Sarah is setting up a garden plot in the shape of a right triangle. One leg off the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show work algebraically.
Answers
The smallest leg of the triangular garden is 5 feet while the biggest leg is 12 feet.
What is a triangle?The three-sided shape known as a triangle is sometimes used to allude to it.
The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.
As the given triangular garden has been drawn below,
By Pythagoras' theorem,
x² + (x + 7)² = (x + 8)²
x² + x² + 49 + 14x = x² + 64 + 16x
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) + 3(x - 5) = 0
(x + 3)(x - 5) = 0
x = -3,5
Since length can never be negative thus x = 5.
The smallest leg = 5 feet
Biggest leg = 5 + 7 = 12 feet
Hence "The triangular garden's smallest leg is 5 feet long, while its longest leg is 12 feet".
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Related Questions
A 95% confidence interval for the slope of the regression line relating the number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696). The confidence interval is based on a random sample of n raw foods. A check of the conditions for inference on the slope shows they are reasonably met. Which of the following is a correct interpretation of the interval?
A. 95% of all such samples of size n will produce a sample slope between 2.505 and 6.696 for the regression line relating grams of carbohydrates and kilocalories per 100- g sample of various raw foods.
B. The probability is 0.95 that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.
C. We are 95% confident that the slope of the regression line for the random sample of n raw foods is between 2.505 and 6.696.
D We are 95% confident that the predicted number of kilocalories per 100-g sample will be between 2.505 and 6.696.
E. We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.
Answers
Answer: E. We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.
Step-by-step explanation:
The interpretation of a 95% confidence interval: A person can be 95% confident that the true population parameter lies in it.
Given: A 95% confidence interval for the slope of the regression line relating the number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696).
Interpretation: We are 95% confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-g sample of various raw foods is between 2.505 and 6.696.
Correct option: E
PLEASE HELP I WILL GIVE BRAINLIEST!
Maria needs to reach a window that is eight feet above the ground. When she placed a ladder so that it reached the bottom of the window, the base of the ladder was 6 feet from the house. How long is the ladder?
DIAGRAM:
WORK:
ANSWER:
Answers
Step-by-step explanation:
First you draw the right triangle and plug in everything you already know
Then you do the pythagoreon theorem
The ladder is 10 ft
whcich expression are equivialant to the one below 3^4*3^x
Answers
Answer:
3x+4
Step-by-step explanation:
Order these numbers from least to greatest:
|-17|
|-18|
-18
|19|
20
Answers
Answer:
-18, |-17|, |-18|, |19|, 20
Step-by-step explanation:
the absolute value of -17 is 17, the absolute value of -18 is 18, and the absolute value of 19 is just 19. Absolute values are never negative.
Hope this helps!
St. Patrick's Day Problem Solving
Use the weight on the scales to determine the weight of each egg.
Note: Identical eggs weigh the same amount,
3.5
6
5.5
Answers
A block of wood measures 5.5 inches by 3.5 inches by 9 inches. What is the volume of the block of wood
Answers
Answer:
V = 173.25 in³Steps:
V = 5.5 × 3.5 × 9
V = 173.25 in³
Victor wants to buy fertilizer for his yard. The yard measure 55 feet by 60 feet the direction on the bag
of fertilizer say that one bag will cover 1,230 sq ft.
How many bags of fertilizer should Victor buy to be sure that he covers the entire yard?
Victor should buy
bags of fertilizer.
Answers
Answer:
3 bags
Step-by-step explanation:
55 x 60 = 3300 ft²
3300/1230 = 2.68 bags
A random sample of 60 was taken from a shipment of 12,500 light bulbs. There were 2 defective bulbs in the sample. How many defective bulbs would you expect in the entire shipment?
250
417
2,500
4,167
Answers
Answer:
417
Step-by-step explanation:
trust me
The defective bulbs in the entire shipment can be 417.
What is proportionality?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given that, a random sample of 60 was taken from a shipment of 12,500 light bulbs, there were 2 defective bulbs in the sample.
We need to find how many defective bulbs would you expect in the entire shipment,
Let there be x defective bulbs in the sample.
using the concept of proportionality,
2 / 60 = x / 12500
x = 417
Hence, the defective bulbs in the entire shipment can be 417.
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The Thompson family is buying a car that can travel 70 miles
Answers
Answer:
The car gets 35 miles per gallons.
Step-by-step explanation:
CLICK ON PHOTO AND NOOOOO LINKS PLSSSS
Answers
Help me I beg u! The pre-image coordinates of a triangle are J(-6,9), K(-6,4), and L(-3,4). The coordinates of the transformed triangle are J'(2,9), K'(2,4), and L'(5,4). What transformation has occurred? A. translation B. reflection C. dilation D. rotation Reset Next Question
Answers
Answer:
A. Translation
Step-by-step explanation:
Given
Preimage
[tex]J = (-6,9)[/tex]
[tex]K = (-6,4)[/tex]
[tex]L = (-3,4)[/tex]
Image
[tex]J' = (2,9)[/tex]
[tex]K' = (2,4)[/tex]
[tex]L' = (5,4)[/tex]
Required
Which transformation occurred
The transformation that occurs is translation because each of the preimage were translated or shifter right by 8 units.
The rule applied here is:
[tex](x,y)=>(x+8,y)[/tex]
So, we have:
[tex]J = (-6,9)[/tex] [tex]==> (-6+8,9) = (2,9)[/tex]
[tex]K = (-6,4)[/tex] [tex]==> (-6+8,4) = (2,4)[/tex]
[tex]L = (-3,4)[/tex] [tex]==> (-3+8,4) = (5,4)[/tex]
Hence, the transformation is (a) Translation
What 1,500 rounded to the nearest hundredth
Answers
Answer:
2,000
Step-by-step explanation:
The two-way table shows the number of students in a school who bring their lunch and/or who ride the bus:
Bring Lunch Do Not Bring Lunch Total
Ride Bus 40 35 75
Do Not Ride Bus 55 2 57
Total 95 37 132
How many more bring lunch than ride the bus? (4 points)
Answers
The correct answer is 20
Answer:
20
Step-by-step explanation:
People who don't ride the bus and bring lunch: 55
People who ride the bus and don't bring lunch: 35
55 - 35 = 20
Hope this helps!
Piper is going to invest $74,000 and leave it in an account for 11 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Piper to end up with $108,000?
Answers
Divide both sides by 74000
1.45946=e^11r
Ln1.45946=11r
.37807=11r
Divide by 11
.03437
3.44%.
Is (4,3) (2,1) endpoints of a vertical line, a horizontal line, or neither?
Answers
Answer:
neither
Step-by-step explanation:
is a diagonal line
Find the measure of angles 1-7
Answers
Answer:
no hablo espanol no mas
Step-by-step explanation:
Question 20(Multiple Choice Worth 2 points) (01.02 LC) Which number has a 9 that is one tenth the value of the 9 in 296? 195 409 981 1,956 NO LINKS HELP ASAP
Answers
Answer:
409 i would say
Step-by-step explanation:
very sorry is its wrong!!! :(
Answer:
prob d im guessing :^)
Step-by-step explanation:
tell me if i got it right or wrong i will fix if needed
joseph left the house at 11:17 A.M and returned at 12:45 P.M how many minutes was joseph gone from the house
Answers
Joseph was gone from the house for 1 hour & 28 minutes.
Please help me I need this due
Answers
There are 10 multiple-choice questions on a math quiz. Each question has four answer choices with one correct
answer. Let X represent the number of questions answered correctly for a student who is randomly guessing each
answer choice.
Have the conditions for a binomial setting been met for this scenario?
O No, the order of the questions is unknown.
O Yes, all four conditions in BINS have been met.
O No, the answers are not independent of one another.
O No, we do not know how many quizzes this teacher will give.
Save and Exit
Next
Submit
Mark this and return
Answers
B.) Yes, all four conditions in BINS have been met.
Jimmy has 6 computers and 7 printers to choose from. How many possible computer- printer combinations are there to make?
O 42
O 13
Answers
Answer:
13
Step-by-step explanation:
Computers=6
Printers=7
Now,
=6+7
=13
please help me .......
Answers
9514 1404 393
Answer:
65°
Step-by-step explanation:
Any sort of bisector divides a geometry into two congruent parts. Here, we have an angle bisector that divides the larger (130°) angle into two equal parts. The measure of each of the resulting smaller angles will be 130°/2 = 65°.
∠JAE = 65°
guys help im bad at math
Answers
Answer:
A = 13
B = 50
C = 22.5
D = 3.5
E = 16.3
Step-by-step explanation:
divide each area by 4
ex: 52 ÷ 4 = 13
A: 13
B: 50
C: 22.5
D: 3.5
E: 16.3
There you go!
Helpp meeeeeeeeeeeeeeeeeee
Answers
Answer:
perimeter = 48 Area = 144
Step-by-step explanation:
was that all?
Please help. Thank you.
Answers
Answer:
-10m-9
Step-by-step explanation:
-3(4m+3)+2m
combine like terms
-12m-9+2m
-10m-9
PLEASE HELP!! NO SCAM LINKS
Answers
9514 1404 393
Answer:
(d) new line is less steep
Step-by-step explanation:
Changing the slope from 3 to 1/3 makes the line less steep.
__
In the attachment, the blue line is the new line.
Gaelle Bosquet Nth Term of an Arithmetic Sequence Apr 10, 12:29:36 AM Find the 60th term of the arithmetic sequence 4,-1,-6, ... Answer: Submit Answer
Answers
Answer:
The nth term is [tex]a_n = 4 - 5(n-1)[/tex]
The 60th term of the sequence is -291.
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and it is called common difference.
The nth term is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
4,-1,-6
The common difference is:
[tex]d = -1 - 4 = -5[/tex]
First term [tex]a_1 = 4[/tex]
So
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n = 4 - 5(n-1)[/tex]
60th term:
[tex]a_{60}[/tex]. Si
[tex]a_{60} = 4 - 5(60-1) = -291[/tex]
The 60th term of the sequence is -291.
A flower bed is in the shape of a triangle, with a base of 11 feet and a height of 7 feet. What is the area of the flower bed
Answers
Answer:
38.5ft²
Step-by-step explanation:
Triangle area formula = [tex]\frac{1}{2} * b * h[/tex]
Triangle area = [tex]\frac{1}{2} * 11 * 7[/tex]
Triangle area = 0.5 * 11 * 7
Triangle area = 38.5ft²
Answer: GIVE THE GUY BRAILIEST PLEASE
henry is 70 inches tall Aaron is 6feey 2inches tall how much taller is Aaron than Henry
Answers
Answer:
4 inches taller
Step-by-step explanation:
aaron is 74 inches
16.
There are two adjacent supplementary angles. The larger angle is 2
more than 3 times the smaller angle. What are the degrees of both
angles? What is the difference in their measurements?