Find the equation of a line perpendicular to another line
Final answer:
To find the equation of a line perpendicular to another, determine the slope of the original line and use the negative reciprocal of that slope for the perpendicular line. Choose a point on the perpendicular line, and apply the point-slope form to get the equation.
Explanation:
The process of finding a perpendicular line involves first understanding the slope of the given line. To find the equation of a line that is perpendicular to another, you need to identify the slope (m) of the original line and use the fact that the slopes of perpendicular lines are negative reciprocals of each other (meaning if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m). In the context of vectors and analytical methods in physics, components can help describe forces or directions. If we consider the example of a skier on a slope, breaking down the weight force into components parallel and perpendicular to the slope helps analyze the motion. However, for strictly finding a perpendicular line in mathematics, we focus on the slopes of the lines. Suppose you have the equation of the original line. If it is in the format y = mx + b, where m is the slope and b is the y-intercept, you can find the slope of the perpendicular line by taking the negative reciprocal of m. If the slope is not readily apparent, you might need to rearrange the equation into this format. Once you have the slope of the perpendicular line, choose a point through which the line passes (this could be the original point or any particular point you're given). Then, use the point-slope form (y - y1) = m(x - x1) to write the equation of the line.
(50 POINTS) Hi, I really need help on this first part of my portfolio it was due last week but I don't really get this part so if someone could explain it to me I could get the other four parts done on my own.
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Use the City Populations table found on the message board and select a city that is experiencing population growth. Determine the percentage growth and use that to write an exponential function to represent the city’s population, y, based on the number of years that pass, x from 2010 (i.e. 2011 means that x = 1)
City: Portland, Oregon 585,256 593,939 603,026 609,456 619,334 630621 639863
This was deleted once and idk why there is plenty of information :(
Ik this is a lot to ask of someone but I haven't had any luck with any function sites.
This is a number that can be divided out of each term in an expression.
Answer:
Hello!
Great question!
The correct answer would be "Common Factor."
Step-by-step explanation:
It is a common factor when it is a factor of two (or more) numbers.
The number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
What is GCF (greatest common factor)?GCF or greatest common factor is the common number which all the term has in a group of terms. It is the number which can divide each number of the group.
For example, let a group of number as,
[tex]\{1,2,4,8,16\}[/tex]
The number which can be divided out of each term in this data is 16 which is the greater common factor of this data set.
Thus, the number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
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I only need number 30 answered
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x − 2, y + 8) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.
Simplify 5 - 2 · 3 + 4. 13 -5 3 21
Consider this equation (csc x+1)/cot x = cot x/(csc x +1) is it an identity?
If f(x)= 2x+8 and g(x) = x^4, what is (g°f)(-3)?
What did the doctor say to the guy who thought he was a wigwam one day and teepee the next? math riddle
Answer:
too tenes
This is the correct answer because it is a play on words comparing tents which describes the native american home structure of a wigwam and a teepee and tense, will which describes a physiological response to high anxiety6.
The formula for the area a of a triangle is a equals 1 half b where is the base and h is the height. solve the formula for h and then find the height of a triangle whose area is 1768 square inches and whose base is 52 inches. round to the nearest tenth if necessary. height = inches
Area of triangle is given as:
A = (1/2) b * h
where b is base and h is height
So given that:
A = 1768 inches^2
b = 52 inches
Rearranging the equation to find for h:
h = 2 A / b
h = 2 * 1768 inches^2 / 52 inches
h = 68 inches
Solve the following equation.75 = –5(–3 – 4x)
x = 3
x = –4
x = –3
x = 5
Evaluate u + xy, for u = 20, x = 9, and y = 8.
For f(x)=3x+1 and g(x)=x squared - 6 find (f- g)(x)
The point p(x, y) on the unit circle that corresponds to a real number t is given. find the values of the indicated trigonometric function at t.
Unit circle : a circle with radius of one. Unit circle is centered at the origin.
Use the formula cot x = base / perpendicular, where x is the angle. Substituting x,y and t to the formula, we get cot (t) = x / y.
To find the trigonometric function values for a point on the unit circle corresponding to a real number t involves using the x and y coordinates, which are derived from the cosine and sine functions at that angle t.
The student's question involves finding the values of trigonometric functions for a point p(x, y) on the unit circle that corresponds to a real number t. This typically involves understanding the relationship between the coordinates of a point on the unit circle and the trigonometric functions sin, cos, and tan. In this context, x(t) and y(t) are understood as the x and y coordinates of a point on the unit circle at a certain angle t. The point p(x, y) would be given by the cosine and sine functions: x(t) = cos(t) and y(t) = sin(t). In more advanced contexts, these functions can take different forms like x(t) = A cos(wt + p) where A, w, and p are constants. The solution to trigonometric equations may involve differential equations or complex numbers in such cases.
Auto insurance options offered by AA Auto Insurance are outlined in the table below. What monthly payment would you expect for an insurance policy through AA Auto Insurance with the following options? Bodily Injury: $25/50,000 Property Damage: $25,000 Collision: $250 deductible Comprehensive: $100 deductible
a.
$43.23
b.
$46.10
c.
$54.85
d.
$64.44
In this exercise we have to use the knowledge of finance to calculate the monthly amount of insurance, so the best alternative that represents this amount is:
Option C
In this exercise we want to calculate the monthly insurance payment amount, so from the given values we find:
[tex]Payment= (Bodily Injury)+ (Property Damage)+ (Collision)+(Comprehensive)[/tex]
Substituting the values in the formula given above we find that:
[tex]Payment= 22.5 + 120.5 + 415.25 + 100 \\= 658.25\\658.25/12 = 54.854[/tex]
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If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is ___.
The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2.
What is probability?Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.
As per the given,
In the first three attempts coming head in the first three times.
In the fourth attempt, the probability will be independent of the first three events.
Thus, the probability of coming ahead in the fourth time will be as,
Number of desire output/number of total output
=> 1 / 2
Hence "The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2".
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Solve for t.
q=r+rst
The equation q=r+rst can be rearranged to isolate t, with the final solution being t=(q-r)/rs.
Explanation:To solve for t in the equation q=r+rst, first, you need to isolate t on one side of the equation. You can do this by subtracting r from both sides so that you have q-r=rst. Next, divide both sides by rs, which gives you the final solution: t=(q-r)/rs.
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Multiplying by a conjugate gives a rational number because (a + b)(a -
b.= _____.
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD.
The value of x in the figure given is E. √70.
The answer is E. √70.
The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.
Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.
We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.
Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.
Here is a proof that shows why the two triangles are similar:
AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.
SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.
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Which number line represents the solutions to |x + 4| = 2?
The number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
Further explanation:
The equation is given as follows:
[tex]|x+4|=2[/tex]
In the above equation [tex]||[/tex] represents the modulus function.
Modulus function is defined as a function which gives positive value of the function for any real value of [tex]x[/tex].
For example: The function [tex]y=|x|[/tex] is a modulus function in which [tex]y>0[/tex] and [tex]x<0[/tex] or [tex]x>0[/tex].
In the given equation [tex]|x+4|[/tex] is a modulus expression.
There are two cases formed for [tex]|x+4|[/tex].
First case: [tex]x>-4[/tex]
If [tex]x>-4[/tex] then [tex]|x+4|\rightarrow (x+4)[/tex].
Substitute [tex]|x+4|=(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}x+4&=2\\x&=2-4\\&=-2\end{aligned}[/tex]
Therefore, for [tex]x>-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-2[/tex].
Second case: [tex]x<-4[/tex]
If [tex]x<-4[/tex] then [tex]|x+4|\rightarrow -(x+4)[/tex].
Substitute [tex]|x+4|=-(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}-(x+4)&=2\\-x-4&=2\\-x&=2+4\\-x&=6\\x&=-6\end{aligned}[/tex]
Therefore, for [tex]x<-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-6[/tex].
This implies that the solution for the equation [tex]|x+4|=2[/tex] or the value of [tex]x[/tex] which satisfies the given equation are [tex]\fbox{\begin\\\ \math x=-2\ \text{and}\ x=-6\\\end{minispace}}[/tex].
Option 1:
The number line in option 1 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 1 is correct.
Option 2:
The number line in option 2 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 2 is incorrect.
Option 3:
The number line in option 3 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 3 is incorrect.
Option 4:
The number line in option 4 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 4 is incorrect.
Therefore, the number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Functions
Keywords: Functions, modulus, modulus function, number line, real line, |x+4|=2, equation, root, zeroes, solutions, absolute function, x=-6 and x=-2.
Option A is correct, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Modulus function always returns a positive value to the equation.
Here, [tex]|x+4|[/tex] will give positive result if [tex]x>-4[/tex] and negative value if, [tex]x<-4[/tex].
Case 1: When [tex]x>-4[/tex]
According to the given equation,
[tex]|x+4|=2\\x=2-4\\x=-2[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x>-4[/tex] is [tex]x=-2[/tex].
Case 2: When [tex]x<-4[/tex]
According to the given equation,
[tex]|x+4|=2\\-x-4=2\\x=-6[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x<-4[/tex] is [tex]x=-6[/tex].
Hence, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Now, according to the options, Option A is correct.
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calculate the rate of change for the quadratic function over the given interval:
f(x)=x^2 + 4x +5 ; -4 =< x =< -2
The rate of change of the quadratic function over the interval −4≤x≤−2 is 2.
To find the rate of change of the quadratic function [tex]$f(x)=x^2+4 x+5$[/tex] , over the interval −4≤x≤−2, we need to find the average rate of change over that interval.
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]Average Rate of Change =\frac{f(b)-f(a)}{b-a}$[/tex]
So, in this case:
a=−4
b=−2
We calculate f(−4) and f(−2):
[tex]$\begin{aligned} & f(-4)=(-4)^2+4(-4)+5=16-16+5=5 \\ & f(-2)=(-2)^2+4(-2)+5=4-8+5=1\end{aligned}$[/tex]
Now we can find the rate of change:
Rate of Change = [tex]$\frac{1-5}{-2-(-4)}=\frac{-4}{-2}=2$[/tex]
The average rate of change of the function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 is -2.
The rate of change for the quadratic function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 can be calculated using the average rate of change formula. This formula is given by:
Rate of Change = [f(x2) - f(x1)] / (x2 - x1)
Where x1 = -4 and x2 = -2. We first calculate f(-4) and f(-2) by plugging these values into the function:
f(-4) = (-4)² + 4(-4) + 5 = 16 - 16 + 5 = 5
f(-2) = (-2)² + 4(-2) + 5 = 4 - 8 + 5 = 1
Now we use these results in our rate of change formula:
Rate of Change = (1 - 5) / (-2 + 4) = -4 / 2 = -2
The average rate of change of the function f(x) over the interval from x = -4 to x = -2 is -2.
A line goes through the points (8,9) and (2,4).
What is the slope of the line?
Write the equation of the line in point-slope form?
Write the equation of the line in slope-intercept form?
What is the value of the 7 digit in 91,764,350?
The perimeter of a rectangular concrete patio is 34 meters. the area is 70 square meters. what are the dimensions of the patio?
To find the dimensions of the rectangular patio, use the equations for perimeter and area and solve for length and width.
Explanation:To find the dimensions of the rectangular patio, we can use the given information about its perimeter and area. Let's assume the length of the patio is L and the width is W.
The perimeter is given as 34 meters, which is equal to 2L + 2W. So, we have the equation 2L + 2W = 34.
The area is given as 70 square meters, which is equal to L * W. So, we have the equation L * W = 70.
We can use these equations to solve for L and W using substitution or elimination method.
If f(x) = 3x2 - x, find f(-2).
10
14
38
f(x) = 3x^2-x
F(-2)
replace x with -2
3(-2)^2 - -2 =
3*4 +2 = 14
Answer is 14
The distance d in feet that dropped object falls in t seconds is givin by the equation d divided 16 = tsquared how long does it take a dropped object to fall 64 feet
The expression 2/+2w is used to find the perimeter of a rectangle with length / and width w.
What is the perimeter of a rectangle with length 14cm and width 4cm?
9cm
18cm
28cm
36cm
THANKS IN ADVANCE, I MARK BRAINLIEST!!!
Answer: 36 cm
Step-by-step explanation:
Given : The expression 2l+2w is used to find the perimeter of a rectangle with length l and width w.
To find : The perimeter of a rectangle with length 14cm and width 4cm.
Substitute l=14 and w=4 in the given expression , we get
Perimeter= [tex]2(14)+2(4) =28+8=36\ cm[/tex]
Hence, the perimeter of a rectangle with length 14cm and width 4cm= 36 cm
A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Answer:
The probability of the event below of rolling a 5 is 0.0625.
Step-by-step explanation:
Given is : A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Total number of faces = 16
So, there is only one way for rolling a 5 on a die
And the probability of rolling a 5 on a die = [tex]\frac{1}{16}[/tex]
= 0.0625
10(2y+2)−y=2(8y−8). please help me
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden. the dirt store sells by the cubic yards. how many cubic yards will you need to order? the store only sells in increments of 1/4 cubic yards.
Answer:
You need to buy 6.5 cubic yards.
Step-by-step explanation:
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden.
We know 1 yard = 3 feet or 1 yard = 36 inches
Then 1 inch = [tex]1/36[/tex] yard.
1 feet = 1/3 yard
The volume of the layer of the topsoil is given by:
= [tex]5(1/36)(23)(1/3)(18)(1/3)[/tex] cubic yards
[tex]2070/324=6.39[/tex] cubic yards
Now, the store only sells increments of 1/4 = 0.25 cubic yards.
So, we need to buy [tex]6.39/0.25=25.56[/tex] increments
Rounded to 26 increments.
Therefore, we need to buy 26 increments of 1/4 cubic yards.
That becomes 6.5 cubic yards.