Answers
Answer:
width = 9/2 inches, length = 18 inches
Step-by-step explanation:
Step-by-step explanation:
l = length
w = width
l×w = 81 in²
l = 2w + 9
we can use the identity of the second equation in the first equation :
(2w + 9)×w = 81
2w² + 9w = 81
2w² + 9w - 81 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 2
b = 9
c = -81
w = (-9 ± sqrt(9² - 4×2×-81))/(2×2) =
= (-9 ± sqrt(81 + 648))/4 =
= (-9 ± sqrt(729))/4 = (-9 ± 27)/4
w1 = (-9 + 27)/4 = 18/4 = 9/2 in
w2 = (-9 - 27)/4 = -36/4 = -9
a negative solution for a side length does not make any sense, so, width = 9/2 in is the only valid solution.
l = 2w + 9 = 2×9/2 + 9 = 9+9 = 18 in
so, the last answer option is correct.
Related Questions
Make and test a conjecture about the given quantity.
18. The product of two negative even integers
19. The sum of two negative odd integers
20. The sum of two even integers and two odd integers
21. When you return from a run, your
friend states, “If you ran 1 mile, then
you ran 5280 feet." Your friend then
asks if you can write the statement as
a biconditional statement. Write the
biconditional statement and decide
whether it is true.
Answers
Answer:
18. The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Decide whether statement is true: So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
Step-by-step explanation:
18. The product of two negative even integers.
Let the integers be -2m and -2n, m and n are positive integers
Product in (-2m) × (-2n) = 4mn = 2(2mn)
= 2p, p = 2mn
The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The sum of two negative odd integers.
Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers
Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1
= -2m - 2n - 2
= -2(+m + 2 + 1)
= -2p, p = m + n + 1
The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The sum of two even integers and two odd integers.
Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)
Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)
= 2r, r = m + n + p + q + 1
The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. Let p: You ran 1 mile
Let q: You 5280 feet
The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Since 1 mile = 5280 feet
So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
7 divided by 89019 long division please answer
Answers
1 2 7 1 7
7 8 9 0 1 9
- 7
1 9
- 1 4
5 0
- 4 9
1 1
- 7
4 9
- 4 9
0
Your answer is 12,717 with a remainder of 0.
Find the value of y. 4y² - 106 The value of y is
Answers
Answer:
7
Step-by-step explanation:
4y²-106=90
4y²=90+106
4y²=196
4y²/4=196/4
y²=49
y=√49
y=7
Janelle plans to paint her bedroom, which is the shape of a
rectangular prism. Its length is 10 feet, its width is 12 feet, and the
ceilings are 9 feet tall. She does not need to paint the floor or ceiling. How many square feet of wall space will she be covering?
Answers
Answer:
31 us the answer but I am not sure about the answer
construct a rectangle with length twice the width and width equal to r.
Answers
Steps provided below .
Take a scale and measure rNow find 2rConstruct two parallel and vertical lines of length rNow construct two adjacent parallel lines of length 2rAnswer:
Properties of a rectangle:
2 pairs of parallel sidesParallel sides are of equal lengthAll interior angles are 90° (right angles)Each side is perpendicular (at a right angle) to its adjacent sideGiven:
width of rectangle = rlength of rectangle = twice width = 2 × r = 2rSee attached for image if the rectangle
Find the circumference.
Answers
Answer:
[tex]2 \times 3.14 \times 6 = 37.68[/tex]
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In a florist shop, the ratio of roses to tulips is 5 : 3. The shop has 72 tulips on Friday morning.
How will the ratio of roses to tulips change if the florist uses half of each type of flower to fill an order for a wedding?
After the order, the ratio is ____ , _____ which is equivalent to 5:3. The ratio does not change.
Answers
Answer: 120:72
Step-by-step explanation:
tulips: 72/3 = 24
so multiply roses to get an equal ratio, 24 x 5 = 120
Za and Zb are complementary angles. Za measures 44°.
What is the measure of Zb?
Answers
Answer:
zb = 46°
Step-by-step explanation:
za + zb = 90
44° + zb = 90°
90° - 44° = zb
zb = 46°
What is the value of b in the equation y = mx + b if the slope is 5 and we have one ordered pair (2, 3)?
Answers
Step-by-step explanation:
the slope is always the factor of x.
so, m = 5.
to get b we use the point coordinates as x and y values :
3 = 5×2 + b
3 = 10 + b
b = -7
Question 10 of 40
Factor this polynomial completely.
x² - 81
O A. (x-2)(x - 9)
B. (x - 81)(x - 81)
C. (x+81)(x - 81)
O D. (x + 9)(x-9)
Answers
Answer:
D) (x + 9)(x-9)
Step-by-step explanation:
[tex]x^2-81[/tex]
Let's Rewrite 81 as → 9^2
[tex]x^2-9^2[/tex]
Now, apply difference two squares formula
[tex]\left(x+9\right)\left(x-9\right)[/tex]
~
In "The Emperor's New Clothes" what does the opening tell you about the narrator?
A. second person narrator
B. third person narrator
C. no narrator
D. first person narrator
Please help me
Answers
Answer: it is first person well it should be
Step-by-step explanation:
In "The Emperor's New Clothes" no narrator does the opening tell you about the narrator. Correct option is c.
In "The Emperor's New Clothes," the opening doesn't provide direct information about the narrator's perspective. The opening typically sets the scene and introduces the main characters and setting. As a result, it does not clearly indicate the narrator's point of view.
Therefore, the correct answer would be:
C. no narrator
In some versions of the story, there may be a narrator providing the context or guiding the reader, but in the traditional fairy tale version, the story is usually presented without a specific narrator.
To know more about Emperor's:
https://brainly.com/question/28148656
#SPJ2
Select which option is most appropriate for describing the number line below.
Answers
Answer:
c
Step-by-step explanation:
choose me as brainly-est
I need help with this one too
Answers
Answer:
10 1/2x + 126 sq. feet
Step-by-step explanation:
Area = length × width
length = 12 + x
width = 10 1/2
(12 + x)(10 1/2)
126 + 10 1/2x
mary needs 50 ft of fence to protect her rectangular garden from squirrels. How long and how wide is the garden if the length is 8 ft more than the width
Answers
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Mary needs 50 ft of fence to protect her rectangular garden from squirrel The length of the garden is 8 ft more than the width To Find :-We have to find the length and breath of the rectangular garden Let's Begin :-Mary needs 50ft of fence to protect her rectangular garden from squirrel
Therefore,We can conclude that
The perimeter of the rectangular garden
[tex]\bold{ = 50\: ft}[/tex]
We know that,
Perimeter of the rectangle
[tex]\sf{ = 2( Length + Breath) }[/tex]
Here, we have Length of the garden that is 8ft more than the widthLet assume the width of the garden be x
According to the question
[tex]\sf{ Perimeter\:of\:rectangle = 2( x + 8 + x) }[/tex]
[tex]\sf{ 50 = 2( x + 8 + x) }[/tex]
[tex]\sf{ 50 = 2( 2x + 8)}[/tex]
[tex]\sf{ 50 = 4x + 16}[/tex]
[tex]\sf{ 50 - 16 = 4x }[/tex]
[tex]\sf{ 34 = 4x }[/tex]
[tex]\sf{ x = }{\sf{\dfrac{34}{4}}}[/tex]
[tex]\sf{ x = 8.5 }[/tex]
Thus, The breath of the garden is 8.5 ft
Therefore,The length of the garden
[tex]\sf{ = x + 8}[/tex]
[tex]\sf{ = 8.5 + 8}[/tex]
[tex]\sf{ = 16.5\: ft }[/tex]
Hence, The length and breath of the rectangle are 8.5ft and 16.5ft .
Given :
Mary needs 50 ft of fence to protect her rectangular garden from squirrels.The length is 8 ft more than the width of the garden.⠀
To Find :
The dimensions of the garden.⠀
Solution :
Let us assume the length of the garden as x ft and therefore, the width will become (x - 8) ft.We know that,
[tex]\qquad{ \sf{ \pmb{2(Length + Width ) = Perimeter_{(rectangle)}}}}[/tex]
⠀
Substituting the values in the formula :
[tex]{ \dashrightarrow\qquad{ \sf{2(x + x - 8 ) = 50}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \sf{2(2x- 8 ) = 50}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \sf{4x- 16 = 50}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \sf{4x = 50 + 16}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \sf{x = \dfrac{66}{4} }}}[/tex]
[tex]{ \dashrightarrow\qquad{ \bf{x = 16.5}}}[/tex]
Therefore,
The Length of the garden is 16.5 ft .⠀
[tex]{ \dashrightarrow\qquad{ \sf{Width_{(Garden)} = x - 8}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \sf{Width_{(Garden)} = 16.5 - 8}}}[/tex]
[tex]{ \dashrightarrow\qquad{ \bf{Width_{(Garden)} = 8.5}}}[/tex]
⠀
Therefore,
The Width of the garden is 8.5 ft .⠀
Hence,
The dimensions of the rectangular garden is 16.5 ft and 8.5 ft.) Supriya makes papadums to sell in her food truck. She uses 12 oz of dough to make each batch.
She has 60 oz of dough and wants to know how many batches she can make.
. Let b equal the number of batches of papadums Supriya can make.
Complete the equation.
(dough for one batch). (number of batches) = (total amount of dough)
b=
?
Answers
The number of batches she can make is = 5 batches
Calculation of total number of batchesThe amount of dough used to make each batch = 12oz
The total amount of dough she has= 60oz
Therefore, the number of batches she can make from the total dough available = b
Using the equation:
(dough for one batch) × (number of batches) = (total amount of dough)
which is = 12× b = 60
b= 60/12
b= 5 batches
Learn more about batches here:
https://brainly.com/question/25770607
Select the correct answer.
What is ?
A.
B.
C.
D.
Answers
Answer:
option C
Step-by-step explanation:
|3 1/2| = 3 1/2
the absolute value of 3 1/2 is 3 1/2
A car requires 15 litres of petrol to travel 200 km.
How much petrol is needed to travel 120 km?
Answers
Answer:
9 litres
Step-by-step explanation:
200 = 15
divide both sides by 200
1 = 0.075
multiply both sides by 120
120 = 9
Please help me with this!
Answers
Answer:
596
Step-by-step explanation:
plato
Answer:
The answer should be 596.
Step-by-step explanation:
542+54=596.
A train is late arriving into a station.
It should arrive at 5 pm
It arrives at 5.15 pm.
Answers
Step-by-step explanation:
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.
Please help
Miguel deposits $2000 into a bank account that earns simple interest. He writes the equation A(t) = 2000(1.07) t to represent the value of the account after t years,
Based on Miguel's equation, how long will it take for the account to grow to $5,000?
Answers
Answer:
based on the equation he would make $2.5 in the first month but realistically he would earn around $30 in the first month
Step-by-step explanation:
2000+2000(.015)(1/12)=2002.5
2002.5-2000=2.5
The account balance will take time for the account to grow to $5,000 in 2 years and 4 months.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
Miguel deposits $2000 into a bank account that earns simple interest. He writes the equation A(t) = 2000(1.07)t to represent the value of the account after t years.
The account is to grow to $5,000. Then the time will be
5000 = 2000(1.07)t
On simplifying, we have
t = 2.33
It will take for the account to grow to $5,000 in 2 years and 4 months.
More about the simple interest link is given below.
https://brainly.com/question/2793278
I'm attracted to the same gender
and don't know how to tell my parents. What are some suggestions
Answers
i dont know. give it in a humorous way? a direct way? indirectly?
but first ask subtly about how they feel about it before you go do anything
A boat heading out to sea starts out at Point AA, at a horizontal distance of 1206 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 9^{\circ} ∘. At some later time, the crew measures the angle of elevation from point BB to be 4^{\circ} ∘. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary
Answers
Answer:
1525.6
Step-by-step explanation:
Find the area of the trapezoid. The median is equal to 25cm and the height is 8cm. (btw if you explained how to find the base would help a lot) :)
Answers
The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².
What is the Area of a Trapezium?Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.
Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:
A = median length × height
Given the following:
Median = 25 cmHeight = 8 cm.Area of trapezium = 25 × 8 = 200 cm².
Learn more about the area of trapezium on:
https://brainly.com/question/16904048
what is it and why?
Answers
Answer:
C
Step-by-step explanation:
the solution to a system of equations given graphically is at the point of intersection of the 2 lines.
the lines here are parallel and never intersect. Thus there is no solution
Help Yall P1z and thx- Will mark if some one else answers Rate 5 stars and thanks
Answers
Answer:
top and bottom because it math
Step-by-step explanation:
Solve the system of equations algebraically using substitution and elimination
Answers
Answer:
my answer is 2x+ 3y=22 because that the answer
Which of the following represents a nonlinear function?
Answers
Which equation represents circle W?
Answers
Answer:
B (x - 6)² + (y + 4)² = 16
Step-by-step explanation:
From inspection of the graph:
center of the circle = (6, -4)radius = 4 unitsGeneral equation of a circle: (x - a)² + (y - b)² = r²
(where (a, b) is the center and r is the radius)
Therefore, substituting the given values into the equation:
equation of the circle: (x - 6)² + (y + 4)² = 16
Answer:
Answer B
Step-by-step explanation:
Centre of Circle (6,-4)
Radius = 4
Substitute in the Equation attached
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
[tex](x-6)^{2} +(y-(-4))^{2} =4^{2}[/tex]
[tex](x-6)^{2} +(y+4)^{2} =16[/tex]
Help me I need the answer for this problem
Answers
Answer:
17.5 sq. in.
Step-by-step explanation:
3.5 in(5 in) =
17.5 sq. in.
Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289. his credit card has an apr of 20%. if julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make. choose the following modification with the least cuts to his current expenses that will allow julius to pay off his credit card balance in 12 months. income wages $2,456.00 expenses rent $900.00 utilities $186.35 food/clothes $298.00 entertainment $330.00 car $385.00 credit card $34.15 cell phone $89.49 net income $233.01 a. julius can eliminate $31 from entertainment and $55 from food/clothes. b. julius can eliminate $80 from entertainment and $60 from food/clothes. c. julius can eliminate $18 from entertainment and $32 from food/clothes. d. the minimum payment is enough to pay off the balance within 12 months.
Answers
Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.
What is APR?APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.
Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289.
His credit card has an APR of 20%.
If Julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make.
Choose the following modification with the least cuts to his current expenses that will allow Julius to pay off his credit card balance in 12 months.
Income wages $2,456.00
Expenses rent $900.00
Utilities $186.35
Food/clothes $298.00
Entertainment $330.00
Car $385.00
Credit card $34.15
Cell phone $89.49
net income $233.01
The net amount will be over 12 months is 1432.92.
Monthly payback will be
[tex]\rm Monthly\ pay = \dfrac{1432.92}{12}\\\\Monthly\ pay = 119.41[/tex]
She was paying 105.68 dollars per month. Then the amount will be
Amount = 119.41 – 34.15 = 85.26
Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.
More about the APR link is given below.
https://brainly.com/question/8846837
Answer:
a
Step-by-step explanation: