orifice, pump, turbine, or pass through a conduit or channel is referred to as flow rate.For, the given question;
Divide the amount of water accumulated by the number of hours to find the rate that the water is leaking out from faucet.
Let 'r' be the flow rate.
The formula for flow rate is;
Flow rate = volume / time
r = 0.25 cup / 1.5 hours
r = 0.167 cup/hour
As a result, the rate of water leaking from faucet is roughly equivalent to 0.167 cup/h.
To know more about the flow rate, here
https://brainly.com/question/1154328
#SPJ9
A water well drilling rig has dug to a height of -30 feet after one full day (24 hours),of continuous use. assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours (5/8 days)?
Answers
The Height of the drill after 15 hours was 18.75 feet deep or (-18.75) feet.
Given that in 24 hours
the water well drilling rig dig -30 feet .
we know that ,
24 hours = 1 day
So,
1 hour =1/24 day
15 hours = [tex]\frac{15}{24} =\frac{5}{8} day[/tex]
Now according to the question ,
in 1 day the drilling rig dug -30 feet
So in [tex]\frac{5}{8} day[/tex] the drilling rig will dig =[tex]\frac{5}{8} *(-30)=-18.75feet[/tex]
in 15 hours (5/8 days ) drilling rig dig -18.75 feet.
Therefore , The Height of the drill after 15 hours (5/8 days) was 18.75 feet deep or (-18.75) feet.
Learn more about Ratio here https://brainly.com/question/17423776
#SPJ4
Three angles are shown, ZHRM, ZHRD, and ZDRM.
D
M
H
If m/HRM = 54°, m/HRD =
m/DRM =
(²7*+11) ².
4
R
(1/22 +22), ar
x
and
what is the value of x?
Answers
Answer:
28
Step-by-step explanation:
By the angle addition postulate,
[tex]54=\frac{1}{2}x+22+\frac{1}{4}x+11 \\ \\ 54=\frac{3}{4}x+33 \\ \\ 21=\frac{3}{4}x \\ \\ x=28[/tex]
Go to school kid and pay attention
Answers
help a soon as possible i don't know how to work this out
Answers
Answer:
the answer of finding highest common factor is 286286
Answer:
24167 ( or 11 x 13^3)
Step-by-step explanation:
x = 2 x 7 x 11 x 11^2 x 13^3 x 13^2
y = 3 x 11 x 13^3
The underlined are common factors of x and y
11 x 13^3 = 24167 is the GCF
The domain and the range of the reciprocal function are the set of all real numbers. True or false?.
Answers
False. All real numbers, with the exception of 0 because f (0) = 1 0, fall inside the reciprocal function's domain and range. Y cannot be 0 if x cannot, either.
What are real numbers?In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are used in measurements of continuously varying quantities such as size and time. They are distinguished from imaginary numbers, which use the symbol I or the square root of 1, by the word "real." A complex number has a real (1) and an imaginary I component, like 1 + i. The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.
Contrary to rational numbers, whose decimal expansions always contain a digit or group of digits that repeats itself, such as 1/6 = 0.16666... or 2/7 = 0.285714285714, irrational numbers have decimal expansions that do not repeat themselves. Since there is no regularly repeating group in the decimal produced as 0.42442444244442, it is irrational.
To learn more about the, real numbers visit:
https://brainly.com/question/9876116
#SPJ4
HELP PLEASE! Use the diagram below to analyze another student's work.
S
80°
45°
Nathan stated that angle q is 20 degrees because 80 degrees + 20 degrees = 100
degrees. Straight lines are measured as 100 degrees.
Did Nathan correctly calculate the measurement for angle q? Justify your answer
1pt for identifying if Nothan was
correct or not
2pts for justification
Answers
Answer: No, Nathan didn't measure angle correctly
Step-by-step explanation:
The sum of angles that are formed on a straight line is equal to 180°
So the value angle q is 80° because the sum of angle q and 100° is 180°
∠q+100°=180°∠q= 180°-100°
∠q= 80°
No, Nathan didn't measure angle correctly.
learn more about angles on brainly.com/question/13954458
#SPJ9
2x+3=7
this equation has multiplication and addition in it. to solve this equation you need to get x by itself which means you need to get 2x by itself first. how can you do this?
Answers
Answer:
Subtract 3 from both sides.
Step-by-step explanation:
Doing this will leave 2x by itself.
Answer:
read below
Step-by-step explanation:
2x + 3 = 7
To isolate 2x, subtract 3 from both sides of the equation.
[tex]2x + \frac{3}{-3} = \frac{7}{-3}[/tex]
3 - 3 = 0
7 - 3 = 4
[tex]2x = 4[/tex]
divide both sides by 2
[tex]x = 2[/tex]