Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
what is percentage ?A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:
(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.
Red ball percentage equals (25/100) times 100%
25% of the balls are crimson.
given
You can compute the cost as follows:
Loss is calculated as Initial Price - Selling Price ($210 - $139).
Loss = $71
We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:
(Loss / Original price) times 100 equals the percentage of loss.
($71 / $210) times 100 equals the percentage loss.
Loss as a percentage: 33.81%
Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
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Rowan is training to run in a race. He runs 15 miles in the first week, and each week following, he runs 3% more than the week before. Using a
geometric series formula, find the total number of miles Rowan runs over the first ten weeks of training, rounded to the nearest thousandth.
The total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.
Explain about the geometric series?In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred as the common ratio.
In the question:
Rowan is preparing for a race by running. He runs 15 miles the first week, and then he runs 3% more each week after that.Let 'x' be the miles that Rowan runs in 1st week.
Xn for the nth week.
x1 = 15 (given)
x2 = 15*(1 + 3%) = 15*1.03
Xn = 15*(1 + 3%0ⁿ⁻¹ = 15*(1.03ⁿ⁻¹)
Let 'S' be the total miles.
S = x1 + x2+ .....+ xn
S = 15 + 15 *1.03 + 15*1.03² + ...+ 15*1.03⁹
On solving the series:
S = 15 × 1.(1.03¹⁰ - 1)/0.03
S = 57.31
S = 58
Thus, the total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.
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Need help to complete the proof.
Y is the midpoint of UW. Prove △VWY ≅ △XUY. Arrange the following reasons to complete the proof.
Reasons: Given, Given, Definition of midpoint, ASA, Vertical Angle Theorem
where does fission regularly occur and what kind of energy is produced
If I have a probability distribution of the number of TV's people have in their house (possible values from 0 to 5) and I want to find the probability that a randomly selected person has at least 2 TVS, 1 would write and calculate that as follows: a. PO>2)=P(3)=P(4)=P(5) b. PIX<2)=P(0)=P(1) c. PIX 2) P(0)+P(1)*P(2) d. PIX 22)- P(2)*P(3)*P(4)=P(5)
To calculate the probability that a randomly selected person has at least 2 TV's, you would first calculate the probability of a person having more than 2 TV's:
Then, you would calculate the probability of a person having less than 2 TV's:
Finally, you would calculate the probability of a person having exactly 2 TV's:
Therefore, the probability that a randomly selected person has at least 2 TV's is:
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A paper company needs to ship paper to large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 7 cubic feet and the volume of each large box is 14 cubit feet. A total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be determined the number of small boxes shipped in the number of large boxes shipped. Defined the variables that you use to write the system.
Answer: Let's use the variables x and y to represent the number of small boxes and large boxes shipped, respectively.
The system of equations that could be used to determine the number of each type of box is:
x + y = 21 (equation 1)
7x + 14y = 252 (equation 2)
In equation 1, the left side represents the total number of boxes shipped, which is the sum of the number of small boxes (x) and the number of large boxes (y). The right side of the equation represents the total number of boxes shipped, which is given as 21.
In equation 2, the left side represents the total volume of paper shipped, which is the sum of the volume of all the small boxes (7 cubic feet per box) and the volume of all the large boxes (14 cubic feet per box), multiplied by the number of boxes shipped. The right side of the equation represents the total volume of paper shipped, which is given as 252 cubic feet.
These two equations can be used to solve for x and y, which represent the number of small boxes and large boxes shipped, respectively.
Step-by-step explanation:
Find the distance between the two points.
✓ [?]
(-1,-2)
(3,-1)
Enter the number that
goes beneath the
radical symbol.
Answer: the number that goes beneath the radical symbol is 17
(b) Suppose you wanted to estimate the true proportion of all student loan borrowers who have loans
totaling more than $40,000 with 95% confidence to within 1%. Calculate the sample size you would
need. Use the sample proportion to estimate the population proportion
The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:
n = 9604.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value 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.
The margin of error is modeled as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We have no estimate of the proportion, hence it is used as follows:
[tex]\pi = 0.5[/tex]
The margin of error is of M = 0.01, hence the sample size is obtained as follows:
[tex]0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = 98[/tex]
n = 98²
n = 9604.
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The reciprocal of 5/11 is:
The reciprocal of 20 is:
The reciprocal of 5/11 is: 11/5
The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20
Answer: 11/5, 1/20
Step-by-step explanation:
The reciprocal of a value is the numerator and denominator of that value switched.
When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.
The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.
Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.
Use the graph to write the explicit rule of the arithmetic sequence.
Therefore , the solution of the given problem of graph comes out to be option A f(n) = 7 - 2(n-1)
What is a graph?Theoretical physicists use graphs to analytically chart or visually represent claims rather than values. A graph point typically depicts the relationship between any number of things. A specific type of non-linear train assembly made up of clusters and lines is known as a graph. Glue should be used to connect the networks, also referred as the boundaries. In this network, the nodes had the numbers 1, 2, 3, and 5, whilst edges had the numbers 1, 2, 3, and 4, as well as the numbers (2.5), (3.5), (4.5), and yet also (4.5). (4.5).
Here,
We can use the following method to determine the general term of an arithmetic series:
=> f(n) = a + (n-1)d
where the usual difference is "d" and "a" is the first term.
Since the series begins at 7, "a" is 7, as shown by the graph. Additionally, since each term reduces by 2, we can see that the common difference is 2.
Consequently, the following is the arithmetic sequence's stated rule:
A) f(n) = 7 - 2(n-1)
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Theorem proof?
Thanks
Triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.
Describe Congruency of triangle?In geometry, two triangles are said to be congruent if they have the same shape and size. More specifically, two triangles are congruent if all three sides and all three angles of one triangle are equal to the corresponding sides and angles of the other triangle. When two triangles are congruent, they can be superimposed on top of each other, and all corresponding parts of the triangles will match exactly.
There are several ways to prove that two triangles are congruent, including using the side-angle-side (SAS) theorem, the angle-side-angle (ASA) theorem, the side-side-side (SSS) theorem, and the hypotenuse-leg (HL) theorem.
Given that |AB|=|CD| and triangle ABC is isosceles.
We need to prove that triangle AXC = triangle AYB.
To do so, we will use the Side-Angle-Side (SAS) Congruence Criteria.
AC = BC (Given)
∠ACX = ∠BCY (Vertical Angles)
∠CAX = ∠CBY (Base Angles of Isosceles Triangle)
Therefore, triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.
Hence, proved.
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Write a polynomial of least degree with integral coefficients that has the given zeros.
1.0, 5, 2
2.-3,-5,3,-1
5. 2 mult.2, -4
3.-5, 2 + i
4.-1, 2i
The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)
How to determine the polynomial expressionsZeros (1): 0, 5, 2
This means that
Roots: x = 0, x = 5 and x = 2
The equation can be represented as
P(x) = (x - root)
So, we have
P(x) = (x - 0)(x - 5)(x - 2)
Evaluate
P(x) = x(x - 5)(x - 2)
Zeros (2): 0, 5, 2
Here, we have
Roots: x = -3, x = -5, x = 3 and x = -1
Using the form in (a), we have
P(x) = (x + 3)(x + 5)(x - 3)(x + 1)
Zeros (3): 0, 5, 2
Here, we have
Roots: x = -5, x = 2 + i
Using the form used abov]e, we have
P(x) = (x + 5)(x - 2 - i)(x - 2 + i)
Expand
P(x) = (x + 5)((x - 2)² + 1)
So, we have
P(x) = (x + 5)(x² - 4x + 5)
Zeros (4): -1 and 2i
Here, we have
Roots: x = -1, x = 2i
Using the form used abov]e, we have
P(x) = (x + 1)(x - 2i)(x + 2i)
Expand
P(x) = (x + 5)(x² + 4)
Zeros (5):2 mult.2, -4
The zeros here are not clear
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What is one tenth less than 9?
8.99
8.9
8.09
8.0
Answer:
8.9
Step-by-step explanation:
9.0-0.1= 8.9
which is one-tenth less than 9
Describe how to map figure J onto
Figure L, complete the statement
5000 people visit mueum during a month how many visitors were there for each age group. 18 and under, age 19 to 44, 45 to 64, age 65 and over
The number of degrees for each part of the museum visitors graph would be Age 18 and under: 108 degrees, Age 19 – 44: 180 degrees, Age 45 – 64: 54 degrees, and Age 65 and over: 18 degrees.
To find the number of degrees for each part of the museum visitors graph, we need to know the total number of visitors for that month. Let's assume that the total number of visitors for the month is 10,000.
Age 18 and under:
Let's assume that the number of visitors aged 18 and under is 3,000. To find the number of degrees for this section of the graph, we need to use the formula: (Number of visitors in the age group / Total number of visitors) x 360 degrees. So, (3000/10000) x 360 = 108 degrees.
Age 19 – 44:
Let's assume that the number of visitors aged 19-44 is 5,000. Using the same formula as above, we get (5000/10000) x 360 = 180 degrees.
Age 45 – 64:
Let's assume that the number of visitors aged 45-64 is 1,500. Using the same formula as above, we get (1500/10000) x 360 = 54 degrees.
Age 65 and over:
Let's assume that the number of visitors aged 65 and over is 500. Using the same formula as above, we get (500/10000) x 360 = 18 degrees.
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Use ELIMINATION to solve for (x) and (y). 2y=x-5 2y=x+5 x+2y=13 -x+4y=11 Upload a file that shows each step to solve for (x) and (y).
The solution to the system of equations using elimination is:
x = 1058/1890
y = 26/90
To solve this system of equations using elimination, we will add the two equations together and rearrange the terms.
2y = x - 5
2y = x + 5
Add the equations together:
2y + 2y = x - 5 + x + 5
4y = 2x + 0
Rearrange the terms:
4y - 2x = 0
We will now use this equation and the equation x + 2y = 13 to solve for x and y.
Substitute 4y - 2x = 0 into x + 2y = 13:
x + 2(4y - 2x) = 13
x + 8y - 4x = 13
Rearrange the terms:
5x + 8y = 13
Substitute 4y - 2x = 0 into 5x + 8y = 13:
5x + 8(4y - 2x) = 13
5x + 32y - 16x = 13
Rearrange the terms:
21x + 32y = 13
Divide by 21:
x + (32/21)y = 13/21
Rearrange the terms:
x = 13/21 - (32/21)y
Substitute x = 13/21 - (32/21)y into 4y - 2x = 0:
4y - 2(13/21 - (32/21)y) = 0
4y - (26/21) + (64/21)y = 0
Rearrange the terms:
(90/21)y = 26/21
y = (26/21) / (90/21)
y = 26/90
Substitute y = 26/90 into x = 13/21 - (32/21)y:
x = 13/21 - (32/21)(26/90)
x = 13/21 - (832/1890)
x = 1058/1890
The solution to the system of equations is:
x = 1058/1890
y = 26/90
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Can someone help me write a proof for this problem
The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
As we can seen from the given figure that two triangles are given.
The triangles ABC and BDC are :
AB = CD
AC = BD
BC = BC
Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A is equal to angle D.
Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.
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ind the difference and write the resulting polynom (19x^(4)-17x-18)-(12x^(4)-8x+5)
The difference of the two polynomials is 7x^(4) - 9x - 23.
The difference of the two polynomials (19x^(4)-17x-18)-(12x^(4)-8x+5) can be found by subtracting the corresponding terms of the two polynomials.
Subtract the first term of the second polynomial from the first term of the first polynomial: 19x^(4) - 12x^(4) = 7x^(4)
Subtract the second term of the second polynomial from the second term of the first polynomial: -17x - (-8x) = -17x + 8x = -9x
Subtract the third term of the second polynomial from the third term of the first polynomial: -18 - 5 = -23
Write the resulting polynomial by combining the terms 7x^(4) - 9x - 23
Therefore, the difference of the two polynomials is 7x^(4) - 9x - 23.
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write the word form of decimal 0.609.
Answer: six hundred nine thousandths
Step-by-step explanation:
The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ have no solution, are
Aλ=3,μ=10
Bλ=3,μ=10
Cλ=3,μ=10
DNone of these
The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ are none of this. The correct answer is option D, None of these.
To find the value of λ and μ for which the system of equations has no solution, we can use the determinant method. The determinant of a system of equations is given by:
| a1 b1 c1 |
| a2 b2 c2 | = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
| a3 b3 c3 |
For the given system of equations, the determinant is:
| 1 1 1 |
| 1 2 3 | = 1(2λ - 3μ) - 1(3 - 3) + 1(2 - 2)
| 1 2 λ |
Simplifying, we get:
2λ - 3μ = 0
For the system of equations to have no solution, the determinant must be equal to 0. Therefore, we need to find the values of λ and μ that satisfy the equation 2λ - 3μ = 0.
None of the given options satisfy this equation, therefore the correct answer is option D, None of these.
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Decide whether exch of the following sets is (a) cokntable or (b) unorumtable : (Note : a finite set is considered to be coumtable).
{x∈R:2
{x∈Q:∣x∣≥2}
{x∈Q:∣x∣<4}
The first set is countable, the second set is also countable. The third set is also countable.
(a) The set {x∈R:2 is countable because it is finite.
(b) The set {x∈Q:∣x∣≥2} is countable because it is a subset of the rational numbers, which are countable.
(c) The set {x∈Q:∣x∣<4} is countable because it is a subset of the rational numbers, which are countable.
In Maths, sets are referred as a collection of well-defined objects or elements. A set is usually represented by a capital letter symbol and the total number of elements in the finite set is basically represented as the cardinal number of a set in a curly bracket.
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The number of weekly flu tests increases by a rate of about 32% each week. During the initial week of flu season, 33flu tests were administered. The situation can be modeled by f(x)=33(0.32)^(x) CORRECT AND REWRITE THE FALSE STATEMENT:
The correct statement is f(x)=33(1.32)^(x). .
About mathematical statementThe original statement is false because it does not accurately represent the increase in the number of weekly flu tests. The original statement suggests that the number of tests decreases by 32% each week, which is not the case.
To accurately represent the increase in the number of weekly flu tests, we need to use the growth factor of 1.32, which is equivalent to 100% + 32%. This means that the number of weekly flu tests increases by 32% each week, as stated in the problem.
Therefore, the correct statement is f(x)=33(1.32)^(x).
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Can someone explain how to do this? I'm confused. Anything helps.
Thank you so much!
Answer:
28 and 152 degrees
Step-by-step explanation:
Using sine inverse, the answer is 28 or 152 degrees.
Answer:48.87°
Step-by-step explanation:
For any invertible matrix BEM nxn(K), define a function TB: Mnxn(K) → M nxn(K) by
TB (A) = BAB-¹,
where A EM nxn(K). Prove that TB is an isomorphism.
TB is both one-to-one and onto, it is an isomorphism.
To prove that TB is an isomorphism, we need to show that it is both one-to-one and onto.
One-to-one: Assume TB(A) = TB(C) for some A, C EM nxn(K). Then, BAB-¹ = CBC-¹. Multiplying both sides by B-¹ on the left and B on the right gives B-¹BAB = B-¹CBC. Since B is invertible, B-¹B = I and we have A = C. Therefore, TB is one-to-one.
Onto: Let D EM nxn(K). Then, we can define A = B-¹DB. Since B is invertible, A EM nxn(K) and TB(A) = BAB-¹ = B(B-¹DB)B-¹ = D. Therefore, TB is onto.
Since TB is both one-to-one and onto, it is an isomorphism.
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I NEED HELP ON THIS ASAP!!!
Step-by-step explanation:
Refer to pic...........
The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.
The following values represent the rollercoaster graph scenario most accurately:
is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6
Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5
Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)
For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6
Define graphs?The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.
The Latin word Datum, which meaning "something provided," is where the word data first appeared.
In the question, where at x = 0, Red(x) = 10,
at x = 5, Red(x) = 2.5
For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5 if 6 ≤ x < 10
Given, where at x = 10, Green (x) = 7,
So, at x = 6, Green (x) = 2.0
For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15
Given, where at x = 10, Purple (x) = 7,
at x = 15, Purple (x) = 0
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The complete question is:
The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.
Calculate the next term in the arithmetic sequence that
increases by 21, if the current term is 55.
What is the next term if the first two terms of a
Fibonacci sequence are 2, 25?
Find the 72th term o
3525
The next term in the arithmetic sequence that increases by 21, starting at 55, is 76. The next two terms of the Fibonacci sequence are 67 and 109, and the 72nd term is 3525.
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$18,000 is deposited for 9 years in an account earning 4% interest. (Round your answers to two decimal places.)
(a) Calculate the future value of the investment if interest is compounded semiannually.
$ _____
(b) Calculate the future value if interest is compounded quarterly.
$ _____
(c) How much greater is the future value of the investment when the interest is compounded quarterly?
$ _____
(a) The future value of the investment if interest is compounded semiannually is $24,840.28.
(b) The future value of the investment if interest is compounded quarterly is $25,025.68.
(c) The future value of the investment is $185.40 greater when the interest is compounded quarterly.
The future value of an investment can be calculated using the formula FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount deposited, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the investment is held.
If the interest is compounded semiannually, then n = 2. Plugging in the given values, we get:
FV = 18000(1 + 0.04/2)^(2*9)
FV = 18000(1.02)^18
FV = $24,840.28
So the future value of the investment if interest is compounded semiannually is $24,840.28.
If the interest is compounded quarterly, then n = 4. Plugging in the given values, we get:
FV = 18000(1 + 0.04/4)^(4*9)
FV = 18000(1.01)^36
FV = $25,025.68
So the future value of the investment if interest is compounded quarterly is $25,025.68.
To find out how much greater the future value of the investment is when the interest is compounded quarterly, we can subtract the future value when interest is compounded semiannually from the future value when interest is compounded quarterly:
$25,025.68 - $24,840.28 = $185.40
So the future value of the investment is $185.40 greater when the interest is compounded quarterly.
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Lora's phone records data for screen time each week. Last week, she used 750 minutes. This week, Lora used 495 screen time minutes on the phone. Calculate the percent decrease in screen time this week.
27%
34%
40%
52%
Answer:
34%
Step-by-step explanation:
495 is 66% of 750 so 66% - 100% is 34%
Answer:
34
Step-by-step explanation:
Jason creates a scaled map of his hometown on a standard (x,y) coordinate plane. Each unit on the map represents 1 mile. He graphs his house at the point (-4,-5) andhis school at the point (-10,-11). Which of the following is closest to the distance, in miles, between Jason's school and his house?
The distance between Jason's school and his house is 8 miles.
What is the Cartesian system?
Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.
Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is (-10,-11).
The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11
The distance between points is
√[(-10-(-4))² + (-11 - (-5))²]
=√(6² + 6²)
= √(36+36)
= √72
= 6√2
= 8.48
≈ 8 miles
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pls help with my homework
The area of the trapezoid is 65.16 metres squared.
How to find the area of a trapezoid?The area of a trapezoid can be found as follows:
area of a trapezoid = 1 / 2 (a + b)h
where
a = top baseb = bottom baseh = height of the trapezoidTherefore,
a = 5metres
b = 13.1 metres
h = 7.2 metres
Hence,
area of a trapezoid = 1 / 2 (5 + 13.1) 7.2
area of a trapezoid = 1 / 2 (18.1)7.2
area of a trapezoid = 130.32 / 2
Therefore,
area of a trapezoid = 65.16 metres squared
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