The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
The area of this triangle, A, is equal to the perimeter of this triangle.
Create a system of equations to model this situation. Determine if there are any solutions, and, if possible, whether or not they are viable.
How many total possible solutions are there to this system?
Of any possible solutions, how many are viable solutions for this situation?
Answers
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Answer:
two possible and one viable
Step-by-step explanation:
hope this helps!
Related Questions
Which sequence could be used to transform pentagon p to pentagon Q
Answers
Four cups of hummingbird food that is 20% corn syrup is mixed with six cups of humming bird food that is 15% corn syrup. What percent of corn syrup is in the mixture??
Answers
What is the median of the data set?
{20, 25, 36, 41, 87, 91, 92, 95, 99}
Enter your answer in the box.
Answers
In your equation, it is already arranged from least to greatest. Since it has odd numbers (9 numbers) in your data, the answer would be 87. (Four numbers is lower and four numbers is higher).
The median number means the middle number so the number in the middle would be the answer
Answer:
87
hope o helped
Have a great day or night
Fossils are remains of organisms found in sedimentary rock. These remains are found in thousands of rock layers around the world and provide evidence for Earth's long history of changing lifeforms. Rock layers that formed more recently A. contain fossils of animals only. B. contain fossils of plants only. C. contain fossils that resemble existing species less closely than do fossils found in older rock layers. D. contain fossils that resemble existing species more closely than do fossils found in older rock layers.
Answers
Rock layers that formed more recently contain fossils that resemble existing species more closely than do fossils found in older rock layers.
Explanation:Fossils found in rock layers provide evidence for Earth's long history of changing lifeforms. Rock layers that formed more recently contain fossils that resemble existing species more closely than do fossils found in older rock layers. This is because the more recent layers contain organisms that are more similar to the species that exist today.
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x^2 + 18x + 50 = 9
Solve by completing the square
Answers
step 2: both sides add (1/2 of 18)², which is 81: x²+18x+81=-41+81
step 3: make the square: (x+9)²=40
step 4: square root both sides: x+9=√40 or x+9=-√40
simplify: x=-9+2√10 or x=-9-2√10
Estimate the circumference of a circle that has a diameter of 13 yards. yards
Answers
Answer:
a little bit more than 37.70 yards
Step-by-step explanation:
How many square feet of outdoor carpet will we need for this hole?
Answers
Yesterday, Jed's bank account balance was –$26.34. He deposited some money into his account so that the balance is now $42.18.
How much did he deposit into his account?
$68.52
$15.84
$68.42
$16.84
PLEASE HELP ME!! I AM DOING AN EXAM
Answers
The solution to 7x = 42 is x = ___.
A.4
B.5
C.6
D.7
Answers
7x = 42 => x = 42/7 = 6
Answer:
the x value equals 6.
Step-by-step explanation:
When you are solving for x, divide the 42 by 7.
An RV leaving Canada is stopped at customs at the border and weighed. The scale shows a reading of 2.5 tons. What is the weight of the RV in tonnes?
Answers
2.5 x 0.907185 = 2.26796 tonnes ( Round the answer as needed)
The weight of the RV in tonnes is approximately 2.26796 tonnes.
Explanation:The weight of the RV can be converted from tons to tonnes using a conversion factor. One ton is equal to 0.90718474 tonnes. To find the weight of the RV in tonnes, we can multiply 2.5 tons by the conversion factor:
Weight in tonnes = 2.5 tons x 0.90718474 tonnes/ton = 2.26796 tonnes
Therefore, the weight of the RV in tonnes is approximately 2.26796 tonnes.
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Tell whether this solution has one, zero or many solutions by solving it -2(z+3)-z=-z-4(z+2)
Answers
-3z - 6 = -5z - 8
-3z - 6 = -5z - 8
2z = -2
z = -1
the equation has 1 solution
The squirrel stored seven more than three times as many nuts as the chipmunk. The chipmunk stored x acorns.Write an expression that shows how many acorns the squirrel stored.
Answers
i think that is the imperresion
sdfasfafsdgagzdgdagdagagda
Answers
We plug into slope-intercept form [tex]y=mx+b[/tex] to get [tex]y=7x+5[/tex].
y = 7x + 5
Explanation:
The equation of line in slop-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept
We are given that the slope = 7. Therefore, the equation becomes:
y = 7x + c
Now, we need to get the value of c. To do so, we will substitute with the given point (0,5) in the equation and solve for c as follows:
y = 7x + c
5 = 7(0) + c
c = 5
Based on the above, the equation of the line is:
y = 7x + 5
Hope this helps :)
what is this expression 2(5x-1)+14
Answers
Your question states: What is this expression 2(5x-1)+14
2 * 5x = 10x
2 * -1 = -2
10x + -2 + 14 = 10x + 12
Your answer is 10x + 12
Hope I helped!
Let me know if you need anything else!
~ Zoe
I'm going to assume you want to simplify the expression:
[tex]2(5x-1)+14[/tex]
First, distribute the parenthesis:
[tex]=2(5x-1)+14[/tex]
[tex]=[(5x)(2)-(1)(2)]+14[/tex]
[tex]=(10x-2)+14[/tex]
Next, you want to combine like terms:
[tex]=(10x-2)+14[/tex]
[tex]=10x+12[/tex]
This is the furthest the expression can be simplified:
[tex]\boxed{10x+12}[/tex]
I hope this helped!
-Benjamin
The function h(t) = 150 – 9t represents the height of a ball dropped from 150 feet after t seconds. What will the height of the ball be after 1.4 seconds?
Answers
h(t) = 150 - 9(1.4)
Multiply 9 by 1.4 to get 12.6.
h(t) = 150 - 12.6
Subtract 12.6 from 150 to get 137.4.
h(t) = 137.4.
The height of the ball would be 137.4 after 1.4 seconds.
Hope this helps!
Final answer:
The height of the ball after 1.4 seconds, using the function h(t) = 150 – 9t, is 137.4 feet above the ground.
Explanation:
To determine the height of the ball after 1.4 seconds using the function h(t) = 150 – 9t, we simply need to substitute the value of t with 1.4 seconds into the equation.
By plugging in the given values in the equation, the solution we get will be:
h(1.4) = 150 – 9(1.4) = 150 - 12.6 = 137.4 feet
Therefore, the height of the ball after 1.4 seconds will be 137.4 feet above the ground.
Multiply. (3x+1)(x−1) Express the answer in standard form.
Answers
Answer:
3x2−2x−1
Step-by-step explanation:
Jeff had $20. He spent 1/8 of his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left?
Answers
total fraction of his expenses on lunch and movies is:
(2/5+1/8)
=21/40
the remaining fraction is:
1-21/40
=19/40
thus the amount of cash that Jeff was left with will be:
19/40×20
=$ 9.5
In the figure, PQ is parallel to RS. The length of RP is 2 cm; the length of PT is 18 cm; the length of QT is 27 cm. What is the length of SQ?
Answers
Step 1
Find the value of TS
we know that
if PQ is parallel to RS. then triangles TRS and TPQ are similar
so
[tex]\frac{TR}{TP} =\frac{TS}{QT}[/tex]
solve for TS
[tex]TS =\frac{TR*QT}{TP}[/tex]
we have
[tex]RP=2\ cm\\TP=18\ cm\\QT=27\ cm[/tex]
[tex]TR=TP+RP\\TR=18+2=20\ cm[/tex]
substitute
[tex]TS =\frac{20*27}{18}[/tex]
[tex]TS =30\ cm[/tex]
Step 2
Find the value of SQ
we know that
[tex]SQ=TS-QT[/tex]
we have
[tex]TS =30\ cm[/tex]
[tex]QT=27\ cm[/tex]
substitute
[tex]SQ=30\ cm-27\ cm=3\ cm[/tex]
therefore
the answer is
the value of SQ is [tex]3\ cm[/tex]
Answer: C. 3cm
Step-by-step explanation:
Order these numbers from least to greatest
Answers
6 5/6 is equal to 6.8333.
Least to greatest, they all are:
6.57, 6 5/6, 6.838, 137/20
Hope this helps!
The train to Sun City travels 150 miles per hour. How long will a trip take if Sun City is 525 miles away?
A. 4 hours
B. 3 hours 30 minutes
C. 3 hours 15 minutes
D. 3 hours
Answers
3.5= 3 hours and 30 mins
answer is b
Speed of train is 3 hours 30 minutes
Given that;Speed of train = 150 miles per hour
Distance of Sun city = 525 miles
Find:Speed of train
Computation:Speed of train = Distance of Sun city / Speed of train
Speed of train = 525 / 150
Speed of train = 3.5
Speed of train = 3 hours 30 minutes
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Question 18 Unsaved
Melody paid $25.00 for 3 movies & a CD. If the price of each movie was 6.50, what was the price of the CD?
Question 18 options:
$5.50
$11.00
$15.50
$19.50
Answers
Each movie is $6.50
6.50 x 3 = 19.5
All 3 movies cost $19.50.
Melody paid $25.00 in all.
She also bought a CD
25-19.5 = 5.5
Melody paid $5.50 for the CD.
Hope this helps you! (:
-Hamilton1757
I believe the answer is A. 5.50
I added 6.50 for 3 movies and got 19.50 then I added 5.50 and got 25.00
You could also do it another way...
You could do 6.50 x 3 and you get 19.50
then she paid 25.00
you will subtract 25 - 19.5 and get 5.50
.
WILL MARK BRAINLIEST! PLEASE HELP MEH!Use the relationship between the angles in the figure to answer the question. Which equation can be used to find the value of x? Drag and drop the equation into the box.
A) x=180−31+40
B)x=90−40
C)x=180−(31+40)
D)x=90−(31+40)
Answers
to find x start with this equation
31 + x + 40 = 180 Now get all the numbers on the right.
(31 + 40) + x = 180
x = 180 - (31 + 40)
Only A or C can be correct. It is C, but you have to be very careful how you eliminate A
C <<<< answer.
x = 180 - 31 - 40 is the correct way to remove the brackets.
x = 180 - 71
x = 109
There are better ways to do this particular question without using brackets.
Answer:
C. [tex]x=180^o-(31^o+40^o)[/tex]
Step-by-step explanation:
We have been given a figure of angles formed on a straight line.
Since we know that the angles on a straight line add up-to 180 degrees. Upon using this property we can set an equation as:
[tex]31^o+x^o+40^o=180^o[/tex]
Let us subtract 40 and 31 degrees from both sides of our equation to solve to x.
[tex]31^o-31^o+x^o+40^o-40^o=180^o-31^o-40^o[/tex]
[tex]x=180^o-31^o-40^o[/tex]
Upon factoring negative sign from right side of our equation we will get,
[tex]x=180^o-(31^o+40^o)[/tex]
Therefore, the equation [tex]x=180^o-(31^o+40^o)[/tex] can be used to find the value of x and option C is the correct choice.
San is five years old. His older brother Tom is 3 times older as Sam. When Sam is 20 how old will Tom be?
Answers
San is currently 5 years old.
Tom is currently 3 times older than San. This means that Tom is 15 years old (multiply San's age by 3 to distinguish this).
San is 5, and in 15 years, he will be 20. To simply put it, add 15 to Tom's age and we will know how old he will be when San is 20.
15 + 15 = 30
When San is 20, Tom will be 30 years old.
I hope this helps!
Why is the library not adding any more fairy tales
Answers
Final answer:
The library may not be adding more fairy tales due to decreased demand, a desire to offer a diverse collection, and a strategic choice to provide a balanced collection.
Explanation:
It is possible that the library is not adding any more fairy tales due to a variety of reasons. One reason could be that the demand for fairy tales has decreased among library patrons. Another reason could be that the library wants to diversify its collection and offer a wider range of books to its readers.
Additionally, the library may be focusing on acquiring books from different genres or themes to cater to the interests of its diverse audience.
It is important to note that libraries regularly make decisions about which books to add to their collection based on factors such as popularity, relevance, and availability. The decision to not add any more fairy tales could simply be a strategic choice made by the library to provide a more balanced and comprehensive collection for its readers.
1. For T (-1,2),(7,8): 10
For E (3,-4), (-2,5): 10.3
For A (-7,0), (-4,12): 12.4
For N (1,-5), (-9,-9): 10.8
2. For S (2,6), (3,10): (2.5, 8)
For F (15,-1),(9,-5): (12, -3)
For T (7,-2), (-10,-8): (-1.5, -5)
For E (-3,0), (-11,9): (-7, 4.5)
Here are the distances and midpoints, calculated step by step:
Distances:
T: (-1, 2), (7, 8)
Difference in x-coordinates: 7 - (-1) = 8
Difference in y-coordinates: 8 - 2 = 6
Distance using the Pythagorean theorem: √(8² + 6²) = √100 = 10
E: (3, -4), (-2, 5)
Difference in x-coordinates: -2 - 3 = -5
Difference in y-coordinates: 5 - (-4) = 9
Distance: √((-5)² + 9²) = √106 ≈ 10.3
A: (-7, 0), (-4, 12)
Difference in x-coordinates: -4 - (-7) = 3
Difference in y-coordinates: 12 - 0 = 12
Distance: √(3² + 12²) = √153 ≈ 12.4
N: (1, -5), (-9, -9)
Difference in x-coordinates: -9 - 1 = -10
Difference in y-coordinates: -9 - (-5) = -4
Distance: √((-10)² + (-4)²) = √116 ≈ 10.8
Midpoints:
S: (2, 6), (3, 10)
Midpoint: ((2 + 3)/2, (6 + 10)/2) = (2.5, 8)
F: (15, -1), (9, -5)
Midpoint: ((15 + 9)/2, (-1 - 5)/2) = (12, -3)
T: (7, -2), (-10, -8)
Midpoint: ((7 - 10)/2, (-2 - 8)/2) = (-1.5, -5)
E: (-3, 0), (-11, 9)
Midpoint: ((-3 - 11)/2, (0 + 9)/2) = (-7, 4.5)
Complete question:
Write the exercise letter in the box above the answer at the bottom of the page. Find the distance between the two given points. If necessary, round to the nearest tenth.
T (-1,2),(7,8)
E (3,-4), (-2,5)
A (-7,0), (-4,12)
N (1,-5), (-9,-9)
Find the midpoint between the two given points.
S (2,6), (3,10)
F (15,-1),(9,-5)
T (7,-2), (-10,-8)
E (-3,0), (-11,9)
What is circumference of a circle if the diameter is 7 ft
Answers
7/2 = 3.5
So the radius is 3.5. Now the circumference.
2(3.14)(3.5) = 21.98 ft
So the circumference is 21.98 ft
Hope this helps :)
3.14 * 7 = 21.98.
Thus the circumference of a circle where the diameter of said circle is 7, is 21.98 [ft].
Line plots display individual data? True or false?
Answers
Use point slope form to write the equation of the line that passes through (-3,4) and has a slope of 7
Answers
y - 4 = 7(x - - 3)
Your class is conducting an experiment to study geometric sequences. The class forms a line . The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line . The next people in line do the same with there slices of pizza . Which portion of the whole pizza does the 7th person in line get ? Please help !!!
Answers
Here is your pattern:
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64.
The first person starts with the 1 whole pizza.
In a geometric pattern, you multiply or divide by the same thing each time.
The 7th person in line get 1/64th part of pizza.
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line .
And, The next people in line do the same with there slices of pizza .
Now,
Since, The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line . The next people in line do the same with there slices of pizza .
Hence, We get the sequence as;
⇒ 1, 1/2, 1/4, 1/8,....
Clearly, The sequence is geometric sequence.
⇒ T (7) = 1 × (1/2)⁶
= 1/64
Thus, The 7th person in line get 1/64th part of pizza.
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Carol wants to find out the favorite foods of students at her middle school. She asks the boys' basketball team about their favorite foods. so would that be random sampling or biased sampling and why?
Answers
the college textbook this year was 197. the following year it was 222. what is the percent change in the price of the book HEEEEELLLLPPPPPP