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
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Answers
Answer:
no solution
Step-by-step explanation:
Which of the options below show a pair of supplementary angles? Select all that apply.
A) 160°, 20°
B) 120°, 40°
C) 45°, 135°
D) 30°, 120°
Answers
Answer:
A and C
Step-by-step explanation:
A) 160 + 20 = 180
B) 120 + 40 = 160
C) 45 + 135 = 180
D) 30 + 120 = 150
All supplementary angles must add up to 180 degrees.
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Answer:
Half of the possible choices as far as I know are not shown in the picture but your answer should be the graph that is 5 units down than the center of the graph.
Aliyah is drawing a ball from one bag and a tile from another bag the first bag contains four green balls and four yellow balls the second bag contains tiles 1 through 5 search
Answers
Complete question :
Aliyah is drawing a ball from one bag and a tile from another bag the first bag contains four green balls and four yellow balls the second bag contains tiles 1 through 5 search
What is the probability that she draws a green ball and a tile numbered with 4?
Answer:
1 / 10
Step-by-step explanation:
Given:
Bag content :
Green balls = 4
Yellow balls = 4
Probability = required outcome / Total possible outcomes
P(drawing a green ball) = 4 / 8 = 1/2
Total number of tiles = 5
P(drawing tile numbered 4) = (number of tiles numbered 4 / total number of tiles) = 1 / 5
P(drawing a green ball) * P(drawing tile numbered 4)
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= 1 / 10
h + 13.4 = -13.4
h = ?
Answers
-2•f(-6)-7•g(-7) help
Answers
Answer:
11
Step-by-step explanation:
-2 • f(-6) -7 • g(-7) = ?
As per graph:
f(-6) = 5
g(-7) = -3
Calculation:
-2 • f(-6) -7 • g(-7) =
-2(5) - 7(-3) =
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Answer:
24.45cm squared
Step-by-step explanation:
(9 x 12) - ((6 x 3.14) / 2)
2x – 5 = 7 to 2x = 12 What property of equality was used?
Answers
Property of Addition and division.
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:
I had a similar question that I solved which helped me here.
Question 3 (2 points)
(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)
population greater than the g(x) population? (2 points)
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)
Thus;
3^(x) > 7x + 6
For option A, month 1 means x = 1.thus;
LHS is 3¹ = 3
RHS = 7(1) + 6 = 13
Our LHS is not greater than RHS as the question demands, thus this option is not correct
For option B, month 2 means x = 2. thus;
LHS is 3² = 9
RHS = 7(2) + 6 = 20
Our LHS is not greater than RHS as the question demands, thus this option is not correct
For option C, month 3 means x = 3. thus;
LHS is 3³ = 27
RHS = 7(3) + 6 = 27
Our LHS IS equal to the RHS and not greater than RHS as the question demands, thus this option is not correct
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LHS is 3⁴ = 81
RHS = 7(4) + 6 = 34
Our LHS is greater than RHS as the question demands, thus this option is correct
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Answers
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A. 153
B. 272
C. 128
D. 135
Answers
Answer and Step-by-step explanation:
To solve, you first divide 7 by 9.
Then, you divide 119 by 7/9.
[tex]\frac{7}{9} = 0.777777777777\\\\\frac{119}{0.77777777777} = 153.\\\\[/tex]
To check your work, divide 119 by 153, and you will get 0.777777777777, which is the same as 7 divided by 9.
So, the answer is A. 153
#teamtrees #WAP (Water And Plant)
Answer:
A
Step-by-step explanation:
I divided 119 by 7 which is 17. Then multiplied that by 2 because theres a gap of 2 between 7 and 9 and got 34. lastly added 119 by 34 and got 153. (Sorry if I got it wrong)
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Determine the length of CB.
Answers
9514 1404 393
Answer:
CB = √6 cm
Step-by-step explanation:
The diagonal of a square is √2 times the edge length, so the length AB will be (1/2)√2(2 cm) = √2 cm.
Then the length CB is given by the Pythagorean theorem as ...
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CB = √6 cm
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Answers
Answer:
x=50 y=25
Step-by-step explanation:
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Answers
Answer:
26
Show Your Work:
Answer:
26 sq.ft.
Step-by-step explanation:
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Answers
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Answer:
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Step-by-step explanation:
UV=3y-5+2z+2
=3y+2y-3
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3x+3=3y+6
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3x-3y=3
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30 =3y+2y this is 30=5y which is y=6
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3=3x-18
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Answers
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A. 1 pound
B. 1 5/9
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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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 :
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Step-by-step explanation:
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Answers
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Answer:
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Step-by-step explanation:
First, add the 7w and the 2w
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Answers
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Step-by-step explanation:
Here,
We have only one variable
So we can multiply it with number
=6×2b
=12b
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Answers
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AC, AB. BC
Step-by-step explanation:
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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
.
Tap for more steps...
x
=
16
2
Divide
16
by
2
.
x
=
8
Answer:
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