Jen wants to create a diagonal walkway through her rectangular garden. If the
garden is 60 yd wide by 105 yd long, how long will the diagonal walkway be?
Answers
Jen's rectangular garden measures 60 yards wide and 105 yards long. She wants to create a diagonal walkway through the garden. We need to calculate the length of the diagonal walkway.
In a rectangular shape, the diagonal is the longest possible straight line connecting two opposite corners. To find the length of the diagonal walkway, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
In this case, the width and length of the garden form the two sides of a right triangle, with the diagonal walkway being the hypotenuse. We can represent the width as the base (b) of the triangle, the length as the height (h) of the triangle, and the diagonal walkway as the hypotenuse (d).
Using the Pythagorean theorem, the equation can be written as:
d^2 = b^2 + h^2
Substituting the given values, we have:
d^2 = 60^2 + 105^2
Calculating further:
d^2 = 3600 + 11025
d^2 = 14625
To find the length of the diagonal walkway, we take the square root of both sides:
d = √14625
d ≈ 120.83 yards
Therefore, the length of the diagonal walkway through Jen's rectangular garden would be approximately 120.83 yards.
By applying the Pythagorean theorem and substituting the width and length of the garden, we can determine the length of the diagonal walkway. The Pythagorean theorem is a fundamental mathematical concept that helps us find unknown sides in right triangles, making it applicable in various real-world scenarios, including calculating distances and lengths in geometric shapes like Jen's garden.
Learn more about the Pythagorean theorem here:- brainly.com/question/14930619
#SPJ11
Related Questions
Find the height of a triangle if the area is 42 square units and the base is 7 units.
Answers
Answer:
your answer is 12
Step-by-step explanation:
Base 7 Area 42
Using the formula
A= hb over 2
Solving for hb
hb=2A
b=2·42
7=12
hope this is not to confusing but the answer is 12.
Elijah was trying to determine whether one triangle is a dilation of the other. Which statements about his solution are true? Check all that apply.One triangle has side lengths of 3, 6, 7.5. Another triangle has side lengths of 5, 10, 12.5.Elijah’s work:3 is not a factor of 5, so it must be a relationship with addition.3 + 2 = 5. 6 + 2 not-equals 10. 7.5 + 2 not-equals 12.5.Therefore, the triangles are not proportional and cannot form a dilation.Elijah did not know that scale factors can be fractions or decimals greater than zero.Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.Elijah should have compared the ratios Five-thirds = StartFraction 10 Over 6 EndFraction = StartFraction 12.5 Over 7.5 EndFraction to determine if they are equivalent.Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.Elijah needs labels on the points to determine which sides correspond when writing the ratios.
Answers
Answer:
The First 3 Statements Are Correct.
Step-by-step explanation:
The statements that are false about his solution is Elijah needs labels on the points to determine which sides correspond when writing the ratios.
We are given that;
The statement one triangle is a dilation of the other
Now,
He did not know that scale factors can be fractions or decimals greater than zero. He did not know that dilations are proportional and the relationships are multiplicative, not additive. He should have compared the ratios
\($\frac{5}{3}=\frac{10}{6}=\frac{12.5}{7.5}$\) to determine if they are equivalent.
So, the statements that are true about his solution are:
- Elijah did not know that scale factors can be fractions or decimals greater than zero.
- Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.
- Elijah should have compared the ratios
\(\frac{5}{3}=\frac{10}{6}=\frac{12.5}{7.5}\)to determine if they are equivalent.
Therefore, by dilation answer will be Elijah needs labels on the points to determine which sides correspond when writing the ratios.
Learn more about dilation here:
https://brainly.com/question/27212783
#SPJ2
Herbert got a 76 on his last unit test. If he increases his score by 30% on the next test, what will his new score be?
Answers
A plumber notices a faucet leaking of a rate of 2 milliliters per second.
What is the rate of the leak in liters per hour?
Answers
Answer:
it is 7200 Liters
Step-by-step explanation:
Brainliest?
What are the three rules for horizontal asymptotes?
Answers
A horizontal asymptote is a horizontal line that a graph approaches but never touches as the input values become larger or smaller.
There are three rules for determining horizontal asymptotes of a function:
If the degree (the largest exponent) of the numerator of a rational function (a function that can be written as a fraction) is less than the degree of the denominator, the horizontal asymptote is a horizontal line at y = 0. This is because as the input values become larger, the numerator will grow at a slower rate than the denominator, and the value of the function will approach 0.
If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. This is because the numerator will grow at a faster rate than the denominator and the value of the function will not approach a constant value as the input values become larger.
If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is a horizontal line at y = the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator. This is because as the input values become larger, the numerator and denominator will grow at the same rate and the value of the function will approach a constant value determined by the ratio of the leading coefficients.
For example, consider the function f(x) = x^2 / x^3. The degree of the numerator, x^2, is 2, and the degree of the denominator, x^3, is 3. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is a horizontal line at y = 0.
On the other hand, consider the function g(x) = x^3 / x^2. The degree of the numerator, x^3, is 3, and the degree of the denominator, x^2, is 2. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
Another example, consider the function h(x) = 2x^3 / 2x^3. The degree of the numerator, 2x^3, is 3, and the degree of the denominator, 2x^3, is 3 as well. Since the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is a horizontal line at y = 1 (ratio of the leading coefficient of numerator and denominator).
Here you can learn more about horizontal asymptotes
https://brainly.com/question/4084552#
#SPJ11
what is the surface area of 4.5 4.5 4.5 4.1 triangular prisms
Answers
The surface area of the triangular prism is S = 63.237 cm²
Given data ,
Let the surface area of the triangular prism be S
where the area of the base = 8.8 cm²
Now , the area of the 2 triangular faces is given by T
where T = 2 [ ( √3/4 )a² ] ( equilateral triangle )
T = 2 ( √3/4 ( 4.5 )² )
T = 2 ( 8.76851 )
T = 17.537 cm²
Now , the area of the two rectangular faces is R
where R = 2 ( 4.5 x 4.1 )
On simplifying , we get
R = 2 ( 18.45 ) = 36.9 cm²
And , S = 8.8 + 17.537 + 36.9
S = 63.237 cm²
Hence , the surface area is S = 63.237 cm²
To learn more about surface area of prism click :
https://brainly.com/question/9183590
#SPJ1
explain how regression toward the mean can describe two friends who have a fight then later go to the movies together.
Answers
Given the circumstances of the question, it is feasible that the two friends would feel that they overreacted during the argument, and as a result, they decide to see a movie together to make up for it.
Regression toward the mean is a statistical condition that involves events that the outcomes produce based solely on chance rather than on real facts. Therefore, it is impossible to forecast with precision what will happen in a regression towards the mean.
Example
Two military units are brought back, one with 20% casualties and the other with 50%. He compliments the first while criticizing the second. The two units return with the opposite outcomes the following time. He "learns" from this experience that praise reduces performance and berating strengthens it.
To learn more about regression toward mean
brainly.com/question/16539587
#SPJ4
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
Learn more about median on
https://brainly.com/question/14532771
#SPJ1
To become a member at an art museum costs $60. If
you are a member art lessons will cost $2 for each
class. If you are not a member lessons will cost $6
each. Which system of equations would be used to
solve for how many lessons it would take member and
nonmemeber to cost the same.
Answers
Answer:
10
Step-by-step explanation:
If your not a member it would cost 6 member lessons because 60 by 6=10
6=1 lesson
12=2 lessons
18=3 lessons
24= 4 lessons
30=5 lessons
36=6 lessons
42=7 lessons
48=8 lessons
54=9 lessons
60=10 lessons
If your are ready and member the 30 because 2$ if for 1 lesson so 30 lessons x 2$ each is 30.
Hope it helps have a great day
While in Manchester, England, Jaslene bought a sweater for £28(GBP). When she returned,
she saw the same sweater for $38CAD. Which sweater cost more? By how much in Canadian
dollars?
Answers
Answer:
The Manchester, England sweater is more expensive.
27 GBP is equal to 49.52 CAD, which is more than the 38 CAD from the afterwards.
Step-by-step explanation:
can yall help im kinda stuck here
Answers
Answer:
Step-by-step explanation:
ummm let me think
Answer:
A. 202.5
Step-by-step explanation:
To find the volume of a square-based pyramid, use the formula V = A(h/3), where V is the volume and A is the area of the base.
Which rectangle has a base to height ratio of 4:3?
(Figures not drawn to scale)
Answers
Answer:
Is prob 8,6
Step-by-step explanation:
3(-3x - 3) + 2x + 4 = -33
Answers
4
Please see the picture attached.
Select the correct answer.
What is the standard form of this complex number?
3i + ( + 2i ) – (3 + 3i)
Answers
Answer:
\(\huge\boxed{A.\ -\dfrac{9}{4}+2i}\)
Step-by-step explanation:
The standard form of a complex number:
\(z=a+bi\\\\a,\ b\in\mathbb{R}\)
\(3i+\left(\dfrac{3}{4}+2i\right)-(3+3i)=3i+\dfrac{3}{4}+2i-3-3i\\\\=\left(\dfrac{3}{4}-3\right)+(3+2-3)i=-2\dfrac{1}{4}+2i=-\dfrac{9}{4}+2i\)
How do you find the square root of an integer
Answers
Step-by-step explanation:
you can find the factors of it then see which two numbers multiply together to form the integer.
the differential euqastion whihc has y =c1ex ce^--2x as its general soution is
Answers
y'' + y' - 2y = 0 is the differential equation which has y = c₁e^x + ce^(-2x) as its general solution.
The differential equation which has y = c₁e^x + ce^(-2x) .A differential equation is a mathematical equation that relates the derivatives of an unknown function to the function itself. Differential equations are used to model real-world situations that involve continuously changing quantities and rates of change. The differential equation which has y = c₁ e^x + c e^(-2x) as its general solution is:y'' + y' - 2y = 0. Differentiate the solution given: y = c₁e^x + ce^(-2x)y' = c₁e^x - 2ce^(-2x)y'' = c₁e^x + 4ce^(-2x). Substitute the derivatives into the differential equation: y'' + y' - 2y = 0(c₁e^x + 4ce^(-2x)) + (c₁e^x - 2ce^(-2x)) - 2(c₁e^x + ce^(-2x)) = 0c₁e^x + 4ce^(-2x) + c₁e^x - 2ce^(-2x) - 2c₁e^x - 2ce^(-2x) = 0
⇒c₁e^x - 2ce^(-2x) = 0.
Let's learn more about differential equation:
https://brainly.com/question/14926412
#SPJ11
help please ASAP!!! Got a lot of math to do here comes an all nighter :(
Answers
Answer:
110
Step-by-step explanation:
2 ( wl+hl+hw ) = 2 (7·1+6·1+6·7 ) = 110
Here Enjoy :)
two angles that add up to 90 degrees are called ________ angles.
Answers
Answer: Right/complementary angles
Step-by-step explanation:
Two angles that add up to 90 degrees are called complementary angles.
Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.
In other words, the sum of the measures of complementary angles is always 90 degrees.
Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ6
Pleaes answer. if its right ill give brainliest
Answers
Answer: X is equal to 55.
Step-by-step explanation:
You can determine that the triangle is an isosceles triangle because of its side lengths.
Therefore you know that value of the angle it's not asking for is also x. Since a triangle's angles always measures 180. You can say that 180 = 70 + 2x.
You can now solve for x.
180 = 70 + 2x
-70 -70
110 = 2x
----------------
2
55 = x
Adding Rational Numbers Using Properties of Operations we can
add integers in any order using the
and
properties of addition.
Consider the integers a, b, c, and -d. We can add this group of
integers in several different ways:
a + (-b) + C+ (-0)
a+c+ (-6) + (-d)
(a + c) + [(-b) + (-d)]
The sum of the integers remains the
regardless of
their arrangement. We can use the commutative and associative
properties to break up numbers by
to find the sum of two or more rational numbers.
Answers
Answer:
First blank: Commutative
Second blank: Associative
Third blank: Same
Fourth blank and fifth blank: Rearranging them? (Not entirely sure)
Hope this helps :)
The average number of credits taken by college students to earn their bachelors degree is normally distributed with a mean of 140 credits and a standard deviation of 10 credits. Using the empirical rule (also called the the 68-95-99.7 rule), what percentage of the total credits earned by students is less than 140 credits
Answers
The given distribution is Normal with a mean of μ = 140 and a standard deviation of σ = 10. Using the empirical rule, we can find the percentage of the total credits earned by students that are less than 140 credits.
The given distribution is Normal with a mean of μ = 140 and a standard deviation of σ = 10. Using the empirical rule, we can find the percentage of the total credits earned by students that are less than 140 credits:
68% of the total credits lie within one standard deviation of the mean. Therefore, the percentage of total credits that are less than 140 credits is 50%. The empirical rule is also called the 68-95-99.7 rule. The empirical rule is a statistical concept that indicates the proportion of the data that falls within certain standard deviations from the mean of a normal distribution. Therefore, the percentage of total credits that are less than 140 credits is 50%.
To know more about standard deviation visit: https://brainly.com/question/29115611
#SPJ11
Eight families live in a subdivision.the number of member in each family are as follow:2,2,5,4,8,3,1,7.What is the arithmetic mean of the number of member in each family
Answers
The arithmetic mean of the number of member in each family is 4.
What is the Arithmetic Mean?Arithmetic mean is the mean or the average of the samples. That means, it is the sum of all values divided by the number of values.
In this question, we have 8 values. So, the arithmetic mean (M) is:
\(\text{M}=\dfrac{2+2+5+4+8+3+1+7}{8}\)
\(\text{M}=\dfrac{32}{8}\)
\(\text{M}=4\)
Thus, The arithmetic mean of the number of member in each family is 4.
Learn more: https://brainly.com/question/29445117
PLEASE HELP!!!!!!!!!!!!!!!!!!!!! THIS IS DUE !!!!!
Answers
Answer:
C
Step-by-step explanation:
In the heirarchy of Quadrilaterals, a square has to become either a rhombus or a square, and then a parallelogram in order to become a quadrilateral, and quadrilaterals are polygons.
Greta is opening a savings account. She starts with $100 and plans to add $50 each week. How do you write an equation she can use to calculate the amount of money she have after any number of weeks. How much money will she have after 1 year?- what is the unit rate of change for this situation
Answers
Answer:
100+50n
n stands for the number of weeks
There are about 52 weeks in a year, so
100+50(52) = 2700
Greta would have $2700 after 1 year
use a venn diagram to illustrate the relationships a ⊂ b and a ⊂ c.
Answers
In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).
A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.
Learn more about Venn diagram here:
https://brainly.com/question/20795347
#SPJ11
Help me it’s due in 20 minutes
Answers
9514 1404 393
Answer:
a) a, b
b) d
Step-by-step explanation:
A line with positive slope goes up to the right. The right end is higher than the left end. Lines a and b have positive slope.
__
A line with negative slope goes down to the right. The right end is lower than the left end. Line d has negative slope.
_____
Vertical line y is said to have "undefined" slope. Horizontal lines c and x have zero slope (neither positive nor negative).
An online store receives customer satisfaction ratings
between 0 and 100, inclusive. In the first 10 ratings
the store received, the average (arithmetic mean) of
the ratings was 75. What is the least value the store
can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?
Answers
The least value the store can receive for the 11th rating = 50.
What is Average number?The sum of a group of numbers divided by the total number of values in the group yields the average of the group. Take the average of 24, 55, 17, 87, and 100 as an example. Simply add up the numbers: 24 + 55 + 17 + 87 + 100 = 283; then, divide that number by five to get 56.6.
According to the given information:The sum of the values in a data set divided by the total number of values in the data set represents the mean of the data set. Finding the average of The first 10 ratings and dividing by 10 yielded a result of 75.
The sum of the first 10 ratings was 750.
For the mean of the first 20 ratings to be at least 85
The sum of the first 20 ratings must be at least
= 85 * (20)
=1700.
The sum of the next 10 ratings must be at least 1700−750
=950.
The maximum rating is 100, so the maximum possible value of the sum of the 12th through 20th ratings is
= 9(100)
=900.
the store to be able to have an average of at least 85 for the first 20 ratings, the least possible value for the 11th rating is:
= 950−900
=50.
The least value the store can receive for the 11th rating = 50.
To know more about Average number visit:
https://brainly.com/question/20450155
#SPJ4
Jason and Jerry are competing at a weightlifting competition. They are both lifting barbells containing 200 pounds of plates. Jason's barbell has 4 large and 10 small plates on it. Jerry's barbell has 6 large and 5 small plates on it. How much does each large and each small plate weigh?
Answers
Answer:
The weight of :
Large plates = x = 25 pounds
Small plates = y = 10 pounds.
Step-by-step explanation:
Jason and Jerry are competing at a weightlifting competition.
Let us represent the weight of
Large plates = x
Small plates = y
They are both lifting barbells containing 200 pounds of plates. Jason's barbell has 4 large and 10 small plates on it.
4x + 10y = 200.... Equation 1
Jerry's barbell has 6 large and 5 small plates on it.
6x + 5y = 200..... Equation 2
Combining Equations
4x + 10y = 200.... Equation 1
6x + 5y = 200..... Equation 2
We solve using Elimination method
Multiply Equation 1 by 6 and Equation 2 by 4 to eliminate x
24x + 60y = 1200..... Equation 3
24x + 20y = 800.... Equation 4
Subtract Equation 4 from Equation 3
40y = 400
y = 400/40
y = 10 pounds
Solving for x using Equation 1
4x + 10y = 200.... Equation 1
4x + 10(10) = 200
4x + 100 = 200
4x = 200-100
4x = 100
x = 100/4
x = 25 pounds
Therefore, the weight of
Large plates = x = 25 pounds
Small plates = y = 10 pounds.
A rectangular living room is 6 meters long and 3 meters wide. What is its area?
Answers
for a line perpendicular to the line y = 2x - 3 through the point (4,-6)
Answers
Answer:
y=2x-14
Step-by-step explanation:
y=mx+c
-6=2(4)+c
-6=8+c
-6-8=c
c=-14
y=mx+c
y=2x-14