Answer:
(a). The length of the field is 1,300 - 2·x
(b) The area of the rectangular field is 1,300·x - 2·x²
(c) x leading to the maximum area is 325 meters
(d) The maximum area is 211,250 m²
Step-by-step explanation:
The given parameters are;
The length of fencing the compound owner has = 1,300 m
The shape of the field he wants to enclose = Rectangular field
The width of the field he wants to enclose = x
The fence on the side along the river = No fencing along the river
(a). Let 'l' represent the length of the field, we, have;
2·x + l = 1.300
∴ l = 1,300 - 2·x
The length of the field, l = 1,300 - 2·x
(b) The area of a rectangular field, A = Length of the field, l × Width of the field, w
Therefore;
The area of the rectangular field, A = x × (1,300 - 2·x) = 1,300·x - 2·x²
The area of the rectangular field = 1,300·x - 2·x²
(c) The coefficient of x² is negative, therefore, the graph of the area has a maximum point
The value of 'x' leading to maximum area is given by differentiating the function representing the area, equating the result to 0, and fining the value of 'x' as follows;
d(A)/dx = d(1,300·x - 2·x²)/dx = 1,300 - 4·x
d(A)/dx = 0 at the maximum point
∴ 1,300 - 4·x = 0
4·x = 1,300
x = 1,300/4 = 325
x leading to the maximum area = 325 meters
(d) The maximum area, [tex]A_{max}[/tex] is given by A = 1,300·x - 2·x², when x = 325
∴ [tex]A_{max}[/tex] = 1,300 m × 325 m - 2 × (325 m)² = 211,250 m²
The maximum area, [tex]A_{max}[/tex] = 211,250 m²
help please asap please
What does the word commute mean
Answer:
travel some distance between one's home and place of work on a regular basis.
Step-by-step explanation:
PLEASE HELP ASAP Find the true measurements (2 answers)
Answer:
(C) Because of the fact that apply for a new number
Solve the question. Explain WHY
Answer:
C
Step-by-step explanation:
Both C and D have the correct ratio. (5/15=1/3)
But I’m thinking the answer is C because it’s orientation is landscape, not portrait, which would be important in artwork.
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
The unit price of the yogurt is given by the equation A = $ 0.45
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the cost of 5 ounces of frozen yogurt be = $ 2.25
So , the cost of 1 ounce of frozen yogurt A = cost of 5 ounces of frozen yogurt / 5
Substituting the values in the equation , we get
The cost of 1 ounce of frozen yogurt A = $ 2.25 / 5
The cost of 1 ounce of frozen yogurt A = $ 0.45
Hence , the unit rate cost is $ 0.45
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What is the value of AB?
Answer:
345
Step-by-step explanation:
Ms. Lee wants to know what kinds of things her students do prepare for her tests. Ms. Lee placed the names of her students into a box. To determine who she would ask about their study habits she asked a student to draw names from the box.
a. What is the sample in this situation?
b. What is the population?
(NOT A MULTIPLE CHOICE)
Answers:
a) The sample is the set of students Ms. Lee selects from the box.b) The population is the set of all students in Ms. Lee's classroom.=============================================
Explanation:
The first sentence tells us what the population is: it's the set of all her students. She's not concerned with any other students in any other classroom. So her "universe", so to speak, is solely focused on this classroom only. Once the population is set up, a sample of it would be a subset of the population.
If set A is a subset of set B, then everything in A is also in B, but not vice versa. For example, the set of humans is a subset of the set of mammals because all humans are mammals. However, a dog is a mammal but not a human. This shows that A is a subset of B, but not the other way around. In this example, A = humans and B = mammals.
Going back to the classroom problem, we have A = sample and B = population. If Ms. Lee has 30 students, and she randomly selects 5 of them, then those 30 students make up set B and the 5 selected make up set A. Selecting the names randomly should generate an unbiased sample. This sample should represent the population overall. If the population is small enough, the teacher could do a census and not need a sample. Though there may be scenarios that it's still effective to draw a sample.
Have an amazing day :)
Will give brainlst! Pls help
Answer:
As the study time increases the test score increases
Step-by-step explanation:
Nonlinear because the points aren't going in a straight line, they points fluctuate over time
Write each phrase as an algebraic expression.
4. Jenny is 5 times as a old
5. Brandon spent 10 dollars more
Mike builds a pen for his dogs near his barn. The pen is a regular hexagon with a side length of 4 feet. What is the area of the pen?
Answer: Roughly 41.57
Step-by-step explanation:
Jackie has a poster that is 7 inches wide by 10 inches long. She wants to
enlarge it so that its length is 20 inches. What should the width be?
Answer: width= 3.5 inches
Step-by-step explanation:
Answer:
★ The width would be 3.5 INCHES
Step-by-step explanation:
Hope you have a great day
A math teacher's homework grading policy states that a homework assignment turned in late will result in the
grade being reduced by a certain percentage each day that the assignment is late. The teacher creates the
table below to illustrate this policy.
Number of Days Late (1)
Homework Grade, g(t)
0
80
60
1
45
2
Based on the table, write an exponential function in the form y= abt that represents the situation.
y =
An exponential function in the form y= abt that represents the situation.
y = 60.75.
What is correlation coefficient and how to interpret it?Correlation coefficient is a measure of how similar two datasets are acting.
The range of correlation coefficient is [-1, 1]
When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.
When the correlation coefficient comes out below 0, values are negatively correlated.
If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated with respect to how we compare them.
When the correlation coefficient comes out > 0, that means both datasets' values are positively correlated.
If correlation coefficient comes out as 1, then the values grow exact similarly, in the same direction.
Given;
y = -0.4x + 98.3
When you increase your homework score by 1 point, you lose 0.4 points on your test.
-0.4x + 98.3 = 74
→ -0.4x = -24.3
→ x = 60.75 ≈ 61
Therefore, the correlation will be y=61.
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please help me answer this
9514 1404 393
Answer:
A. 9
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles.
10x -19 = (3x +2) +(5x -3)
2x = 18 . . . . . . . . . . . . . . . add 19-8x to both sides, simplfy
x = 9 . . . . . . . . . . . divide by 2
Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)
A)
y = 5x -5
B)
y = 5x + 5
C)
y = -5x -5
D)
y-tx-5
what is the absolute value of |4x|- 12 = 4
Answer:
X = 4
Step-by-step explanation:
4 X 4 equals 16 and 16 minus twelve equals 4
A set of 4 chairs cost $56, or you can buy 1 chair for $16. How much less is the cost of 1 chair if you buy the set?
What is the greatest common factor of 15, 75, and 9
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Factors of each number }\huge\boxed{\downarrow}\\\\\large\textsf{9: 1. 3. \& 9}\\\large\textsf{15: 1, 3, 5, \& 15}\\\large\textsf{75: 1, 3, 5, 15, 25, \75}[/tex]
[tex]\huge\text{Like terms between the factors}\\\\\bullet \large\textsf{1 \& 3}[/tex]
[tex]\huge\text{Reason for the factors of the numbers }\huge\boxed{\downarrow}\\\\\large\textsf{9: 1}\times\large\textsf{9 = \bf{9} }\& \large\textsf{ 3}\times\large\textsf{3 = \bf 9}\\\\\large\textsf{15: 1}\times\large\textsf{15 = \bf 15 }\&\large\textsf{ 3}\times\large\textsf{5 = \bf 15}\\\\\large\textsf{75: 1}\times\large\textsf{ 75 = \bf 75}, \large\textsf{ 3}\times\large\textsf{25 = \bf 75}, \& \large\textsf{ 5}\times\large\textsf{ 15 = \bf 75}[/tex]
[tex]\huge\text{BIGGEST NUMBER OUT OF THE LIKE}\\\huge\text{TERMS }\huge\boxed{\downarrow}\\\\\large\textsf{\bf 3}[/tex]
[tex]\huge\text{ANSWER }\huge\boxed{\downarrow}\\\\\large\boxed{\textsf{The GCF (Greatest Common Factor) is: \huge\boxed{\textsf3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\large\text{Amphitrite1040:)}[/tex]the partial circle has a radius of 11 inches
What is the area of this figure? ANSWER ASAP
Answer:
285.1 in.²
Step-by-step explanation:
The circle is a ¾ circle.
Area of the figure = ¾(πr²)
Radius (r) = 11 in.
Plug in the value
Area = ¾(π*11²)
Area = ¾(π*121)
Area = 285.099533 ≈ 285.1 in.² (nearest tenth)
Given AB =6 and BD =8, find the value of x
Answer: x=10
Step-by-step explanation:
Find AD by making a 90 degree triangle with segments AB and BD
a=6 b= 8 c= c
[tex]a^{2}+b^{2} =c^{2}[/tex]
[tex]6^{2} +8^{2} =c^{2} \\36+64=c^{2} \\100=c^{2} \\10=c[/tex]
AD is = to 10- AD is also the radius of the circle. since x is also the radius of the circle, it is also 10
Help please I don’t understand
Answer:
6x-4y+0 is the linear equation
j) You spend $35. Tip is 15%. How much did you pay in total?
Answer:
You paid $40.25 in total.
Step-by-step explanation:
In this question:
Spending of 35%
Tip of 15% means that 15% of 35 will be added to your total spending. So
[tex]T = 35 + 0.15*35 = 35 + 5.25 = 40.25[/tex]
You paid $40.25 in total.
Which step has the mistake in solving for roots?
2x^2 – 7x – 3 = 1
Step 1: 2x^2 – 7x – 4 = 0
Step 2: x^2 – 7x – 8 = 0
Step 3: (x-8)(x+1) = 0
Step 4: (x-8/4)(x+1/4) = 0
Step 5: (x-2)(4x+1) = 0
Step 6: x – 2 = 0 4x + 1 = 0
Step 7: x = 2 x = -1/4
One of these steps is incorrect. List the step that is incorrect, then finish the problem correctly.
Answer:
Step-by-step explanation:
2x² - 7x - 3 = 1
Step 1: 2x² - 7x - 4 = 0
Step 2: incorrect.
Use Quadratic Formula to solve for roots.
x = [7 ± √(7² – 4·2(-4))] / [2·2]
= [7 ± √81] / 4
= [7 ± 9] /4
= -0.5, 4
Which Statements Describe One Of The Transformations Performed On F(x)=x^2 to create g(x)=3(x+5)^2-2? Choose all that apply
Answer:
can you post a picture of the options?
Answer:
A vertical stretch with a scale factor of 3
&
A translation of 5 units to the left
Step-by-step explanation:
An initial investment of $5,000 grows at 9% per year.
Answer:
C. f(t) = 5000(1.09)^t
Step-by-step explanation:
Compound interest formula:
F = P(1 + r)^t
Answer: C. f(t) = 5000(1.09)^t
Circle 1 has a center (−4, 5) and a radius of 6 cm. Circle 2 has (2, −3) and a radius of 9 cm. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the blanks. Enter the scale factor as a fraction in the simplest form.
The circles are similar because the transformation rule (___ , ___ ) can be applied to Circle 1 and then dilate it using a scale factor of ___/___
Answer:
The circles are similar because the transformation rule (+ 5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of 3/4.
Step-by-step explanation:
All the circles are similar.
That is because you can transform one circle onto another by two similarity operations: translation and dilation (scale factor).
For these two circles you have to translate the center of circle 1 to the center of circle 2, which will make that the two circles are concentric (have the same center).
The two centers are (-6,2) and (-1,- 4). To move the center (-6, 2) to (-1,4) you have to shift it 5 units to the right and 6 units down:
- 6 + 5 = - 1
2 - 6 = - 4.
After this translation, you dilate the circle with smaller radius using a scale factor equal to the ratio of the bigger radius to the smaller radius: 8/6 = 4/3.
Enter the scale factor as a fraction in simplest form. 3/4
The circles are similar because the transformation rule (+5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of 3/4.
Answer:
The circles are similar because the transformation rule ( [tex]x + 6, y - 8[/tex]) can be applied to Circle 1 and then dilate it using a scale factor of [tex]\frac{3}{2}[/tex]Step-by-step explanation:
just took the test down. proof down below
What is 7/12 +3/12+7/12=
Answer:
just add them because the denominators are the same and then when u get an answer simplify it but in this case, it is not possible.
so the answer is 17/12 or [tex]\frac{17}{12}[/tex] or 1.46( bar on 6
Answer:
17/12
Step-by-step explanation:
This can be found because the numbers across the top of the fraction all add, as there is a common denominator of 12.
Sebastian has filled a paper grocery bag with food to donate to the food drive. If the paper bag is in the shape of a right rectangular prism with a length of 12 inches, a width of 7 inches, and a height of 17 inches, what volume of food it can hold?
36 Inches cubed
72 Inches cubed
1,428 Inches cubed
2,856 Inches cubed
Answer:
1,428 inches cubed
Step-by-step explanation:
This easy, to find a volume of a cube/rectangular prism you just do lengthxwidthxhight
12x7x17=1428
will someone plz help me
Answer:
minimum value = 18
Step-by-step explanation:
explanation in the picture :) let me know if you have any questions
Dana's pool table is 4 feet wide and 8 feet long. Dana wants to replace the felt on the pool
table. The felt costs $5.00 per square foot. How much would it cost in total to replace the felt
on the pool table?
* Will give brainliest*
Find the third value, given two values for each linear function. Show work.
h(0)= -1
h(5)=1
h(-5) = ?
Answer:
The answer is -3
Step-by-step explanation:
If we use the point slope intercept form we would get the slope of 2/5
which we can apply it to the -5 and we would get the answer.
h(0)= -1 is saying the x is the 0 while the y is the -1.
Same goes for h(5)=1.
so then you would do m=[1-(-1)]/(5-0)
which gives you the slope.
The you put the -5 which is the x value and write an equation for it:
y=2/5(-5)-1
Which gives you the answer of -3
GOOD LUCK
Answer:
-3
Step-by-step explanation:
!:3$$3$3