Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answers
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
Related Questions
pls help:Find all the missing elements:
Answers
Answer:
B = 48.7° , C = 61.3° , b = 12Step-by-step explanation:
In order to find B we must first angle C
To find angle C we use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
From the question
a = 15
A = 70°
c = 14
So we have
[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]
[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]
[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]
C = 61.288
C = 61.3° to the nearest tenthSince we've found C we can use it to find B.
Angles in a triangle add up to 180°
To find B add A and C and subtract it from 180°
That's
A + B + C = 180
B = 180 - A - C
B = 180 - 70 - 61.3
B = 48.7° to the nearest tenthTo find b we can use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]
[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]
[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]
b = 11.9921
b = 12.0 to the nearest tenthHope this helps you
Two points are plotted on a number line: -11.2 and 3.3. What is
the distance between these two points?
Answers
To find the difference you would just subtract. 11.2 - 3.3 = -7.9
-7.9 is the answer
Solve the equation for the given variable x/4=6/8
Answers
Answer:
x = 3
Step-by-step explanation:
This process is called cross multiplication.
Multiply 6 · 4 = 24
Divide 24 ÷ 8 = 3
x = 3
Answer:
x = 3
Step-by-step explanation:
x/4 = 6/8
Using cross products
x*8 = 4*6
8x = 24
Divide by 8
8x/8 = 24/8
x = 3
3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the
ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second.
a) How far is the bottom of the ladder from the wall?
b) How fast is the bottom of the ladder sliding away from the wall?
Answers
Answer:
1. The bottom of the ladder is 4 meters away from the wall
2. I'm not sure about this one, someone else answer please :D
Step-by-step explanation:
We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.
The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.
[tex]a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4[/tex]
I'm sorry I couldn't answer the second one, but I hope this helped!
Answer:
a. 4m
b. 6m/s
Step-by-step explanation:
wall height = y = 3m
ladder length = L = 5m
distance from bottom of ladder to the wall = x
a. y² + x² = L² -----------eq.(1)
3³ + x² = 5²
x = 4 m
b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt
using eq.1 ---- y² + x² = L²
2y (dy/dt) + 2x (dx/dt) = 0
y (dy/dt) + 2 (dx/dt) = 0
we know that (dy/dt) = -8 m/s
3 (-8) + 4 (dx/dt) = 0
dx/dt = -24 / -4
dx/dt = 6 m/s
Select the correct graph.
Answers
Answer:
Graph 1
Step-by-step explanation:
The only graph that could be possible would be graph 1.
As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.
Three times the sum of a number and eight is four more than the number. find the number
Answers
Answer:
3(x+8)=4+x
distribute the 3 by multiplying it with the x and the 8
3x+24=4+x
subtract x from both sides
2x+24=4
subtract 24 from both sides
2x=4-24
2x=-20
divide each side by 2
leaving the variable isolated
x=-10
Step-by-step explanation:
It is important to balance each side by doing the same to both sides such as at the end divide both sides by 2.
The unknown number will be equal to 10.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that three times, the sum of a number and eight is four more than the number.
The equation will be written as,
3(x+8)=4+x
Distribute the 3 by multiplying it with the x and the 8,
3x+24=4+x
Subtract x from both sides,
2x+24=4
Subtract 24 from both sides,
2x=4-24
2x=-20
Divide each side by 2.
x=-10
Therefore, the unknown number will be equal to 10.
To know more about an expression follow
https://brainly.com/question/25968875
#SPJ2
allowing 20% discount on the marked price of a watch, the value of the watch will be rs 6328, when a VAT of 13% is added find it's marked price
Answers
Step-by-step explanation:
let , MP =x
then,
discount amount =D% of MP
= (20/100)× x
= 0.2x
now,Sp without VAT = MP-D
=x - 0.2x
= 0.8x
NoW, SP with VAT = Sp without VAT+ VAT %of SP
or ,6328 = 0.8x + 13% of 0.8x
or, 6328 = 0.8x + (13/100) × 0.8x
or, 6328= 0.8x + 0.104x
or,. 6328= 0.904x
or, X= 6328/0.904
X= 7000 Rs.
Hence ,MP is Rs.7000
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Answers
Answer:
$1344.9Step-by-step explanation:
This problem can be solved using the compound interest formula
[tex]A= P(1+r)^t[/tex]
Given data
A, final amount =?
P, principal = $586
rate, r= 6.6% = 0.066
Time, t= 13 years
Substituting our values into the expression we have
[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]
To the nearest cent the in 13 years the CD will be worth $1344.9
please help answer question
Answers
Answer:
Mark me brainlist please please please please
Answer:
Step-by-step explanation:
what does the inverse of f(x)=2x-3 looks like on a graph
Answers
Step-by-step explanation:
To find this inverse of a graph you have to multiply the current equation by -1.
-1(2x-3)
f(x)=-2x+3.
This graph will start at the point (0,3). Then according to the slope the rest of the points will go down two than right one. So the next two point will be (1,1) and (2,-1).
Need help with the question below.
Answers
Answer:
A
Step-by-step explanation:
r=10 and the angle bln 5√3 and -5 is 330 or 11π/6
Karmen returned a bicycle to Earl's Bike Shop. The sales receipt showed a total paid price of $211.86, including the 7% sales tax. What was the cost of the bicycle without the sales tax? Any help would be very appreciated! Thank you very much!
Answers
Answer:
$198
Step-by-step explanation:
198x.07=13.86
198+13.86=211.86
2 men can build a wall in 10 days. in how many days will 8 men build the wall?
Answers
Step-by-step explanation:
8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da
The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3 cm radius and
6 cm height. What is the depth of the ice-cream, correct to two decimal places?
m
3 cm
Ice-cream
6 cm
depth of
ice-cream
5cm
Answers
Answer:
h = 5 cm
Step-by-step explanation:
Given that,
The volume of ice-cream in the cone is half the volume of the cone.
Volume of cone is given by :
[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]
r is radius of cone, r = 3 cm
h is height of cone, h = 6 cm
So,
[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]
Let [tex]V_i[/tex] is the volume of icecream in the cone. So,
[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]
Let H be the depth of the icecream.
Two triangles formed by the cone and the icecream will be similiar. SO,
[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]
So, volume of icecream in the cone is :
[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]
or
h = 5 cm
So, the depth of the ice-cream is 5 cm.
A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).
1. What is the appropriate test?
2. State the null hypothesis:
3. State the alternative hypothesis:
4. Find the critical value:
5. Calculate the obtained statistic:
6. Make a decision:
7. What does your decision mean
Answers
Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as
H0 :p 0.5 against Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution
Heads (x) Probability (X=x) Cumulative Decumulative
0 1/16384 (1) 0.000061 0.000061
1 1/16384 (14) 0.00085 0.000911
2 1/16384 (91) 0.00555 0.006461
3 1/16384(364) 0.02222
4 1/16384(1001) 0.0611
5 1/16384(2002) 0.122188
6 1/16384(3003) 0.1833
7 1/16384(3432) 0.2095
8 1/16384(3003) 0.1833
9 1/16384(2002) 0.122188
10 1/16384(1001) 0.0611
11 1/16384(364) 0.02222
12 1/16384(91) 0.00555 0.006461
13 1/16384(14) 0.00085 0.000911
14 1/16384(1) 0.000061 0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) = 0.006461 > 0.025
and
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is
∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
I will rate you brainliest!
Answers
Answer:
B
Step-by-step explanation:
X must not be equal to -6, -1, 1 or 3
If 2m−6=8m
2
m
-
6
=
8
m
then 3m=
3
m
=
A. 3
B. -1
C. -3
D. -6
E. I don't know.
Answers
Answer:
3m = -3
Step-by-step explanation:
2m−6=8m
Subtract 2m from each side
2m−6-2m=8m-2m
-6 = 6m
Divide by 6
-6/6 = 6m/6
-1 = m
3m = 3(-1) = -3
2m - 6 = 8m
2m - 8m = 6
-6m = 6
m = -6/6
m = -1
Hence, the answer is -1How to simplify this expression??
Answers
Answer :
1
Step-by-step-explanation :
[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]
[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]
Answer:
(x+1) • (x-5)
Step-by-step explanation:
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .
-5 + 1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
x2 - 5x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-5)
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
Suppose you have read two different books on world war 2 and each book has different arguments about how the war started which of the following sources provides the best support for the authors arguments
Answers
Answer:
Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.
A computer is priced at $2,000. If the sales tax rate is 7.5%, find the total cost of the
computer?
Answers
9514 1404 393
Answer:
$2150
Step-by-step explanation:
The tax is 7.5% of the price, so is ...
$2000 × 0.075 = $150
The total cost is the price with tax added:
$2000 +150 = $2150
Which expression is the factored form of x2-7x+10
Answers
Answer:
[tex]\boxed{ (x - 2)(x - 7)}[/tex]
Step-by-step explanation:
Hey there!
To factor,
[tex]x^2-7x+10[/tex]
We need 2 numbers that multiply to get 10 and add to get -7 which is,
-2 and -5.
-2*-5 = 10
-2x + -5x = -7x
x*x=x^2
Factored - (x - 2)(x - 7)
Hope this helps :)
A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n
Answers
Answer: [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Step-by-step explanation:
[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 1111 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league?
278 303 186 292 276 205 208 236 278 198 208
a. Find the mean.
The mean is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
b. Find the median.
The median is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
c. Find the mode.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The mode(s) is(are) ? pound(s).
(Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.)
B. There is no mode.
d. Find the midrange.
The midrange is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
e. Are the results likely to be representative of all players in that sport's league?
A. The results are not likely to be representative because the median is not equal to the mode.
B. The results are likely to be representative because a championship team is most likely representative of the entire league.
C. The results are not likely to be representative because the median is not equal to the mean.
D. The results are not likely to be representative because the championship team may not be representative of the entire league.
Answers
Answer:
Mean= 242.5 pounds
Median= 236 pounds
Mode= 208 and 278 pounds
Range=117 pounds
Mid-range= 58.5 pounds
B. The results are likely to be representative because a championship team is most likely representative of the entire league.
Step-by-step explanation:
278 303 186 292 276 205 208 236 278 198 208
Arranged in ascending order is
186 198 205 208 208 236 276 278 278 292 303
Mean = (186 +198+ 205+ 208 +208 +236 + 276+ 278 +278+ 292 +303)/11
Mean =2668/11
Mean= 242.5 pounds
Median = the middle number
Median= 236 pounds
Mode = highest occuring number(s)
Mode= 208 and 278 pounds
Range= highest number- smallest number
Range=303-186
Range=117 pounds
Mid-range= range/2
Mid-range= 117/2
Mid-range= 58.5 pounds
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
Answers
9514 1404 393
Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
In a survey of 200 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis (at the 5% level of significance) that the average price-earnings ratio has increased from the past value of 16.8, the null and alternative hypotheses would be:________
Answers
Answer:
Null Hypothesis: H0:μ ≤ 16.8
Alternative Hypothesis: Ha: μ > 16.8
Step-by-step explanation:
We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.
It means that the past value was not more than 16.8.
This follows that the null hypothesis is given as;
H0:μ ≤ 16.8
And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;
Ha: μ > 16.8
Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at Furniture Patch Inc.
$4.0 $6.0 $7.4 $10.6 $12.5 $13.6 $15.4 $15.8 $16.8
$17.4 $19.1 $22.3 $37.1 $43.2 $81.4
a. Determine the mean, median, and the standard deviation. (Round your answers to 2 decimal places.)
Mean $
Median $
Standard deviation $
b. Determine the coefficient of skewness using Pearson
Answers
Answer:
Mean= $21.5067
Median = $15.8
Standard deviation= $19.02
Coefficient of skewness= $0.8991
Step-by-step explanation:
Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8
+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15
Mean =$ 322.6/15
Mean= $21.5067
Median= middle number
Median = $15.8
Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15
Variance=$ 5424.79/15
Variance=$ 361.65
Standard deviation= √ variance
Standard deviation= √361.65
Standard deviation= $19.02
Coefficient of skewness
=3( mean-median)/standard deviation
= 3(21.5-15.8)/19.02
= 3(5.7)/19.02
= 17.1/19.02
Coefficient of skewness= 0.8991
Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.
Please help!!
Answers
Answer:
Hello,
in order to simplify, i have taken the inverses functions
Step-by-step explanation:
[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!
12. The coordinate grid below represents a town.
a. Curtis's house is at (-4, -6) and Jean's house is at (-4, 3). Plot the plots where Curtis's house and Jean's house are located.
b. Each unit on the grid represents 1 mile. If Curtis can ride his bike at a constant rate of 12 miles per hour, how long would it take Curtis to ride from his house to Jean's house?
THIS IS NOT MULTIPLE CHOICE!!!
Answers
We are given:
Coordinates of Curtis's house: (-4, -6)
Coordinates of Jean's house: (-4, 3)
a) Plotting these points:
in the given coordinates, the first number is called the abscissa and denotes the x-coordinate of the point.
the second number is the ordinate. it denotes the y-coordinate of the point
Plotting Curtis's house:
We will start from the origin (0,0). move 4 units to the left because that's where x = -4 is.
Then, we will move 6 units downwards and mark the point.
The point we just marked is (-4, -6), Curtis's house
Plotting Jean's house:
We will go to x = -4 like we just did when plotting curtis's house
then, we will move 3 units upwards and mark the point.
This point is (-4, 3), Jean's house
b) Time taken by Curtis:
Distance between the points:
distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] (distance formula/Pythagoras' Theorem)
where (x₁, y₁) = (-4, -6) and (x₂, y₂) = (-4, 3)
replacing the values in the formula, we get:
distance = [tex]\sqrt{(-4 - (-4))^2 + (3 - (-6))^2}[/tex]
distance = [tex]\sqrt{(0)^2 + (9)^2}[/tex]
distance = [tex]\sqrt{(9)^2}[/tex] = 9 units
since each unit on the grid represents one mile,
distance = 9 miles
speed of Curtis = 12 miles/hour
we know that speed is just (distance covered)/(time taken)
speed = (distance covered)/(time taken)
replacing known values
12 = 9 / time
12 * time = 9 [multiplying both sides by time]
time = 9/12 [dividing both sides by 12]
time = 3/4 hours
time = 0.75 hours OR 45 minutes
9514 1404 393
Answer:
a) see attached
b) 3/4 hour (45 minutes)
Step-by-step explanation:
a) The attached graph shows the points plotted.
__
b) The points lie on the same vertical line. The distance between them is the difference of their y-coordinates: 3 -(-6) = 9 (miles).
The time is related to distance and speed by ...
time = distance/speed
time = (9 mi)/(12 mi/h) = 9/12 h = 3/4 h
It would take Curtis 3/4 hour to ride from his house to Jean's house.