[tex] \mathbb{ANSWER:}[/tex]
The slope is -2 while the y-intercept is -1.
[tex] \mathbb{EXPLANATION:}[/tex]
The slope and the intersection with the y-axis of the graph or the y-intercept is already given if you will just simply look at the equation. An equation written in y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. So, the number being multiplied to x or the coefficient of x is the slope while the constant is the y-intercept.
Given that,
x + 1: 3y = 1:7 and 2x : y + 3 = 2:5
Find x and y
The value of 'x' and 'y' in x + 1 : 3y = 1 : 7 and 2x : y + 3 = 2 : 5.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, We can write a : b as, a/b.
Therefore, The given equations can be formed as,
(x + 1)/3y = 1/7 and 2x/(y + 3) = 2/5.
7x + 7 = 3y.
7x - 3y = - 7...(i)
And,
10x = 2y + 6.
10x - 2y = 6...(ii)
Now, Multiplying eqn(i) by 10 and (ii) by 7 we have,
70x - 30y = - 70...(iii) and 70x - 14y = 42...(iv)
Now, By Subtracting (iii) and (iv) we have,
- 16y = - 112
y = 7 and hence x = 2
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The real number
t
corresponds to the point
P(− 2
1
, 2
3
)
on the unit circle. Evaluate the six trigonometric functions of
t
. Write your answer as a simplified frection, if necessary, Part 2 of 6
cost=
Part 5 of 6
The real number t corresponds to the point P(-2/1, 2/3) on the unit circle. To evaluate the six trigonometric functions of t, we can use the coordinates of point P.
Part 2 of 6:
cost= x-coordinate of point P = -2/1 = -2
Part 5 of 6:
sect= 1/cost= 1/(-2)= -1/2
The other four trigonometric functions can be evaluated similarly using the coordinates of point P:
sint= y-coordinate of point P = 2/3
cott= x-coordinate/y-coordinate = (-2/1)/(2/3) = -3
csc t= 1/sint= 1/(2/3)= 3/2
tant= y-coordinate/x-coordinate = (2/3)/(-2/1) = -1/3
Therefore, the six trigonometric functions of t are:
sint= 2/3
cost= -2
tant= -1/3
csc t= 3/2
sect= -1/2
cott= -3
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Long division what is the quotient
(2x^3+ 6x²- 6x + 2)divided by (2x-3)
The quotient (2x^3+ 6x²- 6x + 2)divided by (2x-3) is: [tex]x^2 + 4x + 3[/tex].
How to find the quotient?Quotients are often used in algebra to solve equations and expressions involving division. They are used in everyday life such as when calculating the average speed of a journey.
[tex]x^2 + 4x + 3[/tex]
[tex]---------[/tex]
[tex]2x - 3 | 2x^3 + 6x^2 - 6x + 2 \\ - (2x^3 - 3x^2)[/tex]
[tex]----------[/tex]
[tex]9x^2 - 6x \\- (9x^2 - 13x)[/tex]
[tex]-----------[/tex]
[tex]7x + 2[/tex]
The quotient is:
[tex]x^2 + 4x + 3[/tex]
Therefore, (2x^3 + 6x² - 6x + 2) divided by (2x-3) is equal to (x^2 + 4x + 3) with a remainder of (7x + 2).
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Find the measure of
We know that sum of all angles of a triangle is 180°,
So,
[tex] \sf2x + 1 + 5x + 5 + 90 = 180 \\ \sf7x + 96 = 180 \\ \sf7x = 180 - 96 \\ \sf7x = 82 \\ \tt \: x = 12[/tex]
Now,
[tex] \tt∠1 = 2x + 1 \\ \tt = 2(12) + 1 \\ \tt = 24 + 1 \\ \tt= 25 \degree[/tex]
&
[tex] \tt∠ 2 = 5x + 5 \\ \tt = 5(12) + 5 \\ \tt = 60 + 5 \\ \tt = 65 \degree[/tex]
The required measure of the angles ∠A and ∠C is 25° and 65° respectively.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Consider the given triangle ABC,
Since we know that the sum of the interior angle of a triangle is equal to 180°.
∠A + ∠B + ∠C = 180,
2x + 1 + 90 + 5x + 5 = 180
7x + 6 = 90
7x = 84
x = 12
Now,
∠A = 2(12) + 1 = 25°
∠C = 5(12) + 5 = 65°
Thus, the required measure of the ∠A and ∠C is 25° and 65° respectively.
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(x+4)^2=15
solving by talking the square root
Answer:
x = -4 + √15 and x = -4 - √15.
Step-by-step explanation:
To solve for x in the equation (x + 4)^2 = 15 using square roots, we can take the square root of both sides of the equation, remembering to include both the positive and negative square root:
(x + 4)^2 = 15
Taking the square root of both sides:
±(x + 4) = √15
Now we can isolate x by subtracting 4 from both sides of the equation:
x + 4 = ±√15
x = -4 ±√15
Therefore, the solutions to the equation (x + 4)^2 = 15 are x = -4 + √15 and x = -4 - √15.
Assume a triangle ABC has standard labeling. Determine whether the law of sines (LOS), law of
cosines (LOC) or neither should be used to begin solving the triangle.
a) ????,????,???????????? c
b) ????,????,???????????? ????
c) ????,????,???????????? c
d) ????,????,???????????? ????
The law of sines (LOS) or law of cosines (LOC) should be used to begin solving a triangle depending on the given information. The law of sines is used when we are given two sides and an opposite angle (SSA) or two angles and an opposite side (AAS). The law of cosines is used when we are given three sides (SSS) or two sides and the included angle (SAS).
a) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).
b) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).
c) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).
d) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. . At that rate, how many hours does it take Carts to earn one dollar
It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
What is the linear functiοns?In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.
Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):
E = 10h
$1 = 10h
h = $1/10
Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
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Carys earns one dollar in one-tenth of an hour, or six minutes.
What exactly are linear functions?The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.
Set E (the amount earned) to $1 and solve for h (the number of hours):
According to the given data:E = 10h
$1 = 10h
h = $1/10
As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.
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You are going to paint one side of a building. The wall is 105 feet long and 35 feet high. One gallon of paint covers 317 square feet with a single coat of paint. Find how many gallons should be purchased to apply one coat of paint to the side of the building.
Amount of paint that should be purchased to apply one coat of paint to the side of the building is 12 gallons.
What is area?Area is the amount of space occupied by a two-dimensional shape. That is, it is a quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is the square unit, commonly expressed in square inches, square feet, and so on.
Given,
length of the wall = 105 feet
height of the wall = 35 feet
Area of the wall
= length × height
= 105 × 35
= 3675 square feet
One gallon paints 317 square feet
Number of gallons to paint 3675 square feet
= 3675/317
= 11.59 ≈ 12
Hence, 12 gallons should be purchased to apply one coat of paint to the side of building.
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If the prices of new cars increase an average of 4 times in one year, find the probability of:
(a) No price hikes in a randomly selected in one year and half. (3 marks)
(b) Four price hikes in 2 years. (2 marks)
(c) At most of one price hikes in one year.
The probability of at most one price hike in one year is 0 + 0 = 0.
No price hikes in a randomly selected one and a half year:
The probability of no price hikes in one year is 0, since the average is 4. Therefore, the probability of no price hikes in one and a half years is also 0.
Four price hikes in 2 years:
The average number of price hikes in one year is 4, so the average number of price hikes in 2 years is 8. The probability of exactly 4 price hikes in 2 years is therefore 0, since it is less than the average.
At most one price hike in one year:
The probability of at most one price hike in one year is the sum of the probabilities of 0 and 1 price hikes. The probability of 0 price hikes is 0, as mentioned before. The probability of 1 price hike is also 0, since it is less than the average of 4. Therefore, the probability of at most one price hike in one year is 0 + 0 = 0.
Overall, the probability of no price hikes in a randomly selected one and a half year, four price hikes in 2 years, and at most one price hike in one year are all 0, since they are all less than the average number of price hikes.
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The total of monthly payments for a 4-year loan is $4,200. 0. The APR is 9. 25%. How much money was originally borrowed?
The original amount borrowed was approximately $34,211.1.
To compute the first sum acquired, we can involve the recipe for the current worth of a customary annuity, which addresses a progression of equivalent installments made toward the finish of every period. The recipe is:
PV = [tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]
where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the total number of periods.
In this case, we have monthly payments, so we need to convert the APR to a monthly interest rate by dividing it by 12. We also have a 4-year loan, which means 48 monthly payments.
APR = 9.25%
Monthly interest rate = APR / 12 = 0.0925 / 12 = 0.00771 (rounded to five decimal places)
Total number of payments = 48
Total amount of payments = $4,200.0
Substituting these values into the formula, we get:
PV =[tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]
PV = [tex]$4,200.0 * (1 - (1 + 0.00771)^{(-48)}) / 0.00771[/tex]
PV = $4,200.0 x (1 - 0.5180) / 0.00771
PV = $34,211.1 (rounded to the nearest tenth)
Therefore, the original amount borrowed was approximately $34,211.1.
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List the decimal numbers 4.76, 4.9, 4.08, and 4.7 in order from least to greatest.
4.9, 4.7, 4.08, 4.76
4.7, 4.76, 4.9, 4.08
4.08, 4.7, 4.76, 4.9
4.08, 4.76, 4.9, 4.7
The order of the decimal number from least to greatest is
4.08< 4.7<4.76<4.9.
What is decimal number?Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
Here the given decimal numbers are,
=> 4.76, 4.9, 4.08,4.7
Now ordering the number from smallest to largest
=>4.08< 4.7<4.76<4.9.
Hence the order of the decimal number from least to greatest is 4.08< 4.7<4.76<4.9.
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1 divided 2/6 and i want to know the answer ASAP
1 divided by 2/6 is equal to 3.
Division is a mathematical operation used to divide one number (the dividend) by another number (the divisor) to find out how many times the divisor is contained within the dividend
To divide 1 by 2/6, we need to find out how many times the denominator (2/6) fits into the numerator (1).
One way to approach this is to convert the fraction 2/6 to an equivalent fraction with a denominator of 1. To do this, we can multiply both the numerator and denominator of 2/6 by the same number, in this case 3:
2/6 = (23)/(63) = 6/18
Now, we can divide 1 by 6/18:
1 ÷ 6/18
= 1 x 18/6 (reciprocal of 6/18 is 18/6, which is equivalent to 3)
= 3
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Are these two matrices equal? Justify your answer. [[3,-1,7],[2,6,-9],[-5,4,-2]]*[[-2,-9,7],[4,6,-1],[-5,2,3]]
No, these two matrices are not equal.
The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.
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Two circles inside a square are externally tangent to each other and are tangent to certain sides of the square as shown. The perimeter of the square is $2+\sqrt 2.$ What is the sum of the circumferences of the two circles?
The sum of the circumferences of the two circles is equal to [tex]$2\pi \sqrt 2.$[/tex]
What is circumferences?Circumference is the distance around a two-dimensional shape, such as a circle or ellipse. It can be calculated by multiplying the circumference of the shape by its diameter. The formula for calculating the circumference of a circle is 2πr, where π is the constant 3.14 and r is the radius of the circle. The circumference of an ellipse is more complicated and requires knowledge of the length of its major and minor axes.
The two circles are externally tangent to each other, which means that the distance between them is equal to the sum of their radii. Since the circles are tangent to the sides of the square, the length of one side of the square is equal to the sum of their radii. Since the perimeter of the square is given to be [tex]$2+\sqrt 2,[/tex] we can calculate the length of each side of the square to be [tex]$\sqrt 2.$[/tex] Hence, the sum of the radii of the two circles is equal to [tex]$\sqrt 2.$[/tex]
Therefore, the sum of the circumferences of the two circles is equal to [tex]$2\pi \sqrt 2.$[/tex]
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A store is having a holiday sale and offers no down payment on each credit items. A sound system will cost $29.99 per week for a year. What is the total price?
Answer:$20.40
Step-by-step explanation:
20% off means that the new price of the skirt will be 80% of the original price:
$30(100% – 20%) = $30(80%)
Converting the percent to a decimal gives:
$30(0.8) = $24.00
There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:
$24(100% – 15%) = $24(85%)
Again converting the percent to a decimal gives:
$24(0.85) = $20.40
Estimate the solution of the linear system graphically and check the solution algebraically: A. A line graph showing 2 intersecting lines, the first line passes through the points (0, 5), (-1, 1), and (-3, -6) and the second line passes through the points (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5). B. A line graph showing 2 intersecting lines, the first line passes through the points (3, 4), (2, 1), (1, -2), and (0, -5) and the second line passes through the points (-5, 4), (-4, 3), (-3, 2), (-2, 1), (-1, 0), (0, -1), (1, -2), (2, -3), and (3, -4). C. A line graph showing 2 intersecting lines, the first line passes through the points (3, 4), (2, 1), (1, -2), (0, -5) and (-1, -8) and the second line passes through the points (5, 4), (4, 3), (3, 2), (2, 1), (1, 0), (0, -1), (-1, -2), (-2, -3), and (-3, -4). D. A line graph showing 2 intersecting lines, the first line passes through the points (2, 5), (1, 2), (0, -1), (-1, -4), and (-2, -7) and the second line passes through the points (-6, 5), (-5, 4), (-4, 3), (-3, 2), (-2, 1), (-1, 0), (0, -1), (1, -2), and (2, -3).
Using graph it is seen that the solution of the linear system is found as (-1, 1).
Explain about graphing linear system?It is as easy to graph two straight lines as it is a set of linear equations. The (x,y) arranged pair where it two lines intersect will be the answer when the lines being graphed (cross).When the crossing point has integer coordinates, the graphing method using graph paper may be helpful. However, it is less useful if the coordinates are still not integers. Use an algebraic optimization technique or get out your graphing calculator if it looks that its intersection point does not sit on the intersections of the grids on the graph paper.The points for the two intersecting lines are-
Red points: (0, 5), (-1, 1), and (-3, -6)
Green points: (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).
Graph of there points are plotted.
Thus, it is seen that the solution of the linear system graphically is found as (-1, 1).
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The correct question is-
Estimate the solution of the linear system graphically and check the solution algebraically:
A line graph showing 2 intersecting lines, the first line passes through the points (0, 5), (-1, 1), and (-3, -6) and the second line passes through the points (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).
Cooper decides to estimate the volume of a grapefruit by modeling it as a sphere. He measures its radius as 6.7 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic............
Let ????(x, y) = 6y(1 − y), 0 ≤ x ≤ y ≤ 1 ???????????? z????????o
????l????e????ℎ???????????? be a valid joint density
function. Find ????(????|???? = y)
The conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.
So the answer is ????(????|???? = y) = 1/y.
The question asks us to find the conditional density function ????(????|???? = y) given the joint density function ????(x, y) = 6y(1 − y), 0 ≤ x ≤ y ≤ 1.
To find the conditional density function, we need to divide the joint density function by the marginal density function of y.
The marginal density function of y can be found by integrating the joint density function with respect to x:
????(y) = ∫????(x, y) dx = ∫6y(1 − y) dx = 6y(1 − y) ∫dx = 6y(1 − y) (x) |0≤x≤y = 6y(1 − y) (y - 0) = 6y^2(1 − y)
Now we can find the conditional density function by dividing the joint density function by the marginal density function:
????(????|???? = y) = ????(x, y)/????(y) = 6y(1 − y)/6y^2(1 − y) = 1/y
Therefore, the conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.
So the answer is ????(????|???? = y) = 1/y.
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Please can someone help me
Answer:
Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Step-by-step explanation:
c is the ansswer
URGENTT
Latasha is painting a mural for a school project. A model of the mural is shown below. In the model, side T is 7 inches and side S is 9.4 inches
Answer:Latasha should ask her mom for help
Step-by-step explanation:
Shea runs a carpet cleaning business. The average cost to shea per cleaning is $30. Shea charges $60 per cleaning. Shea’s fixed plus variable costs per month total $1,500. How many carpet cleaning does shea need to do per year to break even?
Shea needs to do 600 carpet cleaning per year to break even.
What is revenue?
Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.
To break even, the total revenue Shea generates from the carpet cleaning business must be equal to the total cost of running the business.
Let's first calculate the total cost of running the business per year:
Total Cost = Fixed Costs + Variable Costs
Since the fixed plus variable costs per month total $1,500, the total cost per year would be:
Total Cost = $1,500 x 12
Total Cost = $18,000
Now, let's calculate the profit that Shea makes per cleaning:
Profit per Cleaning = Price per Cleaning - Cost per Cleaning
Profit per Cleaning = $60 - $30
Profit per Cleaning = $30
So, Shea makes a profit of $30 per cleaning.
To break even, the total profit generated by the number of cleanings Shea does per year should be equal to the total cost of running the business per year:
Total Profit = Total Revenue - Total Cost
If x is the number of carpet cleaning Shea needs to do per year to break even, then:
Total Revenue = Price per Cleaning x Number of Cleanings per Year = $60x
Total Profit = Profit per Cleaning x Number of Cleanings per Year = $30x
Setting Total Profit equal to Total Cost:
$30x = $18,000
x = $18,000 / $30
x = 600
Therefore, Shea needs to do 600 carpet cleaning per year to break even.
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AABC has vertices A(-4,6), B(-6, -4), and C(2,-2).
The following transformation defines AA'B'C':
AA'B'C' =D 5/2 (AABC)
The required vertices of [tex]$\Delta A'B'C'$[/tex] are A'(-10, 15), B'(-15, -10), and C'(5, -5).
How to find the dilated coordinates of triangle?The transformation that defines AA'B'C' can be described as a dilation with center at the origin and scale factor of 5/2.
To find the coordinates of A', B', and C', we can use the following formulas:
[tex]$\begin{align*}A'(x,y) &= \left(\frac{5}{2}\right)x, \left(\frac{5}{2}\right)y \B'(x,y) &= \left(\frac{5}{2}\right)x, \left(\frac{5}{2}\right)y \C'(x,y) &= \left(\frac{5}{2}\right)x, \left(\frac{5}{2}\right)y \\end{align*}$[/tex]
Using the coordinates of A(-4,6), B(-6, -4), and C(2,-2), we can calculate the coordinates of A', B', and C' as follows:
For point A(-4,6), we have:
[tex]$A'(x,y) = \left(\frac{5}{2}\right) x, \left(\frac{5}{2}\right) y = \left(\frac{5}{2}\right) (-4), \left(\frac{5}{2}\right) (6) = (-10, 15)$[/tex]
Therefore, the coordinates of A' are (-10, 15).
For point B(-6,4), we have:
[tex]$B'(x,y) = \left(\frac{5}{2}\right) x, \left(\frac{5}{2}\right) y = \left(\frac{5}{2}\right) (-6), \left(\frac{5}{2}\right) (4) = (-15, 10)$[/tex]
Therefore, the coordinates of B' are (-15, 10).
For point C(2,2), we have:
[tex]$C'(x,y) = \left(\frac{5}{2}\right) x, \left(\frac{5}{2}\right) y = \left(\frac{5}{2}\right) (2), \left(\frac{5}{2}\right) (-2) = (5, -5)$[/tex]
the coordinates of C' are (5, -5).
Therefore, the vertices of [tex]$\Delta A'B'C'$[/tex] are A'(-10, 15), B'(-15, -10), and C'(5, -5).
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Work out the area of trapezium L.
If your answer is a decimal, give it to 1 d.p.
Step-by-step explanation:
Refer to pic............
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 3x^(2)+3x^(-3)-2
Yes, the algebraic expression [tex]3x^(2)+3x^(-3)-2[/tex] is a polynomial.
A polynomial is an algebraic expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, as well as non-negative integer exponents. The given algebraic expression satisfies these conditions, so it is a polynomial.
To write the polynomial in standard form, we need to rearrange the terms in descending order of exponents. In this case, the term with the highest exponent is [tex]3x^(2)[/tex], followed by the term with the lowest exponent, [tex]3x^(-3)[/tex], and finally the constant term, -2.
Therefore, the polynomial in standard form is:[tex]3x^(2)+3x^(-3)-2 = 3x^(2)-2+3x^(-3)[/tex] So, the polynomial in standard form is [tex]3x^(2)-2+3x^(-3)[/tex].
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Please explain this more in depth. How does the chain rule allow
the first equation to reduce to the second equation? Some simple
explanation of the chain rule would also be helpful.
The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).
In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.
Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.
Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.
In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
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Morganville and Newton are 36 miles apart. On a map, the two cities are 6 inches apart. What is the map scale?
The scale of the map is 1 inch for 6 miles
How to determine the scale of the mapFrom the question, we have the following parameters that can be used in our computation:
Distance apart = 36 miles
Distance on the map = 6 inches
Using the above as a guide, we have the following:
Scale = Distance on the map/Distance apart
Substitute the known values in the above equation, so, we have the following representation
Scale = 6 inches/36 miles
Evaluate
Scale = 1 inch/6 miles
Hence, the scale is 1 inch per 6 miles
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Find y(t) of the following equation.
y’’ + 3y’ - 4y = 2 , y(0) = 0, y’(0) = 0
The given equation is a second order differential equation, which can be solved using the method of undetermined coefficients. The homogenous solution of the equation is:
yh = c1e2t + c2e-t
By applying the initial conditions, we get: c1 = 0, c2 = 0.
Therefore, the homogenous solution is: yh = 0.
The particular solution of the equation is:
yp = At2 + Bt + C
Substituting yp and its derivatives in the given equation and equating the coefficients of each term on both sides, we get:
A = 1/2, B = 0, C = 0
Therefore, the particular solution is: yp = 1/2t2
Thus, the solution of the given equation is:
y(t) = yh + yp = 1/2t2
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Which description best represents the end behavior of the
function f(x)= -x + 5x³ - 2x+5?
Hint: Use the examples in the table to help you answer the
question.
Polynomial End Behavior
Equation Degree Leading Coefficient
y-x²
y=-x²
y=x³
y=-x³
Even
Even
Odd
Odd
Positive
Negative
Positive
Negative
End Behavior
x)+∞, as x-+
F(x), as x--
F(x), as x4+
x), as x--co
x) +∞, as
x-+00
x) +00, as x--
x)-00, as x-+00
Example
The correct description for best represents the end behavior of the
function f (x) = - x⁴ + 5x³ - 2x + 5 is,
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = - x⁴ + 5x³ - 2x + 5
Now, We have;
Degree of the polynomial = 4
Hence, We get;
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
Thus, The correct description for best represents the end behavior of the
function f (x) = - x⁴ + 5x³ - 2x + 5 is,
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
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If g(v)=11v^(4)+29v^(3)+19v^(2)+22v+39, use synthetic division to find g(-2). Submit
The answer is g(-2) = 15.
To find g(-2) using synthetic division, we need to follow these steps:
Write down the coefficients of the polynomial in descending order. The coefficients are 11, 29, 19, 22, and 39.
Write down the value of the divisor in the leftmost column. In this case, the divisor is -2.
Bring down the first coefficient (11) to the bottom row.
Multiply the bottom row value (11) by the divisor (-2) and write the result (-22) in the next column.
Add the coefficient in that column (29) to the result (-22) and write the sum (7) in the bottom row.
Repeat steps 4 and 5 until you reach the last column. The final result in the bottom row is the remainder.
The synthetic division should look like this:
-2 | 11 29 19 22 39
| -22 -14 -10 -24
-------------------
11 7 9 12 15
Therefore, g(-2) = 15.
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2log_(3)(x)=4 log_(3)(x^(2))=4 x^(2)=3^(4) x^(2)=81 x=9,-9 x=9 and x=-9 are true solutions x=9 and x=-9 are extraneous solutions x=9 is an extraneous solution and x=-9 is a true solution x=9 is a true solution and x=-9 is an extraneous solution
Answer:
9
Step-by-step explanation:
