An equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
What is point-slop equation of a line?
The point-slope equation of a line is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
The equation is useful when we know:
one point on the line: ( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) andthe slope of the line: m,and want to find other points on the line.
Given that,
slope , m = [tex]\frac{2}{3}[/tex] and passing through the point is (0,9)
An equation of a line given the slope and a point is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
or y - 9 = [tex]\frac{2}{3}[/tex] (x - 0)
or y - 9 = [tex]\frac{2}{3}[/tex] x
or y = [tex]\frac{2}{3}[/tex] x + 9
or y = [tex]\frac{2x + 27}{3}[/tex]
or 3y = 2x + 27
or 3y - 2x - 27 = 0
Hence, an equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
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Calculate the distance between the points E = (-4 , 5) and L=(1 , -3) in the coordinate plane. Give an exact answer (not a decimal approximation).
The distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is [tex]\sqrt{89}[/tex]
The points are E = (-4,5) and L = (1,-3)
We know the distance between the two points d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Where d is the distance between two points
[tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex] are the coordinates of the points
Here the given points are E = (-4,5) and L = (1,-3)
To find the distance between the given points, we have to substitute the values in the equation
d = [tex]\sqrt{1-(-4))^{2}+(-3-5)^{2} }[/tex]
d = [tex]\sqrt{5^{2}+(-8)^{2} }[/tex]
d = [tex]\sqrt{25+64}[/tex]
d = [tex]\sqrt{89}[/tex]
Hence, the distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is [tex]\sqrt{89}[/tex]
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the equation of the regression line for the data in the table is y = 4.9 - 198 where x represents the height and y is the predicted walking speed
The numerical value of 4.9 in the equation of the regression line
[y = (4.9x - 198)] determines "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.
As per the question statement, the equation of the regression line goes as [y = (4.9x - 198)], where "x" represents the height and "y" is the predicted walking speed.
We are required to determine, what the numerical value of 4.9 expresses in the regression line.
To solve this question, first we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)], where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line, and compare this standard form to our question mentioned equation, to establish the numerical significance of 4.9.
Now, [y = (4.9x - 198)] can be written as [(y - 0) = 4.9(x - 40.41)], and comparing it to the standard point-slope form of a line, we get (m = 4.9), i.e., the slope of our concerned line of regression is 4.9.
Hence, 4.9 in 4.9x signifies "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.
Equation: In mathematics, an equation is a statement that expresses the relation of equality between two or more separate expressions, by connecting them with the "equal to" sign.To learn more about Equations, click on the link below.
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Answer:
For every 1 inch increase in height, walking speed increases by 4.9 m/min.
Step-by-step explanation:
Just took it, hope this helps.
The normal cruising speed of a certain airplane is about 170 m/sec. What is this speed in miles per hour?
The speed of airplane in miles per hour (mph) is 380.2968 .
What is speed?
Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.
Given that
Speed of a certain airplane = 170 m/s or m[tex]s^{-1}[/tex]
We know that
In 1 meter = 0.0006214 miles
In 1 sec = [tex]\frac{1}{3600}[/tex] hour
but 1 [tex]sec^{-1}[/tex] = 3600 hour
Speed of this airplane in miles per hour = 170 × 0.0006214 × 3600 mph
= 0.105638 × 3600 mph
= 380.2968 mph
Hence, the speed of airplane in miles per hour (mph) is 380.2968 .
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I NEEEED HELLPPP LIKE ASAP I ONLY GOT 5 MINS TO DO THIS AND MORE WILL GIVE BRAINLY AND A LOT OF POINTS
Answer:
I can see that (0, 2) is the solution to this equation because that is the point where the lines intersect.
Step-by-step explanation:
[tex] - 3x + 2 = \frac{1}{2} x + 2[/tex]
[tex] - 3x = \frac{1}{2} x[/tex]
[tex]x = 0[/tex]
[tex]y = 2[/tex]
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
The expression which can be used to represent the total owed for 3 months given the cost per month and a one-time equipment fee is 3(c) + 25
The correct answer option is option C
The expression that represents the total owedPrice of the cable per month = cOne time equipment fee = $25Number of months = 3 monthsThe total owed = Number of months(Price of the cable per month) + One time equipment fee
The total owed = 3(c) + 25
I'm conclusion, the expression for the total owed is represented by 3(c) + 25
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Answer: option c
bc 3<c> is the fee for 25
I need help with number 3
Answer: A.
Step-by-step explanation:
Answer:
the perimeter of a triangle is 84 cm and its area is 336 cm? if one of its side is 30 cm find the length of reamining two side
across which axis was point F reflectedF(10, -5) - F'(-10, -5)
y-axis
Explanations:When a figure is reflected about any axis, the coordinate of that axis still remains the same, but the coordinate of the other axis is negated
For example:
If the point A(x, y) is reflected about the x-axis, the reflected image becomes A' (x, -y)
If the point A(x, y) is reflected about the y axis, the reflected image becomes A'(-x, y)
In this exercise, the point F(10, -5), after reflection, becomes F' (-10, -5)
Since the y-axis still remains -5 after reflection, this means that the point F was reflected across the y-axis.
Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\frac{x + 1}{x^2 -4x +4}[/tex] as x approaches 2 is ∞
What is limit?A limit in mathematics is the value that a function, sequence, or index approaches as an input, or an index, approaches a certain value. The definitions of continuity, derivatives, and integrals depend on limits, which are fundamental to calculus and mathematical analysis.
The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, and it is closely related to the concepts of limit and direct limit in category theory.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
[tex]\lim_{x \to 2} \frac{1 + 0}{2x -4 +0}[/tex]
Evalúe 2 as x
⇒ [tex]\frac{1 + 0}{2x -4 +0}[/tex]
⇒ [tex]\frac{1}{2(2) -4 +0}[/tex]
⇒ [tex]\frac{1}{0}[/tex]
⇒ ∞
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Determine if the sequence below is arithmetic or geometric and determine
the common difference / ratio in simplest form.
64, 16, 4, ...
The sequence 64, 16, 4,. is geometric
What is an arithmetic sequence?Arithmetic Sequence can simply be defined as a sequence in which the difference between successive or consecutive terms is known as a constant.
The sequence is in the form a, a + d, a + 2d, a + 3d, a + 4d
Where;
a is the first termd is the common difference of the sequenceThe formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + (n – 1)d
What is a geometric sequence?Geometric sequence can simply be defined as a sequence where the ratio of every two consecutive or successive terms is a known constant.
Given the sequence;
64, 16, 4, ...
We can see that the common ratio between the terms is 4 and hence a geometric sequence
Hence, it is a geometric sequence
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.
The correct pairs of the functions and their inverses are given by the image at the end of the answer.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The first function that we want to find the inverse is:
f(x) = (2x - 1)/(x + 2).
Hence:
x = (2y - 1)/(y + 2)
(y + 2)x = 2y - 1
xy + 2x = 2y - 1
xy - 2y = -1 - 2x
y(x - 2) = -1 - 2x
y = (-1 - 2x)/(x - 2) (which is the inverse function).
The second function which we want to find the inverse is:
y = (x + 2)/(-2x + 1)
Then:
x = (y + 2)/(-2y + 1)
x(-2y + 1) = y + 2
-2yx + x = y + 2
-2yx - y = 2 - x
-y(2x + 1) = 2 - x
y = (x - 2)/(2x + 1) (which is the inverse function).
The third function which we want to find the inverse is:
y = (x - 1)/(2x + 1)
Then:
x = (y - 1)/(2y + 1)
2yx + x = y - 1
2yx - y = -1 - x
y(2x - 1) = -1 - x
y = (-x - 1)/(2x - 1) (which is the inverse function).
The fourth function which we want to find the inverse is:
y = (2x + 1)/(2x - 1)
Then:
x = (2y + 1)(2y - 1)
2yx - x = 2y + 1
2yx - 2y = 1 + x
2y(x - 1) = (1 + x)
y = (x + 1)/(2(x - 1)) (which is the inverse function).
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determine whether the ordered pair is a solution of the given equation Remeber to use alphabetical order for substitution (-6,-2) a solution of the equation r-s=4 is (-6,-2) a solution of the equation r-s=4?
To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.
Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:
[tex](r,s)[/tex]Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:
[tex]\begin{gathered} r-s=4 \\ \Rightarrow(-6)-(-2)=4 \\ \Rightarrow-6+2=4 \\ \Rightarrow-4=4 \end{gathered}[/tex]Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.
HURRY!!!!!!!1Solve the equation −112 = 8x for x. −14 14 −104 120
The solution to the equation, −112 = 8x, is: x = -14.
How to Solve an Equation?To find the value of the variable in an equation, means to solve the equation.
To solve any given equation, we are to apply all necessary properties of equality in other to isolate, as much as possible, the variable of the equation to one side of the equation. Th value of the variable is the solution to the equation.
Given the equation:
-112 = 8x
Divide both sides of the equation by 8:
-112/8 = 8x/8 [division property of equality]
-14 = x
x = -14
Check: Plug in x = -14 into the equation:
-112 = 8(-14)
-112 = -112 [true]
Thus, the solution to -112 = 8x is: x = -14.
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Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to
figure out where they should go along the race course. They also need to determine how long it will take her to run the
race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of
hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.
Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on
the coordinate plane to the right.
Mother's 10K Race
Time
(H. in hours)
Distance Run
(D, in kilometers)
Distance (in kilometers)
12
10
0
0.5
1
1.5
Time (in hours)
3.5
The specific thing about this graph is it forms a straight line, and it extends to point of origin. The time x is on the x-axis and the distance y is on the y-axis. The coordinates on the graph are the same as the pairs in the table. (2, [tex]6\frac{2}{3}[/tex]) means Sam's mother ran [tex]6\frac{2}{3}[/tex] km in 2 hours.
What is a proportional relationship?Relationships between two variables are called as proportional when you see that their ratios are equal. One variable in a proportional connection is always a constant value multiplied by the other. "Constant of proportionality" is the name that is given to this constant.
What is a proportional relationship graph?The graph of a proportionate connection is a straight line that passes through the origin and rises steadily. The graph's unit rate can be represented by the point on this graph.
The graph depicting this proportional relationship formed in the table can be seen in the image attached.
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The complete question is:
"Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to
figure out where they should go along the race course. They also need to determine how long it will take her to run the
race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of
hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.
Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on
the coordinate plane to the right.
a) What are some specific things you notice about this graph?
b) What is the connection between the table and the graph?
c) What does the ordered pair (2,6 [tex]\frac{2}{3}[/tex]) Represent in the context of this problem?"
Pedro has scores of 95, 84, 68, 92 after four tests. what score must he make on his fifth test to have an average of 78 or greater?
Answer:
51 or above
Step-by-step explanation:
He already averages more then 78. But he at least needs a 51 in order for him to average 78. For him to get more than that he just needs a 52 or higher.
78 x 5 = 390
95 + 92 + 84 + 68 = 339
339/ 4 = 84.75 ( just to let you know the average before #5 )
390 - 339 = 51
51 is that last score needed
Wilbert bought a new dirt bike and is now $229 in debt. How much money does Wilbert have? What does $0 represent in this problem? 6.NS.5
Answer:
The money that Wilbert has is -$229 because of the debt.
$0 Represents his current, with no debts.
Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.
The result of the synthetic division of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:
2x³ - 4x² + 2x - 5.
How does synthetic division works?In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.For this problem, the polynomial is given by:
2x^4 - 12x³ + 18x² - 13x + 20.
Hence the coefficients are:
2, -12, 18, -13, 20.
The divisor is:
x - 4.
Hence the left coefficient is:
4.
From the image at the end of the answer, the resulting coefficients are given as follows:
2, -4, 2, -5, with a remainder of 0.
Hence the result is:
2x³ - 4x² + 2x - 5.
For the procedure, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.
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Use front end rounding to round each number. Then add the rounded
numbers to get an estimated answer. Finally, find the exact answer.
35.25
197.39
+ 4.835
Step-by-step explanation:
A35 (whole number )35.3 (1 decimal place)35.28 (2 decimal place)B197 (whole number )197.4 (1 decimal place)197.39 (2 decimal place)C5 (whole number )4.8 (1 decimal place)4.89 (2 decimal place)Write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
The equation in the slope-intercept form will be y = (-2/5)x + 4.4.
What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, point is (-20, 4) and line is 2x + 5y = 10, then the equation will be:
m = -2/5y = (-2/5)x + bNow, solve for b as follows while inserting the values of x and y:
y = (-2/5)x + b4 = (-2/5)-20 + b4 = 40/-100 + b4 = -0.4 + b4.4 = bb = 4.4So, equation will be y = (-2/5)x + 4.4
Therefore, the equation in the slope-intercept form will be y = (-2/5)x + 4.4.
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Find the volume of each figure. Round your answers to the nearest whole, if necessary.
Given that
The figure is of a cone and we have to find the volume of the cone.
Explanation -
The diameter of the cone is 22km and the height is also 22 km.
So the radius will be
radius = r = d/2 = 22/2 km = 11 km
Hence, r = 11 km and h = 22 km
The formula for the volume of the cone will be
[tex]Volume=\frac{1}{3}\times\pi\times r^2h[/tex]On substituting the values we have
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times11^2\times22\text{ km}^2 \\ \\ V=\frac{1}{3}\times\frac{22}{7}\times11\times11\times22\text{ km}^2 \\ \\ V=\frac{58564}{21}\text{ km}^2=2788.7\text{ km}^2 \end{gathered}[/tex]So B is the correct option.
Final answer -
Hence the final answer is 2788 sq km.For a test whose scores are normally distributed, with mean 470 and standard deviation 52, what is the cutoff score separating the bottom 11% of the test scores from the rest (that is, the score so that 11% of all scores are below this score)?
We will employ the z score table in this problem.
The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.
when we ahave a probability of 0.11 or 11%
This corresponds with a z-score of -1.225.
We then substitute into our z-score equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} z=z\text{ score} \\ x=\text{cut off point} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation} \end{gathered}[/tex]Therefore, we have
[tex]\begin{gathered} x=\sigma z+\mu \\ x=52(-1.225)+470 \\ x=406.3 \end{gathered}[/tex]Find the domain and range of the function represented by the graph.
The graph is a filled-in point at ordered pair negative 4 comma negative 1, a line segment from ordered pair negative 4 comma negative 1 to ordered pair 0 comma 3, a line segment from ordered pair 0 comma 3 to ordered pair 2 comma 3, a line segment from ordered pair 2 comma 3 to ordered pair 3 comma 4, and a filled-in point at ordered pair 3 comma 4.
The domain is
$\le x\le$
.
The range is
$\le y\le$
.
Determine the rate of this problem -> A 18-kg bag of cherries for $2.65 =_____per kg
Answer:
$0.14 per kg
Step-by-step explanation:
A 18-kg bag of cherries for $2.65
for 1 kg
[tex] \frac{2.65}{18} = 0.14 \\ [/tex]
so, the answer is $0.14
Calculate the future value of the $9,000 earning 9% interest compounded quarterly for 8 years round answer to two decimal places
Compound interest formula:
A = P (1 + r/n )^nt
Where:
A = future vale
P= Principal investment = 9,000
r = interest rate in decimal form = 9/100 = 0.09
n = number of compounding periods = 4
t = years = 8
Replacing:
A = 9000 ( 1 + 0.09/4)^ (4*8)
A = 9000 (1.0225)^32
A= 18,342.93
The future value is $18,342.93
Answer the following.
To convert 2.21 x 10⁻⁶, place 6 zeros before 2.21 and move the decimal point to the left:
= 0.000021210
To convert 28,000 to scientific notation, write the non-zero digits, placing a decimal after the first non-zero digit: 2.8, then, multiply by 10 elevated to 4 (number of digits after 2):
28,000 = 2.8 x 10
nswer:
#6 and #7 Axioms of Equality
It is proved that ∠2 and ∠3 are supplementary angles.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, according to the given image below:
(A) m∠1 = m∠3 ⇒ Alternate angles.
(B) m∠1 + m∠2 = 180°
Reason:
R is a straight line through which line m asses making two angles m∠1 and m∠2.As we know a straight line has an angle of 180°.And since, line m divides the angle of 180° into two parts ∠1 and ∠2.So w ecam conclude that: m1 + m∠2 = 180°.(C) m∠3 + m∠2 = 180° due to: Linear Pair Axiom.
(D) m∠2 and m∠3 are supplementary because: Since a linear pair of angles always results in a straight line, their sum is always 180°.
Therefore, it is proved that ∠2 and ∠3 are supplementary angles.
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I need help with question 4. The model is at the very top, no need to answer the question that has been scribbled out.
Step 0 ---- 2
2+1
step 1 ------ 3
3+3
step 2 --------- 6
6+5
step 3 ----------11
11 + 7
step 4 ------------ 18
terms are 2, 3, 6,11, 18
There is an increment of odd numbers from a preceding term
2 increase to 3 by the first odd i.e 1
3 increase to 6 by the next odd i.e 3
6 increase to 11 by the next odd i.e 5
Therefore 11 will increase by the next odd, i.e 7
Thus, 11 + 7 = 18
A person invests 1000 dollars in a bank. The bank pays 6% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2100 dollars?
Solution
For this case we have the following information given:
A= 1000
r= 0.06
n = 1
A= 2100
So we can set up the following formula:
[tex]2100=1000(1+\frac{0.06}{1})^t[/tex]We can solve for t on this way:
[tex]\ln (\frac{2100}{1000})=t\cdot\ln (1.06)[/tex]Solving for t we got:
[tex]t=\frac{\ln (2.1)}{\ln (1.06)}=12.73[/tex]Rounded to the nesrest tenth we got:
12.7 years
Use the definition of the derivative to find the derivative of the function with respect to the given variable.
Show steps
The derivative of the given function [g(r) = -2r + 2] is d/dr (rⁿ) = nrⁿ⁻¹.
What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative. In conclusion, the tangent line's slope, or instantaneous rate of change, at any point on the curve is essentially what the derivative is. When you take a function's derivative, you're left with a different function that gives you the slope of the original function.So, g(r) = -2r + 2:
Differentiate with respect to r as follows:
g(r) = -2r + 2Using Power rule:
d/dr (rⁿ) = nrⁿ⁻¹Therefore, the derivative of the given function is d/dr (rⁿ) = nrⁿ⁻¹.
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Use Gaussian elimination to solve.The burkes pay their babysitter $5 per hour before 11p.m. and $7.50 after 11 p.m. One evening they went out for 5 hours and paid the sitter $35.00. Whag time did they come home?
Given the information on the problem, we can write the following system of equations:
[tex]\begin{cases}x+y=5 \\ 5x+7.5y=35\end{cases}[/tex]then, we can write the following augmented matrix:
[tex]\begin{bmatrix}{1} & {1} & {5} \\ {5} & {7.5} & {35}\end{bmatrix}[/tex]now, if we multiply by 5 the first row and then substract it from the second row, we get:
[tex]\begin{bmatrix}{1} & 1{} & {5} \\ {5} & {}7.5 & 35{}{}\end{bmatrix}\rightarrow\begin{bmatrix}{1} & 1{} & 5{} \\ {0} & {2.5} & {10}{}\end{bmatrix}[/tex]notice that from the second equation, we can find the value of y:
[tex]\begin{gathered} 2.5y=10 \\ \Rightarrow y=\frac{10}{2.5}=4 \\ y=4 \end{gathered}[/tex]now that we have that y = 4, we can use this value on the first equation to find x:
[tex]\begin{gathered} x+4=5 \\ \Rightarrow x=5-4=1 \\ x=1 \end{gathered}[/tex]now, we have that the babysitter worked 1 hour before 11pm and 4 hours after 11 pm,then, the Burkes came home at 3 am
The point (-2, 1) is on the graph of which of these functions?
A. y = -x² -1
B. y = -3x -5
C. y = x² + 3
D. Y = 1/2x