The equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.
What is slope of an equation?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Hence, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = (y2 - y1) / (x2 - x1)
The coordinates of the points are:
(-8, 3) and (-6, 0)
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates we have:
m = (0 - 3)/ (-6 + 8)
m = -3/2
Using the point slope form:
y - y1 = m (x - x1)
Substituting the values of slope and coordinates we have:
y - 3 = -3/2(x + 8)
2(y - 3) = -3(x + 8)
2y - 6 = -3x -24
2y = -3x -18
Hence, the equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.
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A sign in the shape of a circle has a radius of 15 cm. What is the area of the sign? Use 3.14 for pi.
Answer:
The area of the sign is 706.5 cm^2.
Step-by-step explanation:
We know,
The formula of area of a circle,
A = πr^26
Here A is area and r is radius.
Here we have radius is 15 cm, so we can put the values in the above equation and find the area,
A = π * 15^2
A = 3.14 * 225
A = 706.5
The area of the sign is 706.5 cm^2.
Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket. Erik had $480 in his school account and sold tickets for $6 per ticket. How many tickets had to be sold before both accounts had the same amount of money?
Using equations, they sold 165 tickets before both accounts had the same amount of money.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The variables that must be included in the equation are also known as the unknowns.
Given that, Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket.
and Erik had $480 in his school account and sold tickets for the fundraiser at a cost of $6 per ticket.
Let they sold x tickets and they have the amount in their account is y.
After sold tickets, Jaelyn accounts had the amount is
y = 150 + 8x
After sold tickets, Erik accounts had the amount is
y = 480 + 6x
the amount in their account is same, so we compare both equation to find x
150 + 8x = 480 + 6x
arranging like terms in same side
8x - 6x = 480 - 150
2x = 330
divide both sides by 2 we get,
x = 330/2
x = 165
So, they sold 165 tickets before both accounts had the same amount of money.
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here are the first four terms of a number sequence 1 5 13 29.
The rule to continue this sequence is mutiply the previous term by 2 then add 3
work out the 5th term of this sequence
Answer:
61
Step-by-step explanation:
using the rule to find the fifth term from the fourth term 29
5th term = 2 × 29 + 3 = 58 + 3 = 61
WILL GIVE BRAINLIEST WHO EVER ANSWERS CORRECTLY, PLS HELP.
Answer:
Below
Step-by-step explanation:
From the image below you can see that
90 F + 60 L = 160 miles
and given F + L = 2 hours re arrange to F = 2 - L
and substitute this "F" into the first equation
90 (2-L ) + 60 L = 160 Solve for L
180 - 90 L + 60 L = 160
180 - 30 L = 160
- 30 L = -20
L = 2/3 hr then F = 1 1/3 hr ( because they add to '2' )
Solve the equation in the complex number system. X^2+x+8=0
(Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
here's a step-by-step explanation with more detail:
The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:
X = (-b ± √(b^2 - 4ac)) / 2a,
where a = 1, b = 1, and c = 8.
Plugging in the values, we get:
X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1
X = (-1 ± √(-31)) / 2
Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.
X = (-1 ± i * √31) / 2
So, the two solutions to the equation are:
X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2
And these are the two solutions expressed in terms of the imaginary unit i.
The graph of f(x)=sin(x) is transformed to a new function g(x), by reflecting it over the x-axis and shifting it 2 units up. What is the equation of the new function g(x)?
On solving the provided question we can say that here trigonometry y = Asin(Bx + C)+D
What exactly is trigonometry?Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.
(x)=sin(x) consider y = Asin(Bx + C)+D adjusts the amplitude of the function (how high or low it is).
if you want to
B determines how many full wavelengths will occur during a certain time period, and C determines the phase shift (left/right on the axis) (positive values will shift left)
The vertical shift, or D, is up or down. For example, a +3 would move the entire function up 3 units.
In your situation, the amplitude is 4 since you wish to stretch vertically.
Additionally, you want to move it right three units. C = -3 (always the opposite of the direction you wish to go) (always the opposite of the direction you want to go)
g(x) = 4sin(x - 3)
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Circles and please answers please just need help Thank you so much
The area of the shaded region is given as follows:
As = 324(2π - 1) in².
What is the area of the shaded region?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:
A = π x [tex](18\sqrt{2})²[/tex]
A = 648π in².
The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:
A = 18²
A = 324 in².
Hence the area of the shaded region is given as follows:
As = 648π - 324
As = 324(2π - 1) in².
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Sheet Metal Trades To determine the average thickness of a metal sheet, a Sheet metal worker measures it at five different locations. Her measurements are 0.0401, 0.0417, 0.0462, 0.0407, and 0.0428 in. What is the average thickness of the sheet?
The average thickness of the metal sheet is 0.0423 inches.
What do you mean by average?In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.
Mean = (sum of all values) / (number of values)
For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:
Mean = (5 + 7 + 9 + 11 + 13) / 5
Mean = 9
Therefore, the mean of this data set is 9.
The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.
To find the average thickness of the sheet, we need to add the five measurements together and then divide by 5 (the number of measurements):
Average thickness = (0.0401 + 0.0417 + 0.0462 + 0.0407 + 0.0428) / 5
Average thickness = 0.0423 in
Therefore, the average thickness of the metal sheet is 0.0423 inches.
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A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called
Answer:
sampling distribution
Step-by-step explanation:
:)
an=−1+3(n−1)
what is the 55th term in the sequence
The 55th term of the arithmetic sequence is 131.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
Given that, the nth term of the sequence is aₙ= -1+3(n−1)
Here, the 55th term in the sequence is
a₅₅= -1+3(55-1)
= -1+132
= 131
Therefore, the 55th term is 131.
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10. How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.
Answer:
20000*4*5/100=4000
Step-by-step explanation:
Hope this helps!
What is the simplest form of
x^2+ 5x-36/
X^2-16
?
Express the integral f(x, y, z) dV E as an iterated integral in six different ways, where E is the solid bounded by the given surfaces. Y = x2, z = 0, y + 4z = 16
The integral f(x, y, z) dV E as an iterated integral can be expressed in six different ways, where E is the solid bounded by the given surfaces.
To express the integral as an iterated integral, we need to determine the limits of integration for each variable.
First, we can find the limits of integration for z The plane z = 0 is the xy-plane, and the plane y + 4z = 16 can be rewritten as z = (16 - y)/4. So the limits of integration for z are 0 to (16 - y)/4.
Next, we can find the limits of integration for y The surface y = x^2 bounds the solid from below in the y direction, and the plane y + 4z = 16 bounds the solid from above in the y direction. So the limits of integration for y are x^2 to 16 - 4z.
Finally, we can find the limits of integration for x There are no explicit surfaces that bound the solid in the x direction, so we can use the limits of integration for y to determine the limits of integration for x.
With these limits of integration, we can express the integral in six different ways over dz dy dx:
∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫x^2^(16 - 4z) ∫0^g(x, y) f(x, y, z) dz dy dx
where g(x, y) = (16 - y)/4
∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^16-4z ∫0^g(x, y) f(x, y, z) dz dx dy
where g(x, y) = (16 - y)/4
∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^g(x, y) ∫0^(16 - 4z) f(x, y, z) dz dy dx
where g(x, y) = 16 - 4z
∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^g(x, y) f(x, y, z) dy dx dz
where g(x, y) = (16 - 4z)
∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫0^(16 - 4z) ∫y^(1/2)^4 f(x, y, z) dy dz dx
∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^(16 - 4z) f(x, y, z) dz dy dx
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Given the function g(n) = 2 n4 + 20 n3 + 42n2
Its g-intercept is
Its n intercepts are
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
What is a function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.
To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:
g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0
Therefore, the g-intercept of the function g(n) is 0.
To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.
We can factor out a common factor of 2n² to simplify the equation:
2n²(n² + 10n + 21) = 0
This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
Hence,
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
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A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? round your answer to the nearest tenth of a foot.
The height that a ladder reaches is determined by the length of the ladder and its distance from the base of the building.
The ladder can be thought of as the hypotenuse of a right triangle, with the height that the ladder reaches up the building being one of the other sides and the distance of the ladder from the building being the other side.
So, the formula for the height that a ladder reaches can be expressed as:
Height =
Where "Ladder Length" is the length of the ladder, and "Distance from Base" is the distance of the ladder from the building.
Using this formula, we can calculate the height that the 14-foot ladder reaches when set up 4 feet from the base of the building:
Height = ([tex]14^2 - 4^2)^0.5[/tex]
= [tex](196 - 16)^0.5[/tex]
= [tex]180^0.5[/tex]
= 13.416407864
Rounding to the nearest tenth of a foot, the height the ladder reaches is 13.4 feet.
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Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.
y2+7y−2=0
The quadratic equation y2 + 7y - 2 = 0 can be solved using the quadratic formula, which states that the solutions for x in the equation ax^2 + bx + c = 0 are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
We can apply the quadratic formula to this equation by letting a = 1, b = 7, and c = -2:
y = (-7 ± √(7^2 - 4 * 1 * -2)) / 2 * 1
y = (-7 ± √(49 + 8)) / 2
y = (-7 ± √57) / 2
So the solutions to the equation y2 + 7y - 2 = 0 are:
y = (-7 + √57) / 2
y = (-7 - √57) / 2
The solutions to the equation are y = (-7 + √57) / 2 and y = (-7 - √57) / 2.
Help me with this question….
Answer:c
Step-by-step explanation:
Andre pidió prestado al prestado al banco un capital de 350,000 por lo cual el banco le cobrará un 6%de interés mensual cuánto debe pagar por un mes de interés
Andre borrowed 350,000 from the bank and the bank will charge him 6% interest per month. To calculate the amount he has to pay for one month of interest, we can use the following formula:
Interest = Capital * Interest rate
In this case, the capital is 350,000 and the interest rate is 6%. So, we can plug in the values:
Interest = 350,000 * 0.06
Interest = 21,000
Therefore, Andre has to pay 21,000 for one month of interest.
The following information is known about a loan time equals seven years interest rate equals 6% interest equals 840 $.00 what was the principal on a loan
Answer:
$2,000
Step-by-step explanation:
Interest = Principal x Rate x Time
840 = .06(7)p
840 = 0.42p
p = 2000
What is the solution to the equation?
2(x + 7) 2/3 = 8
Answer: x = -1
Step-by-step explanation:
simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there
2) Find the sum of the first 15 terms of the sequence *
(2/7) + (4/7) + (8/7) + ...
Answer:32768/7
Step-by-step explanation:
double every term
Hi! Can someone please help me? Please look in the photo
I would appreciate it a lot thanks :)
Answer:
D
Step-by-step explanation:
Count total dots => 30
Amount of dots under x>=5 => 21
21/30 = 7/10 = 70%
What is your monthly take-home pay if your take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance?
Round intermediate calculations and the final answer to the nearest cent; use 365 days in a year.
Your monthly take-home pay is $
The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.
We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.
Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.
In a week there are 20 hours
So, in 4 weeks, there will be 80 hours
Take - home pay before deductions = 80 * $11.66 = $932.8
Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94
This is equal to ¢ 68094.
Hence, the monthly take-home pay is ¢ 68094.
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A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
792,000 over 7 square centimeters
66,000 over 7 square centimeters
26,400 over 7 square centimeters
2,640 over 7 square centimeters
The label covers approximately 4,800 square centimetres of the wheel of cheese.
What is the lateral surface area of a cylinder?
The lateral surface area of a cylinder can be found using the formula:
L = 2πrh
where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:
L = 2 x (22/7) x 30 x 20
L = 4,800 square centimetres
This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.
The area of a circle can be found using the formula:
A = πr²
where A is the area of the circle, and r is the radius of the circle.
In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:
2 x (22/7) x 30²
= 56,400/7 square centimeters
Subtracting this from the total surface area, we get:
4,800 - 56,400/7
= 33,600/7 square centimeters
= 4,800 square centimeters (rounded to the nearest whole number)
Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.
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estimate the population in the year 2040
The population in the year 2040 is 31800.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 4 is an equation.
We have,
The exponential equation is y = m[tex]a^t[/tex].
Where t is a variable
Now,
In 2007 (t = 0). the population was 12,000.
y = 12000
This means,
12000 = m[tex]a^0[/tex]
12000 = m
And,
In 2019 (t = 12). the population was 23,000.
y = 23000
23000 = m[tex]a^{23}[/tex]
23000 = 12000 [tex]a^{23}[/tex]
23000/12000 = [tex]a^{23}[/tex]
1.92 = [tex]a^{23}[/tex]
[tex]1.036^{23}[/tex] = [tex]a^{23}[/tex]
a = 1.03
Now,
y = 12000 [tex]1.03^t[/tex]
The population in the year 2040.
i.e
t = 33
y = 12000 x [tex]1.03^{33}[/tex]
y = 12000 x 2.65
y = 31800
Thus,
31800 is the population in the year 2040.
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Graph the line with the equation
Answer:
See below
Step-by-step explanation:
You should just use a graphing calculator or an online graphing site to do this
If you were to do this manually on a graph sheet, here is how you proceed
Given line is
y = -x - 4
We need to find 2 points to plot a straight line
Choose x = 0 ==> y = - 0 - 4 = -4
So (0, - 4) is one point
Choose another value for x. x = -4 is a good point
At x = - 4, y = -(-4) - 4 = 0
So (-4, 0) is another point.
Plot these two points on the graph and draw a straight line through those points
The attached graph shows this all
Complete the equation that models the curve of best fit for this data.
curve of best fit: f(x) =
(
)x
X = -3 and its substitution into the first equation results in 3y = 9, which can be written as y = 3. As a result, the system of equations' solution's y-coordinate is 6.
What equation that models the curve of best fit for this data?Equation is a mathematical and physical statement that describes physical phenomena and the relationship between various physical quantities.
It usually consists of a simple variable that presents the physical quantity, followed by a personal variable that may be a personal variable that is focused on the energy.
The system of equations has a solution, and its y-coordinate is 6. This is obtained by solving for x and then putting the specified y-value (2/3) into the equation -x+3y=9. In particular, -x+3(2/3) = 9 becomes -x = 3 when -x+3(2/3) = 9.
Therefore, The system of equations has a solution, and its y-coordinate is 6.
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WILL MARK AS BRAINLIEST
PLS 100PTS
1. what is the reciprocal of 0.0002?
2. what is the reciprocal of c/d
3. what is the reciprocal of 1⅔
4. Given that x²-y²=(x-y)(x+y)
5. Evaluate 173²-127²
6. Evaluate (8.70)²- (8.60)²
7. Evaluate 1003²- 9
Reciprocal of 0.0002 is:
1/0.0002 = 1/(2/10000) = 10000/2 = 5000Question 2Reciprocal of c/d:
1/(c/d) = d/cQuestion 3Reciprocal of 1 2/3 is:
1/(1 2/3) = 1/(5/3) = 3/5Use identity x² - y² = (x - y)(x + y) to solve the following questions.
Question 5Evaluate 173² - 127²:
173² - 127² = (173 - 127)(173 + 127) = 46*300 = 13800Question 6Evaluate (8.70)²- (8.60)²:
(8.70)²- (8.60)² = (8.70 - 8.60)(8.70 + 8.60) = 0.10*17.30 = 1.73Question 7Evaluate 1003²- 9:
1003²- 9 = 1003² - 3² = (1003 - 3)(1003 + 3) = 1000*1006 = 1006000A bag with 12 marbles has 12 blue marbles,a marble is chosen from the bag,What's the probability is blue
100%, If 12 of all 12 marbles are blue, its 100%
1/4 (x - 2/5) = -1 1/2
Step-by-step explanation:
-1 1/2 = -3/2
1/4 × (x - 2/5) = -3/2
let's multiply both sides by 4 to remove the first fraction on the left side :
x - 2/5 = -12/2
x = -12/2 + 2/5 = -6 + 2/5
-6 = -6 × 5/5 = -30/5
so,
x = -30/5 + 2/5 = -28/5 = -5 3/5 = -5.6
please pick any form you need for your result.
