6 Equations of parallel and perpendicular lines VEB
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
y = 4/9x +10/3
Step-by-step explanation:
You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.
Slope-intercept equationThe slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . m is the slope, b is the y-intercept
In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.
SlopeThe slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.
The slope of the perpendicular line is the opposite reciprocal of this:
m = -1/(-9/4) = 4/9
Y-interceptSolving the slope-intercept form equation for b, we find ...
b = y - mx
Using the values of x and y for the given point, and the slope we just found, we have ...
b = 2 -(4/9)(-3) = 2 +4/3 = 10/3
Desired equationThe slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...
y = 4/9x +10/3
__
Additional comment
It can also be useful to start from the point-slope equation:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Your line is ...
y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)
y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify
Related Questions
A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store.Use the results to determine how many people use Redbox.60 only use Netflix64 only use Redbox24 only use a video store 8 use only a video store or Redbox38 use only Netflix or Redbox 35 use only a video store or Netflix5 use all three24 use none of these
Answers
SOLUTION
We will use a Venn Diagram for this problem.
Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below
From the Venn Diagram above, the number in each part of a circle, represents the information
Now, how many people use Redbox?
The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have
[tex]n(R)=38+64+5+8=115[/tex]Hence the answer is 115
what is the volume of a cube with sides 3 cm.be sure to include correct units with your answer
Answers
Answer:
27 cubic feet
Explanation:
The volume of a cube with side length L is given by
[tex]V=L^3[/tex]Now in our case, L = 3 ft; therefore, the volume is
[tex]V=3^3[/tex]which simplifies to give
[tex]\boxed{V=27\text{ ft}^3.}[/tex]which is our answer!
Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.
Find the measures of an interior angle and an exterior angle of the indicated regular polygon. Regular 20-gon interior angle exterior angle
Answers
consider the function f(x) = x^1/2 and the function G, shown below. g(x)= f(1/4 • x) = (1/4 •x)^1/2how will the graph of the function g differ from the graph of the function f?
Answers
ANSWER
The graph of function g is the graph of function f stretched horizontally by a factor of 4.
EXPLANATION
Function g(x) is a transformation of function f(x), obtained by multiplying the variable, x, by 1/4. This is described as a horizontal stretch by a factor of 4.
Hence, the graph of function g is the graph of function f stretched horizontally by a factor of 4.
How to graph this and how to solve the equation
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The graphs of the two equations:
[tex]\begin{gathered} y=\text{ }\frac{-1}{5}x\text{ - 6} \\ y=\text{ }\frac{3x}{5}-\text{ 2} \end{gathered}[/tex]is as follows:
CONCLUSION:
From the graphs above, we can see that the solution to the graphs is:
[tex](x,\text{ y \rparen = \lparen - 5, - 5\rparen}[/tex]When water flows across farmland, some of the soil is washed away, resulting in erosion. Researchers released water
across a test bed at different flow rates and measured the amount of soil washed away. The following table gives the
flow (in liters per second) and the weight (in kilograms) of eroded soil:
Answers
The correlation coefficient between flow rate and amount of eroded soil is:
0.967.
Correlation coefficientsThe correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.
If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.
Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:
(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).
Using a calculator, the coefficient is given as follows:
0.967.
Hence the last option gives the correct coefficient.
Missing informationThe complete problem is given by the image at the end of the answer.
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Swine Flu is attacking Springfield. The function below determines how many people have swine where t=time in days and S=the number of people in thousands.
Answers
A.find s(4)
[tex]\begin{gathered} s(4)=9(4)-4 \\ s(4)=36-4 \\ s(4)=32 \end{gathered}[/tex]B. means that in 4 days there will be 32000 infected people
C. find t to S(t)=23
[tex]\begin{gathered} 23=9t-4 \\ 9t=23+4 \\ t=\frac{27}{9} \\ t=3 \end{gathered}[/tex]D. means there will be 23,000 infected people after 3 days
E. Graph
to draw the line we need two points which we already have but we will add another to make a table of 3 values the new value is t=1
[tex]\begin{gathered} s(1)=9(1)-4 \\ s(1)=5 \end{gathered}[/tex]table
graph
A number between 280 and 380 when rounded to the nearest hundred is 45 less than the original number what number is the original number
Answers
If the unknown number is an integer between 280 and 349;
When rounded to the nearest hundred, the unknown number is 300.
If the unknown number is an integer from 350-380;
When rounded to the nearest hundred, the unknown number is 400.
If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.
But;
[tex]300+45=345[/tex]When 345 is rounded to the nearest hundred, it is 300.
And the difference between the approximated value and the original value is 45.
Hence, 345 is the original number.
CORRECT ANSWER: 345
10. If you invest $2000 at 6% compounded monthly, how long will it take the account to double in
value?
Answers
If I invest $2000 at 6% interest compounded monthly, it will take 11.58 years by the account to double in value.
What is compound interest?
The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the lent capital rather than paid out, or required to be paid by the borrower, resulting in interest being created the next period on the principal amount plus any accrued interest. Compound interest is a prominent concept in finance and economics.
The initial investment of $2000 at 6% compounded monthly.
Since, the interest rate of 6% is compounding monthly, then the effective annual interest rate will be
= (1+)−1i = (1+rm)m−1
Here, r = interest rate in decimals
= (1+0.0612)12−1i = (1+0.0612)12−1
= 0.061678i = 0.061678
= ×100 = 6.1678%
Now, we are using Rule 72 to calculate the doubling time
Time to double the initial amount = 72 /effective annual interest rate
Time to double the initial amount = 11.58 years
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Pizza House offers 4 different salads, 5 different kinds of pizza, and 3 different desserts. How many different three course meals can be ordered?...Question content area rightPart 1How many different meals can be ordered?enter your response here
Answers
A three-course meal will contain 1 pizza, 1 salad, and 1 dessert.
The question tells us that there are 4 different salads, 5 different pizzas, and 3 different desserts.
Therefore, the total number of possible ways a three-course meal can be served is calculated as the product of all the numbers. This is shown below:
[tex]\Rightarrow4\times5\times3=60[/tex]60 different meals can be ordered.
Becky borrowed $580.00 from the bank. The loan had a 13.5% simple
annual interest rate, and she paid off the bill over 18 months. What was
the total amount, including interest, Becky paid for the loan?
Answers
Work Shown:
P = 580
r = 0.135
t = 18 months = 18/12 = 1.5 years
A = P*(1+r*t)
A = 580*(1+0.135*1.5)
A = 697.45
Use the given rounded values, the properties of logsand your knowledge of logarithmic functions to find thevalue of each log expression. Show your work.
Answers
We want to find the value for
[tex]\log _425[/tex]To do that, first let's rewrite this expression as
[tex]\log _425=\log _45^2[/tex]Using the following property
[tex]\log _ab^c=c\log _ab[/tex]We can rewrite our expression as
[tex]\log _45^2=2\log _45[/tex]Using the given value on the text, we get our answer
[tex]\log _425=2\log _45=2\cdot1.2=2.4[/tex]Which statement explains whether x=5 is the solution to 5x + 2 = 27? a. Yes, because 5x means x=5.b. No, because 5x doesn't mean x=5.c. No, because when x is replaced by 5 the equation is false. d. Yes, because when x is replaced by 5 the equation is true.
Answers
Given
x = 5
5x + 2 = 27
Procedure
d. Yes, because when x is replaced by 5 the equation is true.
What are the solutions to the equation (x − 21)2 = 25?x= x=
Answers
SOLUTION:
Case: Quadratics equation
Method:
[tex]\begin{gathered} (x-21)^2=25 \\ TakeSquarerootsOfBothSides \\ x-21=\sqrt{25} \\ x-21=\pm5 \\ x=21\pm5 \\ x=21+5\text{ }or\text{ }x=21-5 \\ x=26\text{ }or\text{ }x=16 \end{gathered}[/tex]Final answer:
x= 16
x= 26
20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
Answers
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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Question 5The table below shows the coordinates of a figure that was transformed.Pre-ImageImageA(5,2)B(6, 1)A'(0,0)B'(1, -1)C'(-1,3)C(4,5)Which is a correct description of the transformation?
Answers
You have the following A, B and C points, which are transformed to the points A', B' and C', jus
How come my answer is wrong? It says it’s equal to the correct answer but it’s not the right answer.
Answers
The Adventure Club has scheduled a trip to hike a nearby mountain. Since the group started hiking, they gained 456 feet in altitude from their start position. The current altitude is 437 feet, but there is no record of their starting altitude.write a equation to represent this situation Explain what your variable representssolve your equation please someone help me ill give you a star anything please ♡
Answers
Let h be the altitude of the starting position.
Since the group has gained 456 feet from the start position, then the current altitude is:
Refer to the diagram below to prove that the exterior angle equals the
Answers
To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:
1.- the inner angles of a triangle add up 180 degrees
2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3+\measuredangle4=180^{\circ} \\ \Rightarrow \\ \measuredangle1+\measuredangle2+\measuredangle3=\measuredangle3+\measuredangle4 \\ \Rightarrow \\ \measuredangle1+\measuredangle2=\measuredangle4 \end{gathered}[/tex]Answer:
They are linear pair and therefore supplementary.
Triangle sum theorem.
Substitution.
Subtraction property of equality.
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month
Answers
Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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Determine the angle of rotation of the conic section given by: 32x2 +50xy + 7y2 = 100 (round your answer to the nearest tenth of adegree).
Answers
The formula to obtain the angle of rotation is as follows:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Compare the given equation to the general equation of a conic.
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]Thus, the values of A, B, and C are as follows.
[tex]\begin{gathered} A=32 \\ B=50 \\ C=7 \end{gathered}[/tex]Substitute the values into the equation.
[tex]\begin{gathered} \cot 2\theta=\frac{32-7}{50} \\ \cot 2\theta=\frac{25}{50} \\ \cot 2\theta=\frac{1}{2} \end{gathered}[/tex]Find the value of the θ.
[tex]\begin{gathered} \frac{1}{\tan 2\theta}=\frac{1}{2} \\ \tan 2\theta=2 \\ 2\theta=\tan ^{-1}(2) \\ 2\theta\approx63.4349 \\ \theta\approx31.7 \end{gathered}[/tex]#8 help with algebra 2 question. That’s the only picture I have. I tried writing it out.
Answers
Solution:
Given a cosine function graph;
The general cosine function is
[tex]y=A\cos(Bx-C)+D[/tex]Where
[tex]\begin{gathered} A\text{ is the amplitude} \\ Period=\frac{2\pi}{B} \\ C\text{ is the phase shift} \\ D\text{ is the vertical shift} \end{gathered}[/tex]From the graph,
The midline is y = 1
The amplitude, A, is
[tex]\begin{gathered} A=4-1=3 \\ A=3 \end{gathered}[/tex]The amplitude, A is 3
Where,
[tex]\begin{gathered} Period=12 \\ Period=\frac{2\pi}{B} \\ 12=\frac{2\pi}{B} \\ Crossmultiply \\ 12B=2\pi \\ Duvide\text{ both sides by 12} \\ \frac{12B}{12}=\frac{2\pi}{12} \\ B=\frac{\pi}{6} \end{gathered}[/tex]The phase shift, C = 0, and the vertical, D, is 1
Thus, the equation of the graph is
[tex]\begin{gathered} y=A\cos(Bx-C)+D \\ Where \\ A=3 \\ B=\frac{\pi}{6} \\ C=0 \\ D=1 \\ y=3\cos(\frac{\pi}{6}x)+1 \end{gathered}[/tex]The graph is shown below
Hence, the equation is
[tex]y=3\cos(\frac{\pi}{6}x)+1[/tex]kindly asking for help to clarify this question and mathematical problem .
Answers
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
At which of the following points do the two equations f(x)=3x^2+5 and g(x)=4x+4 intersect?A. (0,5)B. (1,8)C. (0,4) D. (8,1)
Answers
Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
rewrite 2x+5y=10 in slope intercept form then graph them
Answers
The slope intercept of a line is:
[tex]y=mx+b[/tex]We re-write the equation given:
[tex]\begin{gathered} 2x+5y=10 \\ 5y=-2x+10 \\ y=\frac{-2x+10}{5} \\ y=\frac{-2x}{5}+\frac{10}{5} \\ y=-\frac{2}{5}x+2 \end{gathered}[/tex]The graph of this line is shown below:
Is P(A and B) ≠ 0? Explain.
A.) No. P(A and B) = 0.
B.) Yes. Even if P(A) = 0 or P(B) = 0, P(A and B) will always be non-zero.
C.) No. Because both P(A) and P(B) are not equal to 0, P(A and B) = 0.
D.) Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. (b)
Answers
The right option is D as P(A and B) ≠ 0 only for the independent probability events for A and B.
What is an independent event in probability?Two events say A and B are said to be independent if the probability of the intersection of A and B is equal to the product of their respective probability, But same events are said to be mutually exclusive if the probability of the intersection of A and B is equal to zero(0).
In the given question, P(A and B) ≠ 0 can only be true if A and B are independent event and P(A) and P(B) are not equal to zero such that
P(A and B)=P(A)× P(B)≠ 0.
Hence, we can deduce from the axiom of independent events of probability that because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0.
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divide the sum of z and 3 by 7
Answers
Answer:
4 divide the sum of z and 3 by 7
Step-by-step explanation:
z+3=7
or,z=7-3
or,z=4
i need help solving this and also what does the 2 that's on the top of some letters mean
Answers
given the expression :
[tex]a-bc^2[/tex]We need to evaluate the expression when :
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-1 \end{gathered}[/tex]So, substitute with a , b and c at the expression
The result will be :
[tex]\begin{gathered} a-bc^2 \\ =3-2\cdot(-1)^2 \\ =3-2\cdot1 \\ =3-2 \\ \\ =1 \end{gathered}[/tex]There is another expression :
[tex]c^2+a^2b[/tex]By substitute with the values of a, b and c
so, the result will be :
[tex]\begin{gathered} c^2=(-1)^2=1 \\ a^2=3^2=9 \\ \\ c^2+a^2b=1+9\cdot2=1+18=19 \end{gathered}[/tex]covert 6\10 into decimal number and then see if it's a repeating or terminating
Answers
We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:
We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:
[tex]0.6\times10=6[/tex]Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.
A basketball player scored 24 times during one game. she scored a total of 38 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
Answers
The number of two-points shots made is 14
The number of free throws made is 10
What is the number of two-points shots and free throws made?The first step is to formulate a set of linear equations that represent the information in the question:
x + y = 24 equation 1
2x + y = 38 equation 2
Where:
x = number of two-point shots made y = number of free throws madeThe linear equations would be solved using the elimination method.
In order to determine the value of x, take the following steps:
Subtract equation 1 from equation 2
x = 14
Substitute for x in equation 1
14 + y = 24
Combine similar terms:
y = 24 - 14
Add similar terms together
y = 10
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation: