Answers
The correct matrix representation is; [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,
Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)
Given here the points are P₁(1, 3) and P₂(5, 2)
Thus, by the coordinates of the two vectors, we can represent the matrix ;
[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Hence, Option A) is the correct answer.
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Related Questions
I need help with my work
Answers
The area of the interior above the polar axis is -0.858 square units
The area bounded by a polar curveThe area bounded by a polar curve between θ = θ₁ and θ = θ₂ is given by
[tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta[/tex]
Now, since we have the curve r = 1 - sinθ and we want to find the area of the interior above the polar axis, we integrate from θ = 0 to θ = π, since this is the region above the polar axis.
So, [tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}(1 - sin\theta)^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}[1 - 2sin\theta + (sin\theta)^{2}] } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - \int\limits^{\pi}_{0} 2sin\theta \, d\theta+ \int\limits^{\pi}_{0} (sin\theta)^{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{(1 - cos2\theta)}{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{1}{2} } \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} \, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\= [\theta]_{0}^{\pi} - 2[-cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi} \\= [\theta]_{0}^{\pi} + 2[cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi}\\= [\pi - 0] + 2[cos\pi - cos0] - \frac{ [sin2\pi - sin0]}{4}\\= \pi + 2[-1 - 1] - \frac{ [0 - 0]}{4}\\= \pi + 2[-2] - \frac{ [0]}{4}\\= \pi - 4 - 0\\= \pi - 4\\= 3.142 - 4\\= -0.858[/tex]
So, the area of the interior above the polar axis is -0.858 square units
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Compute the monthly payments for the add on interest loan. The amount of the loan is $8,276.17. The annual interest rate is 5.7%. The term of the loan is 5.5 years.
Answers
The monthly payments for this add on interest loan are of $164.71.
Given Information and Formula Used
It is given that for an add on interest loan,
Principal Amount, p = $8,276.17
Annual Interest Rate, r = 5.7%
Term of the loan, T = 5.5 years
The formula for simple interest is given as follows,
I = (p)(r)(t)/100 ............... (1)
The formula for total amount of add on interest is given by,
A = p + I ....................... (2)
Computing the Interest
Substitute the given values of p, r, and t in the formula (1) of interest to get,
I = (8276.17)(5.7)(5.5)/100
I = 259457.9295/100
I = $2,594.58
Computing the Monthly Payment for Add-on Interest Loan
Substituting the values of p and I in the formula (2), we obtain the total amount as,
A = $ (8276.17 + 2594.58)
A = $ 10,870.75
Monthly payment for the add on interest loan = A/t(in months)
= $ (10,870.75/66)
= $164.71
Therefore, monthly payments of $164.71 are to be made for the add on interest loan.
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Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take to ensure that the margin of error is below 29?
Answers
Using the z-distribution, it is found that she should take a sample of 46 students.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:
[tex]6\sigma = 800 - 200[/tex]
[tex]6\sigma = 600[/tex]
[tex]\sigma = 100[/tex]
The sample size is n when M = 29, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]29\sqrt{n} = 196[/tex]
[tex]\sqrt{n} = \frac{196}{29}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]
n = 45.67.
Rounding up, a sample of 46 students should be taken.
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which of the following functions is graphed below?
Answers
The graphed piecewise function is the one in option B.
Which of the given functions is the graphed one?
On the graph, we can see that on the lowest part we have a closed dot at x = 1
And the above part has a open dot at x = 1.
Then the piecewise function is of the form:
y = f(x) for x ≤ 1y = g(x) for x > 1Such that the above part seems to be quadratic, and the part below seems to have a larger degree.
With that, we can conclude that the correct option is:
y = x^2 + 4, for x > 1y = x^3 - 2, for x ≤ 1Which is option b.
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What is the current yield on a 3 year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?
Answers
The current yield of the bond is 9.27%.
What is current yield?
Current yield is the bond rate of return computed as the annual coupon divided by the current price of the bond
The annual coupon is the coupon rate of 10% multiplied by the bond's par value of 100
annual coupon=10%*100
annual coupon=10
current bond price=107.87
current yield=annual coupon/current bond price
current yield=10/107.87
current yield=9.27%
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what is the lower quartile in the following distribution 82, 90, 66, 78, 88, 72, 60, 80 A)69 B)78 C)79 D) 85
Answers
Answer:
A) 69
Step-by-step explanation:
• First , we put the numbers of the distribution in order:
60 , 66 , 72 , 78 , 80 , 82 , 88 , 90
• Notice that the set has 8 numbers which is an even number.
Then
→ the lower quartile is the mean of the set :
60 , 66 , 72 , 78
Which is the average of the two middle numbers 66 and 72.
Then
[tex]\text{the lower quartile}=\frac{66+72}{2} = 69[/tex]
The graph of a quartic function crosses the x-axis at -4 and -2 and touches it at 3. State the equation for the family.
Answers
The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.
How to find the possible equations for a quartic polynomial that passes through the x-axis at three points
Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.
The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:
f(x) = (x - 3)² · (x + 4) · (x + 2)
Now we expand the expression to get the standard form:
f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)
f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72
f(x) = x⁴ - 18 · x² + 6 · x + 72
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Use the information provided to write the general conic form equation of the circle: Ends of a diameter: (11, -2) and (9, 4)
Answers
The equation for a circle is:
[tex](x-a)^{2} + (y-b)^{2} + = r^{2}[/tex]
Where (a,b) is the circle's center and r is the circle's radius.
First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.
The formula to find the mid-point of a line segment giving the two endpoints is:
M = [tex](\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{y} )[/tex]
Where M is the midpoint and the given points are:
[tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} , y_{2})[/tex]
Substituting the values from the two points in the problem gives:
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{-2+4}{2} )[/tex]
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{2-4}{2})[/tex]
[tex]M = (\frac{20}{2} , \frac{2}{2})[/tex]
[tex]M = (10,1)[/tex]
The equations of four lines are given. Identify which lines are parallel.
Line 1: y=−5x−5
Line 2: x+12y=−4
Line 3: y=−2x+4
Line 4: y+8=−15(x−9)
Answers
None of the equation of the line is parallel because there slope are not equal.
How to find lines that are parallel?Parallel line have the same slope.
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence,
y = −5x − 5 , slope = -5
x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12
y = −2x + 4: slope = -2
y + 8 = -15x + 135; y = -15x + 127, slope = -15
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Type 4 points found on the circumference of the following equation. Exact points only, no approximations.
(x-3)^2 +(y+2)^2+49
Answers
The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
How to determine the points on the circumference of the circle?The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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: A native wolf species has been reintroduced into a national forest. Originally 210 wolves were transplanted. After 10 years, the population had grown to 410 wolves. If the population grows exponentially, write an explicit formula for the number of wolves, where w is the number of wolves and t is the number of years.
Answers
The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .
What is the explicit formula?The first step is to determine the growth rate of the wolf species.
Growth rate = [(future population / present population)^(1/number of years)] - 1
[(410 / 210)^(1/10)] - 1 = 6.92
The exponential function would have the form:
FV = P (1 + r)^t
FV = Future population P = Present populationR = rate of growtht = number of yearsw = 210 (1.0692^t)
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Cuál es el número que no pertenece a esta sucesión 99 koma 105 koma 111 koma 117 koma 123 koma 129 koma 135 koma 141 koma 147 koma 153 Cuál es el número que no pertenece esta sucesión 99coma 105 koma 111 koma 117 koma 123 koma 129 koma 135 koma 141 koma 147 koma 153
Answers
Based on the calculations, all of the numbers belong to this arithmetic sequence.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
[tex]a_n = a_1 +(n-1)d[/tex]
Where:
d is the common difference.a₁ is the first term of an arithmetic sequence.n is the total number of terms.Next, we would determine the common difference as follows:
d = a₂ - a₁
d = 105 - 99 = 6.
d = a₃ - a₂
d = 111 - 105 = 6.
d = a₄ - a₃
d = 117 - 111 = 6.
Based on the calculations, all of the numbers belong to this arithmetic sequence.
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Complete Question:
What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153
A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answers
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
The Rangers won five of the first six games. how many of the next 30 games must the rangers wins have twice as many wins as losses?
Answers
Using proportions, it is found that they must win 19 of their next 30 games.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:
The team will have won 5 + x games.The team will have played 36 games.Hence:
[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]
3(5 + x) = 72
15 + 3x = 72
3x = 57
x = 19.
The Rangers must win 19 of their next 30 games.
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Two-thirds of a number x is at least 10. Find the smallest possible prime number x.
Answers
x>15
Smallest prime number of x is 17
The smallest possible prime number x is 17.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
given, Two-thirds of a number x is at least 10.
So,
2/3 x ≥ 10
x ≥ 15
First prime number that is bigger than 15 is 17.
therefore, The smallest possible prime number x is 17.
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Calculate the price elasticity of supply for Bobbie's Bakery's banana bread. When the price changes by 29% the quantity supplied changes by 55%. Round your answer to two decimal places.
Answers
The price elasticity of demand is 1.90.
What is the price elasticity of demand?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.
Price elasticity of supply = percentage change in quantity supplied / percentage change in price
55% / 29% = 1.90
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The inverse of G(x) is a function.
• A. True
• B. False
Answers
Answer: False
Step-by-step explanation:
G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.
tiff basic insurance cost is $613.50 per year. His insurance company offers a typical "safe-driver discount." What would be his rate if he went three years without an accident? Annual premium?
Answers
The rate if he went three years without an accident based on the information about the insurance is $552.15.
How to calculate the insurance?From the information given, his basic insurance cost is $613.50 per year and his insurance company offers a typical "safe-driver discount.
The amount will be:
= 613.50 - (20.45 × 3)
= 552.15
In conclusion, the rate is $552.15.
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AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.
Answers
In the given diagram, the length of CD is 12.7 cm
TrigonometryFrom the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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If 4x+2=5y+3 then y =
Answers
Answer:4x/5-1/5 = y
Step-by-step explanation:
We need to get y by itself
4x+2=5y+3
subtract 3 from both sides
4x-1=5y
divide both sides by 5
4x/5-1/5 = y
Answer:
[tex]4x + 2 = 5y + 3[/tex]
[tex]5y + 3 = 4x + 2[/tex]
[tex]5y = 5x + 2 - 3[/tex]
[tex]5y = 4x - 1[/tex]
[tex] \frac{5y}{5} = \frac{4x - 1}{5} [/tex]
[tex]y = \frac{4x - 1}{5} [/tex]
Find the zeros of polynomial function
X³-4x²-7x+5
Answers
The zeros of the polynomial function are -1.728, 0.56 and 5.167
How to solve the zeros?The polynomial function is given as:
x^3 - 4x^2 - 7x + 5
Next, we plot the graph of the polynomial
From the graph, the polynomial cross the x-axis when
x = -1.728, 0.56 and 5.167
Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167
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x minus 2 is equal to 7
Answers
Add both values 7 + 2 = 9, which is x.
9 - 2 = 7.
3
3
4
Possible inputs for the quadratic when the
output is 3 are
(Note: Fill in the least input first)
or
Answers
[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]
Handre runs a paragliding and adventure touring company. For each paragliding trip (p) he takes he makes $55 and for each adventure tour (a) he makes $75. Last week, he made $2725. Write the equation to represent the relationship between the number of paragliding trips, adventure tours, and his total pay
Answers
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:
55a + 75p = 2725
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
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Landscape artists frequently hand-draw their landscape layouts (blueprints) because this allows them more creativity and precision over their plans. Although done by hand, the layouts must be extremely accurate in terms of angles and distances.
a. A landscape artist has drawn the outline of a house. Describe three different ways to make sure the corners of the house are right angles.
b. A bench needs to be placed in the exact middle of two trees. Describe three different methods the designer can use to find out where to place the bench.
c. The landscape designer has drawn an angle on one side of the yard and wants to draw the same angle on the other side. Describe three different ways he can do this.
Answers
The information given about the landscape is illustrated below:
How to explain the landscape?a. You'll need a measuring tape, two range poles, pegs, and three people.
The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.
Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.
B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.
Method 2; By use of a compass to bisect the distance between both points.
Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.
C The three different ways he can do this.
1) by using a protractor
2) by finding a point
3) by extending the line of the angle until it reaches the other side of the field.
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Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y > 2x + 4
x + y ≤ 6
Answers
The solution to the system of inequalities is (0.667, 5.333)
How to graph the inequalities?The system of inequalities is given as:
y > 2x + 4
x + y ≤ 6
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(0.667, 5.333)
Hence, the solution to the system of inequalities is (0.667, 5.333)
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Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?
The 2 people can arrange themselves in blank ways?
Answers
Using the Fundamental Counting Theorem, it is found that:
The 2 people can arrange themselves in 40 ways.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With one people in the aisle and one in the normal seats, the parameters are:
n1 = 4, n2 = 7
With both in the aisle, the parameters is:
n1 = 4, n2 = 3
Hence the number of ways is:
N = 4 x 7 + 4 x 3 = 28 + 12 = 40.
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The perimeter of a regular hexagon is 72 inches. Find the length of each of its sides.
Answers
12 inches
Step-by-step explanation:A regular polygon is any 2-D shape where all the sides and angles are congruent.
Regular Hexagon
As denoted by the prefix "hexa-", hexagons have 6 sides and internal angles. The perimeter is equal to all 6 sides added together. However, we know that these sides must be congruent because it is a regular hexagon.
Solving for Perimeter
We can create an equation that describes the perimeter of this shape, with "x" representing the length of one side.
6x = 72Since all the sides are equal we can use multiplication instead of addition. To solve this equation, divide both sides by 6.
x = 12This means that all sides must be 12 inches.
Select the story problem that this division problem represent 1/2 2/5 (Repost)
Answers
The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
How to illustrate the division problem?From the information given, it can be seen that 1/2 is divided by 2/5.
In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
In this case, the length is multiplied by width to get the area.
Therefore, the correct option is A.
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A dry Waller wants to order core board for a 15-story elevator shaft. Each floor uses 18.5 sheets.Calculate the number of boards needed. Add 10%of the total for waste.
Answers
Answer:
305.25
Step-by-step explanation:
18.5 for one floor, multiply by 15 to get the amount for 15 floors: 18.5*15 = 277.5 sheets
We need to add 10% for waste, meaning 277.5 plus the waste: 1.1*277.5 = 305.25
The drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
How to determine the number of boards needed. Add 10%of the total for wastecalculate the number of core boards needed for the 15-story elevator shaft, we can follow these
Calculate the total number of sheets for all floors:
Total sheets = Number of floors × Sheets per floor
Total sheets = 15 floors × 18.5 sheets per floor
Total sheets = 277.5 sheets
Add 10% of the total for waste:
Waste percentage = 10% = 0.10 (in decimal form)
Waste sheets = Total sheets × Waste percentage
Waste sheets = 277.5 sheets × 0.10
Waste sheets = 27.75 sheets
Calculate the final number of boards needed (including waste):
Number of boards = Total sheets + Waste sheets
Number of boards = 277.5 sheets + 27.75 sheets
Number of boards = 305.25 sheets
Since you can't have a fraction of a sheet, we need to round up to the nearest whole number.
Therefore, the drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
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