Ryan is putting a clothesline in his rectangular backyard. He wants to put it between two trees on the edge of his
property. He has measured his property, and made the sketch shown below, where all the lengths listed are in
meters.
10
Tree
What is the smallest length of rope that Ryan could buy which would stretch from one tree to the other?
Answers
Answer: 25 meters.
Step-by-step explanation:
The missing figure is attached.
Draw a Right triangle as the one shown in the second picture, where "a" is the smallest length of rope (in meters) that Ryan could buy, which would stretch from one tree to the other tree.
You need to use the Pythagoream Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" are "c" are the legs of the Right triangle.
In this case you can identify that:
[tex]b=25-10=15\\\\c=20[/tex]
Knowing those values, you can susbtitute into [tex]a^2=b^2+c^2[/tex] and then solve for "a" in order to find its value.
You get:
[tex]a^2=15^2+20^2\\\\a=\sqrt{15^2+20^2}\\\\a=25[/tex]
Related Questions
What is the range of 16,17,17,18,18,18,19,19,19,19,20,20,20,21,21,22,22,24,25,25
Answers
In order to find the range we first have to list the numbers from least to greatest:
16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 24, 25, 25
range = largest value - smallest value = answer
range = 25 - 16 = 9
range = 19
so, our final answer would be 19.
~ i hope this helps you have a good day/night afternoon~ ~-gabby~
Answer: The answer is 23.
Step-by-step explanation:
The coordinates of trapezoid ABCD are A (-6,3) B (-3,6) C (9,6) and D (-5,-8). Find the coordinates of trapezoid A’ B’ C’ D’ after the translation whose rule is T 3,4.
Answers
Answer:
A' (-3,7)
B' (0,10)
C' (12,10)
D' (-2,-4)
Step-by-step explanation:
A' (-6+3 , 3+4) = (-3,7)
B' (-3+3 , 6+4) = (0,10)
C' (9+3 , 6+4) = (12,10)
D' (-5+3 , -8+4) = (-2,-4)
Find the 72nd term of the arithmetic sequence 11, 7,3,...
Answers
Answer:
3124
Step-by-step explanation:
Answer: -273
Step-by-step explanation: To determine the 72nd term, we will want use our explicit formula which is shown below.
[tex]^{a}n = ^{a}1 + (n - 1)d[/tex]
Since we want to find the 72nd term, the [tex]^{a}n[/tex]
in the formula will be changed to [tex]^{a} 72[/tex].
Also, the 72 will be substituted in for the n
that is inside the set of parentheses.
Then [tex]^{a} 1[/tex] will be the 1st term given in our sequence or 11.
Lastly, the d outside the parentheses is the difference between
each of the terms in the sequence which is -4.
So we now have [tex]^{a} 72 = 11 + (72 - 1)(-4)[/tex].
Now we have all the information we need.
Now we can simplify from here.
Make sure to apply your order of operations because
this is where a lot of students make mistake.
Start simplifying inside the parentheses!
(72 - 1) is going to be 70.
So we have [tex]^{a} 72 = 11 + (71)(-4)[/tex].
Then, we have to multiply before we add.
So (71)(-4) is going to be -284.
So we have [tex]^{a} 72 = 11 + (-284)[/tex].
Solving from here, 11 + (-284) simplifies to -273.
This means that the 72nd term of this sequence is -273.
which expression is equivalent to 9x2 − 16
Answers
Answer:
[tex]9 \times 2 - 16 \\ 18 - 16 = 2[/tex]
66 times 26 times 60 then multiply 1/2
Answers
Answer:
Step-by-step explanation:
51,480 is the answer.
Answer:
51,480
Step-by-step explanation:
66 x 26 = 1,716
1,716 x 60 = 102,960
102,960 x 1/2 = 51,480
1.
What is the mean for the following scores: 2, 5, 4, 1, 8?
A. 3
B. 4
c. 5
20
Answers
Answer to your question is:
B. 4
Explanation:
2 + 5 + 4 + 1 + 8 = 20
20 ÷ 5 = 4
The mean is found out by adding the scores given and dividing the total by the number of scores.
In the given question the mean of the scores is 4.
The mean is calculated to get an average about something that is given.
Here
n= number of scores= 5
Sum of scores = ∑x= 2+5+4+1+8= 20
Mean = x bar= ∑x/n= 20/5= 4
For different distributions mean may or may not be the middle value.
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Identify the graph of g(x) = –x2 + 9x – 20 from the choices below.
Answers
The graph of the quadratic function g(x) = -x^2 + 9x - 20 will be a downward opening parabola with vertex at (4.5, 0.25), x-intercepts at (4, 0) and (5, 0), and a y-intercept at (0, -20). To graph it, label the axes as 'f(x)' and 'x' and scale them to include these critical points.
Explanation:The student wants to identify the graph of the quadratic function g(x) = –x2 + 9x – 20. To do this, first note that the standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants.
In this case, a = -1 (which makes the parabola open downward), b = 9, and c = -20.
The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b/(2a).
For g(x), this gives h = -9/(2 * -1) = 4.5.
We can then find the value of k by substituting h back into g(x), which gives us k = -4.52 + 9(4.5) - 20.
Therefore, k = 0.25.
The vertex of the parabola is at (4.5, 0.25), and because a is negative, the parabola opens downward. The x-intercepts (or roots) of the parabola can be found by factoring the quadratic equation or using the quadratic formula. In this case, the x-intercepts are (4, 0) and (5, 0). Lastly, the y-intercept occurs when x = 0, which for g(x) is -20.
To label the graph, we'd use 'f(x)' for the vertical axis and 'x' for the horizontal axis. The scale of the axes depends on the maximum and minimum x and y values of the graph, which in this instance would include at least the vertex, x-intercepts, and y-intercept.
convert 20 miles to km
Answers
Answer:
32.1869
Step-by-step explanation:
multiply 20 by 1.609
multiplying miles by 1.609 will give you the answer
Answer:
20 miles =32.1869
Step-by-step explanation:
For an approximate result multiply the length value by 1.609.
What are the roots of the equation 16x2 - 16x + 5 = 0 in simplest a + bi form?
Answers
Answer:
37/16
Step-by-step explanation:
The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.
51,54,57,60,63,66,69,72,75,78,81,84
Which statement about the temperatures in Orlando must be true?
A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.
Answers
Answer:
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
The box ranges from 66 to 75... meaning that most of the days were in those temperatures.
The lines mean that there were only a few days that were in those temperatures.
You're welcome if I'm correct.
The correct answer is about 50% of the days in January had average temperatures between 66 and 75 degrees.
What is the box and whisker plot?A Box and Whisker Plot (also known as a Box Plot) is a visual representation of data distribution through quartiles.
The maximum and minimum value of the function is plotted at the ends of a box and whisker plot.The box in the middle displays the interquartile range, which means that about 50% of values when the data is arranged in ascending or descending order.In the graph given in the question we can clearly see that the interquartile range of the data is lying between the temperatures 66° to 75°, which means that 50% of days in January had the temperature between 66 to 75 degrees.
Hence, Option(c) is correct for the given question.
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please solve this question
Answers
Given:
Number of mice and frequency
Mean = 7
To find:
The value of x.
Solution:
Number of mice = X
Frequency = Y
XY = Multiply X and Y values.
X Y XY
5 4 20
6 13 78
7 16 112
8 x 8x
9 6 54
Sum of Y = 4 + 13 + 16 + x + 6
= 39 + x
Sum of XY = 20 + 78 + 112 + 8x + 54
= 8x + 264
Mean formula:
[tex]$Mean = \frac{\Sigma XY }{\Sigma Y}[/tex]
[tex]$7=\frac{8x+264}{39+x}[/tex]
Do cross multiplication.
[tex]7(39+x)=(8x+264)[/tex]
[tex]273+7x=8x+264[/tex]
Subtract 264 from both sides, we get
[tex]9+7x=8x[/tex]
Subtract 7x from both sides, we get
[tex]9=x[/tex]
The value of x is 9.
Find the area to this please
Answers
Answer:
35
Step-by-step explanation:
please mark brainiest
Hope this helps
2/3 is greater than, less than it equal to 5/8
Answers
Answer:
greater than it
Step-by-step explanation:
Answer:
[tex] \frac{2}{3} > \frac{5}{8} \\ \frac{2}{3} \: greater \: \: \: than \frac{5}{8} [/tex]
Need help!!!!!!
This is so confusing
Answers
Answer:
Omar
Step-by-step explanation:
to find the base, which i am to assume they want to find the triangle base based on the formula they are using,
you should multiply base * height, then divide by 2, since it is a triangle, you not solving for a rectangle.
dividing by 2 and multiplying by 1/2 is the same thing!
so,
1/2 (7* 24) is the right answer to finding the base!
Kari looked at he direct base of 7*28, however, that shape is actually a rectangle... so Kari is wrong because he multiplied that dimension by 1/2, which is the formula for a triangle.
Omar is correct because he chose the dimensions of a triangle, and properly used the triangle formula!
i hope this helped you out!
stay safe!
:)
Can someone please explain how to solve this question? I will give thanks and 5 stars! Whoever answers, thank you!
Answers
Answer:
33 1/3%
Step-by-step explanation:
When you roll a die, the possible outcomes are 1,2,3,4,5,6
getting a number less than 5: 1,2,3,4
P( getting a number less than 5)
= number of outcomes that meet conditions / total outcomes
=4/6
= 2/3
Then we flip a coin heads or tails
We want heads
P (heads) = number of outcomes that meet conditions / total outcomes
= 1/2
Since the event outcomes do not depend on each other
P( getting a number less than 5) *P (heads) = 2/3 * 1/2 = 1/3
as a percent
= 33 1/3%
What is the height of our classroom door is it a statistical or non statistical question
Answers
Answer:
to me should be statistical question
Step-by-step explanation:
not statistical would be only getting one answer but you could have the height in inches, centimeters, feet, meters, etc. which would count as more then one answer being statistical
29+5x=44 whats the valué of x
Answers
Answer:
x=3
Step-by-step explanation:
44-29=15
5*3=15
The value of x in the equation 29 + 5x = 44 is solved by isolating x to find that x = 3.
Explanation:To solve the equation 29 + 5x = 44 for x, you should start by isolating the variable on one side. Here's a step-by-step process:
Subtract 29 from both sides of the equation to get 5x = 44 - 29.This simplifies to 5x = 15.To find the value of , divide both sides by 5, leading to .Finally, you get the solution x = 3.Therefore, the value of x in the given equation is 3.
Express your answer exactly
Answers
Answer:
sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
See the attachment.
Cosine is adjacent over hypotenuse, so since cos(θ) = 3/8, then the adjacent side of the triangle is 3 and the hypotenuse is 8.
Since is opposite divided by hypotenuse. To find the opposite side, which is the unlabelled side on the graph, we need to use the Pythagorean Theorem:
x = [tex]\sqrt{8^2-3^2} =\sqrt{64-9} =\sqrt{55}[/tex]
So, sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex].
Hope this helps!
What is the circumference of the circle? Use 3.14 for pi
r = 6.4 cm
20 096 cm
40 192 cm
200 96 cm
401 92 cm
Answers
Answer:
its
40 192 cm
Step-by-step explanation:
Answer:
40.192cm
Step-by-step explanation:
the circumference of a circle = ?
radius = 6.4cm
recall that,
circumference of a circle = 2πr
circumference of a circle = 2 x 3.14 x 6.4cm
circumference of a circle = 40.192cm
therefore the circumference of a circle whose radius is 6.4cm is evaluated to be equals to 40.192cm.
the answer to your question is option B 40.192cm
This graph shows a car moving at a
constant speed. For example, in 8 hours
the car travels 400 miles.
Which equation shows the line on the
graph?
A y = 2x
B y = 50x
C y = 400x
Answers
Answer:
B
Step-by-step explanation:
If you set x to hours and y to the amount of miles, you can multiply the hours to the numbers and equal out your miles. So, if 8 hours is multiplied to 50, it equals out the 400 miles.
Which of the following statements is true regarding a representative sample?
A.
It is at least 1/2 of the total population.
B.
It focuses on a specific group within the population.
C.
It is a group that is fairly proportional to the population.
Answers
Answer:
B
Step-by-step explanation:
The following statement is true regarding a representative sample
"It is a group that is fairly proportional to the population".
What is the representative sample?
A representative sample is a subset of a population that is selected in such a way that it accurately reflects the characteristics of the entire population. The goal of a representative sample is to ensure that the sample is as representative as possible of the population as a whole so that the results of a study based on the sample can be generalized to the population.
A representative sample is not necessarily at least 1/2 of the total population (Option A) or focused on a specific group within the population (Option B). It is simply a group that is fairly proportional to the population, meaning that it contains a similar mix of characteristics as the population as a whole.
Hence, the correct answer would be an option (C).
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There are 4 green crayons, 6 yellow crayons and 3 blue crayons. P(green
then blue) without replacement. *
Answers
Answer:
0.0769 or 7.69%
Step-by-step explanation:
Number of green crayons = 4
Number of yellow crayons = 6
Number of blue crayons = 3
Total number of crayons = 4 + 6 + 3
= 13 crayons
[tex]Probability=\frac{\text{favorable outcome}}{\text{total number of outcome}}[/tex]
probability to get first green crayon P₁ = [tex]\frac{4}{13}[/tex]
Probability to get second crayon is blue P₂ = [tex]\frac{3}{12}[/tex]
P = P₁ × P₂
= [tex]\frac{4}{13}\times \frac{3}{12}[/tex]
= [tex]\frac{12}{156}[/tex]
= 0.0769
Probability to get green then blue is 0.0769 or 7.69%
Are these shapes similar?
Answers
First one that knows the answer
wins brainliest
Answers
Answer:
The bakery made a profit of $8,013 during the summer months
Step-by-step explanation:
A profit is made when income is greater than expenses while a loss is made when expenses are greater than income
A loss is a negative profit
In June
Income = $750
Expense:
rent = $890
Operating costs = $975
Total expense = $1,865
Profit = income - expense
profit = $750 - $1865
= -$1115
Therefore, a loss of $1115 was made in June
July
Income = $ 925
Expenses:
Rent = $890
Operating costs = $721
Total expenses = 1611
Profit = $925 - $1611
= -$686
A loss of $686 was made in July
August
Income = $11,250
Expenses:
Rent = $890
Operating costs= $546
Total expense = $1436
Profit = $11,250 - $1436
= $9,814
A profit of $9,814 was made in August
Now let's find the difference between the profit and losses that were made during the summer months. This will be the addition of the profit and losses of all three months
Remember that losses carry a negative sign
$9,814 -$686 -$1115 = $8,013
Therefore, the bakery made a profit of $8,013 during the summer months
Find the circumference of a circle that has a diameter of 42 m.
Answers
Answer:
the answer is 131.95m.
Answer:
Step-by-step explanation:
Circumference = πd
r = diameter/2
C= 42π = 42 XX22/7 =- 6x22=132m
Find the measure of Arc JN
Find the measure of arcJN=
Find the m
Answers
Step-by-step explanation:
[tex]m(arc \: JN) = 360 \degree - (60 \degree + 150 \degree) \\ \hspace{57pt}= 360 \degree - 210 \degree \\ \hspace{57pt} = 150\degree \\ \\ m \angle K = \frac{1}{2} \times m(arc \: JN) \\ \hspace{30pt}= \frac{1}{2} \times 150\degree \\ \hspace{30pt} = 75\degree \\ [/tex]
Similar triangles are two triangles with equal ____ angles.
a. vertical
b. corresponding
angles.
c. horizontal
d. elliptical
Answers
Similar triangles are defined as two triangles having equal B. corresponding angles, shown by the congruence of vertical angles, alternate interior angles, and the application of the AAA theorem.
Similar triangles are two triangles with equal corresponding angles. According to the question, in the figure, two triangles named triangle ABC and triangle FCE are observed to be similar because they have three sets of congruent angles - vertical angles (Angle ACB \\<=\ Angle FCE), alternate interior angles (Angle CAB \\<=\ Angle CFE), and another set of alternate interior angles (Angle CBA \\<=\ Angle CEF).
This is summed up by the AAA (Angle Angle Angle) theorem which states that two triangles are similar if all their corresponding angles are congruent. An example will be two right triangles which are equal when the hypotenuse and an acute angle of one are equal, respectively, to the hypotenuse and an acute angle of the other. These principles help us understand the similarity of triangles in geometry.
if 3300 equals 4.5 percent what is the price of 100%
Answers
Answer:
73333.333
Step-by-step explanation:
100/4.5= 22.222
3300*22.222= 73333.333
What is the perimeter of the rhombus below?
Answers
Answer:
16
Step-by-step explanation:
the perimeter of the given rhombus is 8√5.
To find the perimeter of a rhombus, we need to calculate the sum of the lengths of all four sides.
Given the coordinates of the points touching the graph: (-5,-3), (-1,-1), (3,-3), and (-1,-5), we can calculate the distances between these points to find the lengths of the sides.
Let's calculate the lengths of the sides:
1. Side 1: Distance between (-5,-3) and (-1,-1)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - (-5))^2 + (-1 - (-3))^2]
Length = √[4^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
2. Side 2: Distance between (-1,-1) and (3,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(3 - (-1))^2 + (-3 - (-1))^2]
Length = √[4^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
3. Side 3: Distance between (3,-3) and (-1,-5)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - 3)^2 + (-5 - (-3))^2]
Length = √[(-4)^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
4. Side 4: Distance between (-1,-5) and (-5,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-5 - (-1))^2 + (-3 - (-5))^2]
Length = √[(-4)^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
Now, we can calculate the perimeter by adding the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 2√5 + 2√5 + 2√5 + 2√5
Perimeter = 8√5
Therefore, the perimeter of the given rhombus is 8√5.
If a-b = 4 and ab = 60, what is the value of a + b?
Answers
Answer:
a + b = 16 or -16.
Step-by-step explanation:
a - b = 4
ab = 60 so a = 60/b
Substituting for a in the first equation:
60/b - b = 4
60 - b^2 = 4b
b^2 + 4b - 60 = 0
(b + 10)b - 6) = 0
b = 6, -10.
Therefore, from the first equation:
When b = -10 . a + 10 =4 giving a = -6 or
When b = 6, a - 6 = 4 giving a = 10.
So when a = -6, b = -10 and
when a = 10, b = 6.
So a + b is either 16 or -16.