Here is a scale drawing of a garden.
Kim wants to plant a tree in the garden according to the following rules:
It must be 7 m from A and 4 m from C.
Place a cross where Kim can plant the tree.
1 cm represents 2 m
D
2.5 cm
А A
B.
4 cm
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Answers
Answer:
The coordinates of the cross on the scale drawing which locates where Kim can plant the tree is (3.45 cm, 0.58 cm)
Step-by-step explanation:
The question relates to coordinates geometry and the solution can be obtained graphically by construction as shown in the attached drawing
The given parameters of the scale drawing are;
The scale of the drawing is 1 cm = 2 m
The dimensions of the rectangle representing the garden in the scale drawing is given as follows;
The width of the rectangle = 2.5 cm
The length of the rectangle = 4 cm
The required location where the tree is to be planted = 7 m from A and 4 m from point C
Therefore, the location where Kim can plant the tree on the scale drawing is 3.5 cm from point A and 2 cm from point C
Taking the coordinate of point A as the origin, we have;
The coordinates of point A = (0, 0)
∴ The coordinates of point C = (4, 2.5)
The general equation of a circle is (x - h)² + (y - k)² = r²
Where, (h, k) is the coordinate of the center of the circle
The location of the point is on a radius 3.5 cm from point A and a radius 2 cm from point C
Therefore, for point A, we have;
(x - 0)² + (y - 0)² = 3.5²
x² + y² = 12.25...(1)
For point C, we have;
(x - 4)² + (y - 2.5)² = 2² = 4
Which gives;
x² - 8·x + 16 + y² - 5·y + 6.25 = 4
x² + y² - 8·x - 5·y + 22.25 = 4
We have x² + y² = 12.25 from equation (1), therefore, we have;
12.25 - 8·x - 5·y + 22.25 = 4
- 8·x - 5·y = 4 - 22.25 - 12.25 = -30.5
∴ 8·x + 5·y = 30.5
y = (30.5 - 8·x)/5
Therefore, we have;
x² + y² = 12.25 = x² + ((30.5 - 8·x)/5)² = 12.25
Using a graphing calculator we get;
356·x² - 1952·x + 2496 = 0
Which gives;
x = (1952 ± √((-1952)² - 4×356×2496))/(2 × 356)
x = 3.452197227 or 2.03094884081
To two decimal places, we have the coordinates of the points where the tree can be planted given as follows;
Therefore, y = (30.5 - 8×3.452197227)/5 = 0.5764844368
or y = (30.5 - 8×2.03094884081)/5 = 2.8504818547
y = 0.5764844368 or 2.8504818547
To two decimal places, we have the coordinates of the places where Kim can plant the tree are given as follows;
(3.45, 0.58) or (2.03, 2.85)
We note that the point (2.03, 2.85) is at the outside the drawing the area as 2.85 cm is more than 2.5 cm which is the width (height) of the rectangle as shown in the attached drawing created with Microsoft Word.
Therefore, the coordinates of the cross where Kim can plant the tree is (3.45, 0.58)
Answer:
Step-by-step explanation:
Make sure to use protractor and cross tools to get full marks
Thank you
Related Questions
Help pls!! Find the value of DB and AE
Answers
Answer:
B
Step-by-step explanation:
x=2
3x + 10
3(2) + 10
6+10
16
Db=16
16(x)
16(2)
32=AE
Db=16, 32=AE which is B
plz brainliest
Answer:
16, 32
Step-by-step explanation:
BD is midsegment of the ΔACE ⇒ 16x = 2(3x + 10)
16x - 6x = 20 ⇒ x = 2
BD = 3(2) + 10 = 16 units
AE = 16(2) = 32 units
Please help ASAP!!!!
Answers
Answer:
(-2, 0, 1, 3)
Step-by-step explanation:
From the given graph, there are four x-intercepts, which are the points the graph crosses the x-axis
Taking the y-axis as the given vertical line, and each demarcation as representing one unit division, we have;
The x coordinates of the x-intercepts are given as follows;
1) Two lines to the left of the origin which represents "-2"
2) Through the origin, which represents "0"
3) One line to the right of the origin which represents "1"
4) Three lines to the right of the origin which represents "3"
The set of values that represents the x-intercepts of the function are;
(-2, 0, 1, and 3)
HELP ME IM USING ALL MY POINTS MULTIPLE QUESTONS PLZ
Answers
hope it will help you.........
Answer:
UV=UZ+ZV
Step-by-step explanation:
UV=3y-5+2z+2
=3y+2y-3
but UV =27=3y+2y-3
30 =3y+2y
bisect means cut in to two equal parts so
3x+3=3y+6
3x-3y=6-3
3x-3y=3
then combine the two equation
30 =3y+2y this is 30=5y which is y=6
3 = 3x-3y so enter y=6 into this equation
3=3x-3*6
3=3x-18
3x=21
x=7
On a shelf there are 60 novels and 20 poetry books. What is the probability that person A chooses a novel and walks away with it and then person B walks up shortly after and picks another novel?
Answers
Which of the following examples has a unit price of $5.00? Select all that apply.
A) 6 pizzas for $30.00
B) 9 hamburgers for $45.00
C) 7 shirts for $42.00
D) 2 toys for $10.00
E) 5 notebooks for $25.00
Answers
E, D, and A.
well because it can be divide my 5.
In each equation of the form ax + by = c, state a, b, and c.
y=2
In each equation of the form ax + by = c, state a, b, and c.
5x - y = 1
In each equation of the form ax + by = c, state a, b, and c.
4y + 2x = 3
Answers
2) a=5, b=-1, c=1
3) a=4, b=2, c=3
marking Brainlist 7-9g+3g
Answers
Answer:
7-6g
Then you do the 1 step equation.
Divide both sides by 6.
1.16=g
I'm not sure if it's right.
Normally a chef uses 14 ounces to make chocolate chip cookies but he started using 20.44 ounces instead he should advertise the cookies as having percent more chocolate
Answers
(20.44-14)/14
For what value of x must ABCD be a parallelogram?
Answers
Answer:
yes it could be
Step-by-step explanation:
Answer:
5x = 6x-7 subtract 6x from each side-x=-7x=7
does this graph represent a function? if yes why?
Answers
Consider two people where one person is 25% taller than the other but proportion in exactly the same way That the taller person looks like a lager version of the shorter person Suppose the shorter person has a 36%-inch waist what size is the the taller person's waist?
Answers
Answer:
46.8 inches
Step-by-step explanation:
Taller person = 30% more than height of shorter individual
Waist size of shorter person = 36 inches
Since they are proportioned in the same way:
Waist size of the taller person will be 30% larger than the waist size of the shorter person :
30% increase in size 36
(100 + 30)% of 36
130% of 36
(130 / 100) * 36
1.3 * 36
= 46.8 inches
Hi another math question please help:)
Answers
Answer:
1). Yes
2). Yes
3). No
Step-by-step explanation:
1). y = 3
We can rewrite this equation in the slope-intercept form as,
y = 0.x + 3
Here, slope = 0
y-intercept = 3
Therefore, it's a linear relation.
YES.
2). 2x - 5y = 10
5y = 2x - 10
y = [tex]\frac{2}{5}x-2[/tex]
Therefor, it's a linear function.
YES
3). y = x(x + 3)
y =x² + 3x
Since, this equation is a quadratic equation,
It's not a linear function.
NO
Aileen has a total debt of $45. She is trying to pay back $6 each week for the next 4 weeks. If Aileen is successful, which amount will represent the change in the amount of her debt?
Answers
Answer:
$-21
Step-by-step explanation:
Since she is paying $6 for 4 weeks, in total she will pay:
6 x 4 = $24
She has an initial balance of $-45 Because she is in debt
Therefore you just need to add it all up
-45 + 24 = $-21
Answer:
-24
Step-by-step explanation:
6 x (-4) = 24
WILL GIVE BRAINLIEST PLEASE ANSWER ASAP
Answers
Answer:
Circle man ez
Step-by-step explanation:
Answer:
Circle
Step-by-step explanation:
There is no way you could cut this where you would get a circle.
help me plez There are 100 bolts in 5 bookcases.
What is the unit rate in bolts per bookcase?
2 bolts per bookcase
20 bolts per bookcase
50 bolts per bookcase
200 bolts per bookcase
Answers
Answer:
20 bolts per bookcase
Step-by-step explanation:
what does mujer culona
mean
Answers
Identify the correct Triangle Congruence Theorem that describes the figure below.
A. SAS
B. ASA
C. AAS
D. SSS
E. HL
Answers
Answer:
ASA
Step-by-step explanation:
Don't worry I just know
Evaluate the expression for the given value of the variable.
46 + 1/5r
r = -1/2
Answers
Answer:
[tex]45\frac{9}{10}[/tex] or [tex]45.9[/tex]
Step-by-step explanation:
All we have to do here is substitute the given value of [tex]r[/tex] into the given expression. Therefore, after substituting [tex]r=-\frac{1}{2}[/tex] into [tex]46+\frac{1}{5}r[/tex], we get:
[tex]46+\frac{1}{5}r[/tex]
[tex]= 46+\frac{1}{5}*(-\frac{1}{2} )[/tex] (Substitute [tex]r=-\frac{1}{2}[/tex] into [tex]46+\frac{1}{5}r[/tex])
[tex]=46-\frac{1}{10}[/tex] (Multiply)
[tex]=45\frac{9}{10}[/tex] or [tex]45.9[/tex] (Simplify)
Hope this helps!
Hey there!
The answer to your question is [tex]45\frac{9}{10}[/tex]
We can find this by simply plugging in the "r" value into the given equation.
46 + [tex]\frac{1}{5}[/tex] ([tex]\frac{-1}{2}[/tex])
Now we evaluate the equation:
46 + [tex]\frac{1}{5}[/tex] ([tex]\frac{-1}{2}[/tex])
46 + [tex]\frac{-1}{10}[/tex]
[tex]45\frac{9}{10}[/tex]
Hope this helps and have an amazing day!
Consider solving 푥2+12푥+5=0by completing the square. What number should be added to both sides of the equation? 푥2+12푥+_____=−5+_____a. -36b. 36c. 16d. -16
Answers
Answer:
B. 36
Step-by-step explanation:
The equation in question is not well written. Let the equation be;
x²+12x+5 = 0
In order to know what number should be added to both sides of the equation, we will take the square of the half of coefficient of x as shown;
Coefficient of x = 12
Half of 12 = 1/2(12) = 6
Square of 6 = 6² = 36
Hence the required number to add to both sides of the equation by completing the square method is 36
Kristen invested $1,800 in an account paying 6.5% simple interest. After 5 years, what is the balance of her account?
Answers
Answer: 2,385
Step-by-step explanation:
Round off 3.447 g to the nearest 1/100 g
pls help
Answers
Answer: 3.55 g
Step-by-step explanation: 3.447 g rounded to the nearest 1/100 g is 3.55 g.
Hint: nearest 1/100 g also means nearest hundredth!
A House needs to some maintenance one sink is dripping water every 10 minutes and the other sink is dripping every 12 minutes if both sink dripped at the same time how many minutes until they both drip at the same time again
Answers
Answer:
60 minutes
Step-by-step explanation:
We solve this question using Lowest Common Factor method
Find and list multiples of each number of minutes( 12 and 10 minutes) until the first common multiple is found. This is the lowest common multiple.
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80
Multiples of 12:
12, 24, 36, 48, 60, 72, 84
Therefore,
LCM(10, 12) = 60
The number if minutes until they both drip again is 60 minutes
What is the radical form of the expression
2 3/4
Answers
On a map, 1 inch represents 60 miles. The towns of Howell and Edgerton are
2
3
4
inches apart on the map. What is the distance in miles between Howell and Edgerton?
Answers
Answer:
On the map below, 14 inch represents one mile. Candler, Canton, and Oteen are three cities on the map.
Map_problem_figure_aff1d9be1f7b39bb6155b3bcf9b3ddd4
If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?
If Candler and Oteen are 312 inches apart on the map, what is the actual distance between Candler and Oteen in miles?
Commentary
The purpose of this task is for students to translate between information provided on a map that is drawn to scale and the distance between two cities represented on the map. This task is a very straightforward application of the mathematics described in 7.G.A.1. This task would be appropriate for assessment.
Solutions
Solution: 1
A distance of nine miles means 9 quarter inches on the map. This is
9×14=94
or 214 inches between Candler and Canton on the map.
Map_problem_a_425ac563f0de413ec7618e8fe79c1b90
How many 14 inches are in 312 inches? To find this, we divide:
312÷14=72×41=14
So it is 14 miles between Chandler and Oteen.
Step-by-step explanation:
Can someone help w this
Answers
I need help- I’ll give brainlist if it’s right
Answers
Answer:
D. x>[4]
Plzzzzz give me Brainliest!!!!!
Answer:
D. x > 4
Step-by-step explanation:
You have to do the opposite operations to get the variable on one side of the equation by itself.
4 - x + 4 = 8 - 4
x = 4
You only switch the comparison sign if you mutliply or divide by negative numbers when you do opposite operations to get the variable on one side of the equation by itself.
I hope this helps!
Find parallel lines which pair of line are paraelle
Answers
Answer:
Parallel lines are like a square. all sides of a square are parallel.
Step-by-step explanation:
Answer:
Parallel lines are lines that will never clash into one another. Like a rectangle is a shape with parallel lines.
Step-by-step explanation:
The table shows the amount of apple sauce made from one apple of each size. Patrice has 17 medium apples and 23 large apples. What is the total amount of apple sauce that she can make with these apples? here's the table:
Apple size: small medium large
1/3 cup 1/2 cup 3/4 cup
Answers
Answer:
uhhhhh 75
Step-by-step explanation:
A livestock pen is built in the shape of a rectangle that is four times as long as is wide. The total perimeter is 60 ft. Write an equation that models the perimeter in terms of width and/or length, find the length and width.
Answers
Answer:
Perimeter = 60ft = 2(4x + x)
breadth = 6ft
length = 24ft
Step-by-step explanation:
Perimeter = 2 (L + B)
L =length
B = Breadth
x= breadth
4x = length
Perimeter = 60ft = 2(4x + x)
Dividing both sides by 2 :
30ft= 4x + x
30ft = 5x
divide both sides by 5
6ft= x
breadth = 6ft
length = 4x= 4 x 6 = 24ft
Which value of n makes the equation true?
1/2(n+4)=6
Answers
Answer:
8
Step-by-step explanation:
1/2(12)=6
Answer:
8
Step-by-step explanation:
1/2(8+4)=6
