Answer (Please mark as brainliest):
STATEMENTS
∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
BD ≅ BD
∆ABD ≅ ∆DCB
REASONS
Given
Reflexive Property of Congruence
By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.
Therefore, ∆ABD ≅ ∆DCB by SSS.
Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?
A. ask every tenth student she sees ac a concert
B. ask every fifth student entering her school in the morning
C. ask every third student she encounters at the mall
D. ask every student at a local movie theater
the option that is not a way for Isabelle to get a representative sample of the most popular music group of students in her community is D. ask every student at a local movie theater.
The reason is that asking every student at a local movie theater is a form of convenience sampling, where the sample is chosen based on convenience and accessibility, rather than being selected randomly from the entire population of interest. It may not provide a representative sample of the community's music preferences since the population of students who attend a movie theater may not be the same as the general population of students in the community. In contrast, options A, B, and C suggest a form of systematic sampling, where every nth student is selected from a randomly chosen starting point, which can help to ensure that the sample is more representative of the general population of students in the community.
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What is the area, in square inches, of the trapezoid below?
Answer:
A = (1/2)(3.6)(5.1 + 8.5 + 5)
= 1.8(18.6)
= 33.48 square inches
help please
A car was valued at $42,000 in the year 1994. The value depreciated to $11,000 by the year 2006.
A) What was the annual rate of change between 1994 and 2006?
r=------------ Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2010 ?
value=$---------------- Round to the nearest 50 dollars.
(A) Between 1995 and 2003, there was a change at an annual rate of -0.1463
(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.
(C) The automobile would be worth $5,844.24 in 2007.
What is depreciation?Depreciation is an annual income tax deduction that enables you to recoup the purchase price or other basis of a specific item over the course of its use.
It is a provision for the property's normal wear and tear, degeneration, or obsolescence.
As the years pass, the car's value drops.
This process is known as depreciation.
Depreciation is the decrease in asset value brought on by normal wear and tear.
Use this formula to calculate the annual rate of change:
g = (FV/PV)¹⁾ⁿ - 1
Now, using the formula calculate as follows:
(11000/3900)¹⁾⁸ - 1
-0.1463 = -14.63%
The following formula can be used to estimate a car's worth in 7 years:
FV = P (1 + g)ⁿ
$39,000 x (1 - 0.1463)¹²
$39,000 x 0.8537¹² = $5,844.24
Therefore, (A) between 1995 and 2003, there was a change at an annual rate of -0.1463
(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.
(C) The automobile would be worth $5,844.24 in 2007.
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Correct question:
A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.
A)What was the annual rate of change between 1995 and 2003? (Round to 4 decimal places)
B)What is the correct answer to part A written in percentage form?
C)Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007?
Which of the following would a scale be used to measure?
the weight of a fish after it is caught
the length of a piece of wood for building a treehouse
the distance between two points on a trail
the volume of water a fish tank can hold
Answer:
a) The weight of a fish after it's caught
A community college has 1400 parking spots on campus. When it builds its new library, the college will lose 63 of its parking spots. What will be the percent decrease in the number of available parking spots?
According to the question we can conclude that the percent decrease in the number of available parking spots is 4.5%.
What is percentage?In mathematics, a percentage is a number or ratio that's also expressed as just a fraction from 100. Occasionally, the acronyms "pct.," "pct," as well as "pc" are also used. Yet it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that what a number is just a percentage by placing it next to it. For instance, you score a 75% if you properly answered 75 out of questions in total on something like a test (75/100). Divide the money even by total as well as multiply the outcome by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
Given,
To find the percent decrease in the number of available parking spots, we need to calculate the difference between the initial number of parking spots and the new number of parking spots, and express it as a percentage of the initial number of parking spots.
The initial number of parking spots is 1400, and the new number of parking spots after the library is built is 1400 - 63 = 1337.
The difference between the initial number of parking spots and the new number of parking spots is 1400 - 1337 = 63.
To express this difference as a percentage of the initial number of parking spots, we divide the difference by the initial number and multiply by 100:
(63 / 1400) x 100 = 4.5%
Therefore, the percent decrease in the number of available parking spots is 4.5%.
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Paula wants to retire. She has an account that has $250,000. It is earning an APR of 5.63%. What is the monthly yield on the account for a 20-year period?
(Please round your answer to the nearest dollar.)
Paula's account will earn a total of $282,546.60 in interest over the next 20 years, in addition to her initial investment of $250,000.
The monthly yield on Paula's account can be calculated using the following formula:
Monthly Yield = (Account Balance x Annual Percentage Rate) ÷ (12 x 100)
Monthly Yield = (250,000 x 5.63) ÷ (12 x 100) = $1,177.29
So, Paula's account will earn a monthly yield of $1,177.29 for the next 20 years. To calculate the total amount earned over the 20-year period, we can multiply the monthly yield by the number of months in 20 years (i.e., 240):
Total Earnings = Monthly Yield x Number of Months
Total Earnings = $1,177.29 x 240
Total Earnings = $282,546.60
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Need help with HW question 6
When diagonalizing Matrix A = PDP^(-1) and λ1 = (1 + √5)/2 and λ2 = (1 - √5)/2 are the eigenvalues of A, and [0 1] is an eigenvector associated with both λ1 and λ2.
How to diagonalize the matrix ATo diagonalize a matrix, we need to find its eigenvalues and eigenvectors. Let's begin by finding the eigenvalues of A.
The characteristic equation is given by:
det(A - λI) = 0
where I is the identity matrix and λ is the eigenvalue.
For matrix A, we have:
A - λI = [1 - λ 0 ]
[6 -1 - λ]
det(A - λI) = (1 - λ)(-1 - λ) - 6(0) = λ^2 - λ - 1 = 0
Using the quadratic formula, we find that the eigenvalues are:
λ1 = (1 + √5)/2
λ2 = (1 - √5)/2
Now let's find the eigenvectors associated with each eigenvalue. For λ1 = (1 + √5)/2, we have:
(A - λ1I)x = 0
[1 - λ1 0] [x1] = [0]
[6 -1 - λ1] [x2] [0]
which simplifies to:
[-(√5-1)/2 0] [x1] = [0]
[6 -√5-1] [x2] [0]
From the first row, we have x1 = 0. Substituting this into the second row, we get:
(√5+1)x2 = 0
Since x2 cannot be zero (otherwise the eigenvector would be the zero vector), we have:
x2 = 1
Therefore, the eigenvector associated with λ1 is:
v1 = [0 1]
Similarly, for λ2 = (1 - √5)/2, we have:
(A - λ2I)x = 0
[1 - λ2 0] [x1] = [0]
[6 -1 - λ2] [x2] [0]
which simplifies to:
[-(√5+1)/2 0] [x1] = [0]
[6 -√5+1] [x2] [0]
From the first row, we have x1 = 0. Substituting this into the second row, we get:
(√5-1)x2 = 0
Again, since x2 cannot be zero, we have:
x2 = 1
Therefore, the eigenvector associated with λ2 is:
v2 = [0 1]
Now we can use the eigenvectors to diagonalize the matrix. The diagonal matrix D will have the eigenvalues on the diagonal and zeros elsewhere. The matrix P will have the eigenvectors as columns.
D = [λ1 0]
[0 λ2]
P = [v1 v2] = [0 0]
[1 1]
To check that this is the correct diagonalization, we can verify that:
A = PDP^(-1)
where P^(-1) is the inverse of P. Since P is not invertible (the columns are linearly dependent), we can use the pseudoinverse instead:
A = PD†P
where D† is the pseudoinverse of D. We have:
we have diagonalized A as:
A = PDP^(-1)
where:
D = [λ1 0]
[0 λ2]
P = [v1 v2] = [0 0]
[1 1]
and λ1 = (1 + √5)/2 and λ2 = (1 - √5)/2 are the eigenvalues of A, and [0 1] is an eigenvector associated with both λ1 and λ2.
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✓
M
T
S
8
V125°
50
N
Practice Problem 3
Q
In Circle V, mzCVQ = 125° and m/ZVW = 50⁰.
Calculate the mCQW, given that V is the center and Cz
and MQ are diameters.
Submit
After answering the presented question, we can conclude that angles m/CQW = 180° - 125° - 50° => m/CQW = 5° Therefore, m/CQW = 5°.
what are angles?An angle is a shape in Euclidean geometry that is made up of two rays that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are located. When two planes collide, an angle is generated. They are referred to as dihedral angles. An angle in plane geometry is a possible configuration of two radiations or lines that express a termination. The word "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the place where the two rays, also known as the angle's sides, meet.
The measure of an inscribed angle is half the measure of its intercepted arc, according to the inscribed angle theorem.
Because C and Q are on the same diameter MQ, m/CQM = 90°. As a result, the intercepted arc CZQ measures 180° - 90° = 90°.
Similarly, because W and Q are on the CW diameter, we have m/CWQ = 90°. As a result, the intercepted arc WVQ measures 180° - 90° = 90°.
m/CQW = 180° - m/CVQ - m/ZVW
m/CQW = 180° - 125° - 50°
m/CQW = 5°
Therefore, m/CQW = 5°.
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Rework the problem so that you pay off the lower interest card first. 5) How much money do you save by paying off the higher interest card first?
By paying off the higher interest card first, we save $1932 - $1579 = $353 in interest charges over the course of 56 months.
The conventional method is to pay off the credit card with the highest interest rate first if we have two credit cards with differing interest rates. We can figure out how much money we save by reworking the issue to pay off the card with the lowest interest rate first.
Consider that we have two credit cards: Card A, which has a $5,000 debt and a 15% interest rate, and Card B, which has a balance of $3,000 and a 10% interest rate. We can save money by lowering the interest paid on Card B while still making minimum payments on Card A if we pay that card off first.
It would take us around 22 months to pay off Card B and 36 months to pay off Card A if we made the minimum payments of $300 on Card B and $150 on Card A each month. We would pay interest on Card A in total of $1932 and Card B in total of $386 throughout this time.
Instead, if we pay off Card A first, we would devote the remaining $300 to Card A until it is completely paid off while continuing to make the minimum payments on Card B. We would need around 24 and 32 months, respectively, to pay off Card A and Card B. We would pay interest on Card A for a total of $1579 and Card B for a total of $282 during this time.
We therefore save $1932 - $1579 = $353 in interest fees over the course of 56 months by paying off the higher rate card sooner.
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or What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 8 ft 6 ft square feet
The surface area of the cylinder has a radius of 8cm and a height of 6cm is 703.36 square feet.
To calculate the surface area of a cylinder, we need to add the area of the top and bottom circles to the area of the curved side.
The formula for the area of a circle is:
A = [tex]\pi r^2[/tex]
where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius.
The formula for the curved surface area of a cylinder is:
C = 2πrh
where C is the curved surface area, r is the radius, and h is the height of the cylinder.
Given that the radius is 8cm and the height is 6cm, we can calculate the surface area as follows:
Area of top circle =
Area of bottom circle =[tex]\pi r^2[/tex] = 3.14 x [tex]8^2[/tex] = 200.96 cm square
Curved surface area = 2πrh = 2 x 3.14 x 8 x 6 = 301.44 cm square
Therefore, the total surface area of the cylinder is:
Total surface area = Area of top circle + Area of bottom circle + Curved surface area
Total surface area = 200.96 [tex]cm^2[/tex] + 200.96 [tex]cm^2[/tex] + 301.44 [tex]cm^2[/tex]
Total surface area = 703.36 [tex]cm^2[/tex]
What is the surface area of the cylinder? Use 3.14 for pi and round your answer to the nearest hundredth with radius 8ft and height 6ft.
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PLEASE ANSWER ASAP WILL MARK BRAINLIST
given circle B what is angle ADC
The measure of the angle ADC in circle B is 23 degrees.
What is circle?A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles. It resembles a line segment in several ways.
For the given circle B, the measure of angle ABC is 46 degrees.
Now, the angle subtended by the circle is half the angle subtended at the center.
Angle ADC = 1/2(angle ABC)
Angle ADC = 1/2(46)
Angle ADC = 23 degrees.
Hence, the measure of the angle ADC in circle B is 23 degrees.
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(Need Help please and thank you!)
Answer:
The answer is the first graph.
Step-by-step explanation:
f(0) = l0-2l + 1
f(0) =2 + 1
f(0) = 3
(0,3)
f(1) = l1-2l + 1
f(1) = 1 + 1
f(1) = 2
(1,2)
f(2) = l2 -2 l + 1
f(2) = 0 + 1
f(2) = 1
(2,1)
f(3) = l3-2l + 1
f(3) = 1 = 1
f(3)
2
(3,2)
f(4) = l4-2l + 1
f(4) = 2 + 1
f(4) = 3
(4,3)
If you graph each of the ordered pairs that are in bold, you will see that it matches the first graph.
Helping in the name of Jesus.
Answer:
a
Step-by-step explanation:
A ship is traveling at 13 knots bearing 305° from New York. How fast is the ship traveling south?
Which of the following numbers is included in the graph of 3x +8 > -2x - 16
a) -5
b) -6
c) -4
d) -20
The answer is Option (C) -4.
which symbols are represented by a closed circle on a number line?
Answer:
A closed circle on a number line represents an inclusive boundary, meaning that the endpoint is included in the set of values being represented. For example, if a closed circle is placed at the number 2 on a number line, it means that 2 is included in the set of values being represented. In interval notation, this would be written as [2, ...).
The floor of a storage unit is 7 meters long and 2 meters wide. Starting at the far left corner, Irma walks down the length, across the width, and then diagonally back to the far left corner. How far does Irma walk? If necessary, round to the nearest tenth.
Answer: 14.4
Step-by-step explanation:
Please see the attached
After 3 years, there will be $2,810.95 in the Richardsons' account and the interest earned on the Richardsons' investment after 3 years will be around $310.95.
(a) The interest rate per month is r = 1.36% ÷ 12 = 0.01133333. The number of compounding periods in 3 years is n = 3 × 12 = 36. Therefore, the amount A after 3 years is:
A = 2500 × (1 + r)ⁿ
A = 2500 × (1 + 0.01133333)³⁶
A = $2,810.95
Therefore, after 3 years, there is $2,810.95 in the Richardsons' account.
(b) The interest earned is the difference between the final amount and the initial investment:
Interest = A - P
I = $2,810.95 - $2,500
I = $310.95
Therefore, the interest earned on the Richardsons' investment after 3 years is $310.95.
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how do i find these
The value of
1. v = 40cm
2. w= 126°
3. x = 30°
4. y = 63cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
The ratio of corresponding sides of similar triangles are equal.
Therefore ;
60/v = 72/48
48 × 60 = 72v
2880 = 72v
divide both sides by 72
v = 2880/72
v = 40cm
since the two triangles are similar w = 126°
x = 180-(126+24)
x = 180- 150
x = 30°
then;
y/42 = 72/48
48y = 42 × 72
48y = 3024
y = 3024/48
y = 63 cm
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unit 3 homework 7 point slope form: Need answers for front and back
the equation of the line that passes through the 7 points (1, 3), (2, 5),
(3, 7), (4, 9), (5, 11), (6, 13), and (7, 15) is y = 2x + 1.
The point-slope form of a linear equation is a way to write the equation of a line when you have a known point on the line and the slope of the line. The point-slope form is written as:
[tex]y - y_{1} = m(x - x_{1} )[/tex]
where m is the slope of the line, and (x1, y1) is the known point on the line.
The 7-point slope form is a variation of the point-slope form that requires knowing 7 points on the line, rather than just one. It is written as:
[tex](y - y_{1} ) = ((y_{2} - y_{1} ) / (x_{2} - x_{1} ))(x - x_{1} )[/tex]
where[tex](x_{1} , y_{1} ) and (x_{2} , y_{2} )[/tex] are two points on the line with known coordinates, and m is the slope of the line, which can be calculated using the two points.
To use the 7-point slope form to write the equation of a line, you need to know the coordinates of 7 points that lie on the line. Once you have these coordinates, you can choose any two of them to use as [tex](x1, y1) and (x2, y2)[/tex] in the formula, and then solve for the slope m. Once you have the slope, you can plug in the coordinates of any one of the 7 points into the 7-point slope form to find the equation of the line.
For example, let's say we have the following 7 points on a line: (1, 3), (2, 5), (3, 7), (4, 9), (5, 11), (6, 13), and (7, 15).
We can choose any two of these points to use as[tex](x_{1} , y_{1} ) and (x_{2} , y_{2} )[/tex] in the 7-point slope form. Let's choose (1, 3) and (2, 5).
The slope m can be calculated as:
[tex]m = (y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]
m = (5 - 3) / (2 - 1)
m = 2
Now we can plug in the values of[tex](x_{1} , y_{1} )[/tex] , m, and x into the 7-point slope form to get the equation of the line:
[tex](y_{2} - y_{1} ) =m (x_{2} - x_{1} )[/tex]
(y - 3) = 2(x - 1)
y - 3 = 2x - 2
y = 2x + 1
So the equation of the line that passes through the 7 points (1, 3), (2, 5), (3, 7), (4, 9), (5, 11), (6, 13), and (7, 15) is y = 2x + 1.
In summary, the 7-point slope form is a variation of the point-slope form that requires knowing the coordinates of 7 points on a line. Once you have these coordinates, you can use the 7-point slope form to find the equation of the line.
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Which equation correctly uses the value of x to
represent the cosine of angle A?
O cos(53⁰) =
O cos(53⁰) =
O cos(53⁰) =
O cos (53⁰) = 5
PLEASE HELP
Answer: y/5
Step-by-step explanation:
5 is the hypotenuse of the triangle and it always goes at the bottom of the fraction. Cosine is the closest two sides to the angle. Giving the answer y/5
Step-by-step explanation:
For RIGHT triangles ( such as this one) , remember S-O-H-C-A-H-T-O-A .
SinΦ = Opposite LEG / Hypotenuse
Sin (53) = 4/x
pleasee helppppppppppp
The area of the ABCD is 30 square units.
what is parallelogram ?A quadrilateral which have opposite side are parallel and equal to each other.
area of the parallelogram ABCD,
Area = base × height
find the equations of the lines AB and BC:
Line AB passes through the points A(-4,2) and B(-4,-3):
slope = (y2 - y1)/(x2 - x1) = (-3 - 2)/(-4 - (-4)) = -5/0 = undefined
Since the slope is undefined, the line is vertical and has the equation x = -4.
Line BC passes through the points B(-4,-3) and C(2,-3):
slope = [tex]\frac{(y2 - y1)}{(x2 - x1)}[/tex] = [tex]\frac{-3 - (-3)}{(2 - (-4)}[/tex]) = 0
Since the slope is 0, the line is horizontal and has the equation y = -3.
The height corresponding to AB is the perpendicular distance between AB and CD, which is the vertical distance between the lines x = -4 and x = 2. This distance is 6 units.
The height corresponding to BC is the perpendicular distance between BC and AD, which is the horizontal distance between the lines y = -3 and y = 2. This distance is 5 units.
Since the height corresponding to BC is shorter, we use it as the height of the parallelogram. The base is BC, which has a length of 6 units. Therefore, the area of the parallelogram is:
Area = base × height = 6 × 5 = 30 square units.
Therefore, the area of the ABCD is 30 square units.
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12
1. Find a common denominator for 1/3 and 1/12 by dividing each whole into the same number of equal parts.
Answer: To find a common denominator for 1/3 and 1/12, we need to divide each whole into the same number of equal parts. The denominator of 1/3 represents three equal parts, so we can divide the whole into three parts. The denominator of 1/12 represents twelve equal parts, so we can divide the whole into twelve parts.
The smallest number of parts that both 3 and 12 divide into evenly is 12. So, we can represent 1/3 as 4/12 by dividing each of the three equal parts into four smaller equal parts. And we can represent 1/12 as 1/12 by dividing each of the twelve equal parts into one smaller equal part.
Therefore, a common denominator for 1/3 and 1/12 is 12, and we can rewrite the fractions as:
1/3 = 4/12
1/12 = 1/12
Step-by-step explanation:
Find the value of x. Round the length to the nearest tenth. The diagram is not drawn to scale.
SOMEONE, PLEASE HELP!!
The value of x in the given figure, rounding the length to the nearest tenth is 2879.4 meters.
What is Pythagoras' theorem?Pythagoras' theorem says that the hypotenuse's square equals the square of the other two sides.
The value of x in the triangle using the principle of Pythagoras is 2879.4 meters
Given the right angle triangle :
The angle of elevation = 10°
Opposite side = 500 m
x = hypotenuse
Using the relation :
Sin θ = opposite / hypotenus
Sin 10° = 500 / x
Cross multiply :
x(sin 10°) = 500
0.1736481x = 500
x = 500 / 0.1736481
x = 2879.39 meters
Therefore, the value of x in the triangle is 2879.4 meters.
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Suppose you wish to invest money safely and are trying to decide between stock options in two companies. The average rates of return are the same for both companies but, one company has a much larger standard deviation of its rates of return. a. Which company should you invest in? The company with the smaller standard deviation The company with the larger standard deviation b. Why is this the better choice?
Answer:
If the average rates of return are the same for both companies, but one company has a much larger standard deviation of its rates of return. You should invest in a company with a smaller standard deviation.
This is the better choice because a larger standard deviation means that the company's returns are more variable, which implies more risk. While higher risk can result in higher returns, it can also result in significant losses. Investing in a company with a smaller standard deviation of its rates of return will likely result in a more stable return on investment and therefore be a safer investment.
In general, investors should consider both the average and variability returns when making investment decisions. While higher average returns are desirable, they may not be worth the additional risk if the variability of returns is too high.
Question 9
Use algebra to show that 4.57 (5 and 7 recurring) equal 4 and 19/33
o show that 4.57 (5 and 7 recurring) is equal to 4 and 19/33, we can use algebraic equations. First, let x = 4.57 (5 and 7 recurring), then we multiply both sides by 100 to get 100x = 457.5757... Next, we subtract x from 100x to get 99x = 453. Thus, x = 453/99. We can simplify this fraction by dividing both the numerator and denominator by 3, giving us 151/33. Finally, we can write 151/33 as a mixed number, which is 4 and 19/33. Therefore, we have shown that 4.57 (5 and 7 recurring) is equal to 4 and 19/33 using algebraic equations.
Writing equations of lines
Answer:
y=-5x+6
Step-by-step explanation:
Slope-intercept form is y=mx+b, with m being the slope and b being the y-intercept.
The y-intercept is where the line crosses over the y-axis. In this case, there is a point on 6, which means 6 is our y-intercept.
Next, we need to calculate the slope. We know slope = rise/run.
Start at the point -9,3. We rise 5 and go left 1 to get to the point -4,2.
Since we went left, our slope is 5/-1, which simplifies to -5.
Our final answer, written in slope intercept form, is y=-5x+6
URGENT PLEASE HELP!! write a polynomial with zeros 0,-3, and 2 with multiplicities 2,1, and 2 respectively. what is its degree?
the polynomial with zeros 0, -3, and 2 with multiplicities 2, 1, and 2 respectively is: f(x) = x⁵ - 8x⁴ - 4x³ + 48x² - 96xThe degree of this polynomial is 5, since the highest power of x in the polynomial is 5.
what is polynomial ?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.
In the given question,
If the zeros of a polynomial are given, we can construct the polynomial by multiplying its factors. Since the given zeros are 0, -3, and 2 with multiplicities 2, 1, and 2 respectively, we can write the factors of the polynomial as follows:
(x - 0)²(x - (-3))(x - 2)²
Simplifying this expression, we get:
x²(x + 3)(x - 2)²
Expanding this expression, we get:
x^²(x² - 4x - 12)(x - 2)²
Multiplying the factors and combining like terms, we get:
x⁵ - 8x⁴ - 4x³ + 48x² - 96x
Therefore, the polynomial with zeros 0, -3, and 2 with multiplicities 2, 1, and 2 respectively is:
f(x) = x⁵ - 8x⁴ - 4x³ + 48x² - 96x
The degree of this polynomial is 5, since the highest power of x in the polynomial is 5.
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Question 6(Multiple Choice Worth 1 points)
(01.04 LC)
Solve for x: 3x-2 > 5x + 10.
Ox>6
O.x < 6
Ox<-6
Ox>-6
Question 10
10 pts
Jayden has a brother and a sister in college. He traveled 2.5 x 102 miles to visit his sister. He traveled 7.5 x 10³ miles to
visit his brother. The distance Jayden traveled to visit his brother is how many times as much as the distance Jayden traveled
to visit his sister?
Jayden traveled [blank] times as many miles to visit his brother than his sister.
Jayden traveled 30 times as many miles to visit his brother than his sister.
What is travel?
To find how many times as much Jayden traveled to visit his brother than his sister, we can divide the distance he traveled to visit his brother by the distance he traveled to visit his sister:
(7.5 x 10³ miles) / (2.5 x 10² miles) = 30
Therefore, Jayden traveled 30 times as many miles to visit his brother than his sister.
What is distance?
Distance is the measure of the space between two points or objects. It is typically measured in units such as meters, kilometers, miles, feet, or inches. In physics, distance is the scalar quantity that represents the magnitude of the displacement between two positions. In mathematics, distance is a metric that satisfies certain properties, such as being non-negative and symmetric, and it is used to define concepts like convergence and continuity. The concept of distance is fundamental to many fields of study, including physics, mathematics, geography, and engineering.
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The highest temperature ever recorded on Earth was 136 F in Libya. The lowest temperature was -129 F in Antarctica. What is the range of the highest and the lowest temperature on Earth?
Answer:
Range = [-129, 136]
Step-by-step explanation:
If this is not the answer you are looking for, please comment
Answer:
265°
Step-by-step explanation:
from -129° to 0° is 129°
from 0° to 136° there is 136°
you add this numbers together and get an answer, so 129°+136°= 265°