Slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
Solution:Need to find the slope intercept form for the line perpendicular to C(-4,-5) and D(4,9)
And passing through the midpoints of the line CD.
Lets first calculate slope of CD
Let say slope of CD be represented by [tex]m_1[/tex]
General formula of slope of line passing through points [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is as follows:
[tex]m=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}[/tex]
[tex]\text { In case of line } \mathrm{CD} , x_{1}=-4, \quad y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]
[tex]\text {So slope of line } \mathrm{CD} \text { that is } m_{1}=\frac{(9-(-5))}{(4-(-4))}=\frac{14}{8}=\frac{7}{4}[/tex]
Let’s say slope of required line which is perpendicular to CD be [tex]m_2[/tex]
As product of slope of the lines perpendicular to each other is -1
=> slope of line CD [tex]\times[/tex] slope of line perpendicular to CD = -1
[tex]\begin{array}{l}{=>m_{1} \times m_{2}=-1} \\\\ {\Rightarrow \frac{7}{4} \times m_{2}=-1} \\\\ {\Rightarrow m_{2}=-\frac{4}{7}}\end{array}[/tex]
Now let’s find midpoint of CD
[tex]\text { Midpoint }(x, y) \text { of two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { is given by }[/tex]
[tex]x=\frac{x_{2}+x_{1}}{2} \text { and } y=\frac{y_{2}+y_{1}}{2}[/tex]
[tex]\text { So in case of line } \mathrm{CD} , x_{1}=-4, y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]
And midpoint of CD will be as follows
[tex]x=\frac{x_{2}+x_{1}}{2}=\frac{4+(-4)}{2}=0 \text { and } y=\frac{y_{2}+y_{1}}{2}=\frac{9-5}{2}=2[/tex]
So midpoint of CD is ( 0 , 2 )
As it is given that line whose slope intercept form is required is perpendicular to CD and passing through midpoint of CD , we need equation of line passing through ( 0 , 2 ) and having slope as [tex]m_{2}=-\frac{4}{7}[/tex]
Generic equation of line passing through [tex]\left(x_{1}, y_{1}\right)[/tex] and having slope of m is given by
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=0 \text { and } y_{1}=2 \text { and } m=-\frac{4}{7}[/tex]
Substituting the values in generic equation of line we get
[tex](y-2)=-\frac{4}{7}(x-0)[/tex]
As we required final equation in slope intercept form which is y = mx + c, lets rearrange our equation is required form:
[tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
Hence can conclude that slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
To find the equation of the line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint (0, 2), follow these steps: 1) Find the slope of the given line. 2) Find the midpoint of the line. 3) Find the negative reciprocal of the slope. 4) Use the slope and midpoint to write the equation of the perpendicular line in slope-intercept form.
Explanation:To find the equation of a line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint of the line, we need to follow these steps:
Let's go through these steps:
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:
slope = (9 - (-5)) / (4 - (-4))
slope = 14 / 8
slope = 7 / 4
The midpoint of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:
midpoint = ((-4 + 4) / 2, (-5 + 9) / 2)
midpoint = (0 / 2, 4 / 2)
midpoint = (0, 2)
The negative reciprocal of a slope is found by changing the sign of the slope and taking its reciprocal.
In this case, the slope is 7 / 4. So, the negative reciprocal is -4 / 7.
Now that we have the slope (-4 / 7) and the midpoint (0, 2), we can use the slope-intercept form of a line to write the equation:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the values, we have:
y = (-4 / 7)x + b
To find the value of b, we can substitute the coordinates of the midpoint (0, 2) into the equation:
2 = (-4 / 7)(0) + b
2 = 0 + b
b = 2
So, the equation of the line perpendicular to the line passing through C(-4,-5) and D(4,9) and passing through the midpoint (0, 2) is:
y = (-4 / 7)x + 2
write an equation that is not a linear function explain why it is not linear
Answer:
x=y^2
Step-by-step explanation:
cause the definition of equation is one x correspond to one y,but one y can correspond to 2 x,
the picture I give to you a x correspond to 2 y
The function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
According to the question,
A nonlinear equation is given as,
y = x²
Now plotting the curve,
When we see that the relationship does not contain a straight line, and has a varying rate of change are nonlinear functions.
So this function is not linear.
Thus, the function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
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Ratio question. Someone please help me!
Answer:
b is the right answer
Step-by-step explanation:
because the ratio of 98÷10=9.8
when we did the ration of 1078÷110=9.8
we can say that both ratio is same.
Answer: [tex]\frac{98}{10}[/tex] ; x = 110
Step-by-step explanation:
Since the ratio of weight to mass is constant , it implies:
[tex]\frac{490}{50}[/tex] = [tex]\frac{1078}{x}[/tex]
490x = 1078 X 50
490x = 53900
x = 53900/490
x = 110
Therefore the ratio of weight to mass will be :
1078/110
98/10
: Create a story or context for this number sentence
50 1/2 divided by 1/4 + 202
Answer:
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
Step-by-step explanation:
Given:
[tex]\frac{50\frac{1}{2}}{\frac{1}{4}}+202[/tex]
The Story can be created as :
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
what is half of 7 minutes and 24 seconds
Step-by-step explanation:
7 minutes are 7*60=420 seconds
420+24=444
444:2=222 seconds
222 seconds are 3minutes and 42 seconds
Answer:3.7 is half of 7 minutes and 24 seconds
Step-by-step explanation:
could someone help with this inequality?
20≥−3.2(c−4.3)
thanks >o
The solution of inequality would be -
c ≥ 1.95
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
We have the following inequality -
20 ≥ −3.2(c − 4.3)
It is given that -
20 ≥ −3.2(c − 4.3)
−3.2(c − 4.3) ≤ 20
-3.2c + 13.76 ≤ 20
-3.2c ≤ 20 - 13.76
-3.2c ≤ 6.24
c ≥ 1.95
Therefore, the solution of inequality would be -
c ≥ 1.95
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F=9/5c+32 a is there a constant of proportionality? Explain your reasoning
yes because in a standard form that that equation is in, it'd be y=mx=b. the m represents the constant of proportionality or the rate of change. another name for it is the slope. in this case, the 9/5 is the m & c is x. meaning that, there is one & it is 9/5
There are 450 children that attend a high school. Of those students. 23%
are in the marching band. How many students are not in the marching
band?
Answer:
The number of students not in the marching band is 346.5
Step-by-step explanation:
Given as :
The total number of children that attend a high school = 450
The percentage of students in the marching band = 23 %
Let The number of students not in the marching band = x
Now ,
∵ The percentage of students in the marching band = 23 %
∴ The percentage of students not in the marching band = 100 % - 23 % = 77 %
So, The number of students not in the marching band = 77 % of the total number of students in the school
I.e The number of students not in the marching band = 77 % × 450
Or , The number of students not in the marching band = [tex]\frac{77}{100}[/tex] × 450
∴ The number of students not in the marching band = 346.5
And The number of students in the marching band = 450 - 346.5 = 103.5
Hence The number of students not in the marching band is 346.5 Answer
A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students?
4:14
4:10
2:7
2:5
Answer:
2:7
Step-by-step explanation:
There are 4 boys and 14 total students. That ratio is 4:14, and to find the simplest form you divide both numbers by the greatest common factor, which is 2. That leaves you with 2:7, the final answer.
Answer: simple just put boys=4ovrwhole class =14 put it in fraction 4/14 simplify you get 2/7
Step-by-step explanation:
use the rational exponent property to write an equivalent expression for
[tex] \sqrt[5]{n ^{4} } + 3 - 12[/tex]
Using the rational exponent property, an equivalent expression for[tex]\(x^{3/4}\[/tex] can be written as[tex]\(\sqrt[4]{x^3}\).[/tex]
Explanation:The rational exponent property states that for any real number a and positive integer[tex]\(n\), \(a^{m/n} = \sqrt[n]{a^m}\)[/tex] . Applying this property to the given expression[tex]\(x^{3/4}\[/tex] ), where (m = 3) and (n = 4), we can rewrite it as [tex]\(\sqrt[4]{x^3}\)[/tex] . This is derived by taking the fourth root of [tex]\(x^3\),[/tex] which is equivalent to raising [tex]\(x^3\)[/tex] to the power of[tex]\(1/4\).[/tex]
To further understand this, consider the original expression [tex]\(x^{3/4}\).[/tex] This represents the fourth root of [tex]\(x^3\)[/tex] , as the numerator 3 indicates the power to which x is raised, and the denominator 4 indicates the root. Expressing it as [tex]\(\sqrt[4]{x^3}\)[/tex] provides a clearer representation of the same mathematical concept, emphasizing the fourth root of [tex]\(x^3\).[/tex]
In mathematical notation, the rational exponent property is a useful tool for simplifying expressions involving fractional exponents. It allows us to transform expressions between radical form and exponent form, providing flexibility in mathematical manipulations and aiding in the understanding of the underlying concepts.
Round to the nearest tenth: 156.78
So how am I supposed to get my.anwsers
You can look them up on here or other apps/websites.
The mean of 20 observations is 50. If the observation 50 is replaced by 140, what will be the resulting mean?
Answer:
24.5
Step-by-step explanation:
20 + 140-50/20
= 20 + 4.5
=24.5
The system of equations is graphed on the coordinate plane.
y=x−1y=−2x−4
What are the coordinates of the solution to the system of equations.
Answer:
(-1,-2)
Step-by-step explanation:
Hope it helps!
Answer:
the correct answer is (-1,-2)
Step-by-step explanation:
What is the simplified form of 2n ^ 2/3 * 3n^ 3 / 4
Answer: N^5/2 thats the answer thank you :)
3/10 11/12 5/8 in Oder from least to greatest
Answer: 5/8 11/12 3/10 I think
Step-by-step explanation:
Find common denominators (LCM is 120).
3/10 = 36/120
11/12 = 110/120
5/8 = 75/120
Now, we can put them from least to greatest.
3/10, 5/8, 11/12
______
Best Regards,
Wolfyy :)
What is the answer ?
Answer:
353
Step-by-step explanation:
355-42=x-40
I just need to subtract 2 from 355 to get x because I subtracted 2 from 42 to get 40.
355-2=353=x
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer in the box.
y = 17.5 when x = 5
Step-by-step explanation:
When two variables are in direct proportion i.e. change in one variable causes change in other variable it can be expressed mathematically as:
y∝x
when the proportionality symbol is removed a proportionality constant is introduced
So,
[tex]y = kx[/tex]
Putting y = 7 and x = 2
[tex]7 = k * 2\\k = \frac{7}{2}\\k = 3.5[/tex]
So the expression will be:
[tex]y = 3.5x[/tex]
Now putting x = 5
[tex]y = 3.5 * 5\\y = 17.5[/tex]
Hence,
y = 17.5 when x = 5
Keywords: Proportion, variables
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is this a function ?
Answer:
No
Step-by-step explanation:
For the relation to be a function
Each value of x from the domain ( values on left ) must map to exactly one unique value of y in the range ( values on the right )
Here x = 0 → 0 and 1 ( that is 2 values from the range )
Thus this does not represent a function
The expression x2 - 36y2 is equivalent to
Answer:
(x + 6y)(x - 6y)
Step-by-step explanation:
The expression x² - 36y² can be factored.
Since the expression is a difference (subtraction) between two numbers that are square (x² = x*x and 36y² = 6y*6y), the factoring can be done as a "difference of squares".
The rules is generalized as: [tex]x^{2} - y^{2} = (x - y)(x+y)[/tex]
To factor x² - 36y², take each square roots for each of the numbers and add and subtract between them.
x² - 36y²
= (√x² + √36y²)(√x² - √36y²)
= (x + 6y)(x - 6y)
Which of the following represents a geometric series
2+6+18
2,6,10
2+6+10+
2,6,18
good morning,
Answer:
2,6,18
Step-by-step explanation:
6/2=3 and 18/6=3 then 2,6,18 represent a geometric series.
6/2=3 and 10/6≠3 then 2,6,10 doesn’t represent a Géométric series.
:)
on average a person blink 16 times per minute how many times does a person blink in one day. there are 1,440 minutes in a day
Answer:
16 times 1440= 23040 blinks a day
Step-by-step explanation:
So umm... 16 blinks a minute so for every minute is 16 blinks so just multiply the 1440 minutes so yeah..
A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height , in feet above the ground of the concrete block after “s” seconds ?
The function would be h = 270 - 2.5s, where h is the height (in feet) and s it the time (in seconds) that has passed.
The 270 represents the initial value, which is given. We are told that the initial height of the block is 270 feet.
2.5s represents the feet that it has descended. We know the block is lowered at a rate of 2.5 feet per second. Multiplying this by s, the time, will give us how much it has descended.
The height at any point is can be given by function f(s) = 270 - 2.5s.
Given to us,
concrete block top height, H = 270 feet,
speed of the block, v = 2.5 feet/second,
We know that [tex]\rm \bold{speed = \dfrac{Distance}{Time} }[/tex],
thus, [tex]\rm \bold{Distance = speed\times Time}[/tex]
So, we can write, height (distance from the top height) covered is "s" seconds as,
[tex]\bold{h = v \times s}=\bold{2.5\times s} = \rm \bold{2.5s}[/tex]
therefore, we can write,
Height at any point = Top height - height covered
= 270 - 2.5s
Hence, the height at any point is can be given by function f(s) = 270 - 2.5s.
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Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.
Answer:
Number of songs played in commercial are 7 and Number of songs played in movie are 5.
Step-by-step explanation:
Let Number of songs played in commercial be x
and Number of songs played in movie be y.
Total number of songs played =12
Hence,
[tex]x+y=12\ \ \ \ equation \ 1[/tex]
Also
Cost for songs played in commercial = $50
Cost for songs played in movie = $130
Total Money earned = $1000
Hence,
[tex]\$50x+\$130y=\$1000[/tex]
Dividing by 10 on both side we get;
[tex]\$5x+\$13y=\$100\ \ \ \ equation \ 2[/tex]
Now multiplying equation 1 by 5 we get;
[tex]5x+5y=60 \ \ \ \ equation \ 3[/tex]
Now Subtracting equation 3 from equation 2 we get;
[tex](5x+13y=100)- (5x+5y=60)\\8y=40\\y=\frac{40}{8}=5[/tex]
y = 5
x + y = 12
x + 5 = 12
x = 12 - 5
x = 7
Hence, Number of songs played in commercial are 7 and Number of songs played in movie are 5.
What is the equation of a line in slope intercept form that passes through the points (-4,3) and (-2,4)
Answer:
y=1/2x+5
Step-by-step explanation:
y-y/x-x for slope
4-3/-2-(-4) 1/2
Answer:
y= --2/4+5
Step-by-step explanation:
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
Answer:
5 more weeks
Step-by-step explanation:
5 more weeks if he already sold 15. 10 more weeks if you exclude the 15 he already sold.
What are the possible values of the missing term of the geometric sequence 6,....,13.5?
Answer:
THE ANSWER IS 1.5
Step-by-step explanation:
13.5 is the 3rd and last value. 6 is the first value.
The formula you need to use is an= 3r^n-1
13.5=3r^3-1
THE REASON YOU USE 3 IS BECAUSE IN TOTAL THERE ARE 3 TERMS AND WE ARE SOLVING FOR ONE MISSING TERM.
Now we bring 3 over to 13.5 to get r alone because we are solving for r
13.5/3 =r^2
Now we want to get rid of the square root. So we...
√13.5/3 =√r^2
The final answer is 1.5=2
twinlakes on the shelf of a covenience store lose their fresh tastines over time. we say that the taste quality is 1 when the twinkies are first put on the shelf at the store, and that the quality of tastiness declined according to the function Q(t)=0.85^t. Graph this function on a graphing calculator, and determine when the taste will be half of its original value?
Answer:
The graph is shown below.
The time to make the taste to half is 4.265 s.
Step-by-step explanation:
Given:
Initial value of the taste is, [tex]Q_0=1[/tex]
Therefore, the quality of taste over time 't' is given as:
[tex]Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t[/tex]
Now, when the taste reduces to half, [tex]Q=0.5[/tex]
Therefore,
[tex]0.5=1(0.85)^t[/tex]
Taking natural log on both the sides, we get:
[tex]\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=\frac{ln(0.5)}{\ln(0.85)}=4.265\ s[/tex]
Therefore, the time to make the taste to half is 4.265 s.
Find 4(6a−5)−(9a+1).
Answer:
15a-21
Step-by-step explanation:
could be wrong though
5p = 1/15
what does p equal?
Answer:
(:5) 5p=1/15 (:5)
p=1/3
Answer:
p= .3333333
Step-by-step explanation:
An airliner is 9.34 feet wide. The airline wants to install 5 seats in each row. The seats are each 1.46 feet wide. Rounded to the nearest tenth, about how much space would be left for the aisle?
About 2.0 feet space will be left for aisle.
Step-by-step explanation:
Width of airliner = 9.34 feet
Width on one seat = 1.46 feet
Seats to install = 5
Width of 5 seats = 5*1.46 = 7.3 feet
Space left for aisle = Width of airliner - width of 5 seats
[tex]Space\ left\ for\ aisle=9.34-7.3\\Space\ left\ for\ aisle=2.04\ feet[/tex]
Rounding off to nearest 10th
Space left for aisle = 2.0 feet
About 2.0 feet space will be left for aisle.
Keywords: multiplication, subtraction
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To find the space left for the aisle, we first calculate the total seat width (5 seats × 1.46 feet/seat) and subtract it from the airliner width (9.34 feet), resulting in 2.0 feet of space for the aisle when rounded to the nearest tenth.
Explanation:To calculate the available space for the aisle in an airliner, we first determine the total width consumed by the seats. Since each seat is 1.46 feet wide and there are 5 seats in a row, we multiply the width of one seat by the number of seats:
1.46 feet/seat × 5 seats = 7.3 feet
Next, we subtract the total width of the seats from the total width of the airliner to find the space left for the aisle:
9.34 feet (total width) - 7.3 feet (width of seats) = 2.04 feet
Therefore, rounded to the nearest tenth, there would be approximately 2.0 feet of space left for the aisle.