Answer:
[tex]y -10=\cfrac{2}{3} (x -5 )[/tex]========================
Given Two points: (5, 10) and (2, 8)To findThe point-slope form of the equation representing this lineSolutionPoint-slope form is:
[tex]y -y_1=m(x - x_1)[/tex], where (x₁, y₁) is one of the points and m is the slopeFind the slope:
[tex]m=\cfrac{y_2-y_1}{x_2-x_1} =\cfrac{8-10}{2-5} =\cfrac{-2}{-3} =\cfrac{2}{3}[/tex]Use one of the points and the slope to determine the equation of the line:
[tex]y -y_1=m(x - x_1)[/tex], substitute the slope and [tex]y -10=\cfrac{2}{3} (x -5 )[/tex]Answer:
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given: g(5)=10, and g(2)=8.
The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.
So, as points, the values are (5, 10), and (2, 8).
The equation wants to be written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
Solving SlopeWe first want to find the slope of the line.
The slope (m) can be found with two points using the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We can label the values of the points we were given.
[tex]x_1=5\\y_1=10\\x_2=2\\y_2=8[/tex]
Now, substitute these values into the formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{8-10}{2-5}[/tex]
Subtract.
[tex]m=\frac{-2}{-3}[/tex]
Simplify.
[tex]m=\frac{2}{3}[/tex]
The slope is 2/3.
Since we now have the value of the slope, as well as [tex](x_1, y_1)[/tex], we can plug these values into the formula for point-slope form.
Point-Slope FormRecall that [tex]x_1=5[/tex] and [tex]y_1=10[/tex]; plug these in for [tex]x_1[/tex] and [tex]y_1[/tex] respectively.
[tex]y-10=m(x-5)[/tex]
We also just found the slope, which is 2/3. Plug that in for m.
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Topics: Point-slope form, functions
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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
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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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 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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4. How many integers are in the solution set of the inequality x² - 10 ≤ 0?
(a)1
(b) 2
(c) 3
(d) 6
(e) 7
Answer: 7
Step-by-step explanation: There are an infinite number of integers that satisfy the inequality. There are only seven integers that don't satisfy the inequality which are -3, -2, -1, 0, 1, 2 and 3.
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
Given the function (f + g) (x) as
[tex]4x^2+x-7[/tex]The domain of the function above is the set of x values except the for x- values that will make the function undefined
For the function above, the domain is defined at all set of real numbers and the interval notation is given as
[tex]-\inftyHence, the correct option is BI 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
Chloe makes flapjacks.
A pack of flapjacks costs Chloe 60p to make.
She sells the flapjacks for a profit of 30%.
For how much does Chloe sell a pack of flapjacks?
Answer: 78p
Step-by-step explanation:
If she sells them with a profit of 30%, this means she is getting 30% more than they cost to make. They cost 60p, so we will set up an equation. Don't forget that a percent divided by 100 becomes a decimal.
60p * 130% = 60p * 1.3 = 78p
which coordinate is a solution to the system of inequalities
Out of Retries Correct Answer Show Enter an estimate. Round each mixed number to the nearest whole in your estimate. 1 WIN Estimate: 0 Find the difference and enter it in simplest form. 3
The mixed fraction are simplify as :
[tex]a\frac{b}{c}=\frac{(a\times c)+b}{c}[/tex]The given expression is :
[tex]5\frac{1}{4}-3\frac{8}{9}[/tex]Simplify the mixed fraction:
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{(5\times4)+1}{4}-\frac{(3\times9)+8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \end{gathered}[/tex]LCM of ( 4 & 3 ) is 12 So,
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \\ 5\frac{1}{4}-3\frac{8}{9}=5.25-11.6667 \\ 5\frac{1}{4}-3\frac{8}{9}=5-11 \\ 5\frac{1}{4}-3\frac{8}{9}=-6 \end{gathered}[/tex]Answer :
a)
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}\text{ can be express as :} \\ \text{Estimate : 5 - 11 =- 6} \end{gathered}[/tex]b)
Diffreence is :
[tex]\text{ 5}\frac{1}{4}\text{ - 3}\frac{8}{9}\text{ = }-6[/tex]
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 +
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
You deposit $3000 each year into an account earning 8% interest compounded annually. How much will youhave in the account in 20 years?
The rule of the compounded interest is
[tex]A=P\frac{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{\frac{r}{n}}[/tex]A is the final amount
P is the amount each year
r is the interest rate in decimal
t is the time
n is the number of periods per year
Since you deposit $3000 each year, then
P = 3000
Since the annual rate is 8%, then
r = 8/100 = 0.08
n = 1
Since the time is 20 years, then
t = 20
Substitute them in the rule above to find A
[tex]\begin{gathered} A=\frac{3000\lbrack(1+\frac{0.08}{1})^{1(20)}-1\rbrack}{\frac{0.08}{1}} \\ A=\frac{3000\lbrack(1.08)^{20}-1\rbrack}{0.08} \\ A=137285.8929 \end{gathered}[/tex]You will earn $137 285.8929 after 20 years
evaluate(if possible) the sine,cosine, and the tangent of the real number
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].
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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06 WS Solving Systems of Equations and Inequalities Word Problems
Systems of Equations: Use two equations with two variables to solve each of the following problems.
(1) The sum of two numbers is 51 and their difference is 13. Find the two numbers.
som of
One Saturday the theat
The two numbers are 19 and 32 respectively.
What is equation?
Equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
According to question, let x and y be two numbers
x + y = 51 and
x- y = 13
from equation two,
x = 13+y
put this in equation one,
y+13+y = 51
2y = 51 - 13
2y = 38
y = 38/2 = 19
x = 13+y
x = 13+19
x = 32
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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.
Evaluate the expression when c=4 and x=-4.-C+2x
ok
c = 4 x = 4
-c + 2x
Substitution
-4 + 2(4)
-4 + 8
Result
4
The answer for the second question is 2v + 15
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
what is y = -5/2 - 4 in standard form?
The slope-intercept form of the equation of a line is:
y = mx + c
where m is the slope
and c is the y-intercept
The given equation is:
[tex]y\text{ = -}\frac{5}{2}x\text{ - 4}[/tex]Comparing the given equation with y = mx + c:
The slope, m = -5/2
The equation perpendicular to y = mx + c and passing through the point (x₁, y₁) is given by the equation:
[tex]\text{y - y}_1=\frac{-1}{m}(x-x_1)[/tex]Since m = -5/2
-1/m = 2/5
The line passes through the point (5, 4)
x₁ = 5, y₁ = 4
The equation becomes:
[tex]\begin{gathered} y\text{ - 4 = }\frac{2}{5}(x\text{ - 5)} \\ y\text{ - 4 = }\frac{2}{5}x\text{ - 2} \\ \text{y = }\frac{2}{5}x\text{ - 2 + 4} \\ y=\frac{2}{5}x\text{ + 2} \end{gathered}[/tex]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.
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:
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.
Find the distance between (2, 5) and (-5, 8).
Given:
The two points are,
[tex]\begin{gathered} (2,5) \\ (-5,8) \end{gathered}[/tex]Required:
To find the distance between the given points.
Explanation:
The distance between the two points (x1,y1) and (x2,y2) can be calculated by using the formula,
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Now the distance between the points (2,5) and (-5,8) is,
[tex]\begin{gathered} \sqrt{(-5-2)^2+(8-5)^2} \\ =\sqrt{(-7)^2+3^2} \\ =\sqrt{49+9} \\ =\sqrt{58} \end{gathered}[/tex]Final Answer:
The distance between two given points is
[tex]\sqrt{58}units[/tex]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]Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-intercept to the nearest integer.
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
The Equation of line is 3x - y + 24 =0.
Given:
The table is given by:
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
To find the equation of line by using the above data.
Now, According to the question:
From the table, We have
We know that,
Slope (m) = [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]
and, slope (m) = [tex]\frac{-5-(-8)}{1-0}[/tex]
m = (-5 + 8)/ 1 = 3
So, [tex]y - y_{1} = m (x - x_{1} )[/tex]
y - 0 = 3 (x - (-8))
y = 3(x + 8)
y = 3x + 24
Hence, The Equation of line is 3x - y + 24 =0.
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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
:]
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
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]