write an equation in point slope form of the line through point J(4,1) with slope -4
Answer:
y - 1 = - 4(x - 4)Step-by-step explanation:
Point- slope form:
y - y₁ = m(x - x₁), where m- the slope, (x₁, y₁) - the point on the lineGiven:
m = - 4,Point J(4, 1)Substitute into equation to get the line:
y - 1 = - 4(x - 4)A. x² +5
B. +5X
C.X + 5
D.5X
The expression that represents the quotient of the given model is x + 5. The correct option is C. x + 5
Determining the expression that represent the quotient of a modelFrom the question, we are to determine the expression that represent the quotient of the given model
From the given model, we can write that
x | x² + x + x + x + x + x
Dividing by using the long division
x + 1 + 1 + 1 + 1 + 1
x | x² + x + x + x + x + x
Thus, the quotient of the expression is
x + 1 + 1 + 1 + 1 + 1
Further simplification,
NOTE: 1 + 1 + 1 + 1 + 1 = 5
Then,
The expression x + 1 + 1 + 1 + 1 + 1 becomes
x + 5
Hence, the expression is x + 5
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Which pair of lines are perpendicular?
A. y = -8 and y = 2
B. x = 4 and y = -1
C. x-y = 7 and y = x + 3
D. y = -4x + 1 and 8x + 2y = -10
Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
There are 4 different pairs of lines given to us.
We have to find out the pair of lines that are perpendicular to each other.
We know that the general equation of a line in slope-intercept form is represented as -
y = mx + c --- (1)
where
(x, y) = coordinates of the lines
m = slope of the line
c = y-intercept
It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.
A. y = -8 and y = 2
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
B. x = 4 and y = -1
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
C. x - y = 7 and y = x + 3
Now, x - y = 7
=> -y = 7 - x
=> y = x - 7
Comparing this to the equation (1), we have slope of the line, m = 1.
Also, y = x + 3
Comparing this to the equation (1), we have slope of the line, m = 1.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
D. y = -4x + 1 and 8x + 2y = -10
Now, y = -4x +1
Comparing this to the equation (1), we have slope of the line, m = -4.
Also, 8x + 2y = -10
=> 2y = -8x - 10
=> y = -4x - 10
Comparing this to the equation (1), we have slope of the line, m = -4.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
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Find a formula for the polynomial of least degree that is graphed below Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4).
Answer: y=-2x²-6x
Step-by-step explanation:
Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4)
Hence we have three coordinates of the equation y=ax²+bx+c (1):
(0,0) (-3,0) (-1,4)
Let's substitute these coordinates into formula (1):
[tex]0=a(0)^2+b(0)+c\\0=a(-3)^2+b(-3)+c\\4=a(-1)^2+b(-1)+c\\\\0=0+0+c\\0=9a-3b+c\\4=a-b+c\\\\0=c\\0=9a-3b+0\\0=a-b+0\\\\c=0\\9a-3b=0\ \ (1)\\a-b=4\ \ \ \ \ (2)\\\\c=0\\\\[/tex]
Divide both parts of the equation (1) by 3 and multiply both parts of the equation (2) by -1: :
[tex]3a-b=0\\-a+b=-4\\\\[/tex]
Sum these equations:
[tex]2a=-4[/tex]
Divide both parts of the equation by 2:
[tex]a=-2[/tex]
We substitute the value of a=-2 into equation (2):
[tex]-2-b=4\\[/tex]
Divide both parts of the equation by -1:
[tex]2+b=-4\\\\2+b-2=-4-2\\\\b=-6[/tex]
[tex]Thus, \\\\y=-2x^2-6x+0\\\\y=-2x^2-6x[/tex]
solve for missing angle 20 degrees + 40 degrees + 39 degrees + x
The sum of angles at a point is equal 360 degrees and using that, the value of x is 261 degrees.
Angle At a PointAngles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360°.
In this question, when we sum all angles up, it will give us the sum of 360 degrees.
20 + 40 + 39 + x = 360
x + 99 = 360
x = 360 - 99
x = 261
x has a value of 261 degrees.
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Maria is applying for a summer job. Six employees who do various jobs at the company earn $8.00, $8.50, $9.00, $9.50, $10.00, and $23.50 per hour. In the interview, the boss tells Maria that the median of the hourly wages is $9.25. Is the boss’s statement misleading? Why or why not?
Answer:
Boss's statement is not misleading.
Explanation:
To find the median, we need to find the middle number.
8.00, 8.50, 9.00, 9.50, 10.00, 23.50
9.00 and 9.50 are in the middle.
And in the middle of those two is 9.25.
In a model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, are the model’s distances proportional to the actual dimensions of the solar system?(1 point)
Responses
Yes, because the ratios of model length to actual distance are equal for the two planets.
Yes, because the ratios of model length to actual distance are equal for the two planets.
No, because the ratios of model length to actual distance are different for the two planets.
No, because the ratios of model length to actual distance are different for the two planets.
No, because the model is in inches and the actual distances are in millions of miles.
No, because the model is in inches and the actual distances are in millions of miles.
No, because the ratios cannot be reduced.
The model’s distances isn't proportional to the actual dimensions of the solar system as B. No, because the ratios of model length to actual distance are different for the two planets.
What is ratio?Ratio demonstrates how many times one number can fit into another number. It is used to show the comparison between two or more things
In this case, in model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. This can be illustrated as:
= 7/19
= 0.368
If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, the ratio is:
= 91.549 / 2780.5
= 0.0329
Therefore, since they're different numbers, the information doesn't illustrate a proportional ratio.
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Out of 45 times at bat, Raul got 27 hits. Write the decimal that represents the times Raul didn't
get a hit.
Answer:
0.6
Step-by-step explanation:
<7 and <8 are vertical angles can you shoe me how to draw this please
Vertical angles are opposite of each othe. Attached is a picture of how it looks:
I hope this helps!
20. Find the area of each of the following shaded regions in
parts (a)-(d). Assume all arcs are circular with centers marked. Leave all answers in terms of Pi
The area of each of the following shaded regions in parts (a)-(d) is 2
How Find the area of each of the following shaded regions?There is a space in the shaded area. Because we are given two circles inside one larger circle, the size of the darkened zone is equal to the area of the circle less the area of the circle.
They are equal to the circle to an area of circle minus an area of circle three. You can calculate the radius of the larger circle as this is likewise 1 cm. The radius refers to the location of the larger circle's center. Keep in mind that all measurements are in cm square. C2's surface area is the same as that of three.There will only be one square. The area is located in the area that is darkened. The region is equal to the size of C1 minus the areas of C2 and C3. As a result, C will be the first. C 2 and C three are the same, and the area is four pi.The answer is 2, and square meters are not the appropriate unit.
The area of each of the following shaded regions in parts (a)-(d) is 2
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The curve with equation y = x³ +3 has two tangents parallel to the line with equation
y = 12x-1. Find the co-ordinates of the two points.
Answer:
(-2, -5), (2, 11)
Step-by-step explanation:
You want the coordinates of the points on the curve y = x³ +3 where the tangent lines are parallel to y = 12x -1.
SlopeThe slope of the tangent line is the x-coefficient in its equation: 12.
The slope of the curve is given by its derivative:
y' = 3x²
We want the x-values where the slope is 12. These are the solutions to ...
12 = 3x²
4 = x² . . . . . . . . . . divide by 3
x = ±√4 = ±2 . . . . . take the square root
CoordinatesThe coordinates of the points with x = ±2 are ...
y = (±2)³ +3 = ±8 +3 = {-5, 11}
The tangent points are (-2, -5) and (5, 11).
__
Additional comment
The attached graphs and table show the solutions to y'=0 and the corresponding point locations. It also shows the tangent line equations (in point-slope form).
Truck Transport
A truck driver is beginning her haul across the country. The warehouse is 15 miles
from the highway. Once she gets on the highway she maintains a constant rate for
several hours. Complete the table of values for the sequence below that relates hours on
the highway and distance from the warehouse in miles.
Refer to the attachment for the required table:
What is the unit rate?
A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
From the table,
For 0 hours, distance = 15 miles
For 1 hour, distance = 80 miles
Difference between distances= 80-15=65 miles
Since it is given that, it is at a constant rate, for every hour there is an increase of 65 miles in distance.
The completed table is shown in the attachment.
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The data lists the salaries at a company:
#1 - $25,000
#2- $10,000
#3- $15,000
#4- $10,000
#5- $15,000
#6- $10,000
#7- $15,000
#8- $10,000
#9- $10,000
#10- $80,000
a) Identify any outliers in the data.
b) Which measure would you use to describe the central tendency of the
dataset? (mean, median,mode)
a) Examining the data, the outlier in the data are
#1 - $25,000#10 - $80,000b) The measure I would use to describe the central tendency of the data is median
What is outlier as used in data analysis?Outlier as used in data analysis refers to a data that is abnormally away from other data. Outliers show high variability
In the given problem, $80 000 is the data that is farther away than any other data and hence the only outlier
The mean is usually a better measure of central tendency how ever the presence of outliers affects the result projected by mean.
The better choice to use here is the median
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The equity sections for Atticus Group at the beginning of the year (January 1) and end of the year (December 31) follow.
Stockholders’ Equity (January 1)
Common stock—$4 par value, 100,000 shares authorized, 35,000 shares issued and outstanding $ 140,000
Paid-in capital in excess of par value, common stock 100,000
Retained earnings 360,000
Total stockholders’ equity $ 600,000
Stockholders’ Equity (December 31)
Common stock—$4 par value, 100,000 shares authorized, 41,000 shares issued, 5,000 shares in treasury $ 164,000
Paid-in capital in excess of par value, common stock 148,000
Retained earnings ($50,000 restricted by treasury stock) 440,000
752,000
Less cost of treasury stock (50,000)
Total stockholders’ equity $ 702,000
The following transactions and events affected its equity during the year.
January 5 Declared a $0.50 per share cash dividend, date of record January 10.
March 20 Purchased treasury stock for cash.
April 5 Declared a $0.50 per share cash dividend, date of record April 10.
July 5 Declared a $0.50 per share cash dividend, date of record July 10.
July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.
August 14 Issued the stock dividend that was declared on July 31.
October 5 Declared a $0.50 per share cash dividend, date of record October 10.
3. What is the amount of retained earnings transferred to paid-in capital accounts (capitalized) for the stock dividend?
4. What is the per share cost of the treasury stock purchased? (Round your answer to 2 decimal places.)
5. How much net income did the company earn this year?
3. The amount of retained earnings transferred to the paid-in capital accounts (capitalized) for the stock dividend is $72,000.
4. The per-share cost of the treasury stock purchased is $10.
5. The net income earned by the Atticus Group this year was $217,500.
How are stock dividends capitalized?Stock dividends do not affect the cash account, unlike cash dividends.
Instead, the deduction is made from the retained earnings.
When the stock dividends are distributed, they are capitalized to the paid-in capital accounts (common stock and additional paid-in capital).
Transaction Analysis:January 5 Dividend $17,500 Dividends Payable $17,500 (35,000 x $0.50)
Retained Earnings $17,500 Dividend $17,500
March 20 Treasury Stock $20,000 Paid-in Capital in Excess $30,000 Cash $50,000 ($50,000/5,000)
April 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)
Retained Earnings $15,000 Dividend $15,000
July 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)
Retained Earnings $15,000 Dividend $15,000
July 31 Stock Dividend $72,000 Dividends Issuable $72,000 (30,000 x 20% x $12)
Retained Earnings $72,000 Stock Dividend $72,000
August 14 Dividends Issuable $72,000 Common Stock $24,000 Paid-in Capital in excess of par value $48,000
October 5 Dividend $18,000 Dividends Payable $18,000 (36,000 x $0.50)
Retained Earnings $18,000 Dividend $18,000
5) Retained earningsEnding balance $440,000
Add:
Dividend $17,500
Dividends $15,000
Dividends $15,000
Dividends $72,000
Dividends $18,000 $137,500
Less Beginning balance $360,000
Net income = $217,500
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The amount of money that Ryan earns is directly proportional to the number hours that he works. How much does Ryan earn per hour?
The earnings of Rayan per hour is $5 per hour
The first point = (1, 5)
The second point = (2, 10)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = (10-5) / (2-1)
Subtract the terms
= 5 / 1
= $5 per hour
Hence, the earnings of Rayan per hour is $5 per hour
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Solve the linear programming problem.
On the coordinate (0,7) the value of P is maximum 280.
What is a Linear Inequality?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.
Solution:
First of all to solve the Linear Inequality we need to plot the graph of the given equations.
Kindly find the attached graph
To maximise the equation P = 30x + 40y
we need to find the corner values of x and y.
According to the graph, the corner values of (x,y) are
(5,0), (3,4) and (0,7)
putting the values in the equation P = 30x + 40y
at x = 5 and y = 0
P = 150
at x = 3 and y = 4
P = 250
at x = 0 and y = 7
P = 280
So, on the cordinate (0,7) the value of P is maximum i.e. 280.
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what's the skskksks of slskksksk
For the function f(x) = x + 7, construct and simplify the difference quotient
f(x+h)-f(x) Over h
H
The value of f(x+h)-f(x) = h.
Given function:
f(x) = x + 7
difference quotient = f(x+h) - f(x)
= (x+h) - 7 - (x - 7)
= x + h - 7 - x + 7
= x - x + 7 - 7 + h
= 0 + 0 + h
= h
Therefore the value of f(x+h)-f(x) = h.
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The median monthly rent in 2005 was $694 and $810 in 2010. What was the percent increase in the median monthly rent prices from 2005 to 2010? Round to the nearest tenth of a percent.
The percent increase in the median monthly rent prices is 14.3%
How to calculate the percentage?From the information, the median monthly rent in 2005 was $694 and $810 in 2010.
The increase in the amount will be:
= $810 - $694.
= $116
The percent increase in the median monthly rent prices from 2005 to 2010 will be:
= Increase in amount / Old rent × 100
= 116/810 × 100
= 14.3%
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A grocer mixes two kinds of n ur s. One kind costs $5.00/kg and the other $5.80/kg. How many kilograms of each type are needed to make 40kg of a blend worth $5.50/kg?
15 kilograms of the first type should be mixed with 25 kilograms of the other kind
How to determine the kilograms of each type needed to make 40kg?If the blend costs $5.50/kg, then:
on each kg at $5.00/kg, gain = $0.50 ($5.50 - $5.00)
on each kg at $5.80/kg, loss = $0.30 ($5.50 - $5.80)
Hence 3kg of the first kind must be mixed with 5kg of the second so that the gain on the first (3 x $0.50) is exactly the same as the loss on the second (5 x $0.30)
The required proportion is 3:5
In order to find how many kilograms of each type are needed to make 40kg, we will use the proportion obtained:
We have 3:5, total share = 3+5 = 8
First kind share = 3/8 x 40 kg = 15 kg
Second kind share = 5/8 x 40 kg = 25kg
Therefore, 15 kilograms of the first type is needed and 25 kilograms of the other kind is needed
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Freida would like to invest 200 into a saving account that earns 3% interest. how much interest will Frieda have earned at the end of the year
Answer: 6 dollars
Step-by-step explanation:
Freida would have earned at the end of the year an interest of $6 for the $200 investment at 3% interest for 1 year.
The principle amount is $200
The saving account earns a interest of 3%
We need to calculate that Frieda have earned at the end of the year.
Interest = PRT/100
where p is principle
r is rate of interest
and t is the time period
= 200 x 3 x 1 / 100
= 6
Therefore, Freida would have earned an interest of $6 for the $200 investment at 3% interest for 1 year.
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Coffee Roasters has five main markets for the distribution of their premium coffee at the location coordinates given in the table below. The monthly demand at each distribution center (in 000's of lbs.) is also provided. Coffee Roasters is interested in locating a distribution center to serve these markets.
Table 2
Markets
Coordinates Demand
(‘000s lbs.)
A (20, 15) 75
B (10, 12) 50
C (15, 10) 60
D (15, 20) 80
E (12, 12) 50
Use the information in Table 2 above. What are the x and y coordinates for the center of gravity?
The center of gravity of the distribution center is located at (14.84, 12.84)
What is the center of gravity?The center of gravity is a point at which the total weight of a body can be thought to be located for calculation purposes.
The coordinates of the five distribution centers using the x and y coordinates are;
A(20, 15) 75, B(10, 12) 50, C(15, 10) 60, D(15, 20) 80, E(12, 12) 50
The center of gravity is found using the formula;
[tex]x = \dfrac{m_1\cdot g\cdot x_1+ m_2\cdot g\cdot x_2 + m_3\cdot g\cdot x_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
[tex]y = \dfrac{m_1\cdot g\cdot y_1+ m_2\cdot g\cdot y_2 + m_3\cdot g\cdot y_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
Coordinates of the center of gravity of the distribution center is therefore;
[tex]x = \dfrac{75\times 20+ 50\times 10+ 60\times 15+80\times 15+50\times 12}{75+50+60+80+50} \approx 14.92[/tex]
[tex]y = \dfrac{75\times 15+ 50\times 12+ 60\times 10+80\times 20+50\times 12}{75+50+60+80+50} \approx 12.84[/tex]
The coordinates of the center of gravity of the distribution center is; (14.92, 12.840
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The height of the blade of a wind turbine as it turns through an angle of is given by the function h()=8.5sin(+180⁰) + 40, with height measured in meters.
Find the maximum and minimum positions of the blade.
Explain what the value of 40 in the equation represents.
What is the amplitude? Explain what it represents.
Sketch the function over two cycles.
Considering the sine function in this problem, we have that:
The minimum position in the table is of: 31.5The maximum position in the table is of: 48.5.The value of 40 is the vertical shift of the function.The amplitude is of 8.5.The graph of two cycles is given by the image at the end of the answer.How is the sine function defined?
The general sine function has the definition presented as follows:
f(x) = asin(b(x+c))+d.
The coefficients are given as follows:
a is the amplitude of the sine function.b: The period of the sine function is of 2π/b.c is the phase shift of the sine function.d is the vertical shift of the sine function.For this problem, the function is:
h(θ ) = 8.5 sin (θ + 180°) + 40
The amplitude is of:
a = 8.5.
The function should oscillate between:
-8.5 and 8.5.
However, with the vertical shift of 40, the minimum and maximum values are given as follows:
Minimum value: -8.5 + 40 = 31.5.Maximum value: 8.5 + 40 = 48.5.The measure of each cycle of the cosine function is of:
2π = 360º.
The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.
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Multiply the following using repeated addition: 4(-3)
What is the value of 0.3 + 0.4? Write your answer as a fraction in lowest terms
Answer: 7/10
Step-by-step explanation:
This is the lowest term because you add the numbers.
See picture-multiple choice.
find the value of x.....
Answer:
Below
Step-by-step explanation:
All of the angles labeled sum up to a right angle = 90 °
x+4 + x+4 + x+4 = 90
3x + 12 = 90
3x = 78
x = 26°
Answer:
x = 26
Step-by-step explanation:
from the diagram
∠ BFC + ∠ CFD + ∠ DFE = ∠ BFE , that is
x + 4 + x + 4 + x + 4 = 90
3x + 12 = 90 ( subtract 12 from both sides )
3x = 78 ( divide both sides by 3 )
x = 26
Which diagram matches the following situation? The function h relates Kami's age in years to her height in inches on her birthday that year.
The diagram that matches the given situation is as shown below.
The correct answer is an Option C
We know that, in the mapping of functions, we map certain parameters to a set of other parameter functions.
In this question, we have been given the function h relates Kami's age in years to her height in inches on her birthday that year.
It means that her ages would be one-one the left to map her height. that means there were 2 times were despite her age difference, her height remained the same.
From the given options, the correct one that represents the required mapping is:
h(14) = 64
h(15) = 64
Therefore, the diagram that matches the given situation is as shown below.
The correct answer is an Option C
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What is the length of BD?
Answer:
D stays for 1 and as B is -6
the length of BD should be 7
good luck <3!
In a town 100 people need 700 liters of water to drink everyday at a festival time how many liters of water do they need to drink with their 30 guest
Answer: 210 liters
Step-by-step explanation: