The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
[tex]y-y_1=m(x-x_1)[/tex]where m = slope.
[tex]\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}[/tex]Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Step-by-step explanation:
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)
where m = slope.
\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}
y−(−13)=
2
1
(x−0)
y+13=
2
1
(x)
y=
2
1
x−13
Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Sammy is 5 years younger than twice Lizzy's age. Sammy os 15 years old. How old is Lizzy?
Answer:
Lizzy is 40
Step-by-step explanation:
15 + 5 + 20
20 x 2 = 40
Answer:
35
Step-by-step explanation:
15 x 2= 30 + 5=35
the five is because he is 5 years younger than lizzy
adding to her age
I need to write to objective function and the constraints
Let's define:
x: number of Traveler bicycles made
y: number of Tourister bicycles made
The objective function is:
Maximize 300x + 600y
Subject to the following restrictions:
x + y ≤ 300
x + 3y ≤ 360
PLEASE HELP URGENT:
Graph the following function:
y=3sin(2x−π/2)−2
Drag the black dot to shift your graph in the desired direction. Use the blue draggable dot to change the period. Drag the orange dot to change the amplitude and/or reflect with respect to the x-axis. The horizontal distance between the vertical dotted green lines corresponds to one period.
A graph of this sine wave function y = 3sin( 2x + π/2) - 2.
A sine wave, also known as a sinusoidal wave or simply a sinusoid in mathematics, is a basic waveform that is frequently employed to describe periodic oscillations, with each interval's displacement amplitude being directly proportional to the sine of the displacement's phase angle.
This mathematical expression can be used to model or depict a sine wave mathematically:
y = asinbx
Where a represents the amplitude of a sine wave, b represents the periodicity.
After that, we would use the lowest common denominator (LCM) to solve the sine wave function given:
y = 3sin( 2x - π/2 ) - 2
y = 3sin( ( 2(2x) - π)/2) - 2
y = 3sin( ( 4x - π)/2 ) - 2
In conclusion, this sine wave function has an amplitude of 3 and a periodicity is 2.
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find the radius of the circle given the central angle and the area of the Shaded sector
we have the following formula for the area of a sector of a circle:
[tex]A_s=\frac{\theta\cdot\pi}{360}\cdot r^2_{}[/tex]In this case, we have the following information:
[tex]\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}[/tex]then, using the formula and solving for r, we get the following:
[tex]\begin{gathered} 60\pi=\frac{24\cdot\pi}{360}\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=\frac{21600\pi}{24\pi}=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}[/tex]therefore, the measure of the radius is r = 30
discriminant of the equation x squared minus 5x equals -2 is
Recall that the "discriminat" of a quadratic equation of the form:
a x^2 + b x + c = 0
is given by the formula: b^2 - 4 a c
So for our equation:
x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:
x^2 - 5 x + 2 = 0
Now we recognize:
a = 1
b = - 5
c = 2
and write the discriminant
b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17
Then, the discriminat of the equation is: 17.
Ben has a 6 3/5 pound bag of granola. He wants to give his friends 3/4 pound of granola each. To how many friends can Ben
give granola?
Answer:21 to each of his 3 friends
Step-by-step explanation:
Equation fraction X over 9 equals 7
Answer:
x/9= 7
×ing by 9 on both sides
x=9×7
x=63
Step-by-step explanation:
I need to know the answer for this question?
The probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So,
Red socks: 10White socks: 6Blue socks: 8Total number of socks: 10 + 8 + 6 = 24
Formula: P = favourable events/Total number of events
Probability of picking a blue sock first:
P = 8/24P = 1/3Probability of picking a white sock at second:
P = 6/24P = 1/4Therefore, the probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
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Find the cos equation given amplitude: 6, period: 2π, vertical shift: 0, and horizontal shift:OA. y = 6 cos 0 + 2OB. y = 6 cos 0 - 2OC. y = 6 cos (0+²)OD. y = 6 cos (0-3)Reset Selection2T3
Given: A cosine function with amplitude: 6, period: 2 pie, vertical shift: 0, and horizontal shift-
[tex]\frac{2\pi}{3}[/tex]Required: To determine the function.
Explanation: The cosine function is defined as-
[tex]y=Acos(Bx-C)+D[/tex]where
[tex]\begin{gathered} A=Amplitude \\ \frac{2\pi}{B}=Period \\ \frac{C}{B}=Phase\text{ shift} \\ D=Verical\text{ shift} \end{gathered}[/tex]Hence, the required function is-
[tex]y=6cos(x-\frac{2\pi}{3})+0[/tex]Final Answer: The function is-
[tex]y=6cos(x-\frac{2\pi}{3})[/tex]Hence, Option D is correct.
5LATR이S20What is the value of sinEnter an exact value or round to the nearest hundredth.(5)
Sine:
[tex]\sin (x)=\frac{opposite}{hypotenus}[/tex]Using the calculator (in radians), we can get the value:
[tex]\sin (\frac{\pi}{3})\approx0.87[/tex]question will be in picture
ANSWER:
C. 50 fewer people will attend for every dollar the admission price increases.
STEP-BY-STEP EXPLANATION:
The equation in its slope and y-intercept form is as follows
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We have the following equation
[tex]n=800-50p[/tex]We can see that in this case the slope is - 50, therefore the answer would be 50 fewer people will attend for every dollar the admission price increases.
my questions is about. latitude and longitude
Answer
Option B is correct.
The latitude and longitude of the point X is 42.5°N, 77.5°W
Hope this Helps!!!
If r is 2 and s is 3 How do I work this problem 2(r s)+4(x)
The value of the expression 2(r+s)+4(x) when r = 2 and s = 3 is 4x + 10.
What is an expression?An expression is written in terms of variables and constants separated by the operation of addition and subtraction. Expressions can be of many types some of them are algebraic expressions, logarithmic expressions, etc.
Given r = 2 and s = 3, we know substitution in which we replace variables with certain numerical values in an expression.
Given 2(r+s)+4(x). ( we'll replace the numerical values of r and s in the
expression).
∴ 2(2+3)+4(x).
2(5)+4x.
10 + 4x, Or
4x + 10.
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What is g(f(x)) if f(x) = 3x + 2 and g(x) = -2x + 4?
⇒g(f(x)) means that in the function g(x) insert/plug in what f(x) is equal to in the place of x. f(x)= 3x+2 meaning in the place of x in g(x) insert 3x+2 and simplify.
[tex]g(f(x))=-2(3x+2)+4\\g(f(x))=-6x-4+4\\g(f(x))=-6x[/tex]
Attached is the solution of what g(f(x)) is equal to.
PLS HELP ME WITH THIS
Equation of the line in slope-intercept form = y = 8x − 1
How to calculate the equation of the line?
Given:
Co-ordinates of the first line (x, y)=(0,-1), (1,7), (2,15), (3,23),(4,31)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{7+1}{1-0}\\\\=8[/tex]
The slope - intercept form of a line is given by,
y = mx + b ---(1)
Let us substitute ( x, y )= (0, -1) in (1)
-1 =(8)*0+b
-1= b
b = - 1 ----(2)
Let us substitute m and b in the slope-intercept equation (1)
y = 8x − 1
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solve the system of equations using elimination (1/2)x+(1/3)y=4(1/3)x+y=-2
EXPLANATION
Let's consider the system of equations:
(1) (1/2)x + (1/3)y = 4
(2) (1/3)x +
Find the domain and range of the following graph in interval notation. 5+ 4 3 2 1 -5 4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5+ a Domain: Range: NOTE: If you do not see an endpoint, assume that the graph continues forever in the same direction. Entry example: [2,3) or (-00,5). Enter -oo for negative infinity and oo for infinity.
The domain of the function of the graph is the set of all x values of the graph for which the function is defined.
The range of the function is the set of all y values shown in the graph.
Hence, the domain is (-∞, ∞)
The range is (-∞, 0].
Use the graph of the function below to answer the questions.i just need help with b and c
Answer:
a) Yes
b) -3, 0, 2
c) [-1, -3], [3, -4], [5, -1]
Explanation:
a) From the graph, we can see that f(3) = -4.
Therefore, f(3) is negative
b) From the graph, we can see that the values of x for which f(x) = 0 are -3, 0, and 2.
c) From the graph, we can see that the values of x for which f(x) < 0 are -1, 3, and 5.
Using the interval notation, we'll have [-1, -3], [3, -4], [5, -1]
Find the linear equation of the plane through the point (1, 3, 10) and parallel to the plane x+6y+2z+4=0
The most appropriate choice for equation of plane will be given by-
Required equation of plane is [tex]x + 6y +2z=39[/tex]
What is a plane?
A surface which is spanned by two linearly independent vectors is called a plane.
The general equation of plane is [tex]ax + by + c =d[/tex] where
[tex](a,b,c)[/tex] are the components of normal vectors.
Equation of the plane parallel to [tex]x + 6y +2z=-4[/tex] is
[tex]x +6y+2z=c[/tex] [As the perpendicular vector of two parallel planes are same]
The required plane passes through (1, 3, 10)
Putting [tex]x=1, y=3,z=10[/tex] in [tex]x + 6y+2z=c[/tex]
[tex]1 + 6 \times 3 + 2\times 10 = c\\1 + 18+20=c\\c=39[/tex]
So, Required equation of plane is [tex]x + 6y +2z=39[/tex]
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which coordinate is a solution to the system of inequalities
12 feet to how many meters
EXPLANATION
1 feet is equal to 0.3048 meters.
So, 12 feets will be equal to ---> 12*0.3048 = 3.6576 meters.
Answer: 12 feets are equal to 3.65
The system of equations y = -2 + 5 and y = x - 1 is graphed. What is the solution to
the system of equations?
(3,2)
(0,5)
3
2
4-5-3
234
(2, 3)
(1,0)
Given
We have the system of equations:
[tex]\begin{gathered} y\text{ = -x + 5} \\ y\text{ = x - 1} \end{gathered}[/tex]The solution to the system of equation as determined from the graph is the point where the two lines intersect
From the graph, we can determine the point of intersection to be (3, 2)
Answer: (3, 2) Option A
If there is more then one element in the set, separate them with commas
Answer:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
Explanation:
The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Then, the outcome for the event that the select number is 2 is
Event that the number chosen is 2 = {2A, 2B, 2C}
Therefore, the answers are:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
evaluate(if possible) the sine,cosine, and the tangent of the real number
A total of $7000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if the annual interest is $510?
The total invested = $7000
Part of the money at 7% and the reminder at 15%
Let the part at 7% = x
So, the part at 15% = 7000 - x
Given the annual interest = $510
so,
7% of x + 15% of ( 7000 - x ) = 510
0.07 * x + 0.15 * ( 7000 - x ) = 510
0.07 x + 0.15 * 7000 - 0.15 x = 510
0.07 x + 1050 - 0.15x = 510
0.07 x - 0.15 x = 510 - 1050
-0.08 x = - 540
divide both sides by -0.08
x = -540/-0.08 = 6,750
7000 - x = 7000 - 6750 = 250
So, the part that is invested at a rate of 7% = $6,750
And the part that invested at a rate of 15% = $250
Given rectangle ABCD, solve for x and y.
Answer:
x=20, y=10
Step-by-step explanation:
50=2x+y
3x+3y = 90
x+y = 30
x=30-y,
substitute x:
50=2(30-y)+y
50=60-y
y=10, x=20
:]
DeAndre is coding a program for a school project. He uses pre-built Python modules to save himself some time. But when he runs his program, he receives an error. What has he most likely done wrong?
A.
He has not saved his code before running it.
B.
He forgot to put the names of the modules in all uppercase letters.
C.
He forgot to import the library that the modules came from.
D.
He forgot to print the results of the modules.
The thing that he.has done regarding the program is A. He has not saved his code before running.
What is coding?The act of writing computer code using programming languages is referred to as coding. The websites, apps, and other technology we use on a daily basis are programmed using coding.
A series of instructions written in a programming language for a computer to follow is referred to as a computer program. Software, which also contains documentation and other intangible components, comprises computer programs as one of its components. Source code is a computer program's human-readable form.
It should be noted that the fact that he didn't save will lead to the error that was faced.
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I need a run down on how to do multi step equations.Number 3 only
Answer:
x=-7
Explanation:
Given the equation:
[tex]8x-2=-9+7x[/tex]To solve equations of this form, the goal is to try to bring all the terms containing the variable (letter x or any letter) to one side of the equation and the constants to the other side.
First, subtract 7x from both sides.
[tex]\begin{gathered} 8x\textcolor{red}{-7x}-2=-9+7x\textcolor{red}{-7x} \\ x-2=-9 \end{gathered}[/tex]Next, add 2 to both sides.
[tex]\begin{gathered} x-2+2=-9+2 \\ x+0=-7 \\ \implies x=-7 \end{gathered}[/tex]The value of x is -7.
solve for B 25+ 7/9=74
To solve this equation, we need to follow the next steps:
1. Subtract 25 to both sides of the equation:
[tex]25-25+\frac{7}{9}b=74-25[/tex][tex]\frac{7}{9}b=49[/tex]We obtained this result doing the corresponding operations (25 - 25 = 0), and (74 - 25 = 49).
2. Multiply by 9/7 to both sides of the equation:
[tex]\frac{9}{7}\cdot\frac{7}{9}b=\frac{9}{7}\cdot49\Rightarrow\frac{9}{9}\cdot\frac{7}{7}b=9\cdot\frac{49}{7}\Rightarrow b=9\cdot7\Rightarrow b=63[/tex]To check if the solution for this equation is b = 63, we can substitute this val
The functions rands are defined as follows.r(x)=32-4s(x) = -2x+4Find the value of s(r(-5)).s(r(-5)) = 00/0
With the use of factorization, we can state that s and r have values of -2 and 3, respectively.
What is factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a POLYNOMIAL) into a product of another entity, Or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring.The given values are
r(x)= 3x-4 s(x)= -2x+4Solving with the help of factotisation.
s(r(-5))(2x-4)(3x-4-5)2x+4(3x-9)6x² - 6x - 36Dividing the eqn by 6
x²-x-6taking common factors= x(x-3) + 2(x-3)(x+2)(x-3)x= -2,3hence,from above solving we can say that values of s and r are: 2,3
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