A client asked Nathan to design a rectangular garden with an area of 22 square feet. The client also requested that the length of the garden be eight feet less than seven times the width
Answers
The length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
Let the width of the garden be x units.
According to the given question.
The area of the rectangular garden is 22 square feet.
Also, the length of the garden be eight feet less than seven times the width.
⇒ length of the garden = 7x - 8
Thereofore, the area of the rectangular garden is given by
22 = x(7x - 8)
⇒ 22 = 7x^2 - 8x
⇒ 7x^2 - 8x - 22 = 0
⇒ x = [tex]\frac{8 \pm \sqrt{64 + 616} }{14}[/tex]
⇒ x = [tex]\frac{8 \pm \sqrt{680} }{14}[/tex]
⇒ x = [tex]\frac{8\pm 26}{14}[/tex]
⇒ x = 8 + 26/14
⇒ x = 34/14
⇒ x = 2.43 feet
So,
the length of the rectangular garden = 7(2.43) - 8 = 9.01 feet
Hence, the length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
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Related Questions
19yd.28in.-16yd.31in.
Answers
Answer:
2yds 33 in
Step-by-step explanation:
Convert everything to the lowest unit(inches) perform the operation and convert back
1 yard = 3 feet
1 foot = 12 in
1 yard = 3feet x 12in = 36 in
19yd, 28in = 19 x 36 + 28 = 684 + 28 = 712 in
16yd, 31 in= 16 x 36 + 31 = 576 + 31 = 607 inches
19yd, 28in - 16yd, 31 in = 712 - 607 = 105 inches
Divide by 36 to get the whole number of yards as quotient
105/36 with remainder of 33
∴ 19yd, 28in - 16yd, 31 in = 105 inches = 2yds 33 inches
We can verify this by converting 2yds 11inches to inches and seeing the values agree
2 yds 33 in = 2 x 36 + 33 = 105
What is the value of (-2) • (7) • (5) • (-4)= Enter your answer as a number, like this: 42
Answers
Answer:
280
Step-by-step explanation:
-2 x 7 = -14
-14 x 5 = -70
-70 x -4 = 280
Answer:
280
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)According to the order of operations (PEMDAS), when multiplying, work from left to right:
Given expression:
(-2) · (7) · (5) · (-4)
Multiply -2 by 7:
⇒ (-14) · (5) · (-4)
Multiply -14 by 5:
⇒ (-70) · (-4)
Finally, multiply -70 by -4, remembering that if both numbers are negative, the answer is positive:
⇒ 280
Given the line y = -1, write the equation
of the line that is parallel to that line and
passes through (-3,5).
Answers
Answer:
Y+5=0
Step-by-step explanation:
Here,given eqn of line is 0.X+Y+1=0_____(i)
since required eqn is parallel to eqn (i)
0.X+Y+K=0____(ii)
passing point (-3,5)
putting the value of Y
5+K=0
.-.K=(-5)
r required eqn is Y-5=0
I am offering 50 points to answer this and i will do it again and again
Answers
Answer: Between 2 and 7
Answer:
2 to 5
Step-by-step explanation:
i don't know because of i don't this transmission may not have the completed Questionnaire
23 + 10 ÷ 2 − (− 14 ÷ 2)
Please explain it.
Answers
Step-by-step explanation:
23 + 10 - 2 + 14 + 2
33 - 2 + 16
31 + 16 = 47
. f(x) = 2x-5; Find f(-8)
Answers
Answer:
D.
Theres no need for a explanation :)
Tell whether the figure has line symmetry. If so how many lines of symmetry are there?
Answers
Find the volume of this object.
Use 3 for π.
Volume of a Cylinder
V= πr²h
6 in
10 in
8 in
12 in V≈ [?]in³
Answers
The volume of the object which is made up of two different cylinders will be 383 cubic inches.
What is the volume of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,
V = π r²h cubic units
The object is made up of two cylinders. Then the volume of the object will be
V = π x (3)² x 8 + π x (5)² x 2
V = π(72 + 50)
V = 3.14 x 122
V = 383.08 ≈ 383 cubic inches
The volume of the object which is made up of two different cylinders will be 383 cubic inches.
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To the citizens of the country of Merka, there is no meal
better than a hot dog nestled securely in a hot dog bun. Relish is optional, mustard is not. The hypothetical market for hot dogs in Merka is graphed. Suppose that the price of hot dog buns decreases. Illustrate the impact of this change on the
market by manipulating the appropriate curve or curves.
The equilibrium price it hot dogs:
a) decreases
b) increases
c) remains the same
The equilibrium quantity of hot dogs:
a) increases
b) decreases
c) remains the same
The supply curve shifts:
a) left
b) right
The demand curve shifts:
a) left
b) right
Answers
Based on the price of hot dog buns decreasing, the impact on the market would be the equilibrium price of hot dogs decreases.
The equilibrium quantity of hot dogs decreases.
The supply curve shifts left. The demand curve shifts right.
What happens to the supply curve when prices drop?When the price of a good like the hot dog duns decreases, supplier will have less incentive to keep making it and so will reduce the quantity supplied to the market. This would mean that the supply curve would shift left.
The demand curve on the other hand would shift right because more people would demand the cheaper hotdogs. The equilibrium price which had fallen would then have to rise.
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1. There are 2 floors in the initial building.
The workers can build 3 floors each week.
When will the building have 15 more floors
than the INITIAL building?
week #
2
5
0 1
8
2
?
Answers
The number of weeks it would take the workers to build 15 more floors is 5 weeks.
How many weeks would it take to build 15 more floors?
The number of weeks it would take to build 15 more floors can be determined by dividing the number of additional floors by the number of floors the workers can build in one week.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient.
Number of weeks = additional floors ÷ number of floors that can be built in a week
15 ÷ 3 = 5 weeks
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Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
Answers
Answer:
Here SOLUTION: −5x + 4y = 20. 10x − 8y = −40.
Step-by-step explanation:
First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity.
help like rn, like rn rn rn rn , thanks
Answers
Answer: 13π/6 √45
Step-by-step explanation:
[tex]\displaystyle\\\sqrt{11} +3\approx6.32\\\\\pi +3,8\approx6.94\\\\Hence,\\\\6.32 < x,6.94\\\\\frac{61}{10}=6.1 \notin\\\\\frac{13\pi }{6}\approx6.81\in\\\\\sqrt{45}\approx6.71\in \\\\6\frac{1}{9}\approx6.11\notin\\\\\sqrt{83}-3\approx6.11\notin[/tex]
which operation should be used to solve x-5=12
Answers
First you add 5 to both sides (inverse operation)
X-5=12
+5 +5
The 5 cancels out and 12+5 =17
X=17
The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
x - 5 = 12
Now,
Adding 5 on both sides,
x = 17
Thus, The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.
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Please help! And show your work for each answer so I can understand, ty
Answers
Answer:
a=17, R=101
Step-by-step explanation:
10:
We know that if all angles of a triangle are congruent, the angles must be as well. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
We also know that all interior angles of a triangle add up to 180 degrees. If they are all equal this only leaves us with the possibility of every angle equaling 60 degrees, otherwise they wouldn't add up to 180 AND be equal simultaneously.
To find the value of a set the equation equal to 60.
[tex]4a-8=60[/tex]
Solve for a:
[tex]4a-8=60\\4a=68\\a=17[/tex]
19:
We know in a parallelogram all interior angles sum to 360 degrees.
Remember the sum of angle pairs between parallel lines is 180 degrees. Meaning if we add angles T and S and set them equal to 180 degrees we can then find the value of angle S as we would have the value of variable x.
[tex](4x+1)+(3x+4)=180\\7x+5=180\\7x=175\\x=25[/tex]
Now substitute in the known value of x to find angle S:
[tex]3(25)+4\\75+4\\79[/tex]
Angle S measures 79 degrees.
Using our previous knowledge of two angles on a parallel line summing to 180 degrees, we can find the measure of angle R by subtracting 79 from 180.
[tex]180-79=x\\101=x[/tex]
R=101
Pllss helppppppppppp
Answers
Answer: A. x=8
Step-by-step explanation:
0.4(5x-12)+0.5x=15.2
(0.4)(5x)-(0.4)(12)+0.5x=15.2
2x-4.8+0.5x=15.2
2.5x-4.8=15.2
2,5x-4.8+4.8=15.2+4.8
2,5x=20
(2.5)(x)=(2.5)(8)
Divide both parts of the equation by 2.5:
x=8
Find the 6th term of the arithmetic sequence x+2, -6x-3, -13x-8,...
Answers
) consider the following sets s with binary operation ∗. which pairs (s,∗) form a group? if (s,∗) is not a group, which axioms fail? (a) let s be the set of integers z and let a ∗ b
Answers
The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.
The following subsets of Z (with ordinary addition and multiplication) satisfy all but one of the
axioms for a ring. In each case, which axiom fails?
(a) The set S of odd integers.
• The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.
Hence, Axiom 1 is violated.
(b) The set of nonnegative integers.
• If a is a positive integer, then there is no solution of a + x = 0 that is also positive. Hence, Axiom
5 is violated.
In general, to show that a subset S of a ring R, is a subring of R, it is sufficient to show that
(i) S is closed under addition in R
(ii) S is closed under multiplication in R;
(iii) 0R ∈ S;
(iv) when a ∈ S, the equation a + x = 0R has a solution in S.
Let a, b, c ∈ S ⊂ Z with a = rk, b = sk, c = tk.
(i) a + b = rk + sk = (r + s)k ∈ S
(ii) ab = (rk)(sk) = (rsk)k ∈ S
(iii) 0Z = 0 = 0 · k ∈ S
(iv) a = rs ∈ S ⇒ x = −rs ∈ S is a solution ofa + x = 0S
Thus, S is a subring of Z.
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The point P(–5,–5) is translated 1 unit left and 1 unit up. What are the coordinates of the resulting point, P'?
Answers
Jamal has a suitcase that contains only 10 white socks. he wants to add enough black socks so that the probability of randomly selecting a white sock is 1/5. how many black socks should jamal add to the suitcase? f. 30 g. 35 h. 40 j. 45 k. 50
Answers
40 black socks should be added to the suitcase( i.e., option h )
Let's take x = black socks added by Jamal
Based on the given condition, we have
[tex]\frac{10}{10 + x}[/tex] = 1/5
Here x ≠ -10
Because to define the fraction, the denominator should not be 0.
Now we need to find the value of x,
[tex]\frac{10}{10 + x}[/tex] = 1/5
50 = 10 + x
x = 40
Therefore 40 socks should Jamal add to the suitcase.
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Write the following statement in the "if-then" form.
A side of a square measures 3 decimeters if the side's measure is 30 centimeters.
Choose the correct answer below.
OA. If the side of a square measures 3 decimeters, then the side's measure is 30 centimeters.
OB. If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.
Answers
If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters, is the "if-then" form of A side of a square measures 3 decimeters if the side's measure is 30 centimeters.
A statement with an assumption and a conclusion is known as a conditional statement (also known as an if-then statement). The hypothesis is the initial clause, or "if," part of a conditional statement which is followed by the second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.
Thus, option B is correct which is, if the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.
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Help please
An airline charges an extra fee for a checked bag that weighs more than 50 pounds.
Your bag weighs 44.9 pounds.
You have a 2.5 pound hair dryer, a 1.3 pound souvenir, and a 3.6 pound pair of boots.
Which items can you add to the bag without paying the extra fee?
Answers
you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb
Which items can you add to the bag without paying the extra fee?
The maximum weight that your bag can have is 50 pounds.
The actual weight of your bag is 44.9 pounds, so if we define x as the weight you can add, then we can write the inequality:
44.9 lb + x ≤ 50lb
Solving the inequality for x, we get:
x ≤ 50lb - 44.9 lb
x ≤ 5.1 lb
Now, the weight of the items are:
hair dryer = 2.5 lb
souvenir = 1.3 lb
boots = 3.6 lb
So you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb
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The tree in Naomi's backyard lost 120 leaves in 12 days.
Which expression below models the change in the number of
eaves per day?
a. 120 ÷ 12
D. -120 ÷ 12
c. 120
-12
d. -120
-12
Answers
The tree in Naomi's backyard lost 120 leaves in 12 days. Therefore, the required expression is A. 120÷12
Hope this helps :)
WILL CHOOSE THE BRAINLIEST ANSWER!!!
Answers
The difference between the area of the square and the area of the circle is C. 9x²(4 - π).
How to calculate the area?The area of the square will be:
= Side ×Side
= 6x × 6x
= 36x²
The area of the circle will be:
= πr²
= 3.14 × (3x)²
= π × 9x²
= 9πx²
The difference will be:
= 36x² - 9πx²
= 9x²(4 - π)
Therefore, the correct option is C.
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Write 2 decimals that are equivalent to the decimal 9.50?
Please help
Answers
Answer: 9.5 and 9.500
Answer:
One would be 9/5 and another could be 1.8
Ming says that 0.24>1/4 because 0.24=2/4 which best explains Ming’s error
Answers
the numbers from $1$ to $150$, inclusive, are placed in a bag and a number is randomly selected from the bag. what is the probability it is neither a perfect square nor a perfect cube? express your answer as a common fraction.
Answers
The required probability is [tex]\frac{1}{10}[/tex].
This problem is related to probability.
First we have to calculate the number of outcomes and then the number of favorable outcomes.
In this case the numbers are from 1 to 150.
First we have to find the numbers which are perfect square between 1 to 150= {1,4,9,16,25,36,49,64,81,100,121,144}
Now we have to find the numbers which are perfect cube other than those which came in square={8,27,125}
Here the number of favorable outcome is 150 minus number of elements in set of perfect square and perfect cube.
Now the probability of the required problem is = [tex]\frac{15}{150}[/tex]
= [tex]\frac{1}{10}[/tex]
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Emily purchased a pack of 6 shirts for $18. What was the cost per shirt? someone answer this please.
Answers
Answer:
$3
Step-by-step explanation:
Divide 6 from 18 to find the cost per shirt.
18/6=3
3 dollars per shirt.
Hope this helps!
Please mark as brainliest if correct!
Give an angle which has the same sine as 300
Answers
I might me wrong, but i believe that its -36.
Have a nice day <3
What are the minimum and maximum temperatures recorded in this table?
Temperature (°C) 11 0 24.2 -32.4 -0.6 0.5
Answers
The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.
What is comparison of values?The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.
Now, given values :11.0, 24.2, -32.4, -0.6, 0.5
Arranging them in ascending order: -32.4, -0.6, 0.5, 11.0, 24.2Thus, The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.
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2x+3y-4;where x=1 and y=-1 answer
Answers
Answer:
-5
Step-by-step explanation:
2x+3y-4
Evaluate for x=1,y=−1
(2)(1)+(3)(−1)−4
(2)(1)+(3)(−1)−4
=−5