The function that describes the profit earned from the sales of the bikes over a period of x years is: [tex]P(x) = 100x^3 + 6x^2 + 9x[/tex]. The Option A is correct.
Which function describes the profit earned from the sales of the bikes?The profit earned from the sales of the bikes can be calculated by subtracting the cost of manufacturing from the revenue earned. Therefore, the function that describes the profit earned can be represented as:
[tex]P(x) = S(x) - C(x)[/tex]
Substituting the given functions for S(x) and C(x), we get:
[tex]P(x) = (100x^3 + 6x^2 + 97x + 215) - (88x + 215)[/tex]
Simplifying this expression, we get:
[tex]P(x) = 100x^3 + 6x^2 + 9x.[/tex]
Full question "A company sells bikes that are light and fast. The revenue earned over a period of x years can be represented by the function, S(x) = 100x3 + 6x2 + 97x + 215. The cost of manufacturing the bikes can be represented by the function, C(x) = 88x + 215. Which function, P(x), describes the profit earned from the sales of the bikes over a period of x years?"
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L.15 Solve matrix equations using inverses 200 If M=[[7,5,-5]] -8 and N=[[0,7,-7]] 2 xM=N
The solution to the matrix equation is x = [[1.032, -1.226], [-1.226, 0.484]].
To solve matrix equations using inverses, we need to use the inverse of the matrix M and multiply it by the matrix N to find the value of x.
First, we need to find the inverse of matrix M. We can do this by finding the determinant of M and then finding the adjoint of M.
The determinant of M is (7 * -8) - (5 * -5) = -56 + 25 = -31.
The adjoint of M is [[-8, 5], [-5, 7]].
To find the inverse of M, we need to divide the adjoint of M by the determinant of M:
M-1 = (1/-31) * [[-8, 5], [-5, 7]] = [[0.258, -0.161], [0.161, -0.226]].
Now, we can multiply the inverse of M by the matrix N to find the value of x:
x = M-1 * N = [[0.258, -0.161], [0.161, -0.226]] * [[0, 7], [-7, 2]] = [[1.032, -1.226], [-1.226, 0.484]].
Therefore, the solution to the matrix equation is x = [[1.032, -1.226], [-1.226, 0.484]].
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Math part 3 question 1
The value of (g - f) (x) is -3x² + 2x - 4
The value of (f + g) (x) is 3x² + 6x - 6.
The value of (g / f) (x) is (4x - 5) / (3x² + 2x - 1).
The value of (fg) (x) is 12x³ - 7x² -14x + 5.
The solution has been obtained by using operations on functions.
What are operations on functions?
Similar to how we operate on the terms of the functions, we can add, subtract, multiply, and divide functions with overlapping domains using the operations on functions.
We are given f(x) = 3x² + 2x - 1 and g(x) = 4x - 5
(g - f) (x)
⇒(g - f) (x) = g(x) - f(x)
⇒(g - f) (x) = (4x - 5) - (3x² + 2x - 1)
⇒(g - f) (x) = 4x - 5 - 3x² - 2x + 1
⇒(g - f) (x) = 2x - 4 - 3x²
⇒(g - f) (x) = -3x² + 2x - 4
(f + g) (x)
⇒(f + g) (x) = f(x) + g(x)
⇒(f + g) (x) = (3x² + 2x - 1) + (4x - 5)
⇒(f + g) (x) = 3x² + 2x - 1 + 4x - 5
⇒(f + g) (x) = 3x² + 6x - 6
(g / f) (x)
⇒(g / f) (x) = g(x) / f(x)
⇒(g / f) (x) = (4x - 5) / (3x² + 2x - 1)
(fg) (x)
⇒(fg) (x) = f(x) * g(x)
⇒(fg) (x) = (3x² + 2x - 1) * (4x - 5)
⇒(fg) (x) = 12x³ - 7x² -14x + 5
Hence, the required solutions have been obtained.
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Determine the y-intercept.
Answer:
y=-x-2
Step-by-step explanation:
All of them are solved, but I will help to find the relationship.
I found the pattern in my head as I thought about absolute value and proportionality.
Feel free to ask more questions.
A large pickup truck can hold up to 26.4 gallons
of fuel. Which inequality shows this, using g for
the amount of fuel the truck can hold?
Inequality g ≤ 26.4 means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.
What is Inequality ?
In mathematics, an inequality is a comparison between two values that shows whether they are larger than, less than, equal, or greater than or equal to each other.
Common symbols for inequalities include (less than), > (greater than), (less than or equal to), and (greater than or equal to).
The inequality that shows this would be:
g ≤ 26.4
This reads as "g is less than or equal to 26.4".
Therefore, g ≤ 26.4 means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.
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Find the volume of each figure and round awnsers to the nearest tenth if needed
The volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Let us find the volume of the cylinder which has diameter of 22 ft and height of 10 feet.
Diameter=2radius
Radius=22/2=11 feet.
V=πr²h
=3.14×11²×10
=3799.4 cubic feet.
Hence, the volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.
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Zachary earned scores of 20, 25, 22, 18, and 24 on his last five math quizzes. What score will he need to earn on the sixth quiz in order to have a mean score of 22?
Zachary will need to earn a score of 23 on his sixth quiz to have a mean score of 22 for all six quizzes.
How to determine his possible scoreTo find out what score Zachary needs to earn on his sixth quiz to have a mean score of 22,
We need to use the formula for the mean (or average) of a set of numbers:
Mean = (sum of all the scores) / (number of tests)
Zachary's mean score for the first five quizzes is 22.
Using the above as a guide, we have the following:
(20 + 25 + 22 + 18 + 24 + x) / 6 = 22
Evaluate the like terms
(109 + x) / 6 = 22
So, we have
109 + x = 132
Evaluate the like terms
x = 23
Hence, the score must be 23
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Solve x^2 + 7= 43 using square roots
Answer: 6
Step-by-step explanation:
Let's start with what we know. We have the following equation:
x^2 + 7 = 43
Now, we subtract 7 from both sides.
x^2 = 36
Then we take the square root of both sides giving our final answer:
x = 6.
Using Gaussian Elimination to solve an inconsistent system Try & Check: Solve the following system of equati using Gaussian Elimination. x-3y+z=4 -x+2y-5z=3 5x-13y+13z=8
The solution for this system is (x,y,z) = (4,3,-2).
To solve this system of equations using Gaussian Elimination, start by adding 3 times the first equation to the second equation, then add 5 times the first equation to the third equation. This will give you a new set of equations in the following form:
x-3y+z=4
0+y-2z=5
0-8y+10z=24
Now, you can use Gaussian Elimination to solve for y and z. Subtract the second equation from the third equation to solve for z, then use that answer to solve for y in the second equation.
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Using the information from question 2, what is the remaining balance when the lease ends?
$7,516.80
$15,946.50
$12,160.26
$12,660.26
The remaining balance after the lease ends, given the information would be B. $ 12,160.26.
How to find the remaining balance ?The remaining balance after the lease ends can be found by the formula :
= Value of lease - Amount paid towards principal over 3 years - down payment
Amount paid towards principal over 3 years :
= ( 429. 95 x 70 % ) x 12 months x 3 years
= $ 10, 834. 74
The remaining balance is therefore :
= 23, 495 - 10, 834. 74 - 500
= $ 12, 160. 26
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The first part of the question is:
You lease a car valued at $23,495.00 for 3 years at $429.95/month with a $500.00 down payment. If interest is 30% of the payments.
Write an explicit formula for an, the nth term of the sequence 7, -14,28,..
The explicit formula for an, the nth term of the sequence is a(n) = 7(2)^n-1
How to determine the explicit formula of the sequenceFrom the question, we have the following parameters that can be used in our computation:
7, -14,28,..
The above definitions imply that we simply multiply -2 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
First term, a = 7
Common ratio, r = -2
The sequence is represented as
a(n) = a(r)^n-1
So, we have
a(n) = 7(2)^n-1
Hence, the sequence is a(n) = 7(2)^n-1
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Solve for w. (w+7)/(w-1)=(w+5)/(w+2)+1 If there is more than one solution. separa If there is no solution, click on "No solutio
The solution is w = 9/5.
Solve for w.
Start by multiplying both sides by (w-1)(w+2):
(w+7)(w+2) = (w+5)(w-1) + (w-1)(w+2)
Simplifying:
w² + 9w + 14 = w² + 4w + 5
Subtracting w² + 9w + 14 from both sides:
0 = -5w - 9
Dividing by -5:
w = 9/5
The solution is w = 9/5.
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Show that for any triangle ABC, we have line AB intersect
triangle ABC = side AB. That is, the only points of line AB that
lie on the triangle are the points of the side AB.
x = (c - y3) / m
y = m*x + c
Let's prove this using the coordinates of the three points A, B, and C that form triangle ABC. If we take line AB, it will intersect the triangle in the point P.
To prove that the only points of line AB that lie on the triangle are the points of the side AB, we must prove that point P is either point A or point B. We do this by showing that the coordinates of P are the same as the coordinates of either A or B.
The equation of line AB is given by y = mx + c, where m is the slope and c is the y-intercept. We can calculate m and c using the coordinates of points A and B:
m = (y2-y1)/(x2-x1)
c = y1 - m*x1
We can now calculate the coordinates of point P using the equation of line AB and the coordinates of point C:
x = (c - y3) / m
y = m*x + c
Finally, we can compare the coordinates of point P with the coordinates of points A and B. If the coordinates are the same, then point P is either point A or point B, and so line AB intersects the triangle ABC only in the points of side AB.
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Let A be a matrix of size n × n such that
A – 2A^2 -A^4 + 3In = 0
Show that A is invertible and find its inverse.
A is invertible and its inverse is B = (-1/3)(A^3 + 2A - In). To show that A is invertible, we need to find a matrix B such that AB = BA = In, where In is the identity matrix of size
n × n.
First, let's rearrange the given equation:
A – 2A^2 -A^4 + 3In = 0
A^4 + 2A^2 - A + 3In = 0
Next, let's factor out A from the left side of the equation:
A(A^3 + 2A - In) = -3In
Now, let's multiply both sides of the equation by -1/3:
(-1/3)A(A^3 + 2A - In) = In
finally, let's set B = (-1/3)(A^3 + 2A - In):
AB = (-1/3)A(A^3 + 2A - In) = In
Therefore, the inverse of A is B = (-1/3)(A^3 + 2A - In).
To check our answer, we can multiply A and B to see if we get the identity matrix:
AB = A[(-1/3)(A^3 + 2A - In)] = (-1/3)(A^4 + 2A^2 - A) = (-1/3)(0) = In
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Measure the height of the tin in the mm and write down the real height in mm
The measure of the height of the tin in mm can be found using the steps below.
What are Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object.
Here, the activity is to measure the height of a tin.
Height of the tin is the vertical distance from the base of the tin to the top of the tin.
The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.
The measurement has to be in millimeters.
So the best tool is the ruler.
Place the ruler vertically with the point 0 at the base line of the tin.
Mark the point in millimeters that the ruler coincides with the top of the tin.
Read the height to the nearest millimeter.
Hence the height of the tin can be measured as above.
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give the new coordinates of the ordered pair(7,-4) after a 180 degree rotation
The new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the new coordinates of the ordered pair (7, -4) after a 180-degree rotation,
Following the trasformation of 180-degree rotation,
(x, y) ⇒ (-x, -y)
So,
(7, -4) ⇒ (-7, 4)
Therefore, the new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
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200% of what number is 26?
200% of number 13 is 26.
What is percentage?A percentage is a number expressed as a fraction of 100, with the symbol % (percent) added. For example, 50% is the same as 50/100 or 0.5.
To find the number that is 200% of another number, we need to divide the given number by 200% (or 2) and then multiply by 100%. So, to find the number that is 200% of another number that is equal to 26, we can use the following equation:
200% of x = 26
We can simplify this equation by dividing both sides by 200% or 2:
x = 26 ÷ 2
x = 13
Therefore, the number that is 200% of 13 is 26.
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Shan used a surveying tool to map a region of land for his science class. To determine the height of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 43 meters, and the angle was 36°. What is the height of the formation to the nearest meter?
The height of the formation is [tex]31meter[/tex], to the nearest meter.
How is height defined?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Height is used to describe everything that may be measured vertically, high or low.
What types of heights are there?In essence, height relates to elevation, which is the height above a certain level. Furthermore, height refers to any quantifiable distance above a particular level as well as extend upwards (as it is from foot to head). For instance, the elevation of a tower, tree, person, mountain, etc.
We can use the tangent function to calculate the formation's height.
[tex]tan(36^{0} )=\frac{h}{3}[/tex]
Here, we have to multiply both sides by [tex]43[/tex] we get,
[tex]43tan(36^{0} )=h[/tex]
[tex]h=31meter[/tex]
Therefore, the height of the formation to the nearest meter is [tex]31meter[/tex].
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The terminal side of θ in standard position contains the
given point. Find the values of the six trigonometric functions of
θ.
( 4 , 3 )
Answer: Read the step by step explanation for the answer
Step-by-step explanation:
We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):
r = √(4² + 3²) = 5
Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:
sin(θ) = opposite/hypotenuse = 3/5
cos(θ) = adjacent/hypotenuse = 4/5
tan(θ) = opposite/adjacent = 3/4
csc(θ) = hypotenuse/opposite = 5/3
sec(θ) = hypotenuse/adjacent = 5/4
cot(θ) = adjacent/opposite = 4/3
Therefore, the values of the six trigonometric functions of θ are:
sin(θ) = 3/5
cos(θ) = 4/5
tan(θ) = 3/4
csc(θ) = 5/3
sec(θ) = 5/4
cot(θ) = 4/3
help me solve this homework
The correct answer to the listed problems above in their correct scientific notation would be :
1.) 76,450,000 =7.645×10⁷
2.) 0.000327 = 3.27 × 10^-4
3.) 34,000 = 2.4 × 10⁴
4.) 116,000,000,000, = 1.16 × 10¹¹
5.) 0.024= 2.4× 10^-2
6.) 2,800= 2.8× 10³
7.) 100= 1 × 10²
8.) 0.00000qq= q.q × 10^-6
9.) q00,000= q × 10⁵
10.) 0.00633= 6.33 × 10^-3
How to determine the scientific notation of a value?Scientific notation is defined as a form that can be used to represent cumbersome numbers or very small numbers in a way that is most convenient.
The correct scientific notation of the given values are listed below with reasons:
1.) 76,450,000 =7.645×10⁷ and not =7.645×10⁸ when the decimal point is moved so that there is 1 non-zero value in front of the decimal point, the number of zero is 8 not 7.
2.) 0.000327 = 3.27 × 10^-4 and not 3.27 × 10⁴ as the value is less than 1.
3.) 34,000 = 3.4 × 10⁴. Correctly written.
4.) 116,000,000,000, = 1.16 × 10¹¹. Should be 11 not q.
5.) 0.024= 2.4× 10^-2 and not 24 × 10^-2
6.) 2,800= 2.8× 10³. Correctly written.
7.) 100= 1 × 10² and not 1 × 10³
8.) 0.00000qq= q.q × 10^-6. Correctly written.
9.) q00,000= q × 10⁵ and not q × 10^-5
10.) 0.00633= 6.33 × 10^-3 and not 63.3 × 10^-3. This is because the decimal point should be placed immediate after the first whole number.
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the vertices of a polygon are (1,2) (1,6) (7,6) (7,2) (5,0) (3,0) graph the polygon then find its area
Answer:
32 square units
Step-by-step explanation:
You want the area of a polygon with the vertices (1,2) (1,6) (7,6) (7,2) (5,0) (3,0).
CompositionThe graphed figure can be decomposed into a rectangle 4 units high and 6 units wide, together with a trapezoid with bases 6 and 2, and height 2.
FormulasThe area formulas for these parts are ...
A = HW . . . . area of a rectangle of height H and width W
A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h
ApplicationThe rectangle area is ...
A = (4)(6) = 24
The trapezoid area is ...
A = 1/2(6+2)(2) = 8
So, the total area of the polygon is ...
A = 24 +8 = 32 . . . . square units.
The area of the polygon is 32 square units.
Marco bought a pair of jeans on sale for 30% off the regular price of $54.00. What was the discount he
received at the cash register and what was the sale price (not including tax)?
Answer:
Step-by-step explanation:
He received $16.20
because 30% of $54.00 is $16.20
Find the equation of the line perpendicular to y = 35 x − 4 and
passing through the point (1, 2). Write your answer in
slope-intercept form (i.e., y = mx + b)
Answer:
y = -1/35x + 71/35
Step-by-step explanation:
slope of the perpendicular line = -1/35 (the negative reciprocal of 35)
use the point (1,2) and the point-slope form:
y - 2 = -1/35(x - 1) now put it in slope-intercept form
y = -1/35x + 1/35 + 2
y = -1/35x + 71/35
0r, y = -1/35(x - 71)
The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:
1. Find the slope of the given line: The slope of the line y = 35x − 4 is 35.2. Find the slope of the perpendicular line: The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. So, the slope of the perpendicular line is -1/35.3. Use the point-slope form of a line equation to find the equation of the perpendicular line: The point-slope form of a line equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have, we get:y - 2 = (-1/35)(x - 1)
4. Solve for y to get the equation in slope-intercept form: Distribute the -1/35 and then add 2 to both sides of the equation to get y on one side:y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35
So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
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Someone remind me what is the rule for reflecting both x and y on a coordinate plane when you reflect on the x do you change the y or and on the y do you change the x and how would this work on negative example:( -x,y ) and ( x,-y ) *can you show me how to do that using reflection on both x and y* much appreciated (middle school math i don’t why it’s says high school)
Therefore, for the first coordinate point (-x, y), the ultimate reflected points are (-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
Describe coordinate plane.A coordinate system is a technique used to precisely find points or additional mathematical objects on a distance, such as Euclidean space, by using one or so more values or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations.
Here,
The x-coordinate remains constant and the y-coordinate is cancelled when a point on the coordinate plane is reflected over the x-axis (i.e. multiplied by -1). The y-coordinate remains constant and the x-coordinate is cancelled when a point is reflected over the y-axis.
Let's mirror the point (-2, 3) first over the x-axis and then over the y-axis as an illustration:
The x-coordinate remains constant while the y-coordinate is cancelled when reflecting over the x-axis. In light of this, the argument is (-2, -3).
The x-coordinate is cancelled while the y-coordinate remains constant when reflecting over the y-axis. In light of this, the argument is (2, -3).
We can reflect the coordinates (-x, y) and (x, -y) over the x-axis and then over the y-axis:
Therefore, for the first point (-x, y), the ultimate reflected points are
(-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
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In a neighborhood,
out of every
houses participate in a yard sale. What percent of the neighborhood participate in the yard sale?
Let's assume, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.
What is percentage?A number or ratio that can be stated as a fraction of 100 is a percentage. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies. The letter "%" stands for it.
To calculate the percentage of the neighborhood participating in the yard sale, divide the number of houses participating by the total number of houses in the neighborhood and multiply by 100. For example, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.
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URGENT!!! A dolphin swims 665,280 feet in 3 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Rearrange the distance formula, d = rt, to solve for time.
Answer:
Step-by-step explanation:
665,280 dived by 3 = 221760
221760 = distance
221760 = per 1 hour
I tried my best :}
Find the monthly payment on a 30-year, $100,000 mortgage if the
interest rate is 6 percent. hundred.
The monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent is $599.55.
To find the monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent, we need to use the following formula:
Monthly Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))
First, we need to convert the interest rate from a percentage to a decimal by dividing it by 100:
Interest Rate = 6 / 100 = 0.06
Next, we need to calculate the number of payments over the life of the loan. Since there are 12 months in a year, and the loan is for 30 years, the number of payments is:
Number of Payments = 12 * 30 = 360
Now we can plug these values into the formula:
Monthly Payment = ($100,000 * 0.06) / (1 - (1 + 0.06)^(-360)) = $599.55
Therefore, A $100,000 mortgage with a 30 year term and a 6% interest rate has a $599.55 monthly payment.
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How would you describe the graph for the equation |x| = 1 ?
A closed circle on the -1 and a closed circle on the 1.
A closed circle on the -1 and an open circle on the 1.
An open circle on the -1 and an open circle on the 1. A
n open circle on the -1 and a closed circle on the 1.
Answer:A
n open circle on the -1 and a closed circle on the 1.
Step-by-step explanation:
I belive it would be this.
Answer:
A closed circle on the -1 and a closed circle on the 1.
Step-by-step explanation:
|x| = 1
x = 1 or -x = 1
x = 1 or x = -1
Answer: A closed circle on the -1 and a closed circle on the 1.
what time is 4 hours and 47 mins before 3.08pm
Answer:
10:21 AM
Step-by-step explanation:
To get the answer you subtract 4 hours and 47 mins from 3:08 pm
4 hours and 47 minutes before 3:08 pm is 10:21 am.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the time 4 hours and 47 minutes before 3:08 pm, we can subtract 4 hours and 47 minutes from 3:08 pm.
First, let's convert 3:08 pm to 24-hour format:
3:08 pm = 15:08
Now we can subtract 4 hours and 47 minutes:
15:08 - 4:47 = 10:21
Therefore,
4 hours and 47 minutes before 3:08 pm is 10:21 am.
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given a line and a point not on the line , find a plane
containing the point and parallel to the given line
Geometry
To find a plane containing a point P not on a given line l and parallel to l, we can follow these steps:
Choose any point Q on the line l.
Find the vector v that connects point Q to point P, i.e., v = P - Q.
Find the direction vector d of the line l.
Take the cross product of the direction vector d and the vector v, denoted by d x v.
The plane that contains point P and is parallel to line l can be represented by the equation ax + by + cz = d, where (a, b, c) is the vector d x v, and x, y, and z are the coordinates of any point on the plane.
Here's an example to illustrate the process:
Let's say we have a line l that passes through points A(1, 2, 3) and B(4, 5, 6), and a point P(7, 8, 9) not on the line. We want to find a plane containing point P and parallel to line l.
Choose any point Q on the line l. Let's choose Q(1, 2, 3) for convenience.
Find the vector v that connects point Q to point P: v = P - Q = (7-1, 8-2, 9-3) = (6, 6, 6).
Find the direction vector d of the line l: d = (4-1, 5-2, 6-3) = (3, 3, 3).
Take the cross product of the direction vector d and the vector v: d x v = <3, 3, 3> x <6, 6, 6> = <0, 18, -18>.
Write the equation of the plane: 0x + 18y - 18z = d. Since the plane is parallel to line l, we know that the coefficients of x, y, and z are all 0, except for the coefficients of y and z, which are the components of the vector d x v. Therefore, the equation simplifies to 18y - 18z = 0, or y - z = 0.
So the plane containing point P(7, 8, 9) and parallel to the line passing through points A(1, 2, 3) and B(4, 5, 6) can be represented by the equation y - z = 0.
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
The values of x in the given equation, (x-7)^2=36, are x = 13 and x = 1. The correct options are the first and second options - x = 13 and x = 1
Quadratic equation: Calculating the value of xFrom the question, we are to determine the values of x in the given equation. The given equation is:
(x-7)^2=36
To solve the equation (x-7)^2=36, we can take the square root of both sides and solve for x:
(x-7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
So we get two possible values of x:
x = 7 + 6 or x = 7 - 6
x = 13 or x = 1
Hence, the correct values of x are:
x = 13
x = 1
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