Let g and h be the functions defined by g(x)=?2x^2+4x+1 and h(x)=1/2x^2 - x + 11/2. If f is a function that satisfies g(x)?f(x)?h(x) for all x, what is limx?1f(x) ?А. 3B. 4 C. 5 D. The limit cannot be determined from the information given
Answers
The value of the limit \(\lim_{x \to 1}\) f(x) is 5. Therefore, option C. is correct.
To find the limit of f(x) as x approaches 1, given that g(x) ≤ f(x) ≤ h(x) for all x, you need to evaluate the limits of g(x) and h(x) as x approaches 1.
Evaluate \(\lim_{x \to 1}\) g(x):
g(x) = 2x² + 4x + 1
Plug in x = 1:
g(1) = 2(1)² + 4(1) + 1
= 2 + 4 + 1
= 7
Now, evaluate \(\lim_{x \to 1}\) h(x):
h(x) = 1/2x² - x + 11/2
Plug in x = 1:
h(1) = 1/2(1)² - (1) + 11/2
= 1/2 - 1 + 11/2
= 5
Since g(1) ≤ f(1) ≤ h(1), and both g(1) and h(1) have the same value of 5, the limit of f(x) as x approaches 1 is 5. Therefore, the correct answer is C. 5.
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The value of the limit \(\lim_{x \to 1}\) f(x) is 5. Therefore, option C. is correct.
To find the limit of f(x) as x approaches 1, given that g(x) ≤ f(x) ≤ h(x) for all x, you need to evaluate the limits of g(x) and h(x) as x approaches 1.
Evaluate \(\lim_{x \to 1}\) g(x):
g(x) = 2x² + 4x + 1
Plug in x = 1:
g(1) = 2(1)² + 4(1) + 1
= 2 + 4 + 1
= 7
Now, evaluate \(\lim_{x \to 1}\) h(x):
h(x) = 1/2x² - x + 11/2
Plug in x = 1:
h(1) = 1/2(1)² - (1) + 11/2
= 1/2 - 1 + 11/2
= 5
Since g(1) ≤ f(1) ≤ h(1), and both g(1) and h(1) have the same value of 5, the limit of f(x) as x approaches 1 is 5. Therefore, the correct answer is C. 5.
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Related Questions
Plz help me, correct answers will get brainliest <3
Answers
Answer:
∠ B = 48°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180° for ∠ B
∠ B = 180° - (90 + 42)° = 180° - 132° = 48°
Determine the unknown fractional part of the graph
Answers
Answer: 34/105
Step-by-step explanation: The idea here is that the fractional parts of the circle graph will all add up to 1 exactly, but the blue segment represents an unknown fraction.
So, this is an exercise in adding fractions with different denominators to get the total known area and then finding the difference between 1 and that known area.
We cannot directly add fractions with different denominators.
To add 1/7 and 1/5 and 1/3, we need to find the least common denominator (LCD) and then express all three numbers in terms of that denominator. In other words, we want a whole number that is evenly divisible by 7, by 3, and by 5 and we want the smallest number for which that is true.
If we multiply all three numbers together, we get 7*5*3 = 105.
That is the LCD. It divides by all 3 numbers (7, 5, 3) and no smaller number will do.
Tan Segment - To take the denominator of 7 and get 105, we multiply by 5*3 = 15, so we do that to both the numerator and denominator of the fraction. We have 1 * 5*3 = 15 on top and 7 * 5*3 = 105 on the bottom, to get the fraction ---> 15/105
Orange Segment - To take the denominator of 5 and get 105, we multiply by 7*3 = 21, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*3 = 21 on top and 5 * 7*3 = 105 on the bottom, to get the fraction ---> 21/105
Purple Segment - To take the denominator of 3 and get 105, we multiply by 7*5 = 35, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*5 = 35 on top and 3 * 7*5* = 105 on the bottom, to get the fraction ---> 35/105
We add the known areas: 15/105 + 21/105 + 35/105 = 71/105
Now we need the Blue Segment:
1 - 71/105 = 105/105 - 71/105 = (105- 71)/105 = 34/105
Since 34 does not divide by any of the three factors of the denominator (3, 5, and 7) the answer cannot be reduced further.
The blue segment area is 34/105
I hope this helps.
Write an expression that matches; “8 less than z”
Answers
Answer:
ᗴ᙭ᑭᖇᗴՏՏIOᑎ:\(z - 8\)
Find the mean, median, and mode(s) of the data. Calculator use is ok.
18, 21, 22, 18, 19
Mean
Median
Mode(s)
Answers
Answer:
The mean is 19.6. you have to add up all the numbers given and divide it by the number of numbers which in this case it's 18+18+19+21+22=98
98/5=19.6
The median is the middle number when you arrange the numbers in order therefore it's 19
The mode is that number which appears the multiple time in the numbers given therefore it's 18
In which interval does a root exist for this equation? tan(x) = 3x^2
PLEASE HELP
Answers
To determine the interval for which a root exists, you can use the intermediate value theorem.
First, observe that the left-hand side of the equation, tan(x), is undefined for x = (n + 1/2) π, where n is an integer. Thus, we can restrict our attention to the interval (-π/2, π/2) where the tangent function is continuous and strictly increasing.
Next, note that tan(0) = 0 and tan(π/6) = 1/√3 < 3/36 = 1/12. Also, as x approaches π/2 from the left, tan(x) approaches infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (0, π/6).
Similarly, tan(-π/6) = -1/√3 > -1/12, and as x approaches -π/2 from the right, tan(x) approaches negative infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (-π/6, 0).
Therefore, the equation tan(x) = 3x^2 has at least one root in the interval (-π/6, π/6).
Help me please this is due in 10 mins. I’ll mark brainliest for the correct/best answer
Answers
Answer:
ok
Step-by-step explanation:
first graph: 3.5, 3.5, 3.5, 3.5, so this one is yes
second graph: 2.5, 2.3, 2, 1.5, so no
third graph: 2, 2, 2, 2 this one is yes
sorry the first time i was wrong
A small box weighs 1 25 pounds. A large box weighs 3 1/3 time as much as the small box. how much does the large box weigh?
Answers
Answer:
416.7pounds
Step-by-step explanation:
Given parameters:
Weight of the small box = 125pounds
Unknown:
Weight of the larger box = ?
Solution:
The large box weighs \(3\frac{1}{3}\) times as the small box:
So;
= 125pounds x \(\frac{10}{3}\)
= 416.7pounds
23. सरल गर्नुहोस् (Simplify):
Ans:
3
(a-3) (a-5)
1
1
1
+
+
(a - 3) (a - 4) (a-4) (a - 5) (a - 5 ) (a - 3)
Answers
3
(a-3) (a-5)
1
1
1
(a - 3) (a - 4) (a-4) (a - 5) (a - 5 ) (a - 3)
Simplifying the denominators, we get:
3
(a-3) (a-5)
1
1
1
(a - 3) (a - 4) 4(a - 5)^2 3(a - 3)(a - 5)
Now, we can find the least common denominator, which is:
4(a - 5)^2 (a - 4) 3(a - 3)(a - 5)
Multiplying the first term by 4(a - 5)^2 and simplifying, we get:
12(a - 4)
Multiplying the second term by 3(a - 3) and simplifying, we get:
3(a - 4)
Multiplying the third term by 4(a - 4)(a - 5)^2 and simplifying, we get:
4
Multiplying the fourth term by (a - 5)(a - 3)(a - 4)(a - 5)^2 and simplifying, we get:
(a - 3)(a - 5)
Multiplying the fifth term by (a - 4)(a - 3)(a - 5)(a - 5) and simplifying, we get:
1
Adding all the simplified terms, we get:
12(a - 4) + 3(a - 4) + 4 + (a - 3)(a - 5) + 1
4(a - 5)^2 (a - 4) 3(a - 3)(a - 5)
Simplifying further, we get:
15a - 57
12(a - 5)^2
Use Euclid's first book to prove what specific quadrilaterals are produced by perpendicular, unequal, bisecting diagonals.
Answers
By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.
According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.
1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.
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How far is the park entrance to the rides How far are the rides from the restroomsHow far are the rides from the refreshment area The diagram below models the layout at the country fair assume the two triangles in the diagram are similar.
Answers
Given two triangles are similar.
A)
We know that the corresponding sides of similar triangles are in proportion.
Let x be the distance between the park entrance and the rides.
we get the proportions as follows.
\(\frac{140}{112}=\frac{x}{100}\)Multiplying both sides by 100, we get
\(\frac{140}{112}\times100=\frac{x}{100}\times100\)\(x=125\text{ yards}\)Hence the Park entrance is 125 yards from the rides.
B)
Let y be the distance between rides and restrooms.
Since the given triangles are similar, we get the following proportion.
\(\frac{140}{112}=\frac{y}{112}\)Multiplying both sides by 112, we get
\(\frac{140}{112}\times112=\frac{y}{112}\times112\)\(y=140\text{ yards.}\)Hence the rides are 140 yards from the restrooms.
C)
the distance between refreshment area and rides =The distance between refreshment area and restrooms + the distance between rides and restrooms
The distance between the refreshment area and rides=112+140=252 yards.
Hence the rides are 252 yards from the refreshment area.
find each of the following probabilities when n independent bernoulli trials are carried out with probability of success p. a) the probability of no failures b) the probability of at least one failure c) the probability of at most one failure d) the probability of at least two failures
Answers
For n independent Bernoulli's trial , with probability of success as "p" then , the
(a) probability of no failure is ⇒ pⁿ ,
(b) at least one failure is ⇒ 1 - pⁿ ,
(c) at most one failure is ⇒ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ,
(d) at least two failure is ⇒ 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ] .
In the question ,
it is given that ,
number of Bernoulli's trials is = "n" ;
the probability of success is ⇒ p ;
Part (a)
the probability of No Failure is equivalent to probability of all success .
= pⁿ .
Part(b)
The probability of at least one failure can be written as
= 1 - (probability of all success)
= 1 - pⁿ
Part(c)
the required probability of at most one failure is =
= probability of "No Failure" \(+\) probability of "One Failure"
= ⁿCₙpⁿ(1-p)⁰ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)¹
= pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)
Part(d)
the probability of at least two failure is =
= 1 - probability of "at most one failure" ...substituting from part(c)
= 1 - [ ⁿCₙpⁿ(1-p)⁰ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)¹ ]
= 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ]
Therefore , the required probabilities are (a) pⁿ ,
(b) 1 - pⁿ ,
(c) pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) and
(d) 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ] .
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Match the decimal with its equivalent percent.
0.42
A. 4.02%
OB. 42%
OC. 4.2%
D. 402%
Answers
Answer:
42%
Step-by-step explanation:
decimal * 100 to get %
can someone help me with this
Answers
Step-by-step explanation:
\(2p + 2p + 2p + 60 = 360 \\ 6p = 360 - 60 \\ 6p = 300 \\ p = \frac{300}{6} \\ p = 50\)
Si los dos triángulos ABC y DFE son proporcionales, ¿Cuál será la longitud del lado DE del triángulo DFE?
Answers
Answer:
La respuesta esta abajo
Step-by-step explanation:
Un triángulo es un polígono con tres lados y tres ángulos.
Se dice que dos triángulos son proporcionales si la razón de sus lados correspondientes está en la misma proporción.
de la pregunta, el lado AB es proporcional a DF, AC es proporcional a DE y BC es proporcional a FE
Por lo tanto, dado que ambos triángulos son proporcionales, entonces:
DE / DF = AC / AB
x / 10 = 21/15
x = (21/15) * 10 = 14
How would I solve an absolute value this:
|2m+3/5|=|1-3m/6|
I’m really stuck on how to remove the 5 and 6 from the equations separately.
Answers
m = \(\frac{4}{25}\) 0r m = \(-\frac{16}{15}\)
|2m+3/5|=|1-3m/6|
Split into two equations
⇒\(2m + \frac{3}{5} = 1 - \frac{3m}{6}\) or
⇒\(2m + \frac{3}{5} =-( 1 - \frac{3m}{6})\)
\(2m + \frac{3}{5} = 1 - \frac{3m}{6}\)
multiply both side of the equation by the common denominator
⇒2m × 30 + \(\frac{3 * 30}{5}\) = 30 - \(\frac{3 m * 30}{6}\)
⇒2m×30 + 18 = 30 -15m
⇒60 m + 18 = 30 -15m
⇒60m + 15m = 30 - 18
⇒75m = 12
⇒m = \(\frac{12}{75}\)
⇒m = \(\frac{4}{25}\)
\(2m + \frac{3}{5} =-( 1 - \frac{3m}{6})\)
reduce the fraction
⇒\(2m + \frac{3}{5} =-( 1 - \frac{m}{2})\)
remove brackets
⇒\(2m + \frac{3}{5} = - 1 + \frac{m}{2}\)
multiply both side of the equation by the common denominator
⇒2m × 10 + \(\frac{3 * 10}{5}\) = -10 + \(\frac{ m * 10}{2}\)
⇒2m × 10 + 6 = -10 + 5m
⇒20 m + 6 = - 10 + 5m
⇒20m - 5m = - 10 -6
⇒15m = -16
⇒m = \(-\frac{16}{15}\)
we get,
m = \(\frac{4}{25}\) 0r m = \(-\frac{16}{15}\)
Equations with fractions involve solving equations where the unknown variable is part of the numerator and/or the denominator of the fraction.
To solve equations with fractions we need to work out what the value of the unknown variable. We solve equations by using the “balancing method” by applying the inverse operation to both sides of the equation.
The inverse operation of addition is subtraction.
The inverse operation of subtraction is addition.
The inverse operation of multiplication is division.
The inverse operation of division is multiplication.
How to solve equations with fractions
In order to solve equations with fraction:
Identify the operations that are being applied to the unknown variable.
Apply the inverse operations, one at a time, to both sides of the equation.
Write the final answer, checking that it is correct.
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A car traveling at a speed of 70 km/h applies the break. The car needed a 50 m to reach complete stop. Determine the time required to stop the car 3.52 s 5.14 s 15.66 s 3.95 s
Answers
The time required to stop the car is approximately 5.14 seconds for all options.
To determine the time required to stop the car, we can use the equation of motion for deceleration:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car comes to a complete stop)
u = initial velocity (70 km/h = 19.44 m/s)
a = acceleration (deceleration, which is unknown)
s = distance (50 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the values, we get:
a = (0^2 - (19.44 m/s)^2) / (2 * 50 m)
Calculating the acceleration:
a = (-377.9136 m^2/s^2) / 100 m
a ≈ -3.78 m/s^2
Now, we can use the formula for acceleration to find the time required to stop the car:
a = (v - u) / t
Rearranging the equation, we have:
t = (v - u) / a
Substituting the values, we get:
t = (0 m/s - 19.44 m/s) / (-3.78 m/s^2)
Calculating the time for each option:
a) t = (-19.44 m/s) / (-3.78 m/s^2) ≈ 5.14 s
b) t = (-19.44 m/s) / (-3.78 m/s^2) ≈ 5.14 s
c) t = (-19.44 m/s) / (-3.78 m/s^2) ≈ 5.14 s
d) t = (-19.44 m/s) / (-3.78 m/s^2) ≈ 5.14 s
Therefore, the time required to stop the car is approximately 5.14 seconds for all options.
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In a bag there are 5 yellow marbles, 7 green marbles, 2 white marbles, and 6 blue marbles. IfT take 3 marbles without replacing them what is the probability of getting 2 white and a blue marble?
Answers
Answer:
1/190
Step-by-step explanation:
To calculate the probability of drawing 2 white marbles and 1 blue marble without replacement, we need to consider the total number of ways to choose 3 marbles out of the total number of marbles in the bag.
The total number of marbles in the bag is 5 + 7 + 2 + 6 = 20.
First, let's calculate the number of ways to choose 2 white marbles out of the 2 available:
Number of ways to choose 2 white marbles = (2 choose 2) = 1
Next, we need to calculate the number of ways to choose 1 blue marble out of the 6 available:
Number of ways to choose 1 blue marble = (6 choose 1) = 6
Now, we can calculate the total number of ways to choose 3 marbles out of the 20 marbles in the bag:
Total number of ways to choose 3 marbles = (20 choose 3) = 1140
Finally, we can calculate the probability by dividing the number of favorable outcomes (2 white marbles and 1 blue marble) by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= (1 * 6) / 1140
= 6 / 1140
= 1 / 190
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See the figure below If the perimeter of the window is 24 ft, find the value of x so that the greatest possible amount of light is admitted
Answers
The perimeter equation is:
2x + x + (1/2)πx = 24 ft.
Simplifying the equation, we have:
(5/2)πx + 3x = 24 ft.
To find the value of x, we solve the equation:
(5/2)πx + 3x = 24 ft.
This equation can be solved numerically or algebraically to find the value of x.
The perimeter of a Norman window can be calculated by adding the lengths of all its sides. In this case, the perimeter is given as 24 ft.
Let's break down the components of the Norman window:
- The rectangular part has two equal sides and two equal widths. Let's call the width of the rectangle "x" ft.
- The semicircle on top has a diameter equal to the width of the rectangle, which is also "x" ft.
To find the perimeter, we need to consider the lengths of all sides of the rectangle and the semicircle.
The perimeter consists of:
- Two equal sides of the rectangle, each with a length of "x" ft. So, the total length for both sides of the rectangle is 2x ft.
- The width of the rectangle, which is also "x" ft.
- The curved part of the semicircle, which is half the circumference of a circle with a diameter of "x" ft. The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. So, the circumference of the semicircle is (1/2)πx ft.
To summarize, the perimeter equation is:
2x + x + (1/2)πx = 24 ft.
Simplifying the equation, we have:
(5/2)πx + 3x = 24 ft.
To find the value of x, we solve the equation:
(5/2)πx + 3x = 24 ft.
This equation can be solved numerically or algebraically to find the value of x.
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Translation!! Please and thanks a lot !
Answers
Answer: A is the answer
Step-by-step explanation:
The rest of the answers show rotation, flip, and dilation, so A seems like the correct answer
I hope this helps!
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answers
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
hence, you divide 2.25 by 5.
Simplify 9 – 3(4x – 18) + 6x
Answers
The expression is simplified to 7(-x + 9)
What are algebraic expressions?
Algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.
They are also made up of mathematical or arithmetic operations
Given the expression;
9 – 3(4x – 18) + 6x
expand the bracket
9 - 12x + 54 + 6x
collect like terms, we have;
-12x + 5x + 54 + 9
Add or subtract like terms
-7x + 63
Factor out 7
7(-x + 9)
Thus, the expression is simplified to 7(-x + 9)
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Shown is the graph of a parabola, y = f(x), with vertex (2,-1). What is te vertex of the parabola y = f(x + 1)?
Answers
The vertex of the parabola y = f(x + 1) is (1, -1).
To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.
The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.
In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.
Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.
Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).
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Find the 7th term of the arithmetic sequence − 3 � + 5 −3x+5, 2 � + 3 2x+3, 7 � + 1 ,. . . 7x+1
Answers
The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.
What is the 7th term of the arithmetic sequence?To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:
(2x+3) - (-3x+5) = 5x - 2
This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:
a₇ = (-3x+5) + (7 - 1)(5x - 2)
Simplifying the equation:
a₇ = -3x + 5 + 30x - 12
a₇ = 27x - 7
Therefore, the 7th term of the arithmetic sequence is 27x - 7.
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A salesman needed to sell a four–wheeler. He priced it at $3,500 the first day it was on the market. The second day he reduced the price by 15%. What was the price of the four–wheeler after this reduction?
Answers
write a 2 columm proof please help i cant do it
Answers
Two column proof is as follows
Statement Reason
AB ≅ CB Given
AD ≅ CD Given
< BAD ≅ < BCD Given
< ABD = < CBD Definition of angle bisection
AB = CB Definition of equality
BD = BD Reflexive property of congruence
AD = DC Definition of bisection
Δ ABD = Δ CBD SSS postulate of congruence
What is two column proof?
This is a method of proof that consists of five parts which include
the diagram the statement columnthe reason columnthe giventhe propositionSSS postulate of congruenceThe postulate says that when the three sides of the triangles under comparison are equal then the triangles under comparison are said to be congruent.
In the figure,
AB =CB, from the given sides
BD = BD sharing common sides
AD = CD line AC was bisected by line BD
This completes the SSS proof of congruence
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Guys can you please help. I dont understand. Thank you. :))))
Lines AB and CD intersect at E. If the measure of angle AEC=5x-20 and the measure of angle BED=x+50, find, in degrees, the measure of angle CEB.
Answers
Answer: 112.5
Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.
a farmer wants to build a rectangular pen which will be bounded on one side by a river and on the other three sides by a single-strand electric fence. if the farmer has 16 meters of wire to use, what is the largest area that the farmer can enclose?
Answers
The largest area that the farmer can enclose is 32metres²
Since, we have the farmer wants to build a rectangular pen, means that opposite sides are of equal length.
So, let suppose the length of rectangular pen be x meters and width of rectangular pen as y meters.
We know that perimeter of rectangle is =2×(length + breadth)
Therefore, perimeter of rectangular pen =2x+y,and we are given the perimeter of rectangular pen in form of length of electric fence,
So,2x+y=16-------(eq1)
We know that area of rectangle=length × breadth
∴A=x × y
Now putting values of y from (eq1),we get
=>A=x×(16-2x)
For largest area, we need to differentiate the area with respect to x and equate to it to equal to zero.
∴d(A)/dx=16-4x
=>16-4x=0
=>x=4metres
Therefore, y=16-2×4=8metres
Now, area of rectangular pen will be =x × y=4×8=32metres².
Hence, the largest area of rectangular pen which will be bounded on one side by a river and on the other three sides by a single-strand electric fence is 32metres².
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Q5. Evaluate this expression when a=6
Q6. Which option shows this expression simplified correctly?
Q7. Which option shows this expression simplified correctly?
Q8. Find the following:
Q9. Which option shows this expression expanded correctly?
Answers
Question 6: 2w + 3x. There are 2 w’s, and 3 x’s.
Question 7: 2x + 4y. There are 2 x’s, and 4 y’s.
Question 8. 11 + 16 is 27.
Question 9: 3(8y - 5). 3*8y is 24y. 3*-5 is -15. The answer is 24y - 15.
If there are 3 apples for every 4 oranges, how many apples would you have if you had 20 oranges?
Answers
Answer:
6 Apples
Step-by-step explanation:
There would be six apples and 2 oranges left over.
Hope this Helps!
:D
Answer:
I was kind of confused on this one but is it 15 apples?
Step-by-step explanation:
3, 6, 9, 12, 15
4, 8, 12, 16, 20
I think the answer is 15 apples.
PLEASE help, I've been trying to get this for like an hour.
Answers
The solution of the equation is (-2, 3) and to eliminate x we have to multiply equation(i) by 3 and multiply equation(ii) by 4.
How to solve system of equation by elimination method?System of equation can be solved using different method such as elimination method, substitution method and graphical method,
Let's use elimination method to solve the system of equation.
Therefore,
4x + 5y = 7
3x - 2y = - 12
Multiply equation(i) by 3 and equation(ii) by 4 to eliminate x.
Hence,
12x + 15y = 21
12x - 8y = - 48
Subtract the equations
23y = 69
y = 69 / 23
y = 3
Hence,
4x = 7 - 5y
4x = 7 - 5(3)
4x = 7 - 15
4x = -8
x = -8 / 4
x = -2
Therefore, the solution is (-2, 3)
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