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
View One Minute Version
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
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Answers
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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
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If the volume of cylinder of height 7 cm is 448 cm², then the total surface area of cylinder is
(1) 2041 cm?
(2) 2241 cm?
(3) 2481 cm?
(4) 240 cm?
Answers
Answer:
A = 240π cm²
Step-by-step explanation:
Given that,
Height of a cylinder, h = 7 cm
Volume of the cylinder, V = 448π cm³
We need to find the total surface area of the cylinder.
The formula for the volume of the cylinder is given by :
[tex]V=\pi r^2 h\\\\r=\sqrt{\dfrac{V\pi }{\pi h}} \\\\r=\sqrt{\dfrac{448\pi }{\pi \times 7}} \\\\r=8\ cm[/tex]
The formula for the total surface area of the cylinder is given by :
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Answers
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7w + 3 + 2w + 9 simplified
Answers
The answer is 9w + 12
hope this helps!
Answer:
9w + 12
Step-by-step explanation:
First, add the 7w and the 2w
7w + 2w = 9w
Second, add 3 and 9
3 + 9 = 12
Last, add the two together
9w + 12 =
Hope this helps!
Simplify the expression. Explain each step.
6(2b)
Answers
Answer:12b
Step-by-step explanation:
Here,
We have only one variable
So we can multiply it with number
=6×2b
=12b
Hope it helps you
Plz mark me brainliest.
Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|
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Hope this helps
Marie works in a garment factory that makes shirts. Marie’s job is sewing in sleeves. Marie receives .55 for each pair of sleeves she completes. During this pay period, she completed 1, 632 pairs of sleeves. What were Marie’s gross earnings?
Answers
Answer:
879.6
Step-by-step explanation:
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The fence around a circular garden is 18 feet long. What is the area of the garden to the nearest square foot? Use 3.14 for pi.
____square feet
Answers
Answer:
26
Show Your Work:
Answer:
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Step-by-step explanation:
i did the diagnostic
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A. 1 pound
B. 1 5/9
C. 1 2/3
D. 2 7/9
Answers
Answer: 2 7/9
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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(04.07)
Two separate bacteria populations grow each month and are represented by the functions fx) = 3* and g(x) = 7x + 6. In what month is the f(x)
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Answers
Complete question is;
Two separate bacteria populations grow each month and are represented by the functions f(x) = 3^(x) and g(x) = 7x + 6. In what month is the f(x) population greater than the g(x) population?
A. Month 1
B. Month 2
C. Month 3.
D. Month 4
Answer:
Option D: Month 4
Step-by-step explanation:
We are given the functions;
f(x) = 3^(x)
And g(x) = 7x + 6
We want to find the month when f(x) > g(x)
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RHS = 7(3) + 6 = 27
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LHS is 3⁴ = 81
RHS = 7(4) + 6 = 34
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Answers
Move all terms not containing
x
to the right side of the equation.
Tap for more steps...
2
x
=
16
Divide each term by
2
and simplify.
Tap for fewer steps...
Divide each term in
2
x
=
16
by
2
.
2
x
2
=
16
2
Cancel the common factor of
2
.
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x
=
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x
=
8
Answer:
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Answers
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Step-by-step explanation:
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As per graph:
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Calculation:
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Answers
Answer and Step-by-step explanation:
To solve, you first divide 7 by 9.
Then, you divide 119 by 7/9.
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#teamtrees #WAP (Water And Plant)
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A
Step-by-step explanation:
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Complete question :
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Which of the options below show a pair of supplementary angles? Select all that apply.
A) 160°, 20°
B) 120°, 40°
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Answers
Answer:
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Step-by-step explanation:
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B) 120 + 40 = 160
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