Answer:
a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.
b. 25 more trees are to be planted per acre to maximize the total yield.
Step-by-step explanation:
If the no. of trees per acre is doubled then it will be equal to,
[tex]100 \times 2[/tex]
= 200
So, the no. of trees per acre is increased by (200 - 100) = 100
hence, the average yield per tree will be,
(150 - 100) = 50 in that case.
Hence, the total yield will be,
[tex]50 \times 200[/tex]
= 10,000 apples per acre
Now , if x trees are planted, the total no. of apples produced per acre will be,
[tex](150 - x) \times (100 + x)[/tex]
= [tex]15000 + 50x - x^{2}[/tex]
= f(x) [say]
So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)
= 50 - 2x---(1)
taking f'(x) = 0 , we get,
50 - 2x = 0
⇒ x = 25 --------------(2)
Again,
[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25
= -2 (<0)
So, f(x) attains it's maximum value at x = 25
Hence,
25 more trees are to be planted per acre to maximize the total yield.
mio bought a tablet and pays monthly for internet service for it. she graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it.
what does the y-intercept represent in this context?
A) the number of months after which the total cost is 0 dollars
B) the cost of buying the tablet
C) the cost per month
D) none of the above
In the context of the question, the Y-intercept represents the cost of the tablet that Mio purchased before counting the ongoing costs per month for internet service.
Explanation:In the context of this problem, the Y-intercept in the graph represents the cost of buying the tablet. Using the algebraic equation for a line, which is y = b + mx, the 'b' term is the Y-intercept. When x (in this case, the number of months) equals zero, y is the initial cost, which serves as our Y-intercept. This is the starting point on the Y-axis, and in the context of Mio's spending, this would be her initial expenditure which is the cost of the tablet itself.
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Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area
of the cover? Use pi = 3.14 and round the answer to the nearest square foot.
Answer:
The area of the cover for the hot tub must be:
38 square feet.Step-by-step explanation:
First, you must understand that since a hydromassage tub is mentioned and the diameter, it is assimilated that it is round in its upper part, which is why the formula is used to find the area of a circle:
Area of a circle = pi * radius ^ 2 (you must know that the radius is half the diameter)Since the diameter is mentioned, it can be replaced in the formula:
Area of a circle = 3.14 * (3.5 feet) ^ 2 Area of a circle = 38,465 square feet. Approximately 38 square feet.Answer:
I believe it is 38
Step-by-step explanation:
HAVE A GOOD DAY AND GOD BLESS YOU
How are the graphs of the functions f(x) = 16and g(x) = 3/64"related?
Answer:
The graphs of the functions are both straight lines and parallel to x-axis
Step-by-step explanation:
The graph of f(x) is the line y = 16 which is parallel to x-axis.
This is because for every value of x the function f(x) only takes the value 16
Similarly the graph of g(x) is also a straight line but is characterized by y = 3/64. This line is also parallel to the x-axis.
For every value of x the function g(x) only takes the value 3/64
PLEASE HELP ASAP!!!!
Compose two complete sentences that each include a dependent clause and an independent clause. Identify the subject and predicate of each. Do not use any of the examples in #1 above.
Example: After the meal (S) was served (P), we (S) lounged around with full bellies (P).
Answer:
An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.Step-by-step explanation:
What is the solution set of{x|X<-3} n {xl x> 5)?
all numbers except -3 and 5
the numbers between -3 and 5
the empty set
all real numbers
Answer:
C) Solution set of{x|X<-3} n {xl x> 5) is an the empty set.
Step-by-step explanation:
Here, the solution set is given as : set of {x| x < -3 } ∩ {x l x > 5)
Now, defining the each set , we get
{x| x < -3 } = ( .... -6,-5,-4 ,-3) = P
and the SET {x l x > 5} = (5,6,7,........ ) = Q
Now, by taking the intersection of two sets,we get
P ∩ Q = NULL SET as they don not have any element in common.
⇒ {x| x < -3 } ∩ {x l x > 5} is an empty set
Hence, solution set of{x|X<-3} n {xl x> 5) is an the empty set.
6. Suppose an Olympic-size swimming pool in the
shape of a rectangular solid has a volume of 4000
cubic meters, a length of 80 meters, and a width of
20 meters. What is the depth of the pool? Round
your answer to one decimal place.
A) 1.5 meters
B) 2.5 meters
C) 4 meters
D) 6 meters
E) 3.5 meters
To find the depth of the swimming pool, use the formula for the volume of a rectangular solid and substitute the given values to calculate the depth as 2.5 meters.
The depth of the Olympic-size swimming pool can be calculated using its volume, length, and width.
First, use the formula for the volume of a rectangular solid:
Volume = Length x Width x Depth
4000 = 80 x 20 x Depth
Depth = 4000 / (80 x 20) = 2.5 meters
Depth = 2.5 meters
I don’t know where to start with this problem
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
Can someone please help?
Answer:
a. .3
b. .7
c. The car is fairly reliable because there is more people with no mechanical issues than there is people with mechanical issues
Step-by-step explanation:
Answer:
A. 3
B. .7
C. The car is fairly reliable, their is more people with no mechanical issues than their is people with mechanical issues
Step-by-step explanation:
6x - 5y = -10
4x+3y=6 linear equation
Answer:
x = 0 , y = 2
Step-by-step explanation:
Solve the following system:
{6 x - 5 y = -10 | (equation 1)
4 x + 3 y = 6 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{6 x - 5 y = -10 | (equation 1)
0 x+(19 y)/3 = 38/3 | (equation 2)
Multiply equation 2 by 3/19:
{6 x - 5 y = -10 | (equation 1)
0 x+y = 2 | (equation 2)
Add 5 × (equation 2) to equation 1:
{6 x+0 y = 0 | (equation 1)
0 x+y = 2 | (equation 2)
Divide equation 1 by 6:
{x+0 y = 0 | (equation 1)
0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = 0 , y = 2
solve using substitution -x+y=3 and -4x+3y=3
Answer:
x=6, y=9. (6, 9).
Step-by-step explanation:
-x+y=3
-4x+3y=3
-----------------
-x=3-y
x=-3+y
x=y-3
---------
-4(y-3)+3y=3
-4y+12+3y=3
-y+12=3
-y=3-12
-y=-9
y=9
-x+9=3
-x=3-9
-x=-6
x=6
x=6, y=9.
A tree grow 1/4 foot in 1/12 year.
Part A: write the rate at which this tree grows as a fractions.
Part B: how many feet does the tree grow in 1 year? explain how you know.
Answer:
Part A) The rate is [tex]\frac{12}{4}\ \frac{feet}{years}[/tex]
Part B) In 1 year the tree grows 3 feet
Step-by-step explanation:
Part A) write the rate at which this tree grows as a fractions
we know that
To find out the rate at which the tree grows divide 1/4 foot by 1/12 year
so
[tex]\frac{(1/4)}{(1/12)}=\frac{12}{4}\ \frac{feet}{years}[/tex]
Part B) how many feet does the tree grow in 1 year?
we know that
The tree grows at rate of [tex]\frac{12}{4}\ \frac{feet}{years}[/tex]
Simplify
[tex]\frac{3}{1}\ \frac{feet}{year}[/tex]
That means ----> The tree grows 3 ft in 1 year
therefore
In 1 year the tree grows 3 feet
How do you graph 2/5 on a number line
To graph 2/5 on a number line, divide the number line into equal segments and locate the point that represents 2/5.
Explanation:To graph 2/5 on a number line, divide the number line into equal segments and find the point that represents 2/5. Start by labeling the endpoints of the number line with the corresponding values. In this case, you can label 0 on the left and 1 on the right. Since the number line is divided into 5 equal segments, mark the points that correspond to 1/5, 2/5, 3/5, and 4/5 between 0 and 1. Then, locate the point that corresponds to 2/5 and mark it on the number line. Remember to place a dot to represent the point.
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What percent is represented by the shaded area?
Answer:
its represented by my 20 inch pito
the product of a 3x3 and a 6x6 matrix would be
54 54 54
54 54 54
54 54 54
Need help asap !!!!!
Answer:
The answer is x = 5.
Step-by-step explanation:
Given:
Δ ABC is an Isosceles triangle with AB = CA
m∠ ABC = ( 6x + 4 )°
m∠ BAC = 73°
m∠ BCA = ( 8y - 7 )°
To Find:
x = ?
Solution:
Properties of an Isosceles Triangle.
Base angles or two angles are equal.Any two sides are equal.Here , Δ ABC is an Isosceles triangle with AB = CA
∴ m∠ BAC = m∠ BCA
[tex]73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10[/tex]
∴ m∠ BCA = ( 8y - 7 )°
= 8 × 10 - 7
m∠ BCA = 73 Which is same as ∠ CAB
Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.
[tex]\angle ACB + \angle CAB + \angle CBA = 180[/tex]
Substituting the values we get,
[tex]73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\[/tex]
The answer is x = 5.
Directions: Simplify each algebraic expression by combining like terms.
1. 7x2 – 5x + 10x - 8x?
2.-6a3 + 5a3 + 2a? - a?
3. - 4(x + 5) – 5(x - 1)
4. -a + 5b - 6a + 5(a + 1)
5. 18x4 - 3x3 - 2x3 + x2 - 10 + 6
Answer:
Step-by-step explanation:
1) 7x^2-5x+10x-8x=7x^2+5x-8x=7x^2-3x
2) -6a^3+5a^3+2a-a=-a^3+2a-a=-a^3+a
3) -4(x+5)-5(x-1)=-4x-20-5x+5=-9x-20+5=-9x-15
4) -a+5b-6a+5(a+1)=-7a+5b+5a+5=-2a+5b+5
5) 18x^4-3x^3-2x^3+x^2-10+6
=18x^4-5x^3+x^2-4
To simplify algebraic expressions, combine like terms, variables and exponents. We simplified five examples, using techniques such as distribution and combining like terms.
Explanation:To simplify algebraic expressions, one has to combine like terms, which are terms with the same variables and exponents. Here, let's do that:
7x2 – 5x + 10x - 8x simplifies to 7x2 + 5x because -5x + 10x - 8x = 5x.
-6a3 + 5a3 + 2a? - a? simplifies to -a3 + a (assuming the '?' is meant to be a variable).
- 4(x + 5) – 5(x - 1) simplifies first by applying distribution (-4x -20 -5x +5) which then becomes -9x - 15.
-a + 5b - 6a + 5(a + 1) simplifies to -2a + 5b + 5 once you distribute and combine like terms.
18x4 - 3x3 - 2x3 + x2 - 10 + 6 simplifies to 18x4 - 5x3 + x2 - 4 since -3x3 and -2x3 add up to -5x3 and -10 and 6 adds up to -4.
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Translate the variable expression into a word phrase 5c
A. The quotient of five and a number
B. The sum of five and a number
C. The difference of five and a number
D. The product of five and a number
PLZ HELP ME
The answer to your question is D, as 5 is being multiplied by c, and the term product refers to multiplication.
HELP ASAP, NO GUESSING OR ADDING RANDOM ANSWERS OR YOU WILL BE REPORTED
Answer:
3.5 unit right and compressed by 3.5 units respectivleyy
Step-by-step explanation:
2. When Mrs. Romano was pricing cans of tomato sauce, she noticed the following prices.
1 can (28 ounces) cost $1.89
1 can (32 ounces) costs $2.95
Which is the better deal?
need to know the unit rate too please.
Answer:
28 oz can is the better deal.
Step-by-step explanation:
In order to compare the two, we need to find the unit rate for each can. In this case, the unit rate will be in dollars per oz.
For the 28 oz can,
unit rate = $1.89 ÷ 28 = $0.675 / oz
For the 32 oz can
unit rate = $2.95 ÷ 32 = $0.922 / oz
comparing the unit rates, we can see that the unit rate for the 28 oz can is lower (i.e it costs less per oz for the 28 oz can compared to the 32 oz can)
Hence the 28 oz can is the better deal.
-3(×+2)=12 what is x equal to
Answer:
x=-6
Step-by-step explanation:
Follow along:
1. Distribute the -3 to those within the parenthesis.
-3x-6=12
2. Move the whole numbers to one sides, isolate the variable.
-3x=18
3. Divide both sides by -3
x=-6
Mr. Tindell divided a 6th grade class Of 80 students an into equal groups the number of students in each group was a prime number how many groups did he make how many were in each group?
Answer:
He made 16 groups which means 5 Students in each group
Step-by-step explanation:
Because 80 divided by 16 is 5 and 5 is a prime number
On a map drawn to scale, 2 cm represents 870 km. How long would a line segment be thats represents 130 kilometers?
Answer:
0.2988
Step-by-step explanation:
the sum of two numbers is 32. the sum of 3 times the larger and 7 times the smaller is 128
Answer:
Smaller number = 8 (x)
Larger number = 24 (y)
Step-by-step explanation:
x+y=32
7x+3y=128
Solving by Elimination
-3x-3y= -96
7x+3y=128
4x=32
4x/4=32/4
x=8
-7x-7y= -224
7x+3y=128
-4y= -96
-4y/-4= -96/-4
y=24
Check answer
x+y=32
8+24=32
7x+3y=128
7(8)=3(24)=138
56+72=128
128=128
using elimination method, simultaneously solve this equation: 2y+3x=7 and 4x+3y=15
Solve 2y + 3x = 7 and 4x + 3y = 15 by elimination, we get x = -9, y = 17. Multiply and subtract equations to eliminate y, then substitute the result to find x or y.
To solve the system of equations 2y + 3x = 7 and 4x + 3y = 15 using the elimination method, we aim to eliminate one variable to solve for the other. Here's a step-by-step explanation:
Multiply the first equation by 3, and the second equation by 2 to make the coefficients of y equal:The solution for the system of equations is x = -9 and y = 17.
The graph models the speed of an amusement park ride. The coordinates of Point Ware (1,
Tower of Thrills
Distanon (motora)
+ + + + +
0 1 2 3 4 5 6 7
Time (coconds)
What is the meaning and value of rat Point W?
A rrepresents the unit rate of speed of 1 meter per 45 seconds
B rrepresents the unit rate of speed of 45 meters per 1 second
c rrepresents the rate of increase of speed of 1 meter per 45 seconds
D represents the rate of increase of speed of 45 meters per 1 second
Answer:
k
Step-by-step explanation:
;
Identify the vertex, the axis of syn
y = x2 + 8x + 16
The vertex is
. (Type an ordere
What is the min and max porabala
Good evening ,
Answer:
Vertex (-4 , 0)
axis x = -4
It’s a parabola.
Min = 0
Step-by-step explanation:
x2 + 8x + 16 = (x + 4)².
solve quadratic equation using factoring
z^2-5z+4=0
Answer:
[tex]z^2-5z+4=(z-4)(z-1)[/tex]
Step-by-step explanation:
To factorize a cuadratic equation, one must use the well known formula to find the roots of the equation: [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a (a=1) is the coefficient that accompanies the cuadratic term, b is the coefficient that accompanies the linear term (b=-5) and c is the constant (c=4).Then, applied to this specific case, the previous formula results: [tex]\frac{5(+-)\sqrt{(-5)^2-4\times{1}\times{4}} }{2\times1}[/tex]. Then, the two roots of the equation come from [tex]\frac{25(+-)\sqrt{9} }{2}[/tex].Consecuently, [tex]z_1=\frac{5+\sqrt{9}}{2} =4[/tex], and [tex]z_2=\frac{5-\sqrt{9}}{2} =1[/tex].Finally, the cuadratic function can be expressed like this: [tex](z-4)(z-1)[/tex] (which comes from the fact that any polynomial can be expressed as the product of [tex](x-x_i)[/tex], where i are the roots of the polynomial). To corroborate that the procedure is correct, you can resolve this product, and you will obtain the inicial expression.A linear function has an x-intercept of 12 and a slope of 3/8. How does this function compare to the linear function that is represented by the table?
Answer:
We rewrite the statement correctly:
"A linear function has an y-intercept of 12 and a slope of 3/8"
Therefore, the linear function is:
y = (3/8) x + 12
We look for the linear function of the table:
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
m = ((- 3/8) - (- 3/4)) / ((1/3) - (- 2/3))
m = ((- 3/8) - (- 6/8)) / (3/3)
m = ((- 3 + 6) / 8) / (1)
m = 3/8
(xo, yo) = (- 2/3, -3/4)
Substituting:
y + 3/4 = (3/8) (x + 2/3)
y = (3/8) x + 2/8 - 3/4
y = (3/8) x + 1/4 - 3/4
y = (3/8) x + -2/4
y = (3/8) x + -1/2
The lines are:
y = (3/8) x + 12
y = (3/8) x + -1/2
Answer:
It has the same slope and a different y-intercept
Step-by-step explanation:
Answer:
B same slope but different y intercept
Step-by-step explanation:
Please answer this correctly
Is the answer
10:07pm
12:32am
1:32am
11:32pm
Answer:
Step-by-step explanation:
12:32 am
Answer:
1:32 AM
Step-by-step explanation:
Arriving in Oklahoma City, the time is already 12:32 AM since it is past midnight. From Mountains to Central, time moves forward by 1 hour. 12:32 + 1 hour is 13:32 or 1:32 AM. Since the time is still past midnight, the time is AM.
Which expressions are equivalent to 6^-10 6^-8
Answer:
The equivalents are 1/6¹⁰ and 1/6⁸
Step-by-step explanation:
1. Let's recall the rule about the negative exponents to find the equivalents to the expressions provided:
The rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.
Thus, x ⁻ⁿ = 1/x ⁿ
2. Now, let's find the equivalents after following the rule:
6 ⁻ ¹⁰ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ¹⁰
6 ⁻ ⁸ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ⁸