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
What is the measure, in degrees, of
PLEASE HELP
Answers
Answer:
58 degrees
Step-by-step explanation:
Complementary angles add together to 90 degrees
(5x + 8) + (3x + 2) = 90
8x + 10 = 90
x = 10
5(10) + 8 = 58
Can anyone explain and give answer please?
Answers
Answer:
slope = - [tex]\frac{1}{19}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 19x + 57 ← is in slope- intercept form
with slope m = 19
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{19}[/tex] ← slope of line w
BRIDGE Arturo is designing a bridge for science class using parallel supports for the top and bottom beam. Find m angle2 if m angle1=60^
Answers
Answer:
Believe it or not, it would be 60 degrees.
Step-by-step explanation:
Here, we are working with ALTERNATE INTERIOR ANGLES. Since we know the beam supports for the top and bottom are parallel, 1&2 will be the same angle measurement.
Here is a diagram of an example of alternate interior angles, where m1=m2.
Answer:
Step-by-step explanation:
-3(2x-3)+10x=39 what’s the answer
Answers
Pls help, I know the answer but what I wrote in the box isn't correct
How do I show the answer?
Answers
Answer:
AC=11.38 cm
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]
The figure shows two triangles and we are required to calculate the length of the side AC, knowing two sides and the angle between them. Thus, applying the formula:
[tex]AC^2=17^2+13^2-2*17*13*\cos42^\circ[/tex]
[tex]AC^2=289+169-442*0.7431[/tex]
[tex]AC^2=129.53[/tex]
[tex]AC=\sqrt{129.53}[/tex]
AC=11.38 cm
Help plsssssssss????
Answers
Help. I need help with these questions ( see image).
Please show workings.
Answers
9514 1404 393
Answer:
4) 6x
5) 2x +3
Step-by-step explanation:
We can work both these problems at once by finding an applicable rule.
[tex]\text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}[/tex]
where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.
This can be referred to as the power rule.
Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:
lim[h→0](f(x+h)-f(x))/h = 2ax +b
__
4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.
5. The gradient of x^2 +3x +1 is 2x +3.
__
If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.
can someone help me ill give a brainiest
Answers
1. 500% Increase
2. 40% Decrease
3. 75% Increase
4. 62.5% Increase
What is the surface area of a cylinder with a radius of 12 centimeters and a height of 7 centimeters? Use terms of pi.
I’ll give brainliest to whoever answers 1st! :)
Answers
Answer:
1432.57cm²
Step-by-step explanation:
HELP! (On the ?’s I didn’t answer thank you!
Answers
Ross has a season ticket.
In 2013 the season ticket cost £65.
In 2014 the cost of the ticket was increased by 8%.
In 2015 the cost of the ticket was increased by a further 5%.
Calculate the cost of the season ticket after the two price increases.
Answers
Answer:
£73.71
Step-by-step explanation:
Let's compute first for the cost of the ticket in 2014. Let x be the increase in the cost of the ticket. If the cost of the ticket is 8% of £65, then the expression should be like this:
x = 65 x 8%x = 65 x 0.08x = £5.2Let's add £5.2 to £65 ⇒ £5.2 + £65 = £70.2
The cost of the season ticket in 2014 is £70.2.
Next, we'll have to compute the cost of the ticket in 2015. Let y be the increase in cost of the ticket. If the cost of the ticket is 5% of £70.2, then the expression should be like this:
y = 70.2 x 5%y = 70.2 x 0.05y = £3.51Let's add £3.51 to £70.2 ⇒ £3.51 + £70.2 = £73.71
The cost of the season ticket in 2015 is £73.71. This is also the cost of the season ticket after two price increases.
HEEELp PLEASEEEEEEE tank uuuuuuuuuu
Answers
Answer:
they both are because they are not symmetrical??
Step-by-step explanation:
9514 1404 393
Answer:
both figures are parallelograms
Step-by-step explanation:
The diagonals of a quadrilateral bisect each other if and only if that quadrilateral is a parallelogram. Hence, the left figure is a parallelogram.
The opposite angles of a quadrilateral are congruent if and only if that quadrilateral is a parallelogram. Hence the right figure is a parallelogram.
__
Additional comment
Proofs of these conditions can be offered, but these are the conclusions of the respective proofs. The bisected diagonals form pairs of triangles, provably congruent using SAS. (left figure) The angles total 360°, so any adjacent pair must total 180°, making opposite sides parallel. (right figure)
What is the midpoint of the line segment with the equation y=12x+3 between x=−4 and x=8?
(6,6)
(2,−2)
(2,4)
(2,2)
Answers
Answer:
2,4 ((((((((((((((((((((
Which angles in the picture are NOT supplementary?
A.) 2 and 3; 1 and 4
B.) 1 and 3; 2 and 4
C.) 4 and 1; 3 and 4
D.) 1 and 2; 2 and 3
Answers
B.) 1 and 3; 2 and 4 in the picture are not supplementary.
Supplementary angles refers to the type of angles whose sum is 180°. It is not mandatory for the division of angle to be in half. The angles can be 60° and 120°, 130° and 50°, 90° and 90° and so on.
In the figure, we can see two lines intersect each other. Angle 1 and 2 are present on straight line, and hence, their sum will be 180°. Angle 2 and 3 are present on straight line, and hence, their sum will be 180°. Angle 3 and 4 are present on straight line, and hence, their sum will be 180°. Angle 1 and 4 are present on straight line, and hence, their sum will be 180°.
Angle 2 and 3 and angle 1 and 4 are opposite angles, that are not present on same straight line. Therefore, they are not supplementary angles.
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HELP ME PLEASE.......
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Answer:
slope is 2.33
Step-by-step explanation:
Simplify
14^15 over 14^5
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What is the solution for the system of equations shown in the graph?WILL GIVE BRAINLY IF ANSWER
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Answer:
(2,4)
Step-by-step explanation:
thats the point where both lines meet
Which type of transformation is shown in the figure on
the left?
O translation
O reflection
O rotation
O dilation
The answer is reflection
Answers
yea the answer is reflection
The type of transformation that's shown in the figure on the left is; reflection
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs,
A reflection is defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis such as; if we're seeing it in a mirror.
We will find that its symmetric, thus each point is equidistant from the axis of reflection such that of the image of that point.
The answer is; reflection
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2.4, -3.4, -9.2, -15, - 20.8,
If the pattern continues, which expression can be used to find the nth term?
Answers
Answer: c. 8.2-5.8n
Step-by-step explanation:
I got it wrong and it said that c was correct your welcome
An arithmetic sequence is a sequence where the difference between the consecutive term is the same.
The formula for nth terms of an arithmetic sequence.
nth term = a + (n -1)d
The expression that is used to find the nth term of the given arithmetic sequence is
2.4 - 5.8 (n - 1)
What is an arithmetic sequence?An arithmetic sequence is a sequence where the difference between the consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
The common difference is 2.
We have,
2.4, -3.4, -9.2, -15, - 20.8,
This is an arithmetic sequence.
The common difference.
= -3.4 - 2.4
= -5.8
Now,
The formula for nth terms of an arithmetic sequence.
nth term = a + (n -1)d
So,
a = 2.4
d = -5.8
nth term:
= 2.4 + (n - 1)(-5.8)
= 2.4 - 5.8(n - 1)
Thus,
The expression that is used to find the nth term of the given arithmetic sequence is
2.4 - 5.8 (n - 1)
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*************MUST ANSWER!***************
Sebastian has a points card for a movie theater.
-He earns 85 points just for signing up.
-He earns 2.5 points for each visit to the movie theater.
-He needs 115 points for a free movie ticket.
Write and solve an Equation which can be used to determine v, the number of visits Sebastian must make to earn a free movie ticket.
Answers
Answer:
Look Down
Step-by-step explanation:
85+2.5v=115
2.5v=30
v=12
What is the measure of x?
Angles are not necessarily drawn to scale.
63
PLEASE HELPPP
Answers
Answer:
help with what?
Step-by-step explanation:
24x0. 6x1. 21x2. 11x5
Answers
6 x 1 = 6
21 x 2 = 42
11 x 5 = 55
Answer:
Step-by-step explanation:
Use calculator
but anyways here
24 x 0 = 0
6 x 1 =6
21x 2 =42
11x 5 = 55
[tex]y/8=5[/tex]what is "y' in y/8=5
Answers
Answer:
Y=40
Step-by-step explanation:
Y/8=5
(Y/8)*(8)=(5)*(8)
Y=40
The sale amount is $67.50 and the sales Tax is 5% what is the total amount paid?
Answers
Answer:
70.88
Step-by-step explanation:
x/67.5=5/100 cross multiply 100x=337.5 divide 100 x=3.375 or 3.38 67.50+3.38=70.88
70.88 is your correct answer
Joseph runs 2/12 miles on Monday. Each day after that, he runs the same 1/13 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?
What is the least number of days after Monday that Joseph needs to run to reach his goal?
Answers
Answer:
Step-by-step explanation:
At the end of practice, Joseph will need to run another 1.75 miles or 1 3/4 miles.
To determine this we need to subtract the amounts he already has run during practice from the goal of 3 miles.
3 miles - 1/2 miles - 1/4 miles - 1/4 miles - 1/4 miles = 1.75 miles
PLEASE ASAP
What is the equation of the line passes through the point (-6, 6) and is parallel to the y=2/3x-1?
Answers
Answer:
y=2/3 x+10
Evidence:
Picture
Hope it helped!
Please help with these questions please!!!
Answers
Answer:
1). x = 0
2). Option 3
Step-by-step explanation:
1). If the two triangles are similar,
Their corresponding sides will be proportional.
[tex]\frac{5x+2}{6}=\frac{x+4}{12}[/tex]
12(5x + 2) = 6(x + 4)
60x + 24 = 6x + 24
60x - 6x = 24 - 24
54x = 0
x = 0
2). Option 1
2(x - 6) + 3 - 5x = -3x - 9
2x - 12 + 3 - 5x = -3x - 9
-3x - 9 = -3x - 9
True.
Option 2
4(2x - 5) + 10 - 5x = 3x - 10
8x - 20 + 10 - 5x = 3x - 10
3x - 10 = 3x - 10
True
Option 3
5x + 4 = 3x + 4
False
Option 4
8x + 3 - 2 = 8x + 1
8x + 1 = 8x + 1
True.
Therefore, option 3 is False.
MLM BLM any one who says other why come fight me lol
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Answer:
BLM &MLM yasss!!!!!!!!!!!!!1
Step-by-step explanation:
Is this equation proportional? why?
y = 3x + 2x
Answers
Answer:
5x
Step-by-step explanation:
Benjamin and Amelia Hopkins have been married since 2016. Benjamin is a U.S. Citizen with a valid Social Security number. Amelia is a resident alien with an Individual Taxpayer Identification Number (ITIN). They elect to file Married Filing Jointly. Benjamin worked in 2020 and earned wages of $25,000. Amelia worked part-time and earned wages of $15,000. They have two children: Harper, who is 9 years old, and Evelyn, who is 12 years old. Both children were supported by their parents all year. Harper is a U.S. Citizen and has a valid Social Security number. Evelyn is a resident alien and has an ITIN. Benjamin, Amelia, Harper, and Evelyn lived together in the U.S. All year 7. Which credit(s) can the Hopkins claim on their 2020 tax return. Are the Hopkins eligible to claim the earned income credit?
Answers
Answer:
The answer is "Child tax credit for Harper and No, because Amelia has ITIN."
Step-by-step explanation:
In question 1, The answer is "Child tax credit for Harpe" each qualified kid for tax years 2018-2025 should have SSN through employment provided before the returned closing date. Harper is a U.S. national and also has a legitimate SSN, and therefore Hopkins may assert Harper's tax credit.
In question 2, The answer is "No, because Amelia has ITIN" because the IRS problem is an ITIN issue whenever a person has been unable to claim their income tax credit his or she may be not qualified to SSN.